tag:blogger.com,1999:blog-78970134367520339002024-03-21T12:43:57.487-07:00Green of Greece - PhilosophyVerdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-7897013436752033900.post-85679156565001664152011-08-17T16:04:00.000-07:002011-08-17T16:04:45.346-07:00Zeno’s Paradox of Achilles and the Tortoise<div align="LEFT"><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">"There is no motion because that which is moved must arrive at the middle of its course before it arrives at the end." </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">The quotation, from Aristotle’s Physics, expresses the principle underlying Zeno’s parable of the race between Achilles and the tortoise. A tortoise challenges Achilles to a race, asking only that he be given a head start. Achilles scoffs at the suggestion but the tortoise explains that the race need not even take place because it would be impossible for Achilles to catch up with him once he had started running from his vantage point some way down the track. </span></span></div><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> <br />
"When you reach the point from which I started, you must admit that I will have run further still, even though it may be a small distance. When you have run that distance, I shall have run further still, and so on </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">ad infinitum</span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. " </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">At this point, Achilles should have insisted on running the race and proved empirically that the tortoise’s argument was false. This provides a clue to the counterintuitive idea that a fast runner cannot overtake a slow one, which contradicts our quotidian experience. If we stick to the tortoise’s a priori argument we are caught in a logical trap, but if we insist on an empirical refutation the status of logic is downgraded, and we must doubt the applicability of logical argument to physical events. <br />
<br />
The tortoise’s argument is one way of defining the race but there are other ways that exclude the paradoxical trap. For example, Achilles could run the agreed distance L (which might have been 1 stadion = 185.4 metres) separately and the tortoise could then have run the shorter distance L/10 say. Timing both events would show that Achilles runs the full distance faster than the tortoise runs the shorter one, the conclusion being that Achilles must have won, without having to overtake the tortoise. The objection to this in those ancient times would be that there were no clocks capable of accurately measuring such short time spans. Zeno might have objected that this was no race at all, because the events took place at different times. If Achilles runs first, he obviously crosses the finishing line first, but if the tortoise goes first he wins if only because he crossed the finishing line before Achilles even starts to run. <br />
<br />
So, we are forced to consider the mathematics of Zeno’s argument. We can suppose that the tortoise has a starting advantage of </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">K < L </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">which is sufficiently small to allow Achilles to catch up before the race is over. Careful consideration will show that </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">K </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">can always be set so the tortoise can win but that this is not the case here. The decreasing distances defined by Zeno’s argument can be precisely defined in terms of the relative velocities of Achilles and the tortoise. Let these be </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a </span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">and </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t </span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">respectively. Achilles runs the distance </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">0 </span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">in </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">T</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">1 </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">= K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">0</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">/ V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a</span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. The distance run by the tortoise in time </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">T</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">1 </span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">will be </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">K1 = T</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">1. </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">= K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">0</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">/ V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a</span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. A series of geometrically decreasing distances can now be defined </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">as (K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">0 </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">+ K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">1 </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">+ K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">2 </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">+ …+K</span></span><span style="font-family: Calibri,Calibri; font-size: x-small;"><span style="font-family: Calibri,Calibri; font-size: x-small;">n</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">) = K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">0</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">Σ</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">n </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">(V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">/ V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a)</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">n</span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. Since </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">< V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a </span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">the sum will converge to an infinite limit, which is the point where Achilles catches up with the tortoise being </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">D = K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">0</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">/(V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">-V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">)</span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">We can now calculate the time taken by Achilles to cover the distance </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">D </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">which is </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">T</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">D </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">= D/V</span></span><span style="font-family: Calibri,Calibri; font-size: x-small;"><span style="font-family: Calibri,Calibri; font-size: x-small;">a</span></span></i><span style="font-family: Calibri,Calibri; font-size: x-small;"><span style="font-family: Calibri,Calibri; font-size: x-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. At any time between </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">D/V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a </span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">and Achilles’ finishing time </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">L/V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a</span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">, we can claim that the tortoise has been overtaken. This provides an a priori rather than an empirical refutation of Zeno’s argument. However, the objection remains that an infinite summation of the decreasing differences is impossible in the physical world. A way out of this difficulty is to ignore the race track altogether </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">and consider the relative velocity of Achilles and the tortoise, which is </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">– V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t</span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. The time taken by Achilles to close the initial gap </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">K </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">is therefore </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">0</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">/( V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">– V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t</span></span><span style="font-family: Calibri,Calibri; font-size: x-small;"><span style="font-family: Calibri,Calibri; font-size: x-small;">) </span></span></i><span style="font-family: Calibri,Calibri; font-size: x-small;"><span style="font-family: Calibri,Calibri; font-size: x-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">so the distance </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">D = K</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">0</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a</span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">/( V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">– V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t</span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: x-small;"><span style="font-family: Calibri,Calibri; font-size: x-small;">) </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">which is the same formula derived using the infinite summation. </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">The cleverness or inadequacy of Zeno’s argument is that it is an incomplete model which precludes consideration of the race as a whole, focussing only on the vanishingly small distances between the participants. The argument is a </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">petitio principii </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">in that it assumes in advance that motion is impossible and creates a model that favours this assumption. The existence of other theoretical models which do conform to everyday experience and the intuitions based on it resolve the apparent paradox by rejecting Zeno’s model. </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">Water clocks existed in Zeno’s time, so the timing of a race by this means should not be ruled out. However, modern circular clocks do provide continual, empirical refutations of Zeno’s argument. The minute hand of a clock does overtake the hour hand several times a day, but the question is: at what time do the hour and minute hands of a clock coincide? <br />
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The method of calculation is similar to the one used to find the crossover point in Zeno’s race. The minute hand of the clock completes one revolution in the time it takes the hour hand to move the five minute division between one hour and the next. The relative velocity is therefore </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">1/12</span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. The first coincidence after </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">12 O’clock </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">is </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">12/11 </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">hours = </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">1h 5m 27.27 sec</span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. Peculiarly there will only be 11 unique coincidences, with no coincidence between </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">10h 54m 32.72 sec </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">and </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">12h 0m 0sec</span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. Since the coincidences are independent of the clock face divisions, the latter could be dispensed with. The result would be a clock which divides the diurnal cycle into </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">22 </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">equal periods. </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">If a typical clock is observed closely, the minute hand appears to move in one second jerks rather than smoothly. The implication is that it cannot exactly coincide with the hour hand at any time other than </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">12 O’clock</span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">, since there are no other coincidences exactly measured in whole seconds. In this sense, Zeno would be correct in asserting that the minute hand cannot overtake the hour hand at such a coincidental point but would be wrong in concluding that it could not do so after that point. This is because we assume that ‘time’ is a continuous process, rather than more correctly realising it is the nature of the physical process that defines how time is to be interpreted. If physical process involving movement are small but discontinuous, they can be regarded as almost continuous because the smallness of the Planck constant. </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">The movements of Achilles and the tortoise can be regarded as individual steps, or strides. When Achilles has run the overtaking distance D, he may be in mid stride, between and </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">n </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">and </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">n +1 </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">strides, in which case he will overtake the tortoise on completion of the nth stride. His stride cannot exactly coincide with the point </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">D </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">unless </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a </span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">is exactly divisible by </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">a </span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">– V</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">t </span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. If it is, then he must complete </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">n +1 </span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">strides before we can claim that he has overtaken the tortoise. In either case, he is bound to win the race unless Paris shoots him in the heel with an arrow first, but Zeno’s argument would also rule out this possibility too. We can conclude from this that Zeno did not believe Homer’s tale or indeed any myths where mythological figures get pierced by arrows. This must have been comforting since on his theory he could never be hit by a missile of any kind. </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">The idea of a limit that cannot be transcended appears in Einstein’s Theory of Relativity. He argued that, as the velocity of a mass approaches the speed of light, the energy required to accelerate the mass approaches infinity. Since the speed of light is a constant, he concluded that the mass must <br />
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increase without limit, which is impossible. Like Zeno’s argument, this mathematical proof seems counterintuitive, but empirically true according to certain scientific observations. Using the earlier Newtonian model, there appears to be no reason to doubt that a mass could reach the speed of light and possibly exceed it. The point is that different theories may lead to different truths. Putting it the other way round, two theories cannot be different and non-contradictory. <br />
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Einstein’s formula below, which relates the mass of a moving body to its rest mass, also uses the idea of a limit that cannot be exceeded because of an infinite process. The interpretation is that a moving mass increases without limit as its velocity approaches the finite limit of the speed of light. If we switch the rest mass </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">m</span></span><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;">0 </span></span></i><span style="font-family: Calibri,Calibri; font-size: xx-small;"><span style="font-family: Calibri,Calibri; font-size: xx-small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">in the formula with the moving mass </span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">m</span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">, the result would be a different theory where the moving mass decreases to zero as its velocity increases towards the speed of light. </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">Zeno’s interpretation was based on his philosophical beliefs. His teacher Parmenides believed that time was an illusion because the universe was a permanent whole that never changed. From this point of view we experience change because our consciousness is incapable of observing the absolute nature of the universe. This approach is similar to Einstein’s four dimensional space time continuum, where events are frozen by regarding time as another spatial dimension. Even the simple Cartesian diagram of parabolic motion illustrates the principle of representing time as a spatial dimension, so Einstein’s formulation was just an extension of this type of description to a fourth dimension, transcending our usual mode of experience. <br />
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Zeno’s paradox of Achilles and the tortoise relied upon generating an infinite process which frustrated finite resolution, at least until mathematicians devised a satisfactory theory of limits. When it came to Cantor’s thoroughgoing examination of infinity, a great many paradoxes arose which had to be dealt with. Behind his approach to the theory of infinity lay the kind of absolutism espoused by Parmenides, which was a belief in the existence of absolute infinity rather than Aristotle’s comparatively timid potential infinity. Cantor’s achievement was to show that a hierarchy of infinities had to be defined as a consequence of his set theoretic approach. One of his best known achievements was to prove that the set of irrational numbers could not be counted by the natural numbers. He did this by means of his diagonal argument. <br />
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Zeno’s argument was Aristotelian in character, relying on the principle that it was impossible to add up all the increasingly tiny distances that Achilles had to run to catch up with the tortoise. Cantor’s starting point was to assume that the set of natural numbers, like any set, must have a totality, which he called Aleph null. Like Zeno’s argument, Cantor covertly employs the trick of introducing a limit that cannot logically be transcended, to wit the diagonal of digits in a finite square adopted for the purpose of demonstration. This involves the belief that the square can be expanded as far as Omega (the ordinal version of Aleph null) thus preserving the property of excluding certain combinations of digits. <br />
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Once the trap is accepted, that the square cannot be greater than the arbitrary number Omega, the result follows that the power set of the natural numbers is non-denumerable. Since the list of irrational numbers has been defined as a permutational power set, the argument degenerates into a <br />
</span></span><i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span></i><br />
<i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">petitio principii</span></span></i><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"></span></span><span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">. The point being that there is no diagonal associated with a non-square list, so the whole argument is a tautology signifying nothing. While cantor’s diagonal argument is logically sound, like Zeno’s, the model he constructed was erroneous. The consequence is a flawed set theory riddled with paradoxes. </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;"> </span></span><br />
<span style="font-family: Calibri,Calibri; font-size: small;"><span style="font-family: Calibri,Calibri; font-size: small;">The general issue is the extent to which we should accept counter intuitive arguments on the basis of special definitions which purport to render them logically sound. In the case of Zeno’s imaginary race, this should not be done without careful examination of alternative models. The corollary is that sound logical argument is not a sufficient criterion for truth, since the devil lies in the details hidden in the definitions and covert assumptions lying beneath the surface. <br />
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Tony Thomas <br />
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August 2011 </span></span>Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com0tag:blogger.com,1999:blog-7897013436752033900.post-69482255416368271182011-04-08T23:51:00.000-07:002011-04-12T15:19:28.648-07:00The Idea of Truth<div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBlBCfZ3VX6iwtLqEGP9x54gwDSbTJCsgkNzexrXF6VPXuzg_60Apq86-4WONNKxE8tQaNfdgI4-idyf9MfFmD8SB8xmkCzMdX1GoUAlBYBnVX78bXRj44UIDLSlOmXxB2VUYoyeTT3PU/s1600/Oed%2526SphinxRedGkVase.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" r6="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBlBCfZ3VX6iwtLqEGP9x54gwDSbTJCsgkNzexrXF6VPXuzg_60Apq86-4WONNKxE8tQaNfdgI4-idyf9MfFmD8SB8xmkCzMdX1GoUAlBYBnVX78bXRj44UIDLSlOmXxB2VUYoyeTT3PU/s320/Oed%2526SphinxRedGkVase.jpg" width="319" /></a></div><br />
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“Beauty is Truth, Truth Beauty, -That is all<br />
Ye know on earth, and all ye need to know.”<br />
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<em>John Keats, Ode on a Grecian Urn</em><br />
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The last two lines of Keats’s poem have been the subject of much erudite analysis, and it is presumptuous for an undistinguished writer to put in his twopenn’orth, but I will anyway. The intention, however, is not to add to an already overburdened debate but to use this example as a cave entrance to the even more labyrinthine consideration of the nature of truth in general. <br />
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In relation to the statement, “Beauty is Truth, Truth Beauty,” The critic IA Richards had warned against trying to take poetic statements too seriously. TS Eliot responded: “<em>on re-reading the whole Ode, this line strikes me as a serious blemish on a beautiful poem, and the reason must be either that I fail to understand it, or that it is a statement which is untrue.</em>” It is unlikely that Eliot did not understand the several possible meanings of the line, so we must conclude he did believe it was false. I agree with his judgment, albeit from a strictly logical interpretation of the last two lines of the poem.<br />
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As one would expect from a great poet, the multiple assertions in the concluding lines are bound together in a complex construction which does not immediately yield up an unequivocal meaning, either to the casual reader or even to prolonged analysis. Some may consider this to be a poetic virtue, akin to any artistic or mystical mode of thought. However, the resulting ambiguity confounds the kind of clear and unique interpretation demanded by the logical mind.<br />
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The two lines can be broken down as follows, at the risk of destroying any beauty or truth they express in their original form:<br />
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S1: Truth is Beauty. <br />
S2: Beauty is Truth.<br />
S3:S1 and S2 is all ye know.<br />
S4:S1and S2 is all ye need to know.<br />
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Before attempting to interpret each of the four propositions it is worth noting the following points. ‘Truth’ and ‘beauty’ are both abstract nouns that are used as adjectives (attributes) in S1 and S2 as well as nouns. This raises the problem of whether attributes (qualities) can properly have other attributes asserted of them and whether nouns can properly be used as attributes. S1 and S2 appear to be universal statements although they are not explicitly quantified ie “All truth is beautiful” and “All beauty is truthful”. If this were the poet’s intention, then we could logically conclude that beauty is in some sense equivalent to truth and vice versa, a proposition that can be tested by substituting one attribute for another in any and all possible propositions containing these attributes. <br />
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Consider the proposition, “Helen of Troy was (a) beauty”, which would become “Helen of Troy was (a) truth”. This provides an immediate contradiction of the equivalence because the second statement is hardly meaningful. We could elaborate and say, “Helen of Troy told the truth” but I am not sure if this was the case. In general, I am inclined to reject the assertion that either abstract or concrete entities are necessarily true because they are beautiful. One reason for this is that beauty is a subjective judgment which does not command universal agreement. What some find beautiful others find uninteresting or even ugly. Truth, however, has a better claim to objectivity whether it is established empirically or as a valid deduction from first principles. Truth, therefore, is not properly comparable with beauty at all.<br />
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Mathematicians and scientists might object to this negative judgment by declaring that beauty is a good if not infallible guide to truth. The justification for the scientist is that nature determines what we find beautiful, both internally through the mind and externally through the senses, and that this natural beauty is an expression of the perfect harmony that exists in nature. Clearly, this was the sentiment that Keats expressed in his ode, although the urn was a man-made artifact rather than a natural one. The mathematician has an even stronger claim for using aesthetic criteria as a guide to truth. The declaration that Euclid’s proof of the infinity of primes is beautiful is certainly meaningful, and the generalisation that mathematical intuition depends on the detection of such beauty soon follows from this aesthetic point of view. However, beauty is being used here as a guide to enquiry but not as a final criterion of truth. The subjectivist objection might be that truth and beauty are generated in the human mental system and so are not proper attributes to the real world as a noumenal domain. In this case, there might very well be a strong connection between aesthetic and veridical judgments.<br />
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Putting aside the inappropriate comparisons of truth and beauty in S1 and S2, the assertion that knowledge is limited to these two statements is clearly false. Even if beauty cannot be separated from truth, this would not justify ignoring all else that we take for true knowledge of our world. Indeed, if truth and beauty are equivalent then we can drop one of them as redundant. To reject all other knowledge is surely epistemological hubris. Most of the humble facts of daily experience, as well as much of scientific knowledge would be excluded from Keats’s idealistic garden of perfect delight. Of course, he may only have intended to assert what he felt was a special relationship between beauty and truth, rather than to follow up the inherent contradictions of this profession of aesthetic idealism.<br />
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The fourth proposition reinforces the third by insisting that no further knowledge is required beyond the equivalence of beauty and truth. This could only make sense in a metaphysical system of which S1, S2 and their equivalence were the axioms, from which all else could be deduced in the perfect world of the poets imagination. From this exalted point of view, the poet seems to have been striving after the kind of ultimate truth that philosophers had long sought after and latterly rejected.<br />
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In Keats’s time the vogue for Greek art was still highly influential. That supreme example, the Parthenon, had incorporated the highest geometrical knowledge of classical Greece, and so expressed a formal beauty derived from it. Given that mathematical principles are embodied in nature and strongly influence our ideas of beauty, Keats’s perception of the relationship between beauty and truth assumes a clearer meaning. What we mean by beauty is the expression of mathematical form intuitively observed in nature through the senses. One might have expected the nature loving poet to have observed the perfidious function of natural beauty. All manner of deceits are dressed up in nature’s colourful finery. Butterflies open their wings to display imitation eyes and beautiful sexual displays are widely used generally to lure a mate. Such strategies are clearly inconsistent with displays of truth combined with beauty in nature. Deception therefore has long preceded the emergence of mankind and its ability to develop such abstract categories as truth or beauty. But even without such deceptions, there are the illusions that derive from imperfect perception. The fly with its compound eyes is presented with multiple views of its world, and even humans learn the clever trick of seeing a world transformed from the inverted image that falls on the retina. <br />
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Our quotidian experience involves continual judgments, both conscious and unconscious, about the present. Standing upright or walking requires such adjustments which may only enter into consciousness when we stumble, and experience error. In going about our business we make innumerable judgments according to habitual criteria, consciously learned or otherwise, which may turn out to be wrong. Some of these criteria are of a sufficiently high order to qualify as beliefs, although many of them may have been acquired as received knowledge rather than consciously examined and granted the status of truth. So, we live among a welter of beliefs which guide our actions and only occasionally get examined for their veracity. <br />
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For higher animals, truth is intimately bound up with memory, and may be marred by its imperfections. Memories of past events can be compared with present situations and accumulated knowledge acquired through memory and concept formation used to make judgments in the present. This process gives rise to the idea of repeated similarities between prior and current events. One overarching truth we observe is that events, though similar, are unique. The clouds we see today may resemble those of yesterday but cannot possibly be identical because of their random structure. Other more permanent forms, such as rocks, trees, and common animals exhibit a stronger degree of resemblance and form the basis for the belief that their identity persists over time, even while they gradually change. This very complex state of affairs is the basis on which we experience and formulate ideas of truth.<br />
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The fairly recent discovery of non-linear mathematics has demonstrated that nature mimics infinite forms, as in the case of each unique snowflake, river channels, human bronchi and mountain ranges. The corollary is that limitations are placed on human ability to understand and to adapt to a world of potentially infinite complexity. <br />
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One approach to the truth enigma is to ask, what kind of things the attribute ‘true’ can meaningfully apply to. One answer is that it applies to beliefs, but these must at least be encoded in some way, usually in a language, before such judgments can be made. Furthermore, the resulting statements need not be believed at all, or any beliefs in them suspended for purposes of logical or semantic analysis. The essential point is that beliefs can be divided into true and false beliefs, so that the fact of believing something is distinct from the fact that the proposition expressing the belief is true or false. In other words, belief has no effect on whether a state of affairs is true or not, except in those cases where human physical or mental performance is influenced by belief, eg to win a race or pass an examination. <br />
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In the Keats example, there was some uneasiness about whether statements like “truth is beauty” are even meaningful, as in Chomsky’s example: “colourless green ideas sleep furiously”, which is grammatically correct but meaningless and contradictory. To judge whether a state of affairs is true or not, it is necessary to encode the situation clearly, unambiguously, grammatically and meaningfully. The expression of ideas in a language exacerbates the problem by transferring the focus of truth judgments to propositions and away from unformulated beliefs or situations that the propositions represent. For example, if we assert “The King of France is bald” several linguistic problems arise: there is no present King of France, we do not know which past king is being referred to or to what degree of hair paucity constitutes baldness. The power of language is very great, and innumerable propositions about a subject may have to be composed before any factual truth criteria can be considered. The simple assertion, “the earth goes round the sun” is readily understood by our educated minds, but some thought would be needed by the non-specialist to demonstrate this scientific ‘fact’ to a disbeliever. Indeed, it was not until 1838 that the astronomer F.W. Bessel was able to measure the parallax of a nearby star to show that the earth was at a different place from the time of the first measurements compared with observations six months later. Einstein, of course, threw doubt on what the term ‘different place’ might mean. <br />
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In this astronomical example, the truth was established by making not only accurate observations but also by relying on the validity of trigonometry, whose truths are of quite a different kind from facts established by observation of what we call the real world. Fortunately, the delicate observations did not depend on Einstein’s as yet to be discovered facts about the behaviour of light under strong gravitational fields but would have been affected by the refraction of light through the earth’s atmosphere under different atmospheric conditions. The point here is that establishing a fact in one area of science may depend on believing a host of other facts. If any of these should prove to be untrue, there may be significant ramifications for those experiments or theories which assumed they were true. <br />
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From this point of view, our most certain fields of knowledge are a contingent house of cards that must be continually be maintained. Similarly, when we make our casual judgments about our ever day lives, we rely on innumerable beliefs, most of which are received knowledge and many of which we would be incapable of adequately demonstrating as true. <br />
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It is often the case that we form opinions, particularly about people, based on their appearance, manner and a few instances of social behaviour. Hypotheses are formed and tested by observations until beliefs about them become firmly established. Such opinions may be influenced by received ideas about how people of their class, colour, creed, occupation, or physiognomy usually behave. In this arena of unavoidable social interaction and judgment, beliefs are founded intuitively rather than through any systematic assemblage of consistent propositions, as would be required in a science. Human behaviour is very complex, a fact which renders difficult the social sciences from psychology to economics. The veracity of statements in these fields of knowledge is commensurately less certain and often characterised by probability rather than certainty.<br />
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It should be clear even to the most exalted mind that significant truths are hard to come by and that, consequently, we live in a fog of beliefs that fall short of the highest standards of veracity. To make matters worse, psychology makes clear that the human mind can be unreliable in making even simple judgments about recent or even current events. The conjuror makes use of this deficiency by exploiting the tendency of the mind to fill in the gaps between what actually occurs, i.e. as recorded on a video camera, and what they think happened. It seems that the control of the senses by the mind produces a mixture of fact and predictive fiction as it attempts to assess what is likely to happen on the basis of quickly varying events.<br />
Truth, then, depends on the formulation of memories and beliefs and the comparison of these with some kind of independent criteria. The most obvious comparator in the case of everyday events is the memories and beliefs of independent witnesses, as well data from any recording devices. This raw material of quotidian events produces quite a different class of truths from the important generalisations about the human condition and the physical environment on which humans depend. Classification, abstraction and generalisation form the basis of useful knowledge, which is different from the truths of individual observations and events. The truths of science require the additional assumption that what is true in several cases can be generalised to apply to all similar cases, the basis of induction. The failure of a hypothesis might be due to imperfect observations about a few situations of the required type or it might be due to unexpected or unknown factors. A grander scientific assumption is that identical circumstances (ceteris paribus) must produce the same results, or be due to different or improperly controlled factors not included in the theory. Establishing the truth of such fundamental ideas poses a special problem for epistemology. <br />
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The empirical procedures and inductive analyses which form the basis of scientific enquiry, together with informed hypotheses have led to general truths of incalculable benefit to humanity. It is hardly surprising, therefore, that the truths of science have replaced the once ubiquitous religious and philosophical beliefs that sustained earlier societies. The question, what is scientific truth, could be answered by saying that it is the body of knowledge, albeit provisional, that has accumulated as a result of applying legitimate scientific methods to the highest possible standards, and confirming the results by the process of peer review.<br />
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This is a very high standard indeed when compared with the way we form common beliefs in our business and private lives. In general then, truth is the body of the best knowledge that humans are capable of producing in the present state of cultural development. Even in the span of a century or so, great changes have occurred in both philosophy of knowledge and the processes of science and technology which have led to what may be classified as truths. <br />
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Several philosophical theories of truth have been formulated. The correspondence theory assumes that the truth predicate applies to beliefs, and further supposes that every true belief corresponds to a fact. This assumes that there are such things as true facts and that their veracity can be established. The Pragmatist William James objected that this approach was just a lexical trick that did not discuss the nature of truth at all. The salient point is that the idea of truth enters into both beliefs and what are regarded as facts and it is not clear what is meant in either case by saying that a belief or a fact is true, apart from applying the attribute to a fact and a corresponding belief simultaneously. <br />
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In the coherence theory of truth, the objection is that individual statements are incapable of capturing truths about ‘reality’, since states of affairs may be described in different ways from different perspectives and motives. Furthermore, descriptions of events are infected by the meanings inherent in the language used, which imports ready-made concepts into the description of what is supposed to be the factual criteria. Only a wide theoretical context will suffice to judge whether a statement is true or not. This mirrors what we actually do in making casual truth judgments, where comparisons are made with our existing knowledge base to see if any inconsistencies arise from accepting a new idea or supposed fact. William James’s pragmatism supposed that true beliefs were those that we must act upon in order to survive or advance the welfare of humanity, which is a rather partisan notion that fits in well with the American predilection for social Darwinism, as opposed to an impartial and unselfish search for truth for its own sake. <br />
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Tarski’s semantic conception of truth applies truth and falsity to sentences, and consequently focuses on their meaning. He pointed out that a statement such as: (It is true that (Socrates was wise)) are meta-lingual statements, where an assertion is made about another statement in what he called an object language. He provided the gnomic example: “snow is white” if and only if ‘snow is white’. One could interpret the first statement to be a belief and the second to be a statement of an empirical fact, which doesn’t seem to advance matters much beyond the rejected theory of correspondence. The objection to this approach is that the so called real world is lost in the process of linguistic and logical formulations. It is worth observing here that pure logic is not at all concerned with empirical meaning and so can provide no guidance whatever on the vexed relationship between an empirical fact and its description as a thought or a belief.<br />
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The distinction between truths of the mind, a priori truths, and observed or a posteriori truths is an important one. An early system of a priori truth was Euclid’s geometry, which was based on five axioms and five elements of construction. This proved capable of generating innumerable mutually consistent theorems, including the well-known truth that the angles of any plane triangle add up to two right angles. The truth of many of these theorems is not immediately obvious to the uninformed observer of geometrical figures and provided essential knowledge for ancient architects and surveyors. How wonderful that every triangle inscribed in a semi-circle is a right angled triangle, and that every triangle inscribed inside an arc defined by an arbitrary chord generates triangles with a constant angle. It is this power to generate truths about infinite cases which distinguishes mathematics from empirical science. <br />
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The idea that a few basic ideas and rules of logic could generate new knowledge was a powerful one, which dominated philosophy until quite recent times. The false idea was that knowledge of a few fundamental principles in philosophy or science would be sufficient to deduce all possible knowledge. A corollary of this idea is that the resulting totality, realised or not, represented a perfect and consistent body of truths, just like the totality of all possible theorems derived from Euclidean Geometry. An obvious drawback to this epistemological programme is that it could only apply to a priori systems, which would confine the resultant knowledge to logic, mathematics and related disciplines. The unfortunate truth was that there is no obvious connection between empirical truths and the logical means of elaborating facts about the physical world.<br />
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This idealistic view persisted until recent times, until empiricism and the rise of science gradually confined it to speculative philosophy. It still remains a philosophical question as to how the observed behaviour of the physical world conforms to Euclidean geometry or to the more advanced systems of mathematics that are so essential to modern science. However, some philosophers of science think this need have no bearing on how science is conducted in pursuit of knowledge. However, what does seem to restrict the progress of scientific theories is the lack of sufficiently powerful mathematical theories used to formulate and describe them. The calculus is an obvious example in relation to mechanics and other areas of physics, as is matrix theory and probability theory in their many applications to science. This indicates the strong dependence of empirical theories on specialised languages. <br />
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A peculiarity of axiomatic systems, both logical and mathematical is that different axiom sets can lead to different and sometimes inconsistent theorems. A simple example is that the angles of a triangle drawn on a sphere add up to more than two right angles, and so does not even include the corresponding Euclidean theorem as a special case. The distinction between Newton’s and Einstein’s theories of space and time is another example of differing but true systems. This difficulty extends to formulating logical languages for demonstrating the consistency of mathematical truths. The avoidance of paradoxes had doomed Russell’s and Whitehead’s attempts to provide a reliable logical language as a basis for all mathematics. Kurt Gödel upset the apple cart by proving that it was not possible to construct such a language that was both consistent and complete, so that there would always be, potentially, true but unprovable theorems describable in the system. This put an end to the dream of creating a final system of a priori knowledge, and further undermined the kind of certainty associated with grand systems of universal truth, whether empirical or not. <br />
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From one point of view, the pursuit of knowledge requires both the general principle of truth and the philosophical, logical, mathematical and empirical means of establishing the ever changing facts which are generally agreed to be true. Because the body of such knowledge is now so vast, it has become inaccessible to the ordinary citizen, if only because of the cost and deficiency of educational systems and the limits to individual knowledge. One unfortunate result of this divide is that beliefs in the general population fall far short of the knowledge that is available to those with the inclination, means and opportunity to obtain access to them. In other words, general ignorance is a source of discontent and social upheaval, often exploited by unscrupulous politicians for personal power and by corporations who wish to preserve an ignorant and subservient population. <br />
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Access to these huge knowledge bases has been greatly increased through the medium of the Internet, but this has also provided access to many bodies of pseudo-knowledge and speculative thought that lies outside the strict borders of academic and professional knowledge. The term truth has been stretched accordingly to accommodate this burgeoning diversity. One particular example of this is the reactionary movement of creationism which seeks to re-establish forms of authoritarian knowledge prevalent in earlier societies. The tension is between restrictions on free thinking beneath the shadow of the now enormous tree of accepted knowledge and allowing a tangle of speculative and redundant thought to thrive in the jungle outside its shadow. Such a wilderness has often nurtured the kind of mavericks who have contributed greatly to scientific and cultural knowledge, so tolerance of a robust unorthodoxy is preferable to an epistemological monoculture. The counter argument that academia already encourages such diversity of thought is less convincing now that corporations finance and control so much of what constitutes advanced education. The corollary is that the truth, whatever it might be, ought not to be controlled by orthodoxy or by whatever dominant philosophy may declare it to be. <br />
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We continue to search for truth without knowing exactly what it is or how we ought to go about it. The combined efforts of countless generations have shown that such a search is both valuable and necessary for human welfare, and latterly perhaps, continuance as a species. It seems obvious, if not proven, that adherence to truth in its many forms is our best hope for a satisfactory social life and that weeding out false beliefs, albeit in a kindly way, must be an ongoing project. Notwithstanding that great monuments to truth have been erected, their continual replacement, however costly, ought to continue if civilisation is to remain accessible to a majority of humans. The balance of false beliefs seems to be gaining ground and might easily derail the beneficial presence of true if not final beliefs that assist humanity on its journey into the unknown.<br />
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Tony Thomas<br />
April 2011Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com0tag:blogger.com,1999:blog-7897013436752033900.post-8222784899931614182009-10-16T22:57:00.000-07:002009-10-16T23:17:15.985-07:00What is Knowledge?<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2YN5J1sUAq_bTbkqlqxbENNztKQQZoQ8gTNKW3x96WRlitaxer7xcDP8F79xyw5yG4y6zlb_RMccKICU9y0VvKVJRvzsgyoXPvoGMM0d0nN_dQ5AkNH1vCZiOkH2hEQuHVwomM10ypg4/s1600-h/Knowledge.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2YN5J1sUAq_bTbkqlqxbENNztKQQZoQ8gTNKW3x96WRlitaxer7xcDP8F79xyw5yG4y6zlb_RMccKICU9y0VvKVJRvzsgyoXPvoGMM0d0nN_dQ5AkNH1vCZiOkH2hEQuHVwomM10ypg4/s640/Knowledge.jpg" /></a><br />
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Like many fundamental questions, 'what is knowledge' is surprisingly difficult to answer in a satisfactory way. This is because it is an important philosophical question that forms the basis of the division of philosophy called epistemology. A dictionary definition yields the following:<br />
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Knowledge (n)<br />
1 information and skills acquired through experience or education - the sum of what is known. Philosophy true, justified belief, as opposed to opinion.<br />
2 awareness or familiarity gained by experience.<br />
- PHRASES come to one's knowledge become known to one. to (the best of) my knowledge 1 so far as I know. 2 as I know for certain.<br />
- ORIGIN ME (orig. as v. in the sense 'acknowledge, recognize')<br />
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The most basic meaning is of being aware that some thing or situation resembles another one that has been previously experienced and exists as a memory. For example, recognizing a face is a skill that does not require conscious, volitional learning but happens automatically: hence familiarity gained by experience, which is not peculiar to humans but is present in all animals who modify their behaviour in response to pain or pleasure. The usual example given is the pain a child feels before learning to avoid contact with fire. This becomes encoded in language as the proposition, "fire burns" or the more general form, "fire is hot", signifying that fire belongs to a more general category of phenomena which can be harmful or useful to mankind. This introduces the fundamental role of knowledge as not only helpful to the conduct of life but essential for survival. In this sense, both humans and animals are knowing beings.<br />
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The first meaning distinguishes between information and skills. The latter may be motor skills, like sawing a piece of wood or playing the violin which involve a different process of repetitive practice from learning, say the multiplication tables, the latter requiring some minimum understanding of numbers and their properties. When Bertrand Russell was a young child he was reduced to tears by his inability to learn the multiplication tables and he records, in his autobiography, that what delighted him most was learning that blue mixed with yellow produced green. Here is what he had to say about learning some basic algebra.<br />
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The beginnings of Algebra I found far more difficult, perhaps<br />
as a result of bad teaching. I was made to learn by heart:<br />
"The square of the sum of two numbers is equal to the sum of<br />
their squares increased by twice their product." I had not the<br />
vaguest idea what this meant, and when I could not remember<br />
the words, my tutor threw the book at my head, which did not<br />
stimulate my intellect in any way.<br />
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This example of the failure of rote learning by a child of exceptional intelligence shows that the acquisition knowledge is affected by the form in which it is presented to the student. The translation of the symbolic form of the mathematical expression into words, instead of explaining the relationship between the parts of the algebraic expression (a + b)2 = a2 + b2 + 2ab, was the cause of the problem, since Russell had no problem learning his Euclid. For Russell, the linguistic proposition was not knowledge because it was meaningless relative to his understanding. It follows that, for the student, knowledge must be understood and meaningful in relation to existing knowledge. Knowledge, therefore, exists in clusters, not in isolation.<br />
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It is clear from the rest of the definition that, for the philosopher, empirical knowledge is always provisional and subject to revision. This has become a basic principal of science but is often ignored in daily life where certainty about common knowledge is usually assumed. Even apriori knowledge may prove inadequate, as non-Euclidean geometry shows. The lesson here is that absolutely true knowledge is always subject to prior assumptions as expressed by the term ceteris paribus. The experimental scientist must restrict his variables by excluding possible but highly improbable factors from the variables. The discoveries of empirically established 'facts' become knowledge, but always subject to the conditions of the theory and experiments within which they are constructed.<br />
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Outside the laboratory and the University a great deal of information is taken on trust as factual. The inadequacy of human records and memory becomes clear when they are disputed in the adversarial system of the courts, where arriving at the truth is a tedious process of forensic examination. Such analysis is usually impractical in business or government, where highly educated individuals are trusted to use their skills and experience in making informed judgments about what are true facts and what are doubtful propositions. The idea of facts being beyond reasonable doubt or of high probability has become an essential tool of administrators as well as scientists. The necessity for scepticism about unusual proposals is well understood and undermines the simplistic assumptions that we always deal with true facts rather than those that common sense and experience suggest are probably true. For practical purpose, therefore, one is always dealing with facts that may turn out to be false, albeit with a small probability.<br />
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The corollary of all this is that the bulk of what the non-specialist knows is a mish-mash of well established common knowledge, which is probably true, and a great deal of assumptions deduced from this knowledge which might be flawed due to inadequate reasoning. While most intelligent people reason correctly about everyday affairs, when faced with complex circumstances involving a huge number of facts and assumptions, this reasoning proves inadequate, and intuitive judgments are applied instead. While humans are capable of reasoning, it would be wrong to assume that they are predominantly reasonable in their judgments as opposed to intuitive, reactive and emotive.<br />
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The distinction between knowledge and assumptions is latent in human affairs, and the incorporation of statements in printed or electronic media raises the status of such information from provisional to established facts.<br />
Editorial or peer review, or the category opinion rather than fact, goes a long way towards ensuring the quality of recorded knowledge, but the vast quantity of such widely available information reduces the overall quality of such knowledge.<br />
Disputes about whether a certain body of knowledge is true are commonplace. Prior to the 18th Century is was unthinkable or at least unwise to challenge religious orthodoxy, whose vast repositories of doctrine went largely unchallenged, except within the upper reaches of the various churches. Theological debate, like today's science, was the preserve of specialists. In our world, specialists abound and represent a process of creating bodies of knowledge that can be widely applied. Fields of doubtful knowledge abound, including psychoanalysis, literary theory, new age regurgitations of Eastern philosophy and many more fields where pseudo-knowledge stakes its claims. This only matters when they affect important government or business decisions, or individual welfare. Familiar examples are the definitions of human personality that underlie the vexed debate over contraception and abortion. This is a case of a conflict between new knowledge or understanding versus old knowledge based on redundant religious beliefs. A more important example is the more complex question of global warming, which turns upon a vast number of facts and theories developed by many different scientific specialists relevant to understanding climate change.<br />
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Big questions like 'has peak oil been reached' or 'will average temperatures rise by more than 3% in the next 20 years' do not admit of definite answers, only informed opinion arrived at by scientific or technical experts. The problem of deliberately distorted information about these important questions is evident in the biased reports and lobbying that is currently taking place. It is clear that politics, at all levels, has an impact on what can be accepted as true, just as religion is often the enemy of truth in both past and present. Indoctrination by the mass media on these and many other sensitive issues shows that many facts commonly held to be true are artefacts of propaganda. In other words, orthodox knowledge is manufactured by ruling elites to serve their interests. An examination of what constitutes knowledge must take account of this fact of life.<br />
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The import of this is that finding reliable sources of information depends not only on doing enough research but making judgments about these sources based on ones own flawed judgment. When faced with hundreds of thousands of seemingly intelligent people who question, say, Darwin's theory of evolution, it becomes evident that untutored opinions are the norm rather than the exception. Like the esoteric theological doctrines of the past, advanced knowledge of, say, biotechnology lies beyond the competence of the average person. Furthermore, advanced specialist in one discipline lack competence in most others fields of advanced knowledge.<br />
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What is knowledge and what is contestable theory is an ongoing problem when viewing human knowledge as a whole, no more so than in the field of economics, where the ever increasing complexity of society casts doubt on theories widely adopted by governments. Knowledge in the social sciences is generally agreed to be less reliable than in the physical sciences, where controlled experiments are possible. Unfortunately, it is in the human sciences that solutions to social problems exist and the need for reliable knowledge can be critical to control by both government and management. The very idea of such controls calls up the philosophy of ethics, which is yet another field of knowledge which can only be established by making arbitrary assumptions or appealing to 'facts' derived from social sciences such as psychology and anthropology.<br />
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In today's complex societies, stability increasingly depends on narrow specialist, but also on generalists, usually managers or administrators, who specialise in generality, or comprehending and judging the work of specialists and coordinating it towards the achievement of certain goals. Such generalists have always existed as eminence grises in the corridors of power. The training of administrators in Britain and France, as well as other nations has long been focused on the task of making future mandarins. What kind of special knowledge should they be taught to equip them to deal with the great generalisations appropriate to the government of millions? Beginning with the works of Plato and Aristotle seem somehow inadequate but choosing alternatives is a difficult educational decision in itself. Who will train the Guardians and then protect us from them is an insoluble problem.<br />
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From a philosophical point of view, knowledge is the totality of true propositions. Unfortunately this set is potentially infinite and its contents mostly irrelevant to the imperatives of individual or collective purposes. From this point of view, it is the engine of human purposes, rational or not, that create the demand for existing knowledge or for the creation of new knowledge. Knowledge, then, is a mental artefact, discovered or created for human use. The body of pertinent knowledge is what is actually in current use or is being created by science or other disciplines. As pointed out above, a great proportion of this knowledge will be doubtful or false, if only because humans have a preference for the useful or interesting rather than the true.<br />
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Understanding what qualifies as knowledge is an example of what Wittgenstein called a language game, where meanings are not separated by sharp boundaries. A final, complete and perfect definition of knowledge for all purpose, therefore, is not to be expected. Far more useful is to address the prior question, why do I want to know what knowledge means and what use will such a definition be to my present purposes. This question is relative to the individual and would produce a commensurately different set of propositions about what knowledge means to them.<br />
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Tony Thomas<br />
October 2009Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com0tag:blogger.com,1999:blog-7897013436752033900.post-1628274521290011492009-10-14T01:21:00.000-07:002009-10-14T01:40:29.464-07:00Nietzsche's eternal recurrence<div class="separator" style="clear: both; text-align: center;"><br />
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<div>Nietzsche presents the idea of the eternal recurrence in three chapters of Thus Spake Zarathustra (TSZ). These are: On the Vision and the Riddle, The Convalescent and The Seven Seals, the second chapter containing the most detailed explanation; the third being a note on eternity.<br />
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</div><div>Before examining the 'doctrine' of eternal recurrence it is worth asking whether anything in TSZ can be taken at face value or as genuine philosophy. The aim of the work seems to be to establish Nietzsche as a great and unique human being through the poetic fiction of his proxy, the prophet Zarathustra. If the whole work is intentionally ironic, in explaining the difficulties that a great philosopher has in getting his ideas across, then it is entirely acceptable. However, if Nietzsche actually believed in the myth presented in TSZ, it would appear to be the work of a megalomaniac, albeit a significant one of poetic fantasy.<br />
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</div><div>It seems probable that Nietzsche did attach importance to the ideas expressed in TSZ and was convinced of his own greatness to an unhealthy degree. This is consistent with his notion of creativity, where the positive affirmation of the individual and of life in general is a sign of greatness. This positive attitude towards achieving greatness permeates TSZ, and runs counter to the mainstream of philosophical discourse since Descartes, which is characterised by scepticism and doubt. Zarathustra affirms life, with all its suffering, and finally exults in the certainty that the superman will lead humanity to a better life. Contrasted with this is the pessimism and disgust with life that precedes his epiphany in The Convalescent. The role of the eternal recurrence is to render the coming of the overman certain in the way that Christians use their doctrinal framework to ensure the second coming of their saviour. Marx's belief that socialism was inevitable relies on a similar pattern of thinking.<br />
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</div><div>On the Vision and the Riddle<br />
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</div><div>Part 3 of TSZ was written in 1884, a few years after Nietzsche's decline in health had forced his retirement from academic life. However there is no suggestion that he was not mentally competent when it was written. However, the chapter entitled The Convalescent may well have been related to the several severe complaints he suffered from, which included migraines and stomach illnesses. It is interesting that Zarathustra suffers a physical and mental collapse in this chapter but it is in the earlier On the Vision and the Riddle that a psychologist is given an insight into Nietzsche's state of mind several years before his actual collapse.<br />
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</div><div>The chapter opens with Zarathustra on a sea voyage, but quickly turns to an address to, "you bold venturers, adventurers", who are complimented: "because you do not want to probe along a thread with cowardly hands; and because where you can guess, there you hate to deduce". This remark suggests that the story Zarathustra is about to tell is not for the ears of pedantic philosophers but is aimed at more adventurous intellectual spirits.<br />
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</div><div>Zarathustra is then depicted as climbing with great courage and difficulty up a steep mountain path (an exercise that the backpacker Nietzsche was familiar with) impeded by having to carry a "half dwarf, half mole, lame, paralysing, dripping lead in my ear, lead-drop thoughts into my brain." This dwarf aspect of Zarathustra then criticises his efforts rather cleverly, by pointing out "You hurled yourself so high - but every hurled stone - must fall!" This can be read as Nietzsche's internal dialogue convincing himself that he can achieve greatness if he can rid himself of the dwarf, characterised by gravity itself, that is holding him back. The dwarf, then, is his self-doubt. Nietzsche confirms that the dwarf is an aspect of his psyche by having Zarathustra say, "and being at two in such a way truly makes one lonelier than being at one."<br />
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</div><div>Zarathustra continues to bewail his struggles and concludes by saying, "Dwarf - you or I!" He asks, "Was that life? Well then! One More Time!" This appears to be the subtle announcement of the doctrine of eternal recurrence. Although Zarathustra's life has been hard, oppressive and agonizing, he decides that he wants to have more of this life.<br />
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</div><div>Part 2 of the chapter begins with Zarathustra confronting his dwarf with the words, "Stop, Dwarf! "I - or you! But I am the stronger of us two - you do not know my abysmal thought! That - you could not bear!" The dwarf hops down from his shoulder and Zarathustra proceeds to explain to him his abysmal thought. The text continues as follows:<br />
</div><div><br />
</div><div> "See this gateway, dwarf!" I continued. "It has two faces. Two paths<br />
</div><div>come together here; no one has yet walked them to the end.<br />
</div><div>This long lane back: it lasts an eternity. And that long lane outward -<br />
</div><div>that is another eternity.<br />
</div><div>They contradict each other, these paths; they blatantly offend each<br />
</div><div>other - and here at this gateway is where they come together. The name<br />
</div><div>of the gateway is inscribed at the top: 'Moment.'<br />
</div><div>But whoever were to walk one of them further - and ever further and<br />
</div><div>ever on: do you believe, dwarf, that these paths contradict each other<br />
</div><div>eternally?" -<br />
</div><div>"All that is straight lies," murmured the dwarf contemptuously. "All<br />
</div><div>truth is crooked, time itself is a circle."<br />
</div><div><br />
</div><div>The dwarf rightly notices that the metaphor is linear, ceteris paribus, but this is only Zarathustra arguing with himself. The statement that "no one has walked them to the end" seems pointless, since the paths are eternal and humans are mortal. Also, the idea of walking back in time seems impossible whether the path is eternal or not. It is interesting that Nietzsche confounds time and space in this model, as if he were anticipating Einstein's concept of space-time. Similarly, the arbitrary 'moment' where Zarathustra and the dwarf are conversing anticipates the relativistic origin of a local space-time system of coordinates. The two paths contradict because of the 'arrow of time' constraint, but it is unclear whether Nietzsche intends this to be the answer to his question. It seems that the dwarf does not like the linear concept of an infinite path, from indefinite past to indefinite future, but prefers a crooked or circular one. Elsewhere in TSZ, the dwarf is referred to as the Devil, so the confrontation described above can be seen as a variant of the dialogue between Christ and Satan in the desert.<br />
</div><div><br />
</div><div>"You spirit of gravity!" I said, angrily. "Do not make it too easy on<br />
</div><div>yourself! Or I shall leave you crouching here where you crouch, lamefoot -<br />
</div><div>and I bore you this high!<br />
</div><div><br />
</div><div>It is not clear from this remark whether Zarathustra prefers a linear eternity or a circular one, but later it becomes clear he does prefer circularity by adopting a wheel of time model.<br />
</div><div><br />
</div><div>See this moment!" I continued. "From this gateway Moment a long<br />
</div><div>eternal lane stretches backward: behind us lies an eternity.<br />
</div><div>Must not whatever can already have passed this way before? Must<br />
</div><div>not whatever can happen, already have happened, been done, passed by<br />
</div><div>before?<br />
</div><div><br />
</div><div>Here the doctrine is stated, that what can happen, must have already happened. The italicized 'can' is critical, and seems to suggest that anything is possible as opposed to the repetition of some restricted set of possibilities.<br />
</div><div>The implication is that the universal event space comprises everything that is not impossible. For the mathematician, this idea can be expressed as a four-dimensional possibility space, but for the physicist this has to be constrained by those mysterious regularities called laws of nature.<br />
</div><div><br />
</div><div>And if everything has already been here before, what do you think of<br />
</div><div>this moment, dwarf? Must this gateway too not already - have been here?<br />
</div><div>And are not all things firmly knotted together in such a way that this<br />
</div><div>moment draws after it all things to come? Therefore - itself as well?<br />
</div><div>For, whatever can run, even in this long lane outward - must run it once<br />
</div><div>more! -<br />
</div><div><br />
</div><div>It is not clear whether Nietzsche had really thought the consequences of his metaphor through. The statement, "everything has been here before" is too general. The small event that is the gateway and its environs when the conversation takes place is not really a 'here and now' but an ongoing (literary) event that ceases when it passes away into new events. Nietzsche's use of 'everything' seems to suggest that the particular space-time juncture is associated with every conceivable event, which is clearly erroneous. The best that can be said is that the construction is just a fanciful figure of speech that does not bear close analysis. The alternative is that Nietzsche is too clever to be understood by all but those who espouse his obscure idea.<br />
</div><div><br />
</div><div>And this slow spider that creeps in the moonlight, and this moonlight<br />
</div><div>itself, and I and you in the gateway whispering together, whispering of<br />
</div><div>eternal things - must not all of us have been here before?<br />
</div><div>- And return and run in that other lane, outward, before us, in this<br />
</div><div>long, eerie lane - must we not return eternally? -"<br />
</div><div><br />
</div><div>The concept is clarified here, by affirming that the precise 'state of affairs' described will be exactly reproduced, presumably at some other time. This raises the major difficulty of understanding how the space-time of a particular event could be holographically reproduced and distributed throughout Zarathustra's eternal cosmos.<br />
</div><div><br />
</div><div><br />
</div><div>Thus I spoke, softer and softer, for I was afraid of my own thought and<br />
</div><div>secret thoughts. Then, suddenly, I heard a dog howl nearby.<br />
</div><div>Had I ever heard a dog howl like this? My thoughts raced back. Yes!<br />
</div><div>When I was a child, in my most distant childhood:<br />
</div><div>- then I heard a dog howl like this. And I saw it too, bristling, its head<br />
</div><div>up, trembling in the stillest midnight when even dogs believe in ghosts:<br />
</div><div>- so that I felt pity. For the full moon had passed over the house, silent<br />
</div><div>as death, and it had just stopped, a round smolder - stopped on the flat<br />
</div><div>roof just as if on a stranger's property -<br />
</div><div>that is the why the dog was so horror-stricken, because dogs believe in<br />
</div><div>thieves and ghosts. And when I heard it howl like this again, I felt pity<br />
</div><div>once more.<br />
</div><div><br />
</div><div>This passage seems to be a feeble attempt to justify the concept anecdotally, but the relevance of the childhood experience and the dog is doubtful.<br />
</div><div><br />
</div><div>Where now was the dwarf? And the gateway? And the spider? And all<br />
</div><div>the whispering? Was I dreaming? Was I waking? I stood all of a sudden<br />
</div><div>among wild cliffs, alone, desolate, in the most desolate moonlight.<br />
</div><div>But there lay a human being! And there! The dog jumping, bristling,<br />
</div><div>whining - now it saw me coming - then it howled again, it screamed: had<br />
</div><div>I ever heard a dog scream like this for help?<br />
</div><div><br />
</div><div>Now Zarathustra reveals that it was all a dream, but links the dream to his present by reintroducing the dog motif.<br />
</div><div><br />
</div><div>And truly, I saw something the like of which I had never seen before.<br />
</div><div>A young shepherd I saw; writhing, choking, twitching, his face distorted,<br />
</div><div>with a thick black snake hanging from his mouth.<br />
</div><div>Had I ever seen so much nausea and pale dread in one face? Surely he<br />
</div><div>must have fallen asleep? Then the snake crawled into his throat - where<br />
</div><div>it bit down firmly.<br />
</div><div>My hand tore at the snake and tore - in vain! It could not tear the snake<br />
</div><div>from his throat. Then it cried out of me: "Bite down! Bite down!<br />
</div><div>Bite off the head! Bite down!" - Thus it cried out of me, my dread, my<br />
</div><div>hatred, my nausea, my pity, all my good and bad cried out of me with one<br />
</div><div>shout. -<br />
</div><div><br />
</div><div>Zarathustra now launches into a new story, but is not clear whether this is just another fancy. The passage is redolent with symbolic significance but it is not clear how Nietzsche intends the symbols to be interpreted, if at all. The Shepherd may stand for Christ, Apollo, Dionysus or some other mythological figure. If it were based on an actual dream, the obvious interpretation is a childhood experience of fellatio, whether performed on the writer himself, or some relative or merely imagined. The snake is traditionally a symbol of wisdom, so the meaning may be that the shepherd, as some kind of leader, is choking on his own wisdom. The biting off of the head and spitting out of the snake may therefore mean the rejection of old knowledge.<br />
</div><div><br />
</div><div>In Psychology and Alchemy (p.137) Jung says of a dream about a snake, ""This is brought about by the ceremonial use of a reptile, presumably a snake. The idea of transformation and renewal by means of a serpent is a well-substantiated archetype. It is reported of the mysteries of Sabazius...(A golden snake is let down into the bosom of the initiated and taken away again from the lower parts). Among the Ophites, Christ was the serpent...The shepherd's experience with the snake in Nietzsche's Zarathustra would accordingly be a fatal omen (and not the only one of its kind - cf. the prophecy at the death of the rope dancer)." It is notable that Sabazius was confounded with Zagreus, the Roman Dionysus. The Shepherd however is to be found in the Hermetica in the person of Peomandres, the Shepherd of Men. Whatever Nietzsche's sources may have been, the important result of the incident is the trauma and nausea that Zarathustra feels as a result of the 'incident' and the subsequent transformation of the shepherd into the superman.<br />
</div><div><br />
</div><div>You bold ones around me! You searchers, researchers and whoever<br />
</div><div>among you ever shipped out with cunning sails onto unexplored seas!<br />
</div><div>You riddle-happy ones!<br />
</div><div>Now guess me this riddle that I saw back then, now interpret me this<br />
</div><div>vision of the loneliest one!<br />
</div><div>For it was a vision and a foreseeing: what did I see then as a parable?<br />
</div><div>And who is it that must some day come?<br />
</div><div>Who is the shepherd into whose throat the snake crawled this way?Who<br />
</div><div>is the human being into whose throat everything that is heaviest, blackest<br />
</div><div>will crawl?<br />
</div><div>- Meanwhile the shepherd bit down as my shout advised him; he bit<br />
</div><div>with a good bite! Far away he spat the head of the snake - and he leaped<br />
</div><div>to his feet. -<br />
</div><div>No longer shepherd, no longer human - a transformed, illuminated,<br />
</div><div>laughing being!<br />
</div><div><br />
</div><div>Zarathustra has moved on from his perfunctory explanation of the eternal recurrence to the birth of the superman. The shepherd has been transformed by his experience into a "transformed and laughing being". This rebirth is reminiscent of the birth of Dionysus from Zeus's thigh or the birth of Athena from his head.<br />
</div><div><br />
</div><div>Never yet on earth had I heard a human being laugh as he laughed!<br />
</div><div>Oh my brothers, I heard a laughter that was no human laughter - and<br />
</div><div>now a thirst gnaws at me, a longing that will never be still.<br />
</div><div>My longing for this laughter gnaws at me; oh how can I bear to go on<br />
</div><div>living! And how could I bear to die now! -<br />
</div><div>Thus spoke Zarathustra.<br />
</div><div><br />
</div><div>Having witnessed the birth of this superhuman being, albeit in a vision, Zarathustra realizes his own irrelevance but cannot bear to accept his mortality - he must go on living, to glory in the superman.<br />
</div><div><br />
</div><div>The Convalescent<br />
</div><div><br />
</div><div>At the opening of this chapter, Zarathustra suffers an epiphany, behaving like a madman he "screamed with a terrifying voice and behaved as though someone else were lying on his bed, who did not want to get up". He then refers, presumably, to the eternal recurrence by saying, "Up, abysmal thought, out of my depths!... listen! Because I want to hear you!" This latter remark reinforces the separation between the two personalities within, the 'you' being his "most abysmal thought".<br />
</div><div>The first section finishes with "Hail to me! Here now! Give me your hand - ha! Let go! Haha! - Nausea, nausea, nausea - oh no!" The uniting of Zarathustra with his great thought leads first to nausea and then to the complete collapse described in Part 2 of the chapter. From a psychological point of view, Zarathustra seems to have suffered a personality split, with his 'abysmal thought' becoming the dominant identity.<br />
</div><div><br />
</div><div>After a convalescent period of seven days, Zarathustra is persuaded by his<br />
</div><div>animals to "step out of your cave: the world awaits you like a garden. The wind is playing with heady fragrances that make their way to you; and all brooks want to run after you." He returns to the idea of the eternal recurrence by saying, "aren't words and sounds rainbows and illusory bridges between things eternally separated? To each soul belongs another world; for each soul every soul is a hinterworld." He continues with this subjectivist position by saying, "For me - how would there be something outside me? There is no outside!" <br />
</div><div><br />
</div><div>The animals then take over the discourse and tell Zarathustra about the wheel of being, "Everything dies, everything comes back: the wheel of being rolls eternally. Everything blossoms again, the year of being runs eternally." All this is just conventional medieval philosophy about seasonal change, and its illusion of certainty. But then, "Everything breaks, everything is joined anew; the same house of being builds itself eternally. Everything parts, everything greets itself again; the ring of being remains loyal to itself eternally. In every Instant being begins; around every Here rolls the ball There. The middle is everywhere. Crooked is the path to eternity."<br />
</div><div><br />
</div><div>Zarathustra then confirms that he is the shepherd of the earlier vision by saying, "How well you know what had to come true in seven days - and how that monster crawled into my throat and choked me! But I bit off its head and spat it away from me." He confirms that he has been redeemed by saying, "Now I lie here, weary still from this biting and spitting out, sick still from my own redemption."<br />
</div><div><br />
</div><div>After a litany of complaint, including the cruelty and lust of human beings, and their littleness, Zarathustra explains that it was "My great surfeit of human beings - that choked me and crawled into my throat; and what the soothsayer said: 'All is the same, nothing is worth it, knowledge chokes.' "<br />
</div><div><br />
</div><div><br />
</div><div>The animals seem to recognise that this nausea and nihilism is just part of the convalescent process, and urge Zarathustra to, "Go outside to the roses and bees and swarms of doves! Especially to song birds, so that you can learn to sing from them!" The animals urge him to "fashion yourself a lyre first, a new lyre!" Presumably this is a reference to Hermes, who invented the lyre, and is none other than the shepherd Poemandres, but the deeper meaning is that Zarathustra must heal himself, "so that you can bear your great destiny, which was never before a human's destiny." The meaning seems to be that Zarathustra must assume the role of a tutelary god because, "you are the teacher of the eternal recurrence." Hermes Trismegistus was, of course, the tutelary god. The remainder of the chapter focuses on explaining the eternal recurrence.<br />
</div><div><br />
</div><div>That you must teach this teaching as the first - how could this great<br />
</div><div>destiny not also be your greatest danger and sickness!<br />
</div><div>Behold, we know what you teach: that all things recur eternally and<br />
</div><div>we ourselves along with them, and that we have already been here times<br />
</div><div>eternal and all things along with us.<br />
</div><div>You teach that there is a great year of becoming, a monster of a great<br />
</div><div>year; like an hourglass it must turn itself over anew, again and again, so<br />
</div><div>that it runs down and runs out anew -<br />
</div><div>- so that all these years are the same as each other, in what is greatest<br />
</div><div>and also in what is smallest - so that we ourselves in every great year are<br />
</div><div>the same, in what is greatest and also in what is smallest.<br />
</div><div>And if you wanted to die now, oh Zarathustra: behold, we know too<br />
</div><div>how you would speak to yourself then: - but your animals beg you not to<br />
</div><div>die yet!<br />
</div><div><br />
</div><div>There is 'great year' in Hindu cosmology, which is much greater than the 25,765 year precession cycle, known to western astronomy as the Great or Platonic year. This latter precession cycle was probably known to Aristarchos of Samos (280BC). The Hindu cycle is based on Kalpas, or one Brahma day, which endures for 4.32 billion years. The Brahma year is therefore very large indeed. The cosmos is destroyed and recreated in the Hindu system but there is no exact repetition as described in the passage above. Indeed, the stories about the Buddha's previous lives indicate the uniqueness of each reincarnation and the progression towards perfection. What is not clear from Zarathustra's exposition is how long his cycle is or if it is finite or infinite. The hourglass metaphor is quantitative only and does not explain why or how each grain of sand would exactly repeat its flow history in the hourglass.<br />
</div><div><br />
</div><div>You would speak and without trembling, rather taking a deep breath,<br />
</div><div>blissfully; for a great weight and oppressiveness would be taken from you,<br />
</div><div>you most patient one!<br />
</div><div>'Now I die and disappear,' you would say, 'and in an instant I will be a<br />
</div><div>nothing. Souls are as mortal as bodies.<br />
</div><div><br />
</div><div>The death of the soul with the body follows Aristotle's view rather than Plato's where the eternal soul returns to the World Soul.<br />
</div><div><br />
</div><div>But the knot of causes in which I am entangled recurs - it will create<br />
</div><div>me again! I myself belong to the causes of the eternal recurrence.<br />
</div><div>I will return, with this sun, with this earth, with this eagle, with this<br />
</div><div>snake - not to a new life or a better life or a similar life:<br />
</div><div>- I will return to this same and selfsame life, in what is greatest as well<br />
</div><div>as in what is smallest, to once again teach the eternal recurrence of all<br />
</div><div>things -<br />
</div><div><br />
</div><div>The view here is the scientific one, that identical causes will reproduce the same events, ceteris paribus. For example, the birth of suns requires similar conditions, but it is hardly conceivable that Earth's sun would arise for a second time in the same cosmos. If the present cosmos were to collapse into a singularity it is conceivable that a new big bang would reproduce an identical copy of the preceding one, but an empirical proof of this would be impossible. From this point of view, Nietzsche's grand idea is irrefutable but possibly false.<br />
</div><div><br />
</div><div>- to once again speak the word about the great earth of noon and human<br />
</div><div>beings, to once again proclaim the overman to mankind.<br />
</div><div>I spoke my word, I break under my word: thus my eternal fate wills it<br />
</div><div>- as proclaimer I perish!<br />
</div><div>The hour has now come for the one who goes under to bless himself.<br />
</div><div>Thus - ends Zarathustra's going under!'" -<br />
</div><div>When the animals had spoken these words they fell silent and waited<br />
</div><div>for Zarathustra to say something to them: but Zarathustra did not hear<br />
</div><div>that they were silent. Instead he lay still, with eyes closed, like someone<br />
</div><div>sleeping - even though he was not sleeping. Indeed, at this moment he<br />
</div><div>was conversing with his soul. The snake and the eagle, however, finding<br />
</div><div>him silent in this manner, honored the great stillness around him and<br />
</div><div>cautiously slipped away.<br />
</div><div><br />
</div><div>According to the eternal return the 'overman' would have arisen innumerable times in the past, as would multiple Zarathustra's have proclaimed him to mankind. In view of the prophet's attitude to women, one wonders if a superwoman arose too, or if the godlike hero would mate with human women like the Watchers, those angels who could not resist the temptation of the daughters of men after the fall.<br />
</div><div><br />
</div><div>The Seven Seals<br />
</div><div><br />
</div><div>Zarathustra explains in Part 1, "oh how then could I not lust for eternity and for the nuptial ring of rings - the ring of recurrence. Never have I found the woman from whom I wanted children, unless it were this woman whom I love: for I love you, oh eternity!" Nietzsche's lack of success with women is here exacerbated by his desire for the impossible rival of a female goddess of eternity. This seems to be a variant of the Church as Bride of Christ or of Plotinus's World Soul.<br />
</div><div><br />
</div><div>Each of the seven sections of this hymn to eternity repeats this stanza, preceded by the imagined delights of eternity. In section five, ""infinity roars around me, way out there space and time glitter, well then, what of it old heart!" and in section 7, "but bird-wisdom speaks like this: 'see there is no up, no down! Throw yourself around, out, back you light one! Sing! Speak no more! - are not all words made for the heavy? Do not all words lie to the light? Sing! Speak no more!" This desire for absolute freedom from gravity and from thought suggests that Zarathustra is not temperamentally suited to the life his author has been leading, one of intense study, but rather the life of a wandering mystic who longs to be free of earthly constraints.<br />
</div><div><br />
</div><div><br />
</div><div>Conclusion<br />
</div><div><br />
</div><div>If one were to strip away all the poetic literary decoration, what would remain of Nietzsche's two important ideas: the eternal recurrence and the superman? In the world that he inhabited and the much-changed world that we know today, there have developed many radical theories and fictions about the cosmos and the future of human beings transformed by science. The possibility of further advances in human evolution, in terms of enhanced human powers, is not too fanciful. A more complex model of the cosmos as a multiverse is also being explored. What is clear, though, is that these scientific advances are based on work mostly unrelated to Nietzsche's fanciful and poetic notions, although psychoanalysts and others have been influenced by his insights. Consequently, Nietzsche's opinion of his importance in human history is grossly overstated, at least regarding the two main ideas of TSZ. However, this is not to say that they are unimportant elements in the development of non-scientific thought, since TSZ has had a profound influence on philosophy, culture and the arts which may well overshadow the influence of less fanciful philosophers.<br />
</div><div><br />
</div><div>The importance attached by Nietzsche to TSZ and the intensity and complexity of the work suggest that he did view the idea of the eternal recurrence and of the coming superman as more than just poetic expressions upon which to hang his radical view of the human condition and the future of humanity. For a great scholar of antiquity he must have been aware of the hubris inherent in TSZ, despite the thin mask provided by its protagonist Zarathustra.<br />
</div><div><br />
</div><div>Given the extravagant idea that anything that is possibly must have occurred, and must occur again, the emergence of a superior human who can save the human race does not appear unreasonable. Unfortunately the idea founders on the shore of the vast accumulation of scientific and technical knowledge that has occurred since Nietzsche's time. The law of entropy alone precludes the kind of cyclic stability envisioned in Nietzsche's recurring cosmos and the eventual death of all stars promises a Malthusian outcome in the absence of humanity. This reduces Nietzsche's grand idea of eternally recurring future heroes to an empty Valhalla, and certainly one where all great beings have vanished without trace.<br />
</div><div><br />
</div><div><span style="white-space: pre;"> </span><br />
</div>Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com1tag:blogger.com,1999:blog-7897013436752033900.post-31288630497804161672009-08-03T21:16:00.000-07:002009-08-04T01:01:15.602-07:00What is the Relationship Between Mind and Being?<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPMUair-V6Ai0toGMa45CZKBXHOdzXyyg9hsECrl9lESbgXV0VC880kINkQ4HvfvN-0HXDzAeEaTz6qKIznVdbG-teSBeIxAZlFQHyIThvBUml_XHXhlO5IPJNo1mWFlok5JvvBFYPx-0/s1600-h/brain-763982-1.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 320px; DISPLAY: block; HEIGHT: 319px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5365963192374526114" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPMUair-V6Ai0toGMa45CZKBXHOdzXyyg9hsECrl9lESbgXV0VC880kINkQ4HvfvN-0HXDzAeEaTz6qKIznVdbG-teSBeIxAZlFQHyIThvBUml_XHXhlO5IPJNo1mWFlok5JvvBFYPx-0/s320/brain-763982-1.jpg" /></a><br /><div><br /></div><div>As Professor Joad* might have said, that depends on what you mean by mind and being. However, to attempt detailed answers to these important but subsidiary questions would create an interminable delay in answering the main question posed. The approach here will be to allow the meaning of these two terms to emerge as a consequence of the discussion of the relationship between them. Before attempting this it would be useful to investigate the general form of the question and what the relationship between one entity and another means.</div><div><br /></div><div>Relations may be of many kinds, including spatial, temporal, logical, mathematical, legal or just the usual anthropic ones, like love or hate. The relationship between an individual mind and an individual being can be explained as a precursor to tackling the more general question posed. One might meaningfully say, "John's mind is devoted to the study of philosophy". Alternatively, this could be expressed as, "John's mental activity is largely concerned with philosophy". This is like saying "John uses his computer mainly to gather information from the Internet." In the first two cases, 'mind' refers to a mental process that takes place in space and time in the region of John's brain. The object of john's thought (philosophy) is a body of knowledge that may take many forms, including processes in John's brain or memory as well as libraries of information.</div><div><br /></div><div>The characteristic of the relationship between an individual mind and the objects of its thoughts looks like a one-many relation. If we say, "John chases after many women", the beings referred to belong to the class of women and 'chases after' is one of John's activities (when he's not doing philosophy). In this example, it is clear that it is John's whole being (including his mind) that is pursing physical bodies, unless he is just stalking them on the Internet. The sentence, "John's mind is filled with thoughts about women", provides an example of the relationship between an individual mind and female human beings, but this is a non physical relationship.</div><div><br /></div><div>When John is pursuing philosophy, he may well be thinking about the concept of mind, as opposed to his individual mind. In so doing, one could reasonably say that he is creating a relationship within his own mind about the more abstract notion of mind in general. This would be a relationship between an individual mind and the concept of the class to which John's mind belongs. If we grant being to the hypothetical John, his thoughts would be an example of an individual being bound in a relationship with the concept of mind. However, this temporary bond can be described as being a certain kind of thought present in John's brain.</div><div><br /></div><div>Mind has been implicitly defined above as the general name for thoughts and also for the capacity to generate such thoughts by a human individual. The existence of such thoughts depends upon the existence of the thinker (John) and on the mental processes, conscious or otherwise, taking place within his brain. John's individual being, therefore, is a necessary condition for the existence of John's thoughts and his mind. </div><div><br /></div><div>In the example above, it is clear that mind is subordinate to the being of the individual possessing that mind. In general, the existence of human beings is necessary to the existence of human minds or what can reasonably be defined as the class of minds. The word 'mind', therefore, refers to the class of human minds, which clearly depends on the existence of the human race. </div><div><br /></div><div>The initial question can now be answered. The relation between mind and being is just the class of possible relations between the class of human minds and the class of beings in general. In this formulation we have arrived at a many-many relation of the greatest diversity and complexity, the very opposite of what one might have expected from a metaphysical reduction of the question. However, no definition of being in general has been evoked other than the sum of beings involved in human thoughts. </div><div><br /></div><div>Boiling the question down, one could say, "The relationship between mind and being comprises the totality of human thoughts about the world". This would necessarily include all erroneous thoughts as well as those that are generally held to be true. Indeed, one might contend that there are no absolutely true thoughts about beings, as opposed to the pure entities of mathematics and logic, so that the relationship between mankind and being in general is founded on approximate knowledge at best and complete delusion at worst. </div><div><br /></div><div>* Cyril Edwin Mitchinson Joad (August 12, 1891 - April 9, 1953) was an English philosopher and broadcasting personality. </div><div><br /></div><div>Tony Thomas</div><div>August 2009</div>Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com1tag:blogger.com,1999:blog-7897013436752033900.post-32233933524808248362009-07-30T19:34:00.000-07:002009-07-30T19:47:19.989-07:00Infinite Chess<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYPIIc38SEggcoZn3XMuNxS8y0s3MW-9iVDud6ItfngaM0kli_3FBmgVDULhJVCfXFOGNIiazr58Ja_LVAG-cjM3YQuzSOl_W8TqGvSGsrhp-XztSsxJVAjYBnAAWxIg_JUzm_k75UOsk/s1600-h/Chess4.gif"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 316px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYPIIc38SEggcoZn3XMuNxS8y0s3MW-9iVDud6ItfngaM0kli_3FBmgVDULhJVCfXFOGNIiazr58Ja_LVAG-cjM3YQuzSOl_W8TqGvSGsrhp-XztSsxJVAjYBnAAWxIg_JUzm_k75UOsk/s320/Chess4.gif" border="0" alt="" id="BLOGGER_PHOTO_ID_5364450055496501650" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJX4pTTHNUpKU7FuHc-DByy_I3QWj6_68oSkxtiflkmf8dCATxP-eQCMmN3RUSoaUSYEkbYjuX9OWLTsCnz44hT_hjOhuOCEBpWk6mtF-IeqQjknvF0EJipSDeAFCeWQ5-gHK2xnIDNHs/s1600-h/Chess2.gif"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 275px; height: 260px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJX4pTTHNUpKU7FuHc-DByy_I3QWj6_68oSkxtiflkmf8dCATxP-eQCMmN3RUSoaUSYEkbYjuX9OWLTsCnz44hT_hjOhuOCEBpWk6mtF-IeqQjknvF0EJipSDeAFCeWQ5-gHK2xnIDNHs/s320/Chess2.gif" border="0" alt="" id="BLOGGER_PHOTO_ID_5364450051107962002" /></a><br /><div style="text-align: center;"><span class="Apple-style-span" style="font-family:Arial;"><span class="Apple-style-span" style="font-size: medium;">The conventional game of chess provides more than enough challenges for even the strongest player, but many extensions to the game have been proposed. Among these are three-dimensional chess, of Star Trek fame, and designs using an infinite board. These latter attempts use the idea of potential infinity rather than absolute infinity. The designs presented below imply actually infinite domains as well as potentially infinite subspaces.</span></span></div><div class="Section1"> <p class="MsoNormal"><span style="font-family:Arial;"> Extending chess to an infinite domain involves defining the required space and also redefining how the chessmen move within it. The conventional chessboard has 64 squares, which are indexed from a1 at the bottom left hand corner to h8 at the top right. This provides a convenient notation for recording the moves of a game. So, the rows are indexed by the first eight numbers and the files (columns) by the first eight letters, as shown below.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> The board can be rendered unlimited simply by allowing the index to include all the finite numbers and all the finite combinations of letters. For example, a square such as g100 or ay39 would be legitimate. In this way the chessmen could move about in an infinite space, without changing the conventional rules by which they move.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> A peculiarity of this extended index is that the bottom and left hand boundaries of the board are preserved. On such a board the white chessmen can move forward or to the right without limit but remain constrained to the left and behind. However, it is not clear where the opposing black pieces are to be located or whether they should be symmetrically constrained behind and to the left like the white pieces, which would clearly never do.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> One solution is to confine the starting positions of the opposing armies to the dimensions of the standard board but relativise their position in the infinite plane. This can be done by extending the index to include negative values, analogous to the notation of the Cartesian plane. For example, ac42, -ac42,</span></p> <p class="MsoNormal"><span style="font-family:Arial;">ac-42 and -ac-42 would be legitimate and distinct locations, where ac represents 26 + 3 = 29 squares.<o:p></o:p></span></p> <p class="MsoNormal"><span style="font-family:Arial;"> The extension to an infinite board would affect the powers of the chessmen differently. The queen, rook and bishop could make unlimited moves but the king, knight and pawn would be restricted to a single move, and so would gain limited freedom on the extended board. Their relative powers would be diminished accordingly.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> An alternative scheme is to separate the white and black chessmen by an infinite space. The immediate consequence would be that no matter how far the queens, rooks or bishops moved according to their enhanced powers, they could never engage the enemy. To rescue the game from this impasse requires a further extension to the powers of the pieces and the pawns.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"><span style="mso-spacerun: yes"> The solution is to allow all the chessmen to make infinite moves, from one domain to another, according to strict but familiar rules. These rules are as follows:</span></span></p> <p class="MsoNormal"><span style="font-family:Arial;"><span class="Apple-style-span" style=" ;font-family:Georgia;"><b><span style=" ;font-family:Arial;color:black;">Rule 1: </span></b><span style=" ;font-family:Arial;color:black;">A man may either make a short (finite) move or a long (infinite) move but not both.</span></span></span></p> <p class="MsoNormal"><span style=" ;font-family:Arial;color:black;"> <span class="Apple-style-span" style=" ;font-family:Georgia;"><b>Rule 2:</b> In making a long move, a man must move from one domain to another in the same manner as required by a short move.</span></span></p> <p class="MsoNormal"><span style=" ;font-family:Arial;color:black;"> <span class="Apple-style-span" style=" ;font-family:Georgia;"><b><span style=" ;font-family:Arial;color:black;">Rule 3:</span></b><span style=" ;font-family:Arial;color:black;"> A move from one domain to another preserves the finite position of the man.</span></span></span></p> <p class="MsoNormal"><span style=" ;font-family:Arial;color:black;"> The first rule is self-explanatory. The player may either make a move within the domain the man occupies or move the man to another domain, subject to rules 2 and 3.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> The meaning and relation of the infinite domains needs to be explained before elaborating on rules 2 and 3. Each domain is a replication of the infinite space defined above. The domains are arranged in a square matrix, which must be sufficiently large to allow long moves as defined in rule 2. For example, a 5 x 5 matrix is necessary to allow the knights access to every domain. Any larger matrix could be adopted but, for aesthetic purposes, an 8 x 8 matrix of domains is ideal.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> A system of notation can now be defined to locate the men within both domain (board) and its finite subspace. Each of the 64 infinite boards is indexed from A1 to H8, analogous to the indexing of the conventional chessboard. A double reference of the form XYxy locates an individual square within a domain. For example, the white king is located on the square E1e1 at the start of the game and the black king is on square E8e8.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> The initial positions of the 32 men can now be described. The rule for setting up the board is simple. On the conventional board, the white queen sits on square d1: on the infinite board she sits on square D1d1. The trick is to duplicate the local reference in the board reference. The white queen’s pawn conventionally starts on d2, so it occupies D2d2 on the infinite matrix. An infinite bird’s eye view would show the initial set up to be identical to that of the conventional game.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"><span style="mso-spacerun: yes"> Rules 2 and 3 can now be explained more fully. The white king’s knight begins on square G1g1. The knight is free to make a short move to either G1f3 or G1h3. In addition, the knight can make a short move to G1e2, because all the pawns start off in domain 2. The knight can make initial long moves to F3g1 or H3g1 but not to E2g1, because this square is occupied by the king’s bishop’s pawn.</span></span></p> <p class="MsoNormal"><span style="font-family:Arial;"> A notable feature is that all the pieces can make unrestricted finite moves at the opening, because each one is alone in its domain. This allows the players to jump into a new domain from an unlimited number of positions. Like many art forms, it is the constraints rather than absolute freedom that leads to interesting works. No less so in the game of chess. For this reason the proposed game can be modified by restricting each domain to the usual finite 8 x 8 matrix of squares. The result is an extremely complex finite expansion of the traditional game of chess.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> The diagram below shows some examples of long moves. A domain set of 3 x 3 boards has been used for compactness of presentation. It can be seen that knight, bishop and rook can reach across domains. The power of a pawn to take diagonally in a long move is also illustrated. The pawns power to move two squares on its first move allows it to make a double long move. The en passant rule is similarly preserved.</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> Summary</span></p> <p class="MsoNormal"><span style="font-family:Arial;"> The extension of the game of chess to multiple domains generates a family of games, which may be either finite or infinite. This can be achieved by the addition of the three special rules for long moves and by adding a square or rectangular matrix of boards of one’s choice. The double notation allows the computerisation of the game. The implications for geometry and the theory of infinite number will not be considered here. Suffice to say that the examination of such models should provide useful insights in these areas of enquiry.</span></p> <p class="MsoNormal"><br /></p><p style="tab-stops: 27.0pt" class="MsoNormal"><span class="Apple-style-span" style="font-family:Arial;"><br /></span></p> <p class="MsoNormal"><span style="font-family:Arial;"> <o:p></o:p></span></p> <p class="MsoNormal"><span style="font-family:Arial;"> <o:p></o:p></span></p></div>Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com0tag:blogger.com,1999:blog-7897013436752033900.post-31594885089216900362009-07-19T00:52:00.000-07:002009-07-19T00:55:04.972-07:00Ich habe meinen Regenschirm vergessen<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbWG6KOpnGLTFjUE7mlUaULnqIr4d-iGtsUd6tRWVPY94M5sFbZgmjEMb0qCHgRM4z_cXGiQHxHxd0UNLRc0Mv_XceXbbzMLS7sh3NvyjuVlgq0EvU6FHyEDAhitlPDzGiOIfhJgcMXf8/s1600-h/umbrella_print-p228245922705807967vsu7_325.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbWG6KOpnGLTFjUE7mlUaULnqIr4d-iGtsUd6tRWVPY94M5sFbZgmjEMb0qCHgRM4z_cXGiQHxHxd0UNLRc0Mv_XceXbbzMLS7sh3NvyjuVlgq0EvU6FHyEDAhitlPDzGiOIfhJgcMXf8/s320/umbrella_print-p228245922705807967vsu7_325.jpg" border="0" alt="" id="BLOGGER_PHOTO_ID_5360076618147231378" /></a><br /><div>Who would have cared I owned an umbrella,</div><div>let alone that I had forgotten it, </div><div>had I not written that note to myself?</div><div>If it had rained outside Plato's cave, they would</div><div>not have known it, but I know, as I stare</div><div>into the sunlight, that it rains sometimes,</div><div>somewhere, at times and places that I may</div><div>chance to be, sans umbrella in Turin</div><div>or, maybe, mindless in Sils Maria.</div><div><br /></div><div>To bear or not to bear an umbrella,</div><div>that is the unbearable question, since</div><div>we cannot know that it is going to rain</div><div>when we reach our final destination.</div><div>Posterity may never know why I</div><div>wrote, "I have forgotten my umbrella",</div><div>nor what the meaning of my act entailed,</div><div>unless some ingenious Frenchman can</div><div>explain it to future generations.</div><div><br /></div><div>But the paradox remains; I could not</div><div>have truly written, "I have forgotten" it </div><div>at the time of writing the note because</div><div>that was the time when I remembered it.</div><div>Clearly, then, it was not the existence </div><div>of the umbrella that I forgot but </div><div>rather not remembering to take it </div><div>with me to the place where I had not predicted </div><div>that it would rain; a place I now forget. </div><div><br /></div><div>I am in some street, and it starts to rain,</div><div>but I find my umbrella is missing. </div><div>For some reason this seems significant,</div><div>so, I write a note to remind myself</div><div>not to forget it again, when there is rain. </div><div>"I have forgotten to bring my umbrella"</div><div>would have made plain the act is intended,</div><div>not the little shadow I forgot to keep </div><div> by me, as defence against bad weather.</div><div><br /></div><div>But I may have left my umbrella on</div><div>the train, in the café, at the brothel </div><div>or anywhere else where it could have been</div><div>set down carelessly and quite forgotten.</div><div>Would our Frenchman think of that, I wonder?</div><div>No, he would be too busy undermining</div><div>my reputation by analysing</div><div>my forgetfulness, on one occasion,</div><div>as if this were a judgement on my work.</div><div><br /></div><div>What really happened I fear to tell you</div><div>because it links me to an awful crime. </div><div>An acquaintance of mine, Monsieur X, say,</div><div>borrowed my umbrella, but on the way</div><div>home he was attacked by ruffians who tried</div><div>to rob him. In self-defence he stabbed one</div><div>in the chest and the other ran away.</div><div>Needless to say, my umbrella is stuck</div><div>in a place that's best forgotten by all.</div><div><br /></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>*****</div><div><br /></div>Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com0tag:blogger.com,1999:blog-7897013436752033900.post-9156401269360949462009-07-16T22:31:00.000-07:002009-07-16T22:35:48.009-07:00The Old Man of the Woods<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglHMUr_XC2JtNhV-aZ07Y5W0dhDF8tLkkAyRTL00aJRaFkBXWAPeMY7YTSlfcLaVyBhMghepAUzP6CKXhyphenhyphenzCTzHdQt1ij5VSGqFK1jooeHMk-fwuTb0kl2IDXwFehWl0vFVC2PD5W-UVg/s1600-h/Odin.bmp"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 252px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglHMUr_XC2JtNhV-aZ07Y5W0dhDF8tLkkAyRTL00aJRaFkBXWAPeMY7YTSlfcLaVyBhMghepAUzP6CKXhyphenhyphenzCTzHdQt1ij5VSGqFK1jooeHMk-fwuTb0kl2IDXwFehWl0vFVC2PD5W-UVg/s320/Odin.bmp" border="0" alt="" id="BLOGGER_PHOTO_ID_5359298590323178578" /></a><br /><div>The great man sits alone within the hut,</div><div>his peasant face not much to look at, but</div><div>the frigid thoughts that flow within his mind</div><div>are much concerned with time, not humankind.</div><div><br /></div><div>Outside the window change is measured by</div><div>the dripping icicles that signify</div><div>the end of winter's elongated clock,</div><div>days pounded out upon the chopping block. </div><div><br /></div><div>Too far away the prison camps that cleanse</div><div>the nation of its multiethnic wens,</div><div>for myopic philosophers to see</div><div>the discarded piles of humanity.</div><div><br /></div><div><i>The winter pools are deep and cold,</i></div><div><i>his tread is heavy, growing old.</i></div><div><i>Now wearied by the tasks ahead,</i></div><div><i>he scratches runes inside the shed. </i></div><div><i>His mind unpicks the threadbare lore,</i></div><div><i>a cloth worn thin from Grecian shore</i></div><div><i>to Konigsberg, where spiders spun</i></div><div><i>those webs abhorred by Englishmen.</i></div><div><i>I, Hugin know who is to blame.</i></div><div><i>Why should he claim a famous name?</i></div><div><br /></div><div>Once more the wolves have eaten Sun and Moon.</div><div>Dread giants rule the Earth again and soon</div><div>the flow of blood becomes unstoppable.</div><div>Meanwhile the sage ponders at his table.</div><div><br /></div><div>He thinks and scribbles, seeing none of this,</div><div>in his small shelter of domestic bliss. </div><div>What is the import of these mighty words</div><div>that fly above the heads of human herds?</div><div><br /></div><div>Time and being crush down the suffering</div><div>but to him, unbearable lightness of being </div><div>is just reward for self inflicted toil</div><div>in the cultivated land of German soil.</div><div><br /></div><div><i>He delves in mines for Rhenish gold, </i></div><div><i>and grasps the ring that was untold,</i></div><div><i>when time's old serpent's tail uncurled,</i></div><div><i>between its fangs to show our world. </i></div><div><i>We brothers say he has no name,</i></div><div><i>and fly to Odin with the same</i></div><div><i>dire message that his fate is sealed.</i></div><div><i>without our runes, his heart's not healed.</i></div><div><i>I, Munin shall forget his lore,</i></div><div><i>and shall forget it evermore.</i></div><div><br /></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>*****</div><div><br /></div>Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com1tag:blogger.com,1999:blog-7897013436752033900.post-88704802047852344952009-07-04T19:45:00.001-07:002009-07-04T21:16:35.319-07:00Going Home<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuAWmkjx5k_1VQjRQprldbjEwSGkg7YUK9Cd_te3IEoGcmFVILahIS1Mmu9MIeN5WBCV_CJcLl7wn2ZsgR8NgsCF4RzjdWJqEezTH8iSvluxDuHyQzQlLaEeu0SUkifR2umaaDFdB_AOw/s1600-h/LAO.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 320px; DISPLAY: block; HEIGHT: 240px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5354819276174058194" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuAWmkjx5k_1VQjRQprldbjEwSGkg7YUK9Cd_te3IEoGcmFVILahIS1Mmu9MIeN5WBCV_CJcLl7wn2ZsgR8NgsCF4RzjdWJqEezTH8iSvluxDuHyQzQlLaEeu0SUkifR2umaaDFdB_AOw/s320/LAO.bmp" /></a> <div></div><div>The old man sat by the window overlooking the courtyard; his disciple, Lai Tan, sat at the big table, cutting bamboo slips.</div><div></div><div><span lang="EN-GB">“Master, shall I join yesterday’s slips or would you like to dictate today?”</span></div><div><br /><p class="MsoNormal"><span lang="EN-GB"><?xml:namespace prefix = o /><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The sage pulled his worn cloak tighter round his neck. The wind from the gorge was spinning the leaves into golden wreaths, sending gusts of cool air into the dimness of the room.<span style="mso-spacerun: yes"> </span>The clack of footsteps sounded in the corridor and a house servant, head bowed, entered the room.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“What is it? My master is not to be disturbed,” Lai Tan said, looking over to the old man for guidance. The sage raised his eyebrows and held a finger to his lips, then looked towards the servant with a kindly smile.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Well, tell the master what you want,” Lai Tan snapped.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Sir, the Keeper of The Pass respectfully requests an audience, he is waiting outside.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The old man rose unsteadily to his feet, nodded his assent and signalled with his hand to Lai Tan.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Shall I leave you to talk with our jailor alone, Master?” </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The old man nodded again and remained standing, in readiness to meet the gentleman outside.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Tell your master he is welcome to come in but that we are unable to entertain him in the accustomed style,” Lai Tan said to the servant.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The servant left, followed by Lai Tan; His Master, Kuan Yin, swept into the room. </span></p><p class="MsoNormal"><span lang="EN-GB">The keeper, a tall, spare man, was dressed in his red robe of office. Middle-aged with a neatly trimmed beard and bobbed hair, he bowed respectfully to the grey haired figure standing before the window.</span></p><p class="MsoNormal"><span lang="EN-GB">“Master, forgive the intrusion. The King has asked me to enquire about your health and the progress of your book.”</span></p><p class="MsoNormal"><span lang="EN-GB">The old man bowed slightly in return and motioned towards the unoccupied chair. The keeper sat down, after a slight hesitation, and looked enquiringly at the old man. The sage sat down again on the window bench and said, “A cold wind is blowing from the North West.”</span></p><p class="MsoNormal"><span lang="EN-GB">The Keeper waited, expecting more but was disappointed.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“We are all waiting anxiously for your wisdom to be recorded – especially my lord the King.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Has he not wisdom enough from the mouth of Kung Fu Tzu?” the elder replied, smiling softly as he looked out of the window at the clouds, now piled up as if before a storm.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“He teaches the court of familial piety, of bending men to the rule of law, but what do you say?”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“The family is older than Dukes and Kings but the Way of Heaven is older than time.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“But the Empire is in disorder. Isn’t that why you left the capital? The States war with each other and take no heed of the suffering of the people.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“The wind is blowing the leaves about, a storm is coming,” the Old Man replied, looking out over the courtyard to the looming mountains beyond.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“I hope you will forgive me, I dared not let you leave Chou, at least not without some token of your wisdom to appease the King.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">Smiling meekly, the old man turned his head to look at the official.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Does the King of Chou prefer wisdom to its source?”</span></p><p class="MsoNormal"><span lang="EN-GB">The Keeper thought carefully, knowing that the question was a test of his sincerity.</span></p><p class="MsoNormal"><span lang="EN-GB">“The water is sweeter at the source – to benefit the people it must flow down to the sea. Becoming muddied on the way it attains to saltiness.”<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB">The sage sat quietly, looking down at the pattern on the tiles between his feet. The Keeper felt pleased with his reply: it spoke of the Yellow River flowing from the mountains to the sea, rushing through muddy canyons before nourishing the plain in the East. Listening carefully, one could hear its roar over the rising wind.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Autumn has arrived, it will soon be spring,” the old man said, by way of acknowledgement.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">The Keeper glanced at the table strewn with bamboo cuttings and a couple of completed rolls. </span><br /></p><p class="MsoNormal"><span lang="EN-GB">“How long will it be?” he said, worried by the directness of his question.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“About five thousand characters,” the sage replied.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">No stranger to the art of writing, the Keeper calculated from the rolls on the table and the shelves that the work was about half complete. He rose and bowed to the old man.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“I must not disturb your thoughts any longer. I will tell your scribe he can return.”</span><span lang="EN-GB">The old man rose and bowed his head as the official crossed the room and went out through the doorway.</span><br /></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>*****</span></p><p class="MsoNormal"><span lang="EN-GB">As autumn turned to winter the old man and his scribe worked on to complete the great book. When the first plum blossom opened in the capital and the snows had melted, turning the great river into a raging flood, Lai Tan had drawn the last character of the five thousand and twenty five and bound up the final roll.<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Master, what will happen now that you have completed Kuan Yin’s demands?”</span></p><p class="MsoNormal"><span lang="EN-GB">The old man looked at the brightening and fading sunlight in the courtyard.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“The moon will be waxing soon,” he replied. </span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Shall I tell the Keeper that we have finished?”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">The sage turned to look at the young man and nodded.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">Lai Tan went to the Keeper of the Pass and knelt before the official.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Please rise and sit here,” Kuan Yin said, pointing to a low stool set before his chair.</span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span>“Have you come to tell me that it’s finished?”</span></p><p class="MsoNormal"><span lang="EN-GB">“Yes Master Yin, the great work is now complete. I have come to ask you whether we are free to leave. I was wondering what would happen to the book now. It would be unwise for us to risk it on a journey. Will you keep it safe here for wandering scholars to read?”<span style="mso-spacerun: yes"> </span></span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Wandering scholars would soon bring great repute to your master but I must deliver it to the King in Luoyang. When your master has rested from his great task, my servants will make provisions so that you can continue on your way. Return to your master now and give him the good news.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span>Lai Tan rose, bowed low and returned to the room where he had worked for almost two years.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Master Lao, I fear the keeper wishes to steal your book. He intends to present it to the King. What if he claims to have written it himself?”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Why would a wise man claim to have written so much foolishness?” the sage replied.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">Having drawn every character of the book, Lai Tan had often asked himself the same question.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“The Keeper expects us to leave soon. He says he will provide for our journey. When do you intend to leave?”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“When the moon is half full.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“But where will we go?”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">The old man sat with his hands in his sleeves and thought for a while.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“I shall return to the place where I was born.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“To Hu Hsien?” the disciple asked.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">Lao Tzu nodded.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“There too,” he said before nodding off to sleep.</span><br /></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>*****<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB">Three days later the Keeper presented Master Lao with gifts from the King that he had withheld until the book was finished. There was a fine yellow robe and a silk hat for the Master, a blue silk robe and a sash for his scribe and a goodly weight in silver. A mule was loaded with provisions for the journey and with the King’s gifts. </span></p><p class="MsoNormal"><span lang="EN-GB">The old man was helped onto the back of the ox, the same one that had delivered him to the Keepers lodge, now grown fat with good feed and little work. Kuan Yin bade them farewell and watched the little party until it disappeared behind the rocks on the road to the western pass. At the bottom of the winding road, the Master pointed south and Lai Tan led the mule away from the river, into the hills where the village of Hu Sien lay hidden in the mists.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">The next day Kuan Yin rode out with a retinue of guards and servants towards Luoyang, taking the precious rolls with him. The journey was long and dangerous with the constant threat of bandits on the road to the capital. The journey proved uneventful until they came within a few leagues of the city. The captain wheeled his horse round and came up to the Keeper. </span><br /></p><p class="MsoNormal"><span lang="EN-GB">“My Lord, we must find shelter, a storm is brewing in the west.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Very well, we will improvise a camp behind those trees by the river,” Kuan Yin shouted back over the rising wind.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">They left the road and pitched the official’s tent, complete with banner, tethering the horses and mules beneath the trees.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">The storm broke just after dark, tearing rotten branches from the trees and flattening the tent.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Typhoon!” the captain screamed, over the roaring wind, “lie down and cling to the ropes.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">Concerned about the book, the keeper fought his way to the tethered mule and tried to carry the bundle of rolls into the shelter of the trees. The wind was so strong that the big bundle, tied up with hides, was torn from his grasp and rolled down the bank into the foaming waters of the river. Heedless of the danger, Kuan Yin plunged down the muddy bank and tried to drag the bundle back to shore. The raging torrent carried him away with the bundle, towards the distant capital.</span></p><p style="TEXT-INDENT: 36pt; MARGIN-LEFT: 144pt" class="MsoNormal"><span lang="EN-GB">*****</span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB">One-foot dragged himself back through the mud towards the river. A storm always meant good pickings. He had already come across the body of a rich man, clothed in red silk all smeared with mud. He had stripped away the finery and pocketed the ornaments and rings. He had pitched the naked body back into the water for the fishes to pick clean before hiding the booty in his hut. There had been a big bundle too, probably full of valuables, but it had been too heavy for him to shift alone. He cursed the gods. There was nothing to be done, he would have to get help from his partner in crime before dawn or someone else would take the prize.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">He stumbled down the riverbank towards the lights of the tavern. Poking his head through the door<span style="mso-spacerun: yes"> </span>he spied One-tooth slumped over a table strewn with food scraps and empty wine bowls. He lay between a fishwife and some other clod; drool hanging from his gaping mouth, snoring in his stupor. </span><br /></p><p class="MsoNormal"><span lang="EN-GB">One-foot shook him roughly. </span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Get up, quick,” he shouted into a battered ear.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span>One-tooth woke with a snort and recognised his partner.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“What now” another of your wonder finds I suppose; pots of gold, strings of pearls, precious silks fit for a king.”<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">One-foot decided to say nothing of the body. </span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Get up, it’s a big bundle stuck in the mud bound up with hides; it could contain all kinds of valuables. I can’t move it by myself, it’s too heavy.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Curse you! How far is it?” </span></p><p class="MsoNormal"><span lang="EN-GB">“It’s close by. I’ll find someone else if you won’t come.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">One-tooth stumbled to his feet, pushed the woman aside and spat on the dirt floor.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Lead on then.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">With much cursing and muffled shouts the pair dragged the bundle to the hut and cut the hides open.</span></p><p class="MsoNormal"><span lang="EN-GB">“It’s nothing but a bundle of firewood tied up with red string, curse it,” One-tooth shouted angrily.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">”No, there must be something inside; unroll it.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">Holding the lantern over the rolls of bamboo, the scavengers beheld the rows of characters painfully drawn by Lai Tan. </span><br /></p><p class="MsoNormal"><span lang="EN-GB">“It’s just some stupid official’s tax rolls. It’s worth nothing,” spat One-tooth. I’m taking the hides, they’re good quality at least, you can keep the firewood.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">With a final curse, he rolled up the hides and went on his way.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>*****</span><br /></p><p class="MsoNormal"><span lang="EN-GB">The Chief Minister of Chou finished making his report to the King about the storm damage to the city.</span></p><p class="MsoNormal"><span lang="EN-GB">“There was one other matter, my Lord.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Speak then.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“A beggar was captured in possession of a mysterious book.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“A scholarly beggar?”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“No my Lord, a river scavenger and a criminal called One-foot.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“He still lives?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“I don’t know my lord. The local magistrate ordered the lopping of his other foot.</span><br /></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span>“Oh dear, soon there will be nobody left standing.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“A jade disc and a muddied red robe were found in the scavenger’s hut.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Ah, I see. We are in need of a new Keeper it seems. But what of the book?”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“It consists of a great many rolls, Lord. I’ve read some of it. It appears to be some kind of philosophy, so I wondered if it would interest your majesty. Its rather obscure stuff, I’m afraid.”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“How fortunate that Kung Fu Tzu is still within the palace walls. Be so good as to request his presence so that he can explain this mystery to us.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Yes my Lord, I will summon him at once.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">A low table and a stool were arranged before the King and a couple of the damp rolls placed on the table. A short while later the stately figure of the sage appeared. Bowing at the waist only, he sat at the table and opened one of the rolls.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“What does it say?” the king asked, a little impatiently.</span></p><p class="MsoNormal"><span lang="EN-GB">“It’s full of aphorisms and rhymes about the old ways,” Kung Tzu replied without looking up from his reading.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Read some out loud,” the King commanded.</span><br /></p><p style="TEXT-INDENT: 36pt" class="MsoNormal"><span lang="EN-GB">“There is a thing confusedly formed,</span></p><p style="TEXT-INDENT: 36pt" class="MsoNormal"><span lang="EN-GB">Born before Heaven and Earth.</span></p><p style="TEXT-INDENT: 36pt" class="MsoNormal"><span lang="EN-GB">It stands alone and does not change,</span></p><p style="TEXT-INDENT: 36pt" class="MsoNormal"><span lang="EN-GB">Goes round and does not weary.</span></p><p style="TEXT-INDENT: 36pt" class="MsoNormal"><span lang="EN-GB">It is capable of being the Mother of the World.</span></p><p style="TEXT-INDENT: 36pt" class="MsoNormal"><span lang="EN-GB">I know not its name </span></p><p style="TEXT-INDENT: 36pt" class="MsoNormal"><span lang="EN-GB">So I style it ‘The Way’.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Mysticism,” the King said. “You’ve studied the Book of Changes for years, haven’t you?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“That is true,” the sage replied, “but this book speaks of that which lies behind the changes.”</span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB">“Is it worth anything?” the King asked.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“The Dragon’s ascent into Heaven on the wind and the clouds is something which is beyond my knowledge,” Kung Tzu replied, quoting his own words after his meeting with the old man.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Make copies for the library right away,” the King commanded, remembering the famous words quoted by the sage.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>***** </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">On the fourth night of their journey, the Sage and the scribe camped under an old chestnut tree overhanging a lake. The evening was calm and the bright moon reflected in the limpid waters. </span></p><p class="MsoNormal"><span lang="EN-GB">“How far is it now Master? Lai Tan enquired.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“In another day the moon will be full,” the old man replied.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">The next day was a fine spring morning. The old man had already bathed by the time Lai Tan woke up and was sitting under the tree watching the sunrise over the water. </span></p><p class="MsoNormal"><span lang="EN-GB">“Master, why are you all dressed up in your new robe and hat? Surely this is not fitting wear for a humble village.”</span></p><p class="MsoNormal"><span lang="EN-GB">“See how the blossoms have opened on this tree”, the sage replied.</span><br /></p><p class="MsoNormal"><span lang="EN-GB">Lai Tan washed quickly, ate a millet cake and put on the blue gown and sash.</span></p><p class="MsoNormal"><span lang="EN-GB">It was noon when they rode down into the clearing where the houses lay nestled among the trees. The sound of the lyre and flute rose up to meet them, where young boys and girls in bright costumes were dancing on the green.<span style="mso-spacerun: yes"> </span>As they entered the village, the dancers ran to meet them, followed by the headman and the rest of the villagers.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“My Lord, it is years since a magistrate passed through our village; you are most welcome. Let me help you down.” </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The sage dismounted and stood unsteadily among the giggling village girls.</span></p><p class="MsoNormal"><span lang="EN-GB">“Master, is it seemly to be among these women? We must go to the headman’s house at once.” </span><br /></p><p class="MsoNormal"><span lang="EN-GB">The girls liked the look of the young scribe and rushed over to where he stood with the mule. They touched his blue robe and tried to drag him away to the green. The music began again as the young people continued with the spring festival of the new moon.</span></p><p class="MsoNormal"><span lang="EN-GB">“Master, what of your teaching about curbing desire?” Lai Tan shouted over the heads of the dancers.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Time enough for that later,” the sage shouted back gaily as he entered the headman’s house.</span></p><p class="MsoNormal"><span lang="EN-GB">“Will you take a cup of herb tea with me, brother?”</span><br /></p><p class="MsoNormal"><span lang="EN-GB">“Is the moon not full?” the sage replied. “Let’s talk over old times.”</span><br /></p><p style="TEXT-INDENT: 36pt; MARGIN-LEFT: 144pt" class="MsoNormal"><span lang="EN-GB">*****</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"></p></div>Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com1tag:blogger.com,1999:blog-7897013436752033900.post-46798878884567142222009-07-04T04:29:00.001-07:002011-07-17T22:39:03.534-07:00The Combination Room<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2XPQ27yIC1goVk5bp5dxFVoarTe9SxujdhD-XmSv7RiyxHLoNChaXVxYt2V1ykn2FKmQortuSaqfOtUeRmMpHstscoNN1D8aDmWPkvpsYY8gVhdrVUbHqAFMqe-Amgs-BRfABipoRQ60/s1600-h/44508281.jpg" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5354571984721348434" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2XPQ27yIC1goVk5bp5dxFVoarTe9SxujdhD-XmSv7RiyxHLoNChaXVxYt2V1ykn2FKmQortuSaqfOtUeRmMpHstscoNN1D8aDmWPkvpsYY8gVhdrVUbHqAFMqe-Amgs-BRfABipoRQ60/s320/44508281.jpg" style="display: block; height: 213px; margin: 0px auto 10px; text-align: center; width: 320px;" /></a><br />
<h1><span lang="EN-GB">The Combination Room</span></h1><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Dramatis Personae:<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Gordon Handley<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"></span>Professor of Mathematics<span style="mso-tab-count: 1;"> </span><span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-tab-span" style="white-space: pre;"></span>} </span>Trinity College<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Sanjeev Ramangita<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"></span>Handley’s student and protégé<span class="Apple-tab-span" style="white-space: pre;"> <span class="Apple-tab-span" style="white-space: pre;"></span></span>}<span class="Apple-tab-span" style="white-space: pre;"> </span><span style="mso-tab-count: 1;"></span></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-tab-count: 1;">Bernard Rushwell<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"></span>Professor of Philosophy<span class="Apple-tab-span" style="white-space: pre;"> <span class="Apple-tab-span" style="white-space: pre;"></span></span>}<span class="Apple-tab-span" style="white-space: pre;"> </span><span style="mso-tab-count: 1;"></span></span></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Ludolph Wittgemein<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"></span>Rushwell’s student and protégé<span class="Apple-tab-span" style="white-space: pre;"> <span class="Apple-tab-span" style="white-space: pre;"></span></span>}<span class="Apple-tab-span" style="white-space: pre;"> </span><span style="mso-tab-count: 1;"></span></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">James Canard-Means<span style="mso-tab-count: 1;"> </span>Professor of Economics<span style="mso-tab-count: 1;"> <span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-tab-span" style="white-space: pre;"></span>} </span></span>Kings College<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><h1><span lang="EN-GB"><span style="mso-tab-count: 2;"></span><span style="mso-tab-count: 2;"></span><span style="mso-tab-count: 1;"></span><span style="mso-tab-count: 1;"></span>*****</span></h1><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Soft April sunlight filtered through the narrow windowpanes of the Combination Room, gilding the tousled hair of a lone man not yet of middle age. His garb was unconventional; grey herringbone tweed trousers, a cricket sweater and a knitted scarf. He had draped a second sweater, of a drab colour, over a wooden framed mirror, opposite to where he sat in a high backed, wicker chair.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">He was of slight build and rather short, his legs barely touching the floor. A cigarette protruded at an angle from his compressed lips, as he concentrated on aligning a walnut exactly between the jaws of a nutcracker. When the necessary precision had been achieved, he squeezed the nutcracker hard, using both hands. The nut skittered across the wooden floor, disappearing under the oak table.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Blast,” he said, snatching the cigarette from his lips, parking it in the ashtray on the table. He contemplated taking a new nut from the bowl, but his sense of duty, not to mention tidiness, forced him to jump up and search for the nut beneath the table.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">The errant nut had lodged in a crack between the uneven boards. He was just reaching for it when the heavy door to the room creaked open. Jerking upright, his head struck the underside of the table.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span>“Drat it all,” he shouted, backing out without the nut. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">From a kneeling position, he turned his head to see the round, fleshy features of his student peeping round the door.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Handley,” the face hissed, through stained teeth and fleshy lips, “I must speak with you at once.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span>“What is it Sanjeev? You know the senior rooms are reserved for Fellows only.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I know Handley. You are topmost professor and I am still very low, but I have damaged the WC in the staircase, and I don’t know what to do.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“What do you mean damaged?” Handley asked, rising to his feet.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“It’s the pump-action. I pull the chain, many, many times, but always there are many unhappy returns of the bowel motion.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“You should report it to the porter. Well, come in, for God’s sake, you’re creating a draft.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">The door opened to reveal a rather uncouth figure in his late twenties, stout and not recently shaven.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Now you’re here, you’d better sit down. I’ll cover for you if anyone comes.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Oh, thank you Handley. But I must explain, the motion was not mine, but some other dirty fellows’. I am still in need of relief, you see.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I don’t think I need to know the details, thank you, Sanjeev. As long as you do use the WC and not the garden bed, I will be satisfied. I couldn’t open my window for a week after your last escapade.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Most sorry, Handley, but it takes a lot of getting used to this English custom of sitting down to do business.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Yes, yes, I’m sure it does, but you must persevere if you are going to fit in with our quaint little ways.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I will persevere, Handley, I will be most deciduous.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Assiduous, Sanjeev, from the Latin assidere.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Sanjeev Ramangita sat down on the floor with crossed legs, his large eyes rolled, looking round the room. His gaze lighted on the bowl of nuts, lips moving in the act of silent counting. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Seventeen nuts, Handley and one on the floor. What do you think it means? Shall I calculate the Goldbach ratio?”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“It means that I accidentally dropped one of the nuts on the floor.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Butterfingers. Why do they say that Handley, do the English butter their fingers? ”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“No they don’t; it means dropping a ball in the game of cricket.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“But what if your ball has already dropped, and what about buttery boards?”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“If you keep asking silly question you will become a butt yourself. Now, if you don’t mind, I would rather like to look at the cricket scores now,” Handley said. He sat down and picked up a crumpled copy of the times from the table.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I could crack nuts for you.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“No thank you, I prefer to crack my own nuts.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Sanjeev fell silent. The ticking of the black clock on the mantelpiece, interspersed with the occasional rustle of Handley’s paper marked the passage of time.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">The sound of footsteps and voices echoed in the passage outside the door. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Shall I hide, Handley?” Sanjeev whispered. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Well, you might try the wardrobe but I don’t think the smell of naphtha and vegetable curry is an ideal combination. Just stand by the window, and gaze intelligently into the distance.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Like Rabindranath Tagore?”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Yes, something like that.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">While Sanjeev moved to the window, Handley quickly smoothed down his hair and lit another cigarette. He just had time to arrange The Times on the table, with the completed crossword prominently displayed, before striking a pose.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">A slim man of medium height entered, talking in fluting tones over his shoulder. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">He looked like an animated turtle, snapping out his words with exaggerated clarity. His companion, a decade and a half younger, was very tall and of athletic build. The tall man’s face was gloomy, with dark circles under the eyes. Unusually, he wore no tie. He listened intently as the older man spoke. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“It’s all up to you, now that my Magnum Opus has been published. You must take over the torch and build on what I have achieved. You can see more clearly than I what must come next in the great story of philosophy. It’s a great burden, I know, but I believe you are the only one who can carry the work forward.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">The tall man closed the door behind them and then stopped, transfixed in front of the mirror that Handley had covered with his pullover.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Isn’t that a bit of a mixed metaphor?” Handley said, “Unless he’s going to burn down the old building first.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I thought I might find you here,” Bernard Rushwell said, advancing towards the table where Handley sat. “Perusing the cricket scores, I bet. I wanted to tell you that the prodigal son has returned from Norway, but only on a flying visit. He has some important results to communicate. I was sceptical at first - we had a terrible row - but he has almost won me over.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Handley wondered why he ought to care about Wittgemein’s return. He knew the Austrian by sight, but had hardly spoken to this new Apostle. He was an Angel himself, but disapproved of some of the newer members of the society, particularly Canard-Means’ Bloomsbury friends.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">When Ludolph Wittgemein came over to shake his hand, Handley thought of Mary Shelley’s monster. The Austrian’s grip was surprisingly limp and brief for such a muscular man, but Handley had no desire to hold hands with the chap. He would leave that sort of thing to Canard-Means and company. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">With a pang of guilt, he turned to the window, where Sanjeev was casting his broad shadow into the room. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I would like to introduce my pupil, Sanjeev Ramangita. Bernard, this is Mr Ramangita. Sanjeev, this is the renowned philosopher Professor Bernard Rushwell.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I am most honoured to meet you, Sir. I have only just arrived in England, and have yet to conquer the plumbing, but I hope soon to appreciate the greatness of your work.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“It’s already out of date, I’m afraid,” Rushwell said, “so it may not be worth your while. Ludolph, you should meet Professor Handley’s protégé, Handley expects great things from him when he has learned the ropes. A future Apostle, eh Handley?”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Like the contact between Adam and God on the ceiling of the Sistine Chapel, their hands barely touched; the worlds of philosophy and mathematics repelling each other like oil and water, despite Rushwell’s struggle to make them mix.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Well, we might as well sit down,” Rushwell said. “Sherry is in order, I think. Ludolphus. Would you do the honours, please. It’s really rather important, you see. Whitehorn and I have laboured in the vineyard all these years and we might have produced a barren crop.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Er, no sherry, for Sanjeev, Wittgemein, he’s a Hindu,” Handley said.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Save it for Canard-Means,” Rushwell interjected, “I asked him to pop in later so we could get his views on Ludolph’s new ideas. Right, sit down Ludolph, we might as well begin.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Wittgemein moved a wooden chair a little way back from the group, as if delivering a tutorial, and rummaged in a voluminous jacket pocket. He pulled at a battered spiral bound notebook, whose wire had become entangled in the lining. After a brief struggle and the tearing of cloth, he got it out and located the starting point of his notes.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“The world is all that is the case,” he began, in a hoarse voice.<span style="mso-spacerun: yes;"> </span>“It is the totality of facts, not of things. The world is determined by the facts, and by their being all the facts.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Right, this is very compressed,” Rushwell interrupted, “I’d like to say why I think this approach is so important. In the Principia, we tried to forge a link between the most primitive logical ideas to the objects and relations of mathematics. The underlying assumption was that logic was the proper place to start. But, unless we know what we mean by logic we can’t know that it is fundamental to our enquiries.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Well, where else could you start?” Handley said, “You could have left well alone. Most mathematicians of sufficient calibre can get on with their business without worrying too much about the philosophical underpinnings.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“There is the question of rigour. While few could match your standards, Gordon, they still fall a long way short of axiomatic proofs as we have defined them,” Rushwell said. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Yes, but there is quite a difference between doing real mathematics and merely laying down the law about how it should be done. You may be forgetting that mathematical beauty often determines the direction of an enquiry into fundamental problems rather than a philosophical roadmap. Where we aspire to go there are no maps.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Yes, Handley, you are right,” cried Sanjeev, jumping up from his chair, “if you cannot follow the beautiful things in your head, you will never reach the topmost heights.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Thank you, Sanjeev. But of course, you do need a very considerable technique to climb the highest mountains, and I suppose that is where you logicians can give us a leg up. Anyway, if you don’t know what you mean by logic by now, you may be in the wrong game, Bernard.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“But do you know what you mean by mathematics?” Rushwell retorted, adopting his frozen, defensive smile. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Probably not, but I expect you’re going to tell me,” Handley replied, brushing fallen ash from his trousers.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Rushwell paused for a moment, drew breath and said, “mathematics is the science in which we do not know what we are talking about and do not care whether what we say is true.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Handley lit a cigarette and paused for reflection. “By the first part, I understand you to mean that we do not know what the objects of mathematics are exactly, since they clearly are not among the things of this world. I’m not too keen on the use of the word science though in this context. For me, a science is not just a systematic enquiry but also one that has empirical connotations. This sort of science has nothing to do with pure mathematics, which is quite unrelated to worldly things. The second part of your reply is more complex. Mathematicians do care a great deal about whether their theorems are true or not, but I suppose you mean true in some absolute, ontological sense. I’m not much of a philosopher, so I can’t instruct you about whether mathematical truth is fatally confined to its own domain or has some mysterious relation to what happens in the real world.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Perhaps we should ask Ludolph what he thinks, Rushwell said, looking expectantly at his protégé.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">The Austrian had gone pale and was leaning forward slightly, as if in pain.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“It’s the words, the language, you see, it’s just no good.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I’m not sure I understand you, Ludolph, could you explain more clearly?”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I’m sorry, Bernard, I’m rather tired from the journey. So much is about to happen in the world, all this seems so remote now, even though I know it is the most important thing for people like us. I’m an Austrian remember. If the Balkan war continues much longer, Austria will have to intervene. If She does, She could be at war with Russia, and that will be the end of the world, as we know it. Of course, I would have to return home and fight for my country.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Nonsense, it doesn’t mean that at all. I hope Asquith would have the good sense to keep Britain out of it. There is no reason why you should leave England, just to satisfy some chauvinistic instinct.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I don’t think you would say that if our country were threatened and you were abroad somewhere,” Handley said. “We all hate war, but we can’t turn our backs on our homeland.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Rushwell made an impatient gesture with his hand. “If you are able, Mr Wittgemein, we would be interested to hear your latest views on the matter in question.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Ludolph put his hand to his temple and massaged it a bit before replying. “Very well, what I really would like to say is that you’ve got it all wrong. I know how important you think it is to pin down exactly what logic is, Bernard, but I have come to believe this is a hopeless task. Like Sanjeev said, you see some wonderful truth in your head, but you can’t express it clearly without a great deal of analysis, maybe years of work.“<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Exactly,” Rushwell interjected.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“No, not exactly,” Ludolph said, his eyes lighting up for the first time. “That’s what I’m trying to tell you. Not only is this kind of discussion a waste of time, at least for the purpose of arriving at the truth about the world, it entirely misses the point.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“And exactly what is the point, Ludolph,” Rushwell asked icily.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“If you keep that frozen smile up much longer, I think I shall go quite mad,” Ludolph said, getting up from his chair to pace up and down parallel to the wall. What is that bally pullover doing over the mirror, anyway?”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Need to confirm your existence, do you?” Rushwell snapped, his mouth finally hardening into a thin line.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“For Christ’s sake, Bernard, not now. No wonder Othalia has chucked you over. Don’t you realise how cold and cruel you can be sometimes?”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Perhaps we should continue this another time, when we have all calmed down a bit,” Handley said, stubbing out his cigarette without looking at the antagonists.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">”The pullover belongs to Gordon,” Rushwell said, jumping up. “If he accidentally catches sight of himself he will realise the futility of his existence and have to do away with himself. That’s it, isn’t it Gordon. It’s just one of those Trinity things we all have to get used to. We’re all mad in one way or another but we have to learn to get along. Being a cry-baby does nobody any good.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“But who is this ‘nobody’?” Ludolph asked, turning to smile at Bernard.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Very funny,” the older philosopher replied. “What now?”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I do feel rather unwell. I haven’t eaten since dinner last night at High Table.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“It could be your last, if you don’t pull yourself together. You know damn well how much faith I’ve invested in you. You can’t suddenly walk out now and throw everything away. You could be a Fellow in a few years; we would all support you, wouldn’t we Gordon?”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Ludolph stood up, clutching his belly. “I have a frightful cramp in my stomach.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Pie,” observed Handley. “<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Yes,” cried Sanjeev eagerly, “ pi is most important. I have devised many new ways to calculate this wonderful number.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“No, mutton pie; for dinner; last night at High Table, I’ve been feeling a bit off colour myself,” Handley said.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“That’s why the WC is broken,” Sanjeev said, excitedly. All those dirty fellows have been ridding themselves of impure food and wearing out the pump.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I had the mutton pie too, it had no effect on me,” Bernard said, “but then I was weaned on Pembroke pies.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“A little lamb enclosed within a wheaten shell,” Handley mused.<span style="mso-spacerun: yes;"> </span>“Sanjeev, would you be so kind as to escort Mr Wittgemein to the staircase, so that he can relieve himself. Meanwhile we will await the appearance of Apostle number 243.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span>“243, Handley that is a nice number. It is three to the power of five.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I was aware of that,” Handley said, “but it is also the membership number of Professor Canard-Means.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“But what about the broken WC, Handley?” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I’m sure a man of Mr Wittgemein’s intellect will find a way round any local difficulties,” Handley replied.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">When they had left, Rushwell said, “I hope you will forget what I said in the heat of the moment. I too have been under considerable strain lately.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I think we have known each other long enough not to attach too much importance to such little spats,” Handley replied. “You ought to take up something a bit more relaxing than logic.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Fortunately for you, you never married. Domestic bliss can end up being an unforeseen torment.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“And your diversions?”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Even worse,” Rushwell replied, “the very Devil. Speaking of whom, I think he has arrived.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">A soft-featured man in his thirties with a large moustache entered the room and strolled over to the seated pair.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Your sherry’s gone cold, James,” Rushwell observed, pointing to the full glass on the table. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Many thanks,” canard-Means replied. “I just saw your acolyte, accompanied by his Indian bearer, going into the male lavatory. I hope Lindon has not been leading him astray.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“You’re a little out of touch, Ludolph found the Apostles were not to his taste after all. He’s resigned.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Pity, he became so much more animated among his peers.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><span style="mso-spacerun: yes;"></span>“He has important work to do. I think it best if he isn’t distracted by too much empty prattle,” Rushwell replied<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“And what is this important work, pray? Some pet scheme of yours in disguise, perhaps.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“On the contrary, he is working on finding the fundamental object that underlies all propositional forms. Without it, the primacy of logic remains in doubt ” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“And what do you think of these endeavours? I mean, doesn’t this cast doubt upon your theory of types?”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Exactly. I had to invent that theory to obviate the pernicious antinomies of sets. These infect the basic propositional form, as you know, so a new, primitive notion of the proposition is essential if the whole enterprise is not to collapse like a house of cards.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Hark, I think I hear genius approaching now,” Canard-Means said.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">Sanjeev entered the room, beaming, followed by Ludolph. <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I trust your expedition has met with more success than Captain Scott’s,” Handley said.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“Oh, yes Handley, much more. Ludolph is truly a great engineer. He pulled the chain many times and listened to the harmonics of the machine. Without even looking, he knew that there was a blockage in the cistern, by the way it sang to him.” <o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“And what was this blockage?” Rushwell asked.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN-GB" style="font-family: Arial;">“I am very ashamed to say it was </span><span lang="EN" style="font-family: Arial; mso-bidi-: EN;">Carr's Synopsis, Handley. I know you told me to get rid of it, but I still love it very much.”<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;">“What was it doing in the cistern?” Handley asked.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;">“I need something to read in the WC when your British food causes a blockage.<span style="mso-spacerun: yes;"> </span>I wrapped it in an oilskin to keep it dry. See, I have it here.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;">Sanjeev held up the dripping package, which began to form a pool of water on the floor.<o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;">“I think this meeting is adjourned,” Rushwell said, taking Ludolph’s arm and leading him back to the door. “I’ll see you in my rooms, James, should you wish to learn more about the future of philosophy.”<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;"><o:p></o:p></span></div><div class="MsoNormal"><span lang="EN" style="font-family: Arial; mso-bidi-mso-ansi-language: EN;"><span style="mso-tab-count: 2;"></span><span style="mso-tab-count: 2;"></span><span style="mso-tab-count: 1;"></span>*****<o:p></o:p></span></div>Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com0tag:blogger.com,1999:blog-7897013436752033900.post-39020495046192881702009-07-04T03:59:00.000-07:002009-07-04T23:36:47.716-07:00Conversations With Myself<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJXYIdCwCYpwTWs5z9zouKzllOeJh_xZO-VyblHAzyz2d0kWCvh970daq1N4ooVkqLvW3jjGklLrv3-BFvHxp1C4WKUVQj2k9yjDS2WIWyFTjx61kgpiQ4vEQRCWl61W9AupfhbS7DbpM/s1600-h/Nietzsche_Olde_11.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 320px; DISPLAY: block; HEIGHT: 236px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5354559005163153090" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJXYIdCwCYpwTWs5z9zouKzllOeJh_xZO-VyblHAzyz2d0kWCvh970daq1N4ooVkqLvW3jjGklLrv3-BFvHxp1C4WKUVQj2k9yjDS2WIWyFTjx61kgpiQ4vEQRCWl61W9AupfhbS7DbpM/s320/Nietzsche_Olde_11.jpg" /></a><br /><p class="MsoNormal">A sparsely furnished room; white walls, black furniture, a little morning sunlight falling on the uneven boards of the floor from a window. A rigid figure sits in an upright, leather backed chair, clutching the wooden armrests. Parchment skin drawn tightly over broad cheekbones, haunted eyes staring into nothingness beneath craggy brows, burning within twin caves of forgetfulness. A veined and mighty forehead looms above, crowned with a shock of dark hair, still unsalted by half a century of unremitting toil. No mouth is visible beneath the shaggy growth, blooming from nostrils to jutting chin. The whole fearful aspect weakened, somehow, by small ears, as if to deny the soaring music within.<span style="mso-spacerun: yes"> </span></p><p class="MsoNormal"><span lang="EN-GB"><?xml:namespace prefix = o /><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">An old woman dressed in black enters, followed by another, a middle-aged simulacrum of the first.<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Elisabeth is here to see you, Friedrich; you know who she is, don’t you?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The older woman reaches out with obvious concern, touching the veined hand clasped tightly round the arm of the chair. In a while, the leonine head turns in her direction, as if hearing rather than seeing the stooping woman. </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">”Is your name Franziska, by any chance?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The voice is gentle, cultured, kind.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The hausfrau puts her hand to her mouth, stifling a spontaneous reply.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Of course it is mother, who else could it be?” the younger woman says, with ill concealed annoyance.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Ah! Die Mutter, Die Mutter, ha-ha, yes..”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Friedrich, please try and pull yourself together.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“And you, who are you?” the seated man replies, with the authority of a king.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“You know very well who I am. Elisabeth, your sister.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“What do you want with me now, is it time for my walk?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“We have received a letter from Oehler, your work is to be published in England; isn’t that wonderful?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Ha, pearls for the other swine!”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“I felt I should let you know. Mama has agreed, but I thought you should be told.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“More light, more light, more..”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The old woman moves to the window and pulls on the already fully open curtains.</span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB">“Dead, summarily dead. More light, soon it will be dawn, more light..” the man continues to mutter, almost inaudibly now. </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“It’s no good Mother, I shall have to proceed alone, I’m the only one who can act for him now.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>*****</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB">The women have left the room. Alone now, the invalid turns his head from side to side, as if scenting the sunlight from the window. Faint sounds drift up from the street, the shaft of sunlight moves slowly to illuminate the wall. He stares at the light reflected from the dark wood of a polished table, standing along the wall. Several leather-bound but unread volumes are arranged on the table, in a row. Above them hangs a wooden crucifix, its doleful figure looking down at the books. </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The eyes of the author, too, come to rest for a while on his works, then look up at the crucifix. An inner voice reverberates from within.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">‘Am I understood? Were you understood? Your time is past, your will is done; mine is yet to come. Let my song go forth to greet the new day and the new man who will be born, fit for a new beginning, for a new dawn.’<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">He glowers at the figure on the wall.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“What say you, son of man?” he says out loud.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The crucifix looms large in his vision; he strains to hear the voice rising from the abyss.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">‘Yima, son of Vivanghat, why do you persecute me?’ </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The sage leans forward in his chair, smiling maliciously.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Without persecution, where would you be? Just one of countless men crucified by your betters; just another body rotting on a tree. Was your pain worth the pain of all those who suffered in your name? Was it greater than the pain of even one of those millions, whose lives were twisted and tormented by your priests?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">He strains to hear the faint reply.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">‘And were you not born out of yourself, as I was born, son to the father and father to the son?’<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Heh, heh. Why ask what you already know? From the Earth I was born and of the Earth I shall remain. No imaginary spirit I, but a real spirit, a spirit of the future born out of a dying past.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">‘None shall enter the Kingdom of Heaven, except through me.’</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Ha, then empty it shall remain, for my kingdom is here on Earth, a kingdom freed from the sickness of ideals and maundering ghosts.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">‘And what of suffering humanity?’</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Bah! How can there be joy without pain? Without pain man would be no better than some mindless sheep, grazing thoughtless in your father’s pastures. Great suffering, great agony, such as I have known, breeds great men, men fit to serve the one yet to be born – the Superman.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">‘Will this Superman choose the path of righteousness or the path of sin?’</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“He will be beyond good and evil, he will follow his own creative path, unbound by the chains of history.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">‘In my father’s house, there are many mansions, fit for such as these, but none may set himself above the Almighty.’</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Have you not heard, then? Your God is dead.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">‘I am the way, the truth and the light; none shall be redeemed except through me.’</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The light from the window fades, and the room darkens. The man closes his eyes and waits.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>*****</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The servant, Alwine, enters the room, places a candle on the table and closes the curtains. She lights a taper from the candle flame, switches on the gaslight over the bed and ignites it. She adjusts the pressure until the mantel glows white-hot. The light hisses and illuminates the cavernous features of the seated man, casting a stark shadow on the wall, and on the crucifix.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">Franziska enters the room, extinguishes the soft candle flame and turns down the covers on a narrow, wooden bed. As in a ritual, the two women haul the tall man to his feet. He stands patiently while they help him to undress. They put a white nightgown over his head and seat him at the table. Alwine leaves the room and returns with a meal of bread and soup. The man grunts with satisfaction and eats with gusto, washing down the food with a glass of water.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">When the meal is over, the man is led to the bed. While Alwine clears the table, Franziska waits until he has finished with the bedpan before pulling up the covers. She kisses the domed forehead and turns off the gaslight, leaving only the flickering candle to illuminate the room.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Alwine,” she calls.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">In a while, the servant returns with a candle and removes the bedpan. Franziska follows her out of the room and closes the door. </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The man stares at the ceiling for a while, and then at the candle, which casts distorted shadows of the crucifix on the wall. His eyes follow the flickering shapes until they finally close. His breathing assumes the regular pattern of sleep. </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>*****<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">An old Hermit emerges from a cave and stands staring into the East at the brightening sky. A few grey clouds still hang over the horizon. A quickly moving speck catches his attention. He watches until it assumes the shape of a large bird, flying towards the mountain where he stands. He half raises a hand in greeting as the bird flies overhead. He sees that it is clutching a snake in its talons.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“My animals,” he calls out, in a raspy voice, long unused to speech, “you have returned.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The eyes of the man in the bed move rapidly beneath the eyelids.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“A sign! I too must return to my people and give them the glad tidings.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The sleeping eyes see a youthful figure walking up the slope towards the cave, his features hidden by the long shadow of the morning sun. </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“You have come at last,” the hermit cries, running eagerly towards the approaching youth. </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Are you not afraid, old man, to finally meet your God?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“I fear nothing, certainly not a figment of my imagination!”<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Have you not heard about the fate of Pentheus and of all those who oppose my will?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Ah! I was mistaken; you are not the one. Just an old Arcadian spirit whom I loved when I was young.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Beware, old man, lest you dance to my tune. You shall know my madness before Morpheus claims you.” </span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB">“I fear nothing, I have seen all that was and that will be. No one before me has seen so much.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“I do not speak of your crazy dreams or of the fear of death but of that unknown terror, that eternal anguish of the self torn to pieces and scattered to the winds. It is I who was rent asunder, until my father retrieved my still beating heart and sewed it in his thigh.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Another bleeding heart; why not join your successor on his cross?”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“I too am merciful and accord the foolish a second chance, but you have dared too much.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The old man cries out as the venom of the God enters his mind. A pit opens up beneath his feet, seething with corruption. Clawing hands and ravening mouths suck and tear at his body. In the distance, he hears the laughter of the young God as he is drawn down into the bowels of the earth. A tangle of vines and ivy boil up into the air, marking the place where the hermit stood.<span style="mso-spacerun: yes"> </span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">The man jerks upright in his bed. A strangled cry escapes his gaping jaw. His hands feel his face convulsively in the flickering candlelight. He stares, wide eyed, at the dark shadows cast by the crucifix.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Ask and you shall receive,” a gentle voice says from the shadow on the wall.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Never, never! The man replies.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">Elisabeth enters the room, followed by Franziska. </span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Friedrich, whatever is the matter?” the old woman asks.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">Elisabeth opens a drawer in the table and takes out a brown bottle and a metal spoon. She goes to the bed and forcefully administers the opiate. The man resists feebly, seemingly unaware of the identity of his carers.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Light, more light!” he cries out, droplets of elixir running down his chin from beneath the luxurious moustache. He soon slumps back on the pillows, his head moving from side to side. The women wait until his fitful movements subside into a drugged sleep.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>*****</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">His body is suffused with a blissful warmth. A soft but ample breast is pressed against his cheek. He turns his head and suckles blissfully on the proffered teat. He feels a powerful erection. Soft hands caress his tightening scrotum and he feels his penis enveloped in the firm softness of a woman’s clasp. Sweet lips kiss his face, crooning his name softly, a heavy body moves rhythmically over his.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Lou?” he mutters, revelling in waves of perfumed delight.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">Voices whisper softly about him: many hands reach for him and many arms and legs entwine his body. His virility increases but without climax, like a Wagnerian aria. The women begin to cry out in ecstasy, and then in anger, fighting with each other, clawing at his flesh in a frenzy. They scratch his skin, pinch and bite, until the blood runs from the welts. Spurred on by the taste of blood, their teeth chew and rip strips of flesh from his neck, sharp nails open up holes in the softness of his side and pull at the organs within. </span></p><p class="MsoNormal"><span lang="EN-GB">Like vultures, they probe into every orifice and finally pick out his eyes.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>*****<span style="mso-tab-count: 1"> </span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB">Alwine enters the room and draws the curtains. She looks at the dishevelled figure on the bed. The bedclothes lie on the floor and the nightdress is pulled up to reveal the still strong body, scarred and scratched from self-inflicted wounds. Elisabeth comes in.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Alwine, quickly; fetch hot water and towels.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“We should clip his nails too, Madam.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">“Yes, but don’t tell Frau Nietzsche about this, it upsets her so.”</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">When the servant has left, the woman kneels at the bedside and begins to pray.</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 2"></span><span style="mso-tab-count: 1"></span>*****</span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB">Tony Thomas </span></p><p class="MsoNormal"><span lang="EN-GB">28 August 2003</span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><span style="mso-spacerun: yes"></span></span></p><p class="MsoNormal"><span lang="EN-GB"><o:p></o:p></span></p>Verdigrishttp://www.blogger.com/profile/11044361509380813613noreply@blogger.com0