Paul Klee

Friday, October 16, 2009

What is Knowledge?

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:

Knowledge (n)
1 information and skills acquired through experience or education - the sum of what is known. Philosophy true, justified belief, as opposed to opinion.
2 awareness or familiarity gained by experience.
- 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.
- ORIGIN ME (orig. as v. in the sense 'acknowledge, recognize')

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.

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.

The beginnings of Algebra I found far more difficult, perhaps
as a result of bad teaching. I was made to learn by heart:
"The square of the sum of two numbers is equal to the sum of
their squares increased by twice their product." I had not the
vaguest idea what this meant, and when I could not remember
the words, my tutor threw the book at my head, which did not
stimulate my intellect in any way.

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.

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.

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.

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.

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.
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.
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.

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.

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.

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.

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.

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.

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.

Tony Thomas
October 2009

Wednesday, October 14, 2009

Nietzsche's eternal recurrence

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.

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.

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.

On the Vision and the Riddle

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.

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.

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."

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.

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:

 "See this gateway, dwarf!" I continued. "It has two faces. Two paths
come together here; no one has yet walked them to the end.
This long lane back: it lasts an eternity. And that long lane outward -
that is another eternity.
They contradict each other, these paths; they blatantly offend each
other - and here at this gateway is where they come together. The name
of the gateway is inscribed at the top: 'Moment.'
But whoever were to walk one of them further - and ever further and
ever on: do you believe, dwarf, that these paths contradict each other
eternally?" -
"All that is straight lies," murmured the dwarf contemptuously. "All
truth is crooked, time itself is a circle."

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.

"You spirit of gravity!" I said, angrily. "Do not make it too easy on
yourself! Or I shall leave you crouching here where you crouch, lamefoot -
and I bore you this high!

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.

See this moment!" I continued. "From this gateway Moment a long
eternal lane stretches backward: behind us lies an eternity.
Must not whatever can already have passed this way before? Must
not whatever can happen, already have happened, been done, passed by

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.
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.

And if everything has already been here before, what do you think of
this moment, dwarf? Must this gateway too not already - have been here?
And are not all things firmly knotted together in such a way that this
moment draws after it all things to come? Therefore - itself as well?
For, whatever can run, even in this long lane outward - must run it once
more! -

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.

And this slow spider that creeps in the moonlight, and this moonlight
itself, and I and you in the gateway whispering together, whispering of
eternal things - must not all of us have been here before?
- And return and run in that other lane, outward, before us, in this
long, eerie lane - must we not return eternally? -"

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.

Thus I spoke, softer and softer, for I was afraid of my own thought and
secret thoughts. Then, suddenly, I heard a dog howl nearby.
Had I ever heard a dog howl like this? My thoughts raced back. Yes!
When I was a child, in my most distant childhood:
- then I heard a dog howl like this. And I saw it too, bristling, its head
up, trembling in the stillest midnight when even dogs believe in ghosts:
- so that I felt pity. For the full moon had passed over the house, silent
as death, and it had just stopped, a round smolder - stopped on the flat
roof just as if on a stranger's property -
that is the why the dog was so horror-stricken, because dogs believe in
thieves and ghosts. And when I heard it howl like this again, I felt pity
once more.

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.

Where now was the dwarf? And the gateway? And the spider? And all
the whispering? Was I dreaming? Was I waking? I stood all of a sudden
among wild cliffs, alone, desolate, in the most desolate moonlight.
But there lay a human being! And there! The dog jumping, bristling,
whining - now it saw me coming - then it howled again, it screamed: had
I ever heard a dog scream like this for help?

Now Zarathustra reveals that it was all a dream, but links the dream to his present by reintroducing the dog motif.

And truly, I saw something the like of which I had never seen before.
A young shepherd I saw; writhing, choking, twitching, his face distorted,
with a thick black snake hanging from his mouth.
Had I ever seen so much nausea and pale dread in one face? Surely he
must have fallen asleep? Then the snake crawled into his throat - where
it bit down firmly.
My hand tore at the snake and tore - in vain! It could not tear the snake
from his throat. Then it cried out of me: "Bite down! Bite down!
Bite off the head! Bite down!" - Thus it cried out of me, my dread, my
hatred, my nausea, my pity, all my good and bad cried out of me with one
shout. -

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.

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.

You bold ones around me! You searchers, researchers and whoever
among you ever shipped out with cunning sails onto unexplored seas!
You riddle-happy ones!
Now guess me this riddle that I saw back then, now interpret me this
vision of the loneliest one!
For it was a vision and a foreseeing: what did I see then as a parable?
And who is it that must some day come?
Who is the shepherd into whose throat the snake crawled this way?Who
is the human being into whose throat everything that is heaviest, blackest
will crawl?
- Meanwhile the shepherd bit down as my shout advised him; he bit
with a good bite! Far away he spat the head of the snake - and he leaped
to his feet. -
No longer shepherd, no longer human - a transformed, illuminated,
laughing being!

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.

Never yet on earth had I heard a human being laugh as he laughed!
Oh my brothers, I heard a laughter that was no human laughter - and
now a thirst gnaws at me, a longing that will never be still.
My longing for this laughter gnaws at me; oh how can I bear to go on
living! And how could I bear to die now! -
Thus spoke Zarathustra.

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.

The Convalescent

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".
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.

After a convalescent period of seven days, Zarathustra is persuaded by his
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!"

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."

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."

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.' "

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.

That you must teach this teaching as the first - how could this great
destiny not also be your greatest danger and sickness!
Behold, we know what you teach: that all things recur eternally and
we ourselves along with them, and that we have already been here times
eternal and all things along with us.
You teach that there is a great year of becoming, a monster of a great
year; like an hourglass it must turn itself over anew, again and again, so
that it runs down and runs out anew -
- so that all these years are the same as each other, in what is greatest
and also in what is smallest - so that we ourselves in every great year are
the same, in what is greatest and also in what is smallest.
And if you wanted to die now, oh Zarathustra: behold, we know too
how you would speak to yourself then: - but your animals beg you not to
die yet!

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.

You would speak and without trembling, rather taking a deep breath,
blissfully; for a great weight and oppressiveness would be taken from you,
you most patient one!
'Now I die and disappear,' you would say, 'and in an instant I will be a
nothing. Souls are as mortal as bodies.

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.

But the knot of causes in which I am entangled recurs - it will create
me again! I myself belong to the causes of the eternal recurrence.
I will return, with this sun, with this earth, with this eagle, with this
snake - not to a new life or a better life or a similar life:
- I will return to this same and selfsame life, in what is greatest as well
as in what is smallest, to once again teach the eternal recurrence of all
things -

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.

- to once again speak the word about the great earth of noon and human
beings, to once again proclaim the overman to mankind.
I spoke my word, I break under my word: thus my eternal fate wills it
- as proclaimer I perish!
The hour has now come for the one who goes under to bless himself.
Thus - ends Zarathustra's going under!'" -
When the animals had spoken these words they fell silent and waited
for Zarathustra to say something to them: but Zarathustra did not hear
that they were silent. Instead he lay still, with eyes closed, like someone
sleeping - even though he was not sleeping. Indeed, at this moment he
was conversing with his soul. The snake and the eagle, however, finding
him silent in this manner, honored the great stillness around him and
cautiously slipped away.

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.

The Seven Seals

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.

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.


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.

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.

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.

Monday, August 3, 2009

What is the Relationship Between Mind and Being?

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.

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.

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.

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.

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.

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.

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.

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.

* Cyril Edwin Mitchinson Joad (August 12, 1891 - April 9, 1953) was an English philosopher and broadcasting personality.

Tony Thomas
August 2009

Thursday, July 30, 2009

Infinite Chess

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.

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.

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.

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.

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,

ac-42 and -ac-42 would be legitimate and distinct locations, where ac represents 26 + 3 = 29 squares.

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.

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.

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:

Rule 1: A man may either make a short (finite) move or a long (infinite) move but not both.

Rule 2: In making a long move, a man must move from one domain to another in the same manner as required by a short move.

Rule 3: A move from one domain to another preserves the finite position of the man.

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.

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.

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.

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.

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.

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.

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.


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.

Sunday, July 19, 2009

Ich habe meinen Regenschirm vergessen

Who would have cared I owned an umbrella,
let alone that I had forgotten it,
had I not written that note to myself?
If it had rained outside Plato's cave, they would
not have known it, but I know, as I stare
into the sunlight, that it rains sometimes,
somewhere, at times and places that I may
chance to be, sans umbrella in Turin
or, maybe, mindless in Sils Maria.

To bear or not to bear an umbrella,
that is the unbearable question, since
we cannot know that it is going to rain
when we reach our final destination.
Posterity may never know why I
wrote, "I have forgotten my umbrella",
nor what the meaning of my act entailed,
unless some ingenious Frenchman can
explain it to future generations.

But the paradox remains; I could not
have truly written, "I have forgotten" it
at the time of writing the note because
that was the time when I remembered it.
Clearly, then, it was not the existence
of the umbrella that I forgot but
rather not remembering to take it
with me to the place where I had not predicted
that it would rain; a place I now forget.

I am in some street, and it starts to rain,
but I find my umbrella is missing.
For some reason this seems significant,
so, I write a note to remind myself
not to forget it again, when there is rain.
"I have forgotten to bring my umbrella"
would have made plain the act is intended,
not the little shadow I forgot to keep
by me, as defence against bad weather.

But I may have left my umbrella on
the train, in the café, at the brothel
or anywhere else where it could have been
set down carelessly and quite forgotten.
Would our Frenchman think of that, I wonder?
No, he would be too busy undermining
my reputation by analysing
my forgetfulness, on one occasion,
as if this were a judgement on my work.

What really happened I fear to tell you
because it links me to an awful crime.
An acquaintance of mine, Monsieur X, say,
borrowed my umbrella, but on the way
home he was attacked by ruffians who tried
to rob him. In self-defence he stabbed one
in the chest and the other ran away.
Needless to say, my umbrella is stuck
in a place that's best forgotten by all.


Thursday, July 16, 2009

The Old Man of the Woods

The great man sits alone within the hut,
his peasant face not much to look at, but
the frigid thoughts that flow within his mind
are much concerned with time, not humankind.

Outside the window change is measured by
the dripping icicles that signify
the end of winter's elongated clock,
days pounded out upon the chopping block.

Too far away the prison camps that cleanse
the nation of its multiethnic wens,
for myopic philosophers to see
the discarded piles of humanity.

The winter pools are deep and cold,
his tread is heavy, growing old.
Now wearied by the tasks ahead,
he scratches runes inside the shed.
His mind unpicks the threadbare lore,
a cloth worn thin from Grecian shore
to Konigsberg, where spiders spun
those webs abhorred by Englishmen.
I, Hugin know who is to blame.
Why should he claim a famous name?

Once more the wolves have eaten Sun and Moon.
Dread giants rule the Earth again and soon
the flow of blood becomes unstoppable.
Meanwhile the sage ponders at his table.

He thinks and scribbles, seeing none of this,
in his small shelter of domestic bliss.
What is the import of these mighty words
that fly above the heads of human herds?

Time and being crush down the suffering
but to him, unbearable lightness of being
is just reward for self inflicted toil
in the cultivated land of German soil.

He delves in mines for Rhenish gold,
and grasps the ring that was untold,
when time's old serpent's tail uncurled,
between its fangs to show our world.
We brothers say he has no name,
and fly to Odin with the same
dire message that his fate is sealed.
without our runes, his heart's not healed.
I, Munin shall forget his lore,
and shall forget it evermore.


Saturday, July 4, 2009

Going Home

The old man sat by the window overlooking the courtyard; his disciple, Lai Tan, sat at the big table, cutting bamboo slips.
“Master, shall I join yesterday’s slips or would you like to dictate today?”

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. The clack of footsteps sounded in the corridor and a house servant, head bowed, entered the room.

“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.

“Well, tell the master what you want,” Lai Tan snapped.

“Sir, the Keeper of The Pass respectfully requests an audience, he is waiting outside.”

The old man rose unsteadily to his feet, nodded his assent and signalled with his hand to Lai Tan.

“Shall I leave you to talk with our jailor alone, Master?”

The old man nodded again and remained standing, in readiness to meet the gentleman outside.

“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.

The servant left, followed by Lai Tan; His Master, Kuan Yin, swept into the room.

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.

“Master, forgive the intrusion. The King has asked me to enquire about your health and the progress of your book.”

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.”

The Keeper waited, expecting more but was disappointed.

“We are all waiting anxiously for your wisdom to be recorded – especially my lord the King.”

“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.

“He teaches the court of familial piety, of bending men to the rule of law, but what do you say?”

“The family is older than Dukes and Kings but the Way of Heaven is older than time.”

“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.”

“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.

“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.”

Smiling meekly, the old man turned his head to look at the official.

“Does the King of Chou prefer wisdom to its source?”

The Keeper thought carefully, knowing that the question was a test of his sincerity.

“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.”

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.

“Autumn has arrived, it will soon be spring,” the old man said, by way of acknowledgement.

The Keeper glanced at the table strewn with bamboo cuttings and a couple of completed rolls.

“How long will it be?” he said, worried by the directness of his question.

“About five thousand characters,” the sage replied.

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.

“I must not disturb your thoughts any longer. I will tell your scribe he can return.”The old man rose and bowed his head as the official crossed the room and went out through the doorway.


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.

“Master, what will happen now that you have completed Kuan Yin’s demands?”

The old man looked at the brightening and fading sunlight in the courtyard.

“The moon will be waxing soon,” he replied.

“Shall I tell the Keeper that we have finished?”

The sage turned to look at the young man and nodded.

Lai Tan went to the Keeper of the Pass and knelt before the official.

“Please rise and sit here,” Kuan Yin said, pointing to a low stool set before his chair.

“Have you come to tell me that it’s finished?”

“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?”

“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.”

Lai Tan rose, bowed low and returned to the room where he had worked for almost two years.

“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?”

“Why would a wise man claim to have written so much foolishness?” the sage replied.

Having drawn every character of the book, Lai Tan had often asked himself the same question.

“The Keeper expects us to leave soon. He says he will provide for our journey. When do you intend to leave?”

“When the moon is half full.”

“But where will we go?”

The old man sat with his hands in his sleeves and thought for a while.

“I shall return to the place where I was born.”

“To Hu Hsien?” the disciple asked.

Lao Tzu nodded.

“There too,” he said before nodding off to sleep.


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.

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.

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.

“My Lord, we must find shelter, a storm is brewing in the west.”

“Very well, we will improvise a camp behind those trees by the river,” Kuan Yin shouted back over the rising wind.

They left the road and pitched the official’s tent, complete with banner, tethering the horses and mules beneath the trees.

The storm broke just after dark, tearing rotten branches from the trees and flattening the tent.

“Typhoon!” the captain screamed, over the roaring wind, “lie down and cling to the ropes.”

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.


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.

He stumbled down the riverbank towards the lights of the tavern. Poking his head through the door 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.

One-foot shook him roughly.

“Get up, quick,” he shouted into a battered ear.

One-tooth woke with a snort and recognised his partner.

“What now” another of your wonder finds I suppose; pots of gold, strings of pearls, precious silks fit for a king.”

One-foot decided to say nothing of the body.

“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.”

“Curse you! How far is it?”

“It’s close by. I’ll find someone else if you won’t come.”

One-tooth stumbled to his feet, pushed the woman aside and spat on the dirt floor.

“Lead on then.”

With much cursing and muffled shouts the pair dragged the bundle to the hut and cut the hides open.

“It’s nothing but a bundle of firewood tied up with red string, curse it,” One-tooth shouted angrily.

”No, there must be something inside; unroll it.”

Holding the lantern over the rolls of bamboo, the scavengers beheld the rows of characters painfully drawn by Lai Tan.

“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.”

With a final curse, he rolled up the hides and went on his way.


The Chief Minister of Chou finished making his report to the King about the storm damage to the city.

“There was one other matter, my Lord.”

“Speak then.”

“A beggar was captured in possession of a mysterious book.”

“A scholarly beggar?”

“No my Lord, a river scavenger and a criminal called One-foot.”

“He still lives?”

“I don’t know my lord. The local magistrate ordered the lopping of his other foot.

“Oh dear, soon there will be nobody left standing.”

“A jade disc and a muddied red robe were found in the scavenger’s hut.”

“Ah, I see. We are in need of a new Keeper it seems. But what of the book?”

“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.”

“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.”

“Yes my Lord, I will summon him at once.”

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.

“What does it say?” the king asked, a little impatiently.

“It’s full of aphorisms and rhymes about the old ways,” Kung Tzu replied without looking up from his reading.

“Read some out loud,” the King commanded.

“There is a thing confusedly formed,

Born before Heaven and Earth.

It stands alone and does not change,

Goes round and does not weary.

It is capable of being the Mother of the World.

I know not its name

So I style it ‘The Way’.”

“Mysticism,” the King said. “You’ve studied the Book of Changes for years, haven’t you?”

“That is true,” the sage replied, “but this book speaks of that which lies behind the changes.”

“Is it worth anything?” the King asked.

“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.

“Make copies for the library right away,” the King commanded, remembering the famous words quoted by the sage.


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.

“How far is it now Master? Lai Tan enquired.

“In another day the moon will be full,” the old man replied.

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.

“Master, why are you all dressed up in your new robe and hat? Surely this is not fitting wear for a humble village.”

“See how the blossoms have opened on this tree”, the sage replied.

Lai Tan washed quickly, ate a millet cake and put on the blue gown and sash.

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. As they entered the village, the dancers ran to meet them, followed by the headman and the rest of the villagers.

“My Lord, it is years since a magistrate passed through our village; you are most welcome. Let me help you down.”

The sage dismounted and stood unsteadily among the giggling village girls.

“Master, is it seemly to be among these women? We must go to the headman’s house at once.”

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.

“Master, what of your teaching about curbing desire?” Lai Tan shouted over the heads of the dancers.

“Time enough for that later,” the sage shouted back gaily as he entered the headman’s house.

“Will you take a cup of herb tea with me, brother?”

“Is the moon not full?” the sage replied. “Let’s talk over old times.”


The Combination Room

The Combination Room

Dramatis Personae:
Gordon Handley Professor of Mathematics } Trinity College
Sanjeev Ramangita Handley’s student and protégé }
Bernard Rushwell Professor of Philosophy }
Ludolph Wittgemein Rushwell’s student and protégé }
James Canard-Means Professor of Economics } Kings College


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.
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.
“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.
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.
“Drat it all,” he shouted, backing out without the nut.
From a kneeling position, he turned his head to see the round, fleshy features of his student peeping round the door.
“Handley,” the face hissed, through stained teeth and fleshy lips, “I must speak with you at once.”
“What is it Sanjeev? You know the senior rooms are reserved for Fellows only.”
“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.”
“What do you mean damaged?” Handley asked, rising to his feet.
“It’s the pump-action. I pull the chain, many, many times, but always there are many unhappy returns of the bowel motion.”
“You should report it to the porter. Well, come in, for God’s sake, you’re creating a draft.”
The door opened to reveal a rather uncouth figure in his late twenties, stout and not recently shaven.
“Now you’re here, you’d better sit down. I’ll cover for you if anyone comes.”
“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.”
“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.”
“Most sorry, Handley, but it takes a lot of getting used to this English custom of sitting down to do business.”
“Yes, yes, I’m sure it does, but you must persevere if you are going to fit in with our quaint little ways.”
“I will persevere, Handley, I will be most deciduous.”
“Assiduous, Sanjeev, from the Latin assidere.”
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.
“Seventeen nuts, Handley and one on the floor. What do you think it means? Shall I calculate the Goldbach ratio?”
“It means that I accidentally dropped one of the nuts on the floor.”
“Butterfingers. Why do they say that Handley, do the English butter their fingers? ”
“No they don’t; it means dropping a ball in the game of cricket.”
“But what if your ball has already dropped, and what about buttery boards?”
“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.
“I could crack nuts for you.”
“No thank you, I prefer to crack my own nuts.”
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.
The sound of footsteps and voices echoed in the passage outside the door.
“Shall I hide, Handley?” Sanjeev whispered.
“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.”
“Like Rabindranath Tagore?”
“Yes, something like that.”
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.
A slim man of medium height entered, talking in fluting tones over his shoulder.
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.
“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.”
The tall man closed the door behind them and then stopped, transfixed in front of the mirror that Handley had covered with his pullover.
“Isn’t that a bit of a mixed metaphor?” Handley said, “Unless he’s going to burn down the old building first.”
“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.”
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.
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.
With a pang of guilt, he turned to the window, where Sanjeev was casting his broad shadow into the room.
“I would like to introduce my pupil, Sanjeev Ramangita. Bernard, this is Mr Ramangita. Sanjeev, this is the renowned philosopher Professor Bernard Rushwell.”
“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.”
“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?”
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.
“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.”
“Er, no sherry, for Sanjeev, Wittgemein, he’s a Hindu,” Handley said.
“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.”
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.
“The world is all that is the case,” he began, in a hoarse voice. “It is the totality of facts, not of things. The world is determined by the facts, and by their being all the facts.”
“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.”
“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.”
“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.
“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.”
“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.”
“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.”
“But do you know what you mean by mathematics?” Rushwell retorted, adopting his frozen, defensive smile.
“Probably not, but I expect you’re going to tell me,” Handley replied, brushing fallen ash from his trousers.
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.”
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.”
“Perhaps we should ask Ludolph what he thinks, Rushwell said, looking expectantly at his protégé.”
The Austrian had gone pale and was leaning forward slightly, as if in pain.
“It’s the words, the language, you see, it’s just no good.”
“I’m not sure I understand you, Ludolph, could you explain more clearly?”
“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.”
“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.”
“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.”
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.”
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.“
“Exactly,” Rushwell interjected.
“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.”
“And exactly what is the point, Ludolph,” Rushwell asked icily.
“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?”
“Need to confirm your existence, do you?” Rushwell snapped, his mouth finally hardening into a thin line.
“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?”
“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.
”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.”
“But who is this ‘nobody’?” Ludolph asked, turning to smile at Bernard.
“Very funny,” the older philosopher replied. “What now?”
“I do feel rather unwell. I haven’t eaten since dinner last night at High Table.”
“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?”
Ludolph stood up, clutching his belly. “I have a frightful cramp in my stomach.”
“Pie,” observed Handley. “
“Yes,” cried Sanjeev eagerly, “ pi is most important. I have devised many new ways to calculate this wonderful number.”
“No, mutton pie; for dinner; last night at High Table, I’ve been feeling a bit off colour myself,” Handley said.
“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.”
“I had the mutton pie too, it had no effect on me,” Bernard said, “but then I was weaned on Pembroke pies.”
“A little lamb enclosed within a wheaten shell,” Handley mused. “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.”
“243, Handley that is a nice number. It is three to the power of five.”
“I was aware of that,” Handley said, “but it is also the membership number of Professor Canard-Means.”
“But what about the broken WC, Handley?”
“I’m sure a man of Mr Wittgemein’s intellect will find a way round any local difficulties,” Handley replied.
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.”
“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.”
“Fortunately for you, you never married. Domestic bliss can end up being an unforeseen torment.”
“And your diversions?”
“Even worse,” Rushwell replied, “the very Devil. Speaking of whom, I think he has arrived.”
A soft-featured man in his thirties with a large moustache entered the room and strolled over to the seated pair.
“Your sherry’s gone cold, James,” Rushwell observed, pointing to the full glass on the table.
“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.”
“You’re a little out of touch, Ludolph found the Apostles were not to his taste after all. He’s resigned.”
“Pity, he became so much more animated among his peers.”
“He has important work to do. I think it best if he isn’t distracted by too much empty prattle,” Rushwell replied
“And what is this important work, pray? Some pet scheme of yours in disguise, perhaps.”
“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 ”
“And what do you think of these endeavours? I mean, doesn’t this cast doubt upon your theory of types?”
“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.”
“Hark, I think I hear genius approaching now,” Canard-Means said.
Sanjeev entered the room, beaming, followed by Ludolph.
“I trust your expedition has met with more success than Captain Scott’s,” Handley said.
“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.”
“And what was this blockage?” Rushwell asked.
“I am very ashamed to say it was Carr's Synopsis, Handley. I know you told me to get rid of it, but I still love it very much.”
“What was it doing in the cistern?” Handley asked.
“I need something to read in the WC when your British food causes a blockage. I wrapped it in an oilskin to keep it dry. See, I have it here.”
Sanjeev held up the dripping package, which began to form a pool of water on the floor.
“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.”