Читать книгу The Woods - Vladimir Bibikhin - Страница 15

Something very notable is our widespread, distraught nostalgia for the forest, our hopeless dream of somehow still being able to escape back into it: for example, by concealing upmarket residential estates in its depths. That is about as sensible as trying to get back to nature by swimming or sunbathing on the beach.

The desire to gain a suntan, or to move out of the city, or to agonize about the environment, all point to the fact that our present way of life is manifestly unsustainable, ‘marked’ in the sense of structural linguistics. Ask anyone why it is unsustainable, since when and, most importantly, to what end. One person may say that human life on earth has always been stressful and under threat. Maybe so. That certainly seems to be the case today. For us, all that is noteworthy about this is that the voices around us vehemently assert that ‘today it is clearer than ever before’, or that this or that ‘continues to be crystal clear’, or that humankind needs to do one thing, was wrong to do another thing, will have to pay if it does not do something else, or has really got it coming to it this time. Stress is difficult to bear without talking fearfully. Our definition of the core of human nature as being religion and philosophy, as unceasing mindfulness, and, in response to stress, even more mindfulness, tells us to be wary of all clichés but pay attention to everything people say. What is, is: what is not, is not. We may perhaps even agree that the earth is sick, not because we have made a diagnosis, but simply because that is what a lot of people are saying and there seems to be no great harm in it. Or is there? At all events, science by its very nature will be unable to reach any conclusion about that because it has no experience of diseases of cosmic entities. Well, unless Mars is a precedent.

Let us draw a slightly curious conclusion, probably uncontroversial, but which we shall shortly need. The state of the forest, the terrestrial forest, and of matter, the global forest, the birthplace of humanity, is extreme but indefinable. This unexpectedly brings us back to an old paradox in the history of philosophy: for Aristotle, and effectively also for Plato, matter plainly exists but no less plainly is very elusive; it is important because it occupies a place at the opposite end of the spectrum from something as important as form, eidos, but that is precisely why it is indefinable.

The situation is ‘marked’, and loudly proclaims, demonstrates, that eidos and matter are coupled, but eidos does not magisterially dictate its form to matter merely because matter is elusive and indefinable. Eidos is intertwined with matter in such a way that all matter is predisposed to certain forms and not to others, as if it were already charged with eidos. The eidos of a statue, for example, can be dictated to bronze but hardly to air; a statuette of the human figure might be carved from bone and a bust might be made of marble or clay but hardly of water.

We find this complex interweaving of eidos and matter being considered already in Plato’s dialogue Timaeus, where the place we now expect to find occupied by matter is occupied by χώρα, khora, which is also eidos, only a darker, more complicated and elusive eidos because it is wide enough to accommodate many different concepts of eidos.¹ Khora is all-accepting nature which knows no birth or emergence. It is obscure and problematical and, needless to say, also needs to be treated with caution.

At our first approach to Aristotle’s concept of matter, we obtain a result that is reassuringly trivial. There is general agreement that the concept of matter was ‘introduced’ by Aristotle: that is, he heard the word, took the risk of using the term, and was so successful that it has been found useful by everybody since, right up to the present. We are shocked by the use made of materialism in Russia, by the way people of the worst kind wielded it as a weapon and a bludgeon to crush and smash everything. We are reluctant now to use it ourselves, just as we would shrink from picking up an executioner’s axe, even if it was much needed, if it was covered with blood and we knew it had been used for beheadings. Even if it was made of good steel, even if it had been rinsed clean. We would much prefer to take a different axe, and point out that executioners are not the only people who use axes.

Everything we find ourselves ignorantly handling has properties, and these are not just something we attribute to it. We have talked in an earlier lecture series about property and ownership.² That, however, was about property, and if we now look in more detail we will find that we are short of words to distinguish between what we think of as owned by us and what someone else may think of as owned by them. That is why I said then that the formulation proposed by Yury Lotman and Boris Uspensky, ‘our own/of others’, is incomplete. ‘Our’ Leonardo da Vinci is ours because we have mentioned him, but as I was writing that I was reminded of Pavel Florensky, who thought and felt his way so deeply into substance that he seemed to become immersed in it, as if he were no longer writing about substance but taking down dictation from it.³ For a true artist or musician, the colour or the sound are his own; he himself is the colour and sound, the mood. A craftsman begins by feeling his way into his material, the wood or the clay, and we constantly see that, for those who fail to do so, nothing comes out quite right. The Russian word ‘khaltura’, hack work, is derived from a word meaning a funeral wake (which is also ‘chaltury’ in Polish). A funeral is a hallowed occasion at which all are fed. They may be asked to eat rice, raisins, and honey, kut’ya, food for the dead. Hack work, too, is dead; it is what Heraclitus meant when he said that what was dead should be thrown out even before what was insanitary.⁴

We can rest content for now with finding that our similes for the forest have one thing in common: they give the lie to the idea that there is such a thing as ‘lifeless nature’. We can never be too sensitive in seeking to understand materia. We should quote so many agreeable cultural clichés that no genuine theoretical physicist will insist there is a boundary between his own science and the humanities.

But these are all, as I say, agreeable clichés that only seem to be important. All the positive attitudes of thoughtful, humane, artistic people towards the world we live in will remain no more than hot air, because what will decide not only the fate of things, not only what people do with them, but their very emergence will be mindfulness. ‘You look at the forest from the sidelines,’ a certain knowledgeable and sympathetic person told me. In fact, however, we are looking at it from the standpoint of mindfulness, which is crucial.

There are different kinds of mindfulness. A hack is attentive: he pays attention to where and how there is dead money to be made. Investigative, probing attention will see what needs to be seen in the forest by someone who is assured of three good meals a day in comfortable surroundings and whose priority is to ensure that situation continues.

Mindfulness is not a tool to be used by humans but a state into which they can and should fall. It is not targeted at the forest. Let us instead attempt a provisional conjecture about how it is that the forest captivates us and lifts us out of metric space. It is in fact possible for mindfulness and the forest, two polar opposites, to come together. Nicholas of Cusa’s coincidentia oppositorum develops something that Aristotle all but explicitly spells out.⁵ We are moving towards our reading of Aristotle with a working hypothesis that for him matter, like that of Plato, will prove to be eidos.

Before we read them, let me dictate this to you: we expect to find in Plato and Aristotle conclusions that we have arrived at ourselves. What arrogance, to attribute our own concepts to distant classical authors! For anyone inclined to that view, let us add insult to injury by saying that not only do we expect to find our own viewpoint in Aristotle but that, if he does not confirm our hypotheses, we will consider there has been no point in reading him.

To anyone complaining that this is a departure from the proprieties of the history of philosophy and philology, we can and will argue that, on the contrary, it is the only proper way to read Aristotle. The history of thought, and history in general, will crumble and I will find myself a New Russian in the most deplorable sense of the word if we do not insist that the most important occupation of humans has never changed: it is working on themselves, digging down to their true self. All our talk about the classical world will prove empty (the ‘Axial Age’, the ‘beginnings of our civilization’) if we fail to notice that these were different times, when the air was purer and visibility was better. The millennia act as a filter, so that in our modern, murky, unfiltered thinking we can presently only have conjectures as to what we will find there, in the classical world, taken as if it lay in the future. We shall be capable of rising to the challenge of the future, of modernizing, only if we lose no time in rising to the challenge of the classical world, and before we can do that we must once and for all repudiate the mentality that avers ‘they had not yet …’. If there is something we talk about now that we do not find in them, that means only that we for some reason are still talking about something they long ago gave up talking about. Their silence is not because they have nothing to say: it conveys a more important message.

One such thunderous silence is Plato’s doctrine of physical bodies. They are, he tells us, composed of geometrical shapes, so that, for example, fire is composed of tetrahedra.⁶ Did Plato really not know that a point, a line, a triangle, a plane surface, have no volume? That they are abstractions and that the ideal tetrahedron will never be found? That we can spend the rest of time trying to establish the exact line of its perfect edge, just as Achilles will never catch up with the tortoise? Not only the edge but the ideal tetrahedron in its entirety is wholly elusive. What has happened to matter? Where is it? Well, that’s just philosophical idealism for you! It needs to be fixed with materialism!

Let’s try to fix it. Let’s point out to Plato: you have failed to understand, you have failed to notice that there is matter in this tetrahedron we have drawn. There is the wood of the blackboard, the chalk, even the energy used in drawing the lines: these are all material. We find your tetrahedron bewildering, but we do understand chalk on a blackboard (materialism deals with tangible things). But these soon melt away, along with the Platonic solid! The blackboard, the line, the classroom, the ‘solid’, are all clear and easy to understand until we come to mindfulness. When we come to mindfulness, we find, to our amazement, that we must take our leave of metric space, and these material things become no more familiar and comprehensible to us than they would be to someone who was drunk out of their mind. We can have absolutely no doubt that Plato managed to do what we can do: namely, he crossed the threshold of unceasing mindfulness which grinds up the material objects of traditional perception.

Plato’s silence in response to our bewilderment, our indignant ‘Where has matter gone?’ and ‘How can they burn, these ideal tetrahedra nobody has ever seen?’, firstly results from his reluctance to chop logic with us in the delusive space of traditional thinking and, secondly, delivers a message we are not yet ready, not yet mature enough, to hear. In the forest, there is not only indefinability, a superseding of images, a silencing of thought, wonder and horror. There is also geometry. More than that, there is actually nothing there but geometry. There is a sign at the entrance that reads:

‘Anyone Who Has Never Studied Geometry: Keep Out!’⁷ Geometry is our introduction to philo-sophy, the love of wisdom.

This is all the more unexpected because the first thing we noticed about the forest, and it is the reason we chose it as the topic for these two semesters, is what it inspires and instils by propelling us out of metric space. Of course, in the forest there is none of the geometry of lines and projections such as get drawn on a blackboard. The ungeometrical nature of the organic was noted some time ago, if by geometry we understand nothing beyond diagrams. So, is there another geometry, and is the forest pushing us out of metric space in order to make us finally understand geo-metry? Geometry as taking the measure of the earth? What would that be? It would be pre-Euclidean geometry, in the sense of not giving Euclid what he is asking for (or demanding) in his postulates and, first and foremost, not accepting his points as something that can be determined or found. Let us again follow the path of our heuristics, of expecting something we already surmise. The point in this early geometry will be Parmenidean and Zenonian, an unattainable focus on precision extending to everything. There is only one point and it coincides with everything. The small difficulty that my work on points in various courses about porosity and Wittgenstein has not been published⁸ will be put right shortly, so I will not repeat myself, and anybody interested can look up the coincidence of opposites, of the absolute minimum and absolute maximum in a point, in my index to the two-volume collection of the works of Nicholas of Cusa.⁹

Given that our concern is not with the problems of geometry, we need go no further than the ‘point’. The more so because the fundamental issue, which we should never have forgotten, is that Euclid asked to be conceded his point, that it was a convention. We conceded it and promptly forgot all about it. The result is that now that point seems to have as much right to exist in reality as a cup of coffee. We ought to have remembered, as Euclid himself always did, that the point on which all his geometry is based is only a convention. That, thank God, was finally recalled in the twentieth century.

Toward the end of the nineteenth century the keenest thinkers in the field of geometry became increasingly concerned about the lack of true rigour in Euclid’s presentation. Undoubtedly, the invention of non-Euclidean geometries did much to spur the search for a correct and complete treatment of classical geometry. The most notable work of the new type was Hilbert’s Grundlagen der Geometrie [Principles of Geometry], published in 1899.¹⁰ David Hilbert (1862–1943) began by stating 21 axioms involving six primitive or undefined terms. [Chief among these was the point, Bibikhin.] He once made a famous comment (not actually published until 1935) to emphasize the importance of keeping the undefined terms totally abstract, that is, devoid of preconceived meaning: ‘One must be able to say at all times – instead of “point, line, and plane” – “tables, chairs, and beer mugs.”’ Such a viewpoint was not widely accepted until well into the twentieth century and, of course, had never occurred to Euclid or his followers.¹¹

That is a good rule for keeping the debate on the ground. We should take a beer mug and place it on a table that extends as far as another beer mug. This would be the best way to talk until such time as we actually know what a point is, and that becomes less clear every time we encounter one. Up until the present day, the ‘point’, as well as other geometrical terms, has existed only thanks to our ability to grasp and hold an object. It was not the point we could see and hold; all we had was our ability to grasp and hold, and the thing we did that to most often, and with great gusto, we called a point or something derived from a point.

Everything about geometrical constructs is beautiful and indisputable, but the elements of geometry are floating in thin air. The fact that they are mere conventions is blindingly obvious, and they hold true only because people have agreed to believe that they should. In Euclid’s original definition, a point ‘is that which has no part’. The ungraspability of a point is established with a deliberate paradox. I say it was deliberate, because in the classical world it was a commonplace that something that has no parts has nothing with which to have contact with anything else. If it merged with something else, it would add nothing to the whole of that other, or, if it entered as a constituent part of that other, it would rend it apart, because nothing in the other would be able to be in contact with a thing that had no part.

Whether it is easy, difficult, or impossible to obtain a point, the only way it can be done is by concentration. The still unresolved paradoxes of Zeno and Parmenides show that concentration of the mind alone is insufficient. I have no time to repeat what has been said in earlier lectures, and would ask those who are thinking about this for the first time to take on trust, without ifs or buts, that in the most literal manner, in the problem of the point, the basis of geo-metry, we come back to mindfulness. All the observations on the relationship of the point to time, about the point as the present, according to Aristotle and Hegel, which has also been previously discussed in detail, provide the context of what we need now to engage with. Our topic is Plato’s unexpected geometry where we would have expected to find matter, the geo-metry of the forest, the forest as geo-metry without Euclidean metric space. Here is what a modern historian of thought has to say about Plato’s ‘eidetic atomism’, which means that in place of the expected atoms of matter we encounter pure eide: ‘Diese kühne und in ihrer Weise großzügige Theorie der Materie ohne Prinzip der Materie hat weder im Altertum noch später Nachahmung, ja auch nur Verständnis gefunden.’ ‘This bold and, in its way, ambitious theory of matter without the actual principle of matter was not taken up, or even understood, either in classical times or subsequently.’¹²

Whether or not it was understood, whether it is easy or difficult, we need to buckle down. As Plato says in The Epinomis (992a), ‘[T]his is the way, this the nurture, these the studies, whether difficult or easy, this the path to pursue.’¹³ The Epinomis here is a legacy, bequeathing the law of bliss, the law in the sense we have been speaking of, the law of humankind, of its nature; happiness in the sense that it was experienced by the Pilgrim when he discovered unceasing prayer, constant mindfulness. The whole history of thought speaks with striking unanimity of the happiness of humanity when it returns to the law. We read the final pages of The Epinomis, and this is so similar to the joyous pages of The Pilgrim. When he comes back to the law, to religion and faith, Plato tells us, a man will be freed from his distress (which we referred to, following the Gospels, as ‘the issue of blood’):

And the man who has acquired all these things in this manner is he whom I account the most truly wise: of him I also assert, both in jest and in earnest, that when one of his like completes his allotted span at death, I would say if he still be dead, he will not partake any more of the various sensations then as he does now, but having alone partaken of a single lot [i.e. he will be vouchsafed wholeness, unity, monasticism, Bibikhin] and having become one out of many, will be happy and at the same time most wise and blessed. (992b)

We shall need to return to The Epinomis, because our main themes of the law, religion, constant mindfulness, and the forest in the sense of matter come together there really very clearly. But we shall remain firmly focused on what has just intrigued us most: matter as number; the forest whose very breeze, we cannot doubt, despatches metric space; and geography, which, according to Plato, has pure geometry as its law. We are not ready for this, to proceed by way of clues and glimpses, such as one that has been suggested to us, of seeing the pillars of a mosque, symbolizing the pillars of the universe, as a forest, as trees, and in some way subordinate to the sacred number of ‘17’. We can, if so inclined, link anything to anything else, any idea to any other. We, however, will prefer to admit failure, inability, rather than rush to associate the forest with a number, or agree with the majority of historians of thought who believe Plato was getting a bit carried away here, coming up against the limitations of idealism, or even, as Alexey Losev manages to claim in line with his preoccupations, that Plato was a man of his time who ‘lived and worked’ in slave ownership, with the result that he projects the callousness of a slave owner on to the world of ideas, and that his geometry is based on heartlessness. ‘Because number, devoid of qualities or indifferent to them, is precisely his basic principle, lacking any personal or “spiritual” dimension. Accordingly it is entirely predictable that Plato’s philosophy, having developed as far as its limitations allowed, ends up with the doctrine that his eternal and divine forms are numbers.’¹⁴

This is sad. I do not think Marxism was the cause of this blunder. More probable is what Nicolai Hartmann noted: that matter as number is such an amazing leap in Plato’s thinking that it has not been understood to this day.¹⁵ If Losev effectively passed on this, preferring to say nothing, that is because in his curious formulation he only hinted at a strict, harsh discipline, also to be found in the structure of the ancient polis, which succeeded in binding in slavery anybody unwilling to accept the risk of being free and taking responsibility for themselves. It was a degree of disciplining of thought that we have forgotten, but which is no less unyielding than mathematics. We have worked our own way round to the discipline and school of constant mindfulness. There is, of course, plenty about that in Plato. It is clear that without schooling, without strict discipline, it will be impossible for us to understand the riddle and mission of Plato, namely matter as number. Discipline is undoubtedly a necessary condition here, but is it a sufficient condition? We may not have enough vision. Does anybody know why the forest is digital?

The forest is wood, and wood is fuel. We take heat and light from fire, the burning of matter. Fire, according to Plato, is a tetrahedron. Not something in the form of a tetrahedron, not a tetrahedron filled up with something, just a tetrahedron. It is not that somewhere baffling processes are taking place with the primary elements in attendance and the tetrahedron is a kind of assembly or abstract function signalling or symbolizing them.

To our difficulties, deadlock actually, must be added the fact that if Plato understands the element of number, the one, in what is called a substantialist way, as a simple concentration, a happy totality, as a blessed fulfilment of everything, how is he to get anything out of such a one, which is clearly singular and clearly equivalent to the maximum integer of the universe? How is he to construct anything with it when a tetrahedron requires at least four different points? We land ourselves in the problem of the difference between the substantialist so-called Pythagorean number and the arithmetical number, which are completely different things. A lot of care has been needed to avoid getting burned by this distinction.

Again the admirable Nicolai Hartmann warns us:

The theory of Timaeus represents, in terms of its content, a synthesis of atomism and the doctrine of forms, which should be considered impossible in view of the natural antithesis of these two doctrines. There has to this day been no thorough investigation of this historical topic. This is one of the numerous gaps in classical historiography of philosophy in the last hundred years that result from its deficient understanding of the problem.¹⁶

That is, the problem is not in the method and apparatus, but in too much understanding: everything is immediately abundantly clear to the researcher, just as the slave-owning undertow of Plato’s idea was, unfortunately, only too clear to Losev. Hartmann sees no problem where Plato did, and is perhaps even a little smug at having been able to sort it out as Plato, unable to resolve the contradictions between materialism and idealism, failed to.

Owing to the fact that the ‘contradictions’ between Plato and Aristotle have by and large been invented, it is even constructive to read the two philosophers as, on the contrary, complementary to each other. There is the brilliant, characteristic, and generally accepted denial by Aristotle of the existence of species and genera – ‘the animal in general’ exists only in the imagination, the species of donkeys perhaps a little more but still not really – and all that really exists is this particular donkey, and another one over there. He places a taboo, in other words, when inspecting this particular donkey, with those particular ears and those big eyes, on hypostasizing donkeyness; a taboo on extending it any further than this particular donkey. Or, if you like, we can eliminate donkeys altogether by counting them as one, two, and three but remembering while doing so that we are counting something that does not exist, and take full responsibility for the fact that we are doing, operating, something that does not exist. That makes all applied mathematics a risky business when, if you forget when counting ‘one thing, two things, three things’, no matter what they may be, it has already slipped into the realm of things that are not there.

And what if applied mathematics is calculating without including what is being counted after the number? The number will have reality if we see it as counting ‘this thing here’: that is, if we are viewing the donkey, not abstracting the number back to a general species or genus. At this point, Aristotle seems unable to help us further and it looks as though (although there can always be a surprise in store) we need to go back to Plato, to see the number itself no less specifically, as ‘thisness’ (haeccaeitas), than the donkey. Can we see the number, can we look straight at it in the same way we can look a donkey straight in the eyes?

Yes, we can, and, oddly enough, the experience will affect us more directly and strongly than our encounter with the donkey.

This experience is not possible with a denumerable number, an element of mathematical operations, because any number there as an element of a set of integers must be abstract and generalized, totally indistinguishable from any other number, since otherwise the set will fall apart. But actually, to our relief, we find we are not being called upon to distinguish between a number with which a close encounter is possible and a mathematical number, because modern mathematics gets by perfectly well without the concept of number and deals instead with structures and processes. In other words, just as geometry repudiates the indefinable and undefined concept of the point and is entirely willing, according to Hilbert, to talk instead about a beer mug, so modern mathematical terminology does not include the concept of number. Philosophy was all for donating number to mathematics (at least, general and philosophical reference books say that number is ‘one of the basic concepts of mathematics’), but now mathematics is returning the gift and philosophy will have to return to it, which is something else for us to look forward to.

Aristotle has experience of encounters with ‘this thing here’, Plato of encounters with forms or, later, with numbers. Just as ‘this thing here’ cannot be part of a calculation, since otherwise it will cease to exist, so Plato’s forms cannot be counted in terms of one, two. This is what I call moving out of metric space. Let us tentatively, without becoming prematurely confident, say that by moving out of the space of counting, auditing, and structuring, we are returning to the early geometric number. I am setting myself that as a task for the future. Just as Plato has long been urging us to think more thoroughly about number, so he is also calling upon us to review geometry. I am merely accepting the challenge which, as an old man, he left at the very end of The Epinomis.

In order to train minds capable of mastering this knowledge,

one must teach the pupil many things beforehand, and continually strive hard to habituate him in childhood and youth. And therefore there will be need of studies: the most important and first is of numbers in themselves; not of those which are corporeal, but of the whole origin of the odd and the even, and the greatness of their influence on the nature of reality. (990c)

I understand this to mean the invariable symmetry of all that exists, which is called real number.

When he has learnt these things, there comes next after these what they call by the very ridiculous name of geometry … and this will be clearly seen by him who is able to understand it to be a marvel not of human, but of divine origin. (990d)

Numbers themselves, like geometry itself rather than the ridiculous way in which it may be understood, are an invitation and a task for us. Let us initially try to approach this task from a fairly easy and uncontroversial direction. A confident counting of things, ‘one window, two windows’, or, which is essentially the same, of numbers, ‘one number, two numbers’, is possible because the generalizations are, as it were, ready and, indeed, waiting for content. Let us imagine a pit that we want to fill up. Who dug the pit, and how, into which the set of natural numbers is thrown? The series can be very long, but the pit is invariably bigger, as if anticipating and inviting it in. Counting things such as the stars in the sky will surely run into difficulties, not because of any lack of space, but only because it is difficult to count them.

Now at this point there is something to which I want to draw your attention, namely what might be called the ‘lure of the pit’, or ‘the lure of the heap’,¹⁷ which seems to have a will of its own to grow bigger, to accumulate, and which, if we did not keep our eyes open, did not protest and resist, would level things down even more. A random example: 300 years ago, a census of the population, conducted as it is nowadays, would have been impossible. The difference between a working man and a woman seemed just too great, and this was even more true of an old man or a child, so the count was based on households or smallholdings. In a modern census, all classes of the population are, as it were, lumped together, levelled out. What is causing this virtually limitless trend towards generalization? Obviously, the fact that ultimately everything belongs to one primal category, the totality of all that exists, is, as it were, sucking everything into itself, demanding enumeration, and avidly seeking to be filled up. Moreover, we know in advance that there is no danger of the categories running out of space, that there might not be a receptacle to count everything into. Everything – and that is a lot of stuff – belongs ultimately to the One, to one world, one universe. We have always enumerated too little, ascribing things to the universe. Everything always fits into it. It has room. Everything ultimately can be generalized by the very fact of belonging to one and the same universe.

This power of unity, of wholeness, encompassing, drawing in, clearly can never be captured by counting. The universe is of a size that, no matter how much you put into it, there will still be room for more. Trying to put more and more into One is clearly an inadequate, negative, or deluded response to the challenge of unity. We can see that the numerical series gets its power from its infinity, from the negative knowledge that the power of unity cannot be exhausted by endless listing. The origin of number is thus negative. A numerical series, infinite counting, are based on a tacit assumption that we can safely engage in endless enumeration because unity is strong enough to accommodate that. We enumerate all the constituent parts and abilities of a human being, but then realize that they can be further subdivided, and that there are others yet to be discovered, not yet investigated.

We encounter something analogous with time: its infinity stems from our own irremediably late arrival on the world scene, from our being late for the event of the world. No matter how many years we add to our own lifespan or to that of humankind, we can be reassured by our intuitive certainty that the event of the world has infinite room to draw on. A supply of unified, official time is reliably provided by our lateness; it can, and should, never end.

Just as, apart from official, levelled-down time, there is being-time, so, apart from the negatively defined unit of arithmetic, there is a unit or unity in the experience of the whole, but as a unit of experience we are much more directly affected by it. More directly, I would say, than the live donkey in front of us: the latter affects us on a living and organic level, but the experience of unity is, by definition, everything, integral. The experience of unity is the same as of the point as concentration, of mindfulness, of prayer as the submission of everything to the one who is no part of being, no part of anything, and yet has the most intimate and direct relationship to everything of anything.

For the time being, we do not see how this all-encompassing unit can move, create order, a set or calculation, and yet the Pythagoreans and Plato talk of substantial numbers, not a substantial unit.¹⁸ This difficult question we shall address next time.

A request for papers, on this topic, or more general. A competition is to be announced nationally. Those submitted now will be eligible.