The Woods. Vladimir Bibikhin
quantity has been transformed into quality? This is a bad law of dialectical materialism that results from poor eyesight: the new quality derives not from some quantitative addition but because the set under consideration has, barely perceptibly, unexpectedly, been drawn towards unity. The whole is beginning to shine in it more strongly.
It would be more precise to say that the way of viewing it has switched; there has been a change of viewpoint from one unity to a different one. The inclusive, attractive power of unity cannot be encapsulated by enumerating its components. The universe is a heap, and no matter how many components you throw on to it, there will still be room for more. And that is true of virtually any unity. Behind the family, we detect the genus, and here is where we need to seek the cause of the inexhaustible bounty of nature. We cannot construct a cell from its constituents because it is a unity. Why it is a unity is a separate matter, and it is as difficult to find an answer to that as it is impossible to create a unity, a wholeness: it has to be found, intuited; it has to give itself away. It is impossible to detect elementary particles, neutrinos or quarks; it is impossible because of the ‘natural’ method of physics. The reason it is called natural science is because it is unable, is not supposed to, has never learned how to, deal with anything that is not a whole. Any whole, any unity, cannot by definition be mechanically assembled from parts. That is a peculiarity of the structure of any unity in nature.
The issue of the elusiveness of wholeness in nature is different from the issue of wholeness in technology, where, for example, there is no difficulty in enumerating how many parts a wheel consists of, and I cannot raise it here. Some other time.
For now, let us hold on to our thread of how and why the forest proves to be geometry. It is so tempting to try to fill up unity with quantity, because we feel the need to respond to it in some way. It challenges us, but perhaps the purest way to redeem thought is to leave unity alone.
So leave it alone we shall, but whether we worry at it or leave it alone and in peace, it remains unassailable. Nevertheless, we understand the origin of numbers and their strength: their infinite reserves. We know negatively and not necessarily consciously, perhaps intuitively, that mere enumeration will never exhaust the power of unity. So let us rest assured that there will be no end to our enumeration.
The origin of number is, then, negative. Numbers with their infinite counting have as their base the hidden intuition that it is possible to carry on safely enumerating till the end of time: unity is strong enough to cope with any amount of enumeration. We have enumerated all the constituent parts and capabilities of the cell, but that is not the end: there are more fragmentary parts, newly discovered, unresearched. We encountered something similar in the computation of mechanical time. Its boundlessness is explained by our ineradicably late arrival in the occurrence of the world. No matter how many years we add to ourselves or to humankind, we can do so secure in the knowledge that, precisely because of our secret awareness that we know nothing of its origin, the event that is the world will be sufficient for us to draw on it indefinitely. The steady movement of unified or official time is reliably ensured, again negatively, by our late arrival, by the fact that the world was already there when we arrived. It can never come to an end.
Just as, separate from the official, standardized time of negative origin there is positive being-time, so, separate from the negatively founded unit of counting, there is the unity of the whole. To use Wittgenstein’s expression, any unit of counting is a test or a measure of the unassailable whole. We approach it this way and that, calling it our experimental number. The more we operate with these measures, these tests of unity, the more the experience of unity recedes into the unfamiliar, something we do not know how to deal with. Plato needs to remind us that the experience of number affects us more directly and fully than, say, the experience of our encounter with the donkey. The latter concerns, let us say, the living, the vegetative in us, and even then not always; while the experience of unity affects us always and completely. The experience of unity is at the same time both very rare and definitive, like the full stops we put at the end of every sentence. We can put them anywhere and everywhere, but do not even notice the charge of a full stop, the experience of concentration, because we have become completely used to operating with them. Prayer as the exposing of everything to what is nothing out of everything is something we undertake very rarely; we are usually busy with something else. In reality, though, we are showing ourselves constantly, always posturing, only we have become confused about who we are, and who it is that we are posing in front of. For a child, for example, the face of the person to whom it tells everything and before whom it poses, until emancipated from the family, is identified with the face of the parent, simply because the parent is constantly imposing a particular agenda. God does not impose himself.
So, number is a measure of unity as a whole, and not the other way round. Unity is not the measure of number. The dimensional number comes from a different, negative, space than unity. The shadow takes its orientation from the tree and not vice versa. But, even while recognizing this, we do not see for the present how all-embracing unity can move, or count, give form to order, a series. For now all we see is one unity, and yet the Pythagoreans and Plato speak of substantial numbers, not only about a substantial unit. I understand one wholeness. Two wholenesses, however, by virtue of there being two of them, will immediately cease to be joint or separate wholeness. Or am I wrong?
Substantial numbers are a difficult issue, and I have no confidence at all we will be able to resolve it; there may not be enough mindfulness, our attention may stray to other matters. It is tempting to say that there simply are no such numbers. The main problem is that we have no idea how to set about resolving this issue. For the time being, therefore, I will skirt round it. Actually, I do have a negative hypothesis, so here it is. Aristotle says clearly and distinctly that number is matter: ἀριθμὁν … ὓλην τοῖς όὔσι (986a, 16–17), but in the context of criticizing the Pythagoreans and Plato. Number and eidos seem to be the same thing for him and he uses the terms interchangeably in Metaphysics A6 and elsewhere.5 Or so, at least, people say. It is said that if we listen attentively, as we did, to Plato’s idea that the forest is number, we will find Aristotle among our critics.
This problem really is one we are going to have to face up to here and now. It would be highly distasteful to try refereeing philosophers’ opinions: ‘In this instance, we agree with Plato and oppose Aristotle.’ We need either to agree with Aristotle’s criticism of Plato or to disagree with it. We are really not going to start haranguing Aristotle along the lines of progressivist scholarship: ‘He committed the error of … failed to take account of, did not understand …’ It would be just too grotesque to ‘referee’ in this manner a thinker who lived 2,300 years ago. The only respectable and elegant way out of our predicament over Aristotle’s criticism of Pythagoreanism is either to manfully jettison everything we have said about number within the forest, about the forest as number, or find precisely that same thought in Aristotle: the forest as number; the forest as the Cross, pure geometry.
Immediately, as if for our boldness, we are rewarded, although matter is one of the most difficult topics in Aristotle. The difficulties are of two kinds. Aristotle does not tie himself down: having propounded one thesis, he does not consider himself disqualified from later putting forward a different one. His truth is on the move. The second difficulty, which is a difficulty for Aristotle himself, is that primal matter must not be ‘like this here’, because then it would be possible to imagine a different kind of matter, meaning there were two or maybe more. There needs to be just one kind of primal matter, but if that is so, where does the difference between substances come from? From different structures of the primal matter? But if we are saying that there are within it proto-structures with the potential for further formation, we are back to dealing with structures, and we wanted to be dealing with pure matter. Certainly, we find different kinds of matter in Aristotle, but the difference comes about from the depth of our scrutiny of it: the immediate matter for illness, for example, is humankind, but humankind itself is eidos, and matter is placed at one remove.
One thing Aristotle is predictably definite about is his refusal to accept that matter can be located anywhere beyond the boundaries of things and separate from them. Just as there is only imaginary donkeyness separate from this particular donkey in front of us,