I had the thought yesterday that I had been going about it all backwards: instead of attempting to characterize the *experience* of disjunction — even if we *do* declare that “we are talking in very definite ways about experiences that never happen” — we should simply be asking, in an abstract way, what is it that disjoins our experience?

There is an great scene in Faulkner’s *Was* about a poker game — well, the highlight of that short story is indeed a poker game, and poker itself is — even if this sounds cliche — an excellent metaphor for life. Because in poker games, you never know what is happening until the cards are finally turned — you never know whether someone is honest, bluffing, or faking the bluff, etc. In poker we experience everything all at once, in a sudden rush of holism at the end — which resembles, not the linear, reactive way in which normal life experienced but rather the way in which *liminal *states are experienced — such, as, for example, these moments of intensity, when man is pushed to his limits, that Conrad is fascinated in. So the task, I realized last night, was not the attempt to describe everyday life, or even its liminal states — there are some *serious problems* with asking about “liminal states”, since the word itself is almost an oxymoronic — problems that we are probably familiar with, ie, we with our bitterness towards society — the way in which all of society is about a crisis that is *not really a crisi* but an accepted “state” — but rather to start from scratch and ask how liminal states are even possible.

2 further comments or corrollaries — first, we wish here, I mean, we hope we can, finally take a very definite break from all the *declared* crises of society — we’ve been trapped here too long — it feels like an enormous impasse. We cannot even *start* with what society considers “events”, “disruptions” — that is *already too late* — but we need to make a fresh start as only theorizing and speculation can — perhaps — bring us. Second, and this is personal, I feel I have been stuck for too long on this notion of “darkness and labor” — it feeels like an enormous impasse to me. We cannot not (unwittingly) presuppose that labor will bring us any sort of insight or knowledge, we cannot *look *for disruptions with the very ‘eyes” that is meant to be disrupted — eyes in quotes here because we are talking about the *linear eye*… If my hunch is correct, then we are on the verge of overcoming an great problem, often stated but never clearly understood — the problem of dealing with *genuine crisis* and the way in which it is lost as soon as it is known.

– The Zero –

The time is shattered, experience is shatterd, *because of representation*, *because of the trace*. In other words, the world is shattered because we have before us the puzzle peices to represent the puzzle of experience, and not because experience has, via some kind of intensity, been shattered beforehand. Poker shatters experience and disrupts the flow of time, it is not merely the *representation* of an experience that was shatterd a priori.

I’ve been reading — well, I mean, I tend to skim things nowadays — I’ve figured out long ago that you can understand what you read only if you *already* understand it — I’ve been reading a lot of Brian Rotman lately, I’ve been reading his book on the history of the zero, the mathematical zero. His major argument, I believe, is that plays a special role in the holisticizing of experience, at the moment when the cards are laid out, the traces brought together.

His account of numbers, arithmetic,etc. is highly pragmatic — related closely to *accounting*, trade, bookkeeping, and so forth, and not to anything like pure mathematics. In retrospect, I seem in myself a vicious *religious* streak (cf, “labor”, “darkness”, etc) that I really need to address. Mathematics is basically a set of techniques used for the manipulation of numbers, specifically, for adding and counting numbers. The zero greatly simplifies arithmetic but there is definitely a kind of blindness to it as well. I mean, working without the zero is conceptually easier but pragmatically difficult — think about, for example, adding Roman numerals — it can be done. The shfit, I believe, towards the zero can be considered a trace from a *linear* sort of experience to a *holisticized *one, I mean, a reassembled one.

Algorithms itself are a kind of gathering together of traces — an algorithm is put together from shattered peices.

Let me digress momentarily and tell you about an experience I had recently, and the lessons I drew from that, upon reflection. I don’t mean to self-aggrandize or anything, even if it may sound like that.

Anyways, the basic story is that I was able to rather quickly solve a problem that some of my roommates had been working on for hours. This is not because I’m a genius or anything, but mostly because of all those years of high school math competitions. Yet I want to also make some cliams about a sort of “insight” or perspectival shift that “cracks” such a problem. It is a very interesting problem in elementary combinatorics: how does one enumerate the set of n-element combinations selected from a set of m elements? So, for example, if you had the set of lowercase letters, {a,b,…z}, and you considered all the 4 element combinations (ie, unordered, so that {e,j,z,a} would be the same as {a,e,j,z}) then what would be a technique for enumerating the set of all 4-element subsets, that is, assign a unique natural number to a given subset?

So this problem is hard if you try to do this… “directly” in some way. One must not have faith in work, in a sense. You have to sort of step away from the imagination of a person “counting” and incrementing each set. Since we are considering unordered sets then we might as well consider them in alphabetical order — so the problem becomes enumerating all the alphabetical 4-tuples, or whatever the technical term is. It’s a problem of counting — we obviously know how to count to 100, it’s very easy, but how does one count if one can only count increasing, non-repeating 2-digit numbers? Like:

12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, … etc. — and how would one (easily) map this to the series 1, 2, 3, 4, 5, 6? How would we know, quickly, what the 27th element of this series would be?

So this is the obvious but also the wrong way to approach the problem. It is very computationally intensive, especially as one considers, say, 3-digits, or 4 digits. Yet there is also the mistaken belief — and this is why they were at an impasse — that there is some underlying *reference* to this problem. One gets caught in a kind of mathematical impasse of translation — that is, doesn’t this number *necessarily refer to* that moment of counting? Isn’t this problem asking about that *procedure*, that linear procedure, and nothing else? Isn’t our only mode of progress the *mental observation* of that procedure?

This reminds me of a famous story about Gauss — which is in fact, now that I think about it, pretty much the very same story. The story goes, that Gauss was told, along with some classmates, by a bored teacher — who wanted a break apparently — to add all the numbers from 1 to 100 and produce an answer. Of course Gauss, via a leap of insight, was able to produce the number within seconds: (1+100)*100/2 = 5050. So the other students are similarly faced with a kind of referential, linear imapsse.

But here we consider that working with the trace has a way of shattering or exploding this scene. We do not observe, like a scientist, but arrive afterwards, like a detective to the scene of the crime, and make deductions about what *must have* happened. (Maybe this is why proof by contradiction, too, can leave one with an uneasy feeling — since there is never the moment of direct observation.) With the construction of addition around the zero — well, there is nothing natural about this.

You know, I’ve had for a long time this incorrect imagination of the zero as a sort of “foolhardy leap” over the problem. Like, although the zero is this strange, almost unthinkable number, let’s just treat it as any number and carry on, and if it works, then we are home free. … this actually reminds me of that story about Schuvalkin if you are familiar with it. But anyways any algorithm involving the zero must have been *painstakingly* constructed — an algorithm makes operations faster but does not itself come fast or easily. Once we *have* an algorithm, then we have the tendency to float along blissfully unaware of the enormous dangers we may be facing — since we usually end up in the right place anyways, which we find comforting.

Numbers themselves are traces, they are representations of an earlier act of counting — so they say. So that the natural numbers are an abbreviation of what Rotman called, I think, “ur-marks”, which are the actual marks of counting: 1, 11, 111, 1111, 11111 … corresponding to 1, 2, 3, 4, 5. But they are also, on the other hand, traces, marks, themselves. Even when abstracted and abbreviated from the ur-marks, it seems as though our imagination persists in seeing numbers as the trace of some given, prior experience of counting. And so this is what addition, without the zero, becomes, merely a kind of *abbreviation* — and thus, still representations — of the process of counting.

But numbers, in the very act of marking, as mark, becomes also divorced from representation. It becomes possible, does it not, to ask about traces directly, like a detective: for example, to ask about what sort of process produced this trace:

1 1 1 1 1

1 1 1 1 1

1 1 1 1

The zero is the absence of the mark, it *seems* like a reprentation but it can be represented *only when the mark gains an independent status*, ie, becomes freed from representation. There is no prior experience assocated with the zero — well, it is precisely the absence of an experience — the experience of *not counting*, or of the origin, of just starting to count — which itself comes, afterwards, to be considered an experience.

TBC

Tags: mark, math, philosophy, poker

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