A place to begin

Here is what you might call an ordinary math problem to inaugurate this the new improved version of The Journal of Time and Sound.

Either: Subtraction is not universally applicable to finite sets

Or: 0=1

Suppose we want to obtain the result for the argument 4-4

If there is an answer, it will be 0. However, this requires that we undertake the solution using the set

{O, 1, 2, 3, 4}

–which contains five numbers. Where did the number five come from? We might simply propose that the subtraction of four from itself implies a universe larger than four. This is all well and good, except that the consequences are that 3-3 derives from a universe implying four numbers, with 2-2 and 1-1 proceeding likewise. But then we come to 0-0, which must derive from a universe containing the number one.

How can 0-0=0 imply a number greater than 0? If we say that one is presumed to be “already there,” we are claiming something different than when we assumed a universe of five for the subtraction of four from itself, because in that case we “borrowed” the zero and counted it as one element. But with the subtraction of zero from zero, we run out of elements to borrow. Zero must be one in some way.

Of course a consequence of this outcome is also that 1-1=1, because zero has been established as one. Moreover, the mere contemplation of zero and one gives us a total of two elements. And off we go.

A century ago, the set theorists pronounced the becoming-one of zero as the successful production of the natural numbers from nothing. But in their haste to tackle all those infinities, did they perhaps neglect this instability in ordinary arithmetic, where the choice is either that no number remains itself, or that enumeration as such expires, like a command to erase the hard drive?

It must be the case that numbers are themselves and that one can answer for the disappearance of a quantity — but how? My proposal: the mind rejects both choices, in a kind of constitutional disgust. This in turn suggests that we only retain the sanity of numbers so long as we project their irrational behavior onto a somewhere or someone else of which we cannot be rid.

Mathematics begins as circulation, disgust, hyperbolic donation, the sovereign exception, face, monstrosity — thoughts?


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