zero not on number line

30 04 2011

If we consider -x as being “not x”, then the natural conclusion is to say that absolute zero is not on the number line.

Zero was adopted in western maths relatively recently as a means of ascribing a symbol for the lack of something. Namely in dark and middle ages when using counting boards, there were no beads on a particular power of ten space. Hence, “0” represented no units, or tens, or hundreds. A digit to represent no beads.

Seems natural, therefore, to have it starting counting in a number line since 0 precedes 1, and the distance between 6 and 7 say is the same as the distance between 0 and 1. Yes, for sure, if we are measuring things. But, if we are not measuring and counting things, how does this effect our use of zero? Again, the direction of XQ.

If we have -7 as meaning not 7 specifically, and -3 as being not 3 specifically, then the absence of all number, not x of any kind, can be indicated by the number zero, the absence of all numbers.

(The reason things get tricky, is because we are using iteration — the ten symbols to represent digits, combined with place value; thus 7 may mean 7 units or 7,000. This folding in of itself, gives the power of modern mathematical notation. The playing around with zero in this context might confuse us. To keep things straight, not twenty has no “zero” in it; there are twenty things, there are precisely not twenty things. The zero used in the number-glyph is “20” is not significant wrt the number, but our notation system. There is no “not” in twenty, as a number of things.)

There are certain mathematical progressions that do not have zero in them, zero as meaning not any and every number. It is not reached, it can not be, it is not part of the same substance as number. x^y. For every number x>0, there is no value of y that brings the total x^y to be equal to zero. On this path lies the significance of the mathematical constant e.

This relates to something Leon came up with a long time ago. I am a person who approaches zero; zero is part of what I do, deeply, experientially. Whereas, Leon had as a basic metaphor, the Egyptian binary number system. He did not appear to have a zero in his being vocabulary. His closest association was, and I bet still is, with one. In the old context of our conversation, I think I related this to identity, of the individual, as well as tot he mathematical sense of identity: 0 is the identity for addition, and 1 is the identity of the function of multiplication. That is, a number is not altered if we add 0 to it; a number is not altered if we multiply it by 1. In this context, we have completely different number systems,: one where zero is part of the number line, and one where it is not.

That is, the notion of zero included in our number line gives rise to the potential of negative as we commonly understand it. It is the pivot around which negative may come into being; it is the means by which opposition enters into maths; the gateway for duality of mind to find itself on the page. Without zero as part of our contiguous number line, we can not have negative.

What, then, comes of a mathematical system that does not have zero as part of the number line? And what of a person who has this… metaphor… identifying idiom… as a part of their character? Their being? A person without negative…?

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