Dark Math and the Vanishing of Zero
Some bits of Facebook conversations that I have been waiting to have about math. I don’t claim to be even a little bit competent as a mathematician, but I do feel like there is a chance that these ideas might just happen to be so absurd that they are profound. Among these ideas has been the consequences of making zero disappear, and redefining the number one so that it is the container of mathematics itself.
There was another idea that I proposed today of “Dark Math”. I asked the question “Does math have a language/theory to represent its own opposite (independent of consciousness even, just like imaginary numbers, but imaginary anti-math instead)?”
If we turn Incompleteness around, for example, we get something like intuition. Any informal-non-system contains unanticipated reflections of formality..surprising quasi-truthful insights from out of thin air, like an oracle. If we turn Church-Turing around, we get non-universal, non-machines = unique individuals. My suspicion is that such a language would help define or model previously undefinable phenomenological conditions. Anti-numbers, (names which are intrinsically semi-proprietary?), Anti-operators (metaphorical and synchronistic?)
Then the zero idea came up again…
OH: A complex number z is said to be purely imaginary. If it has no real part, i.e., R[z] = 0. The term is often used in preference to the simpler “imaginary” in situations where z can in general assume complex values with nonzero real parts, but in a particular case of interest, the real part is identically zero. 0 is a pure imaginary number .
S33: If the part is identically zero, but zero is entirely imaginary, does that mean that its identicality is also imaginary? If we carry through the idea that 0 is imaginary, then any time we qualify something as being ‘not’ we are being figurative, and the reality would always be some infinitessimal fragment. Not would literally be ‘almost not’.
S33: But what I’m proposing is that vanishing itself is identically zero, then vanishing may be infinitesimally figurative. Nothing can vanish completely in reality, even the difference between A and A.
Can zero be said then to be ‘that which is not anything, *not even itself*. When we apply this to ontology (and I think we should) it means we must accept that nothing has vanished. What happens instead is that things nearly vanish from some set of perspectives. The gap between nearly vanishing and vanishing is entropy. Entropy is how perception compensates, fudges, fills in, etc so that what is for all practical purposes absent (i.e. the past) becomes elided or removed. Even the removal is not total, not real, its just a delay. Eventually all that has been denied must be revealed as unvanished from some perspective or encounter.
The reverse of this entropic clipping of the infinitesimally unvanished would be what I call significance. An augmentation of sensitivity or motive so that a near-vanished experience is encountered first as fiction. In other words, entropy makes things seem to disappear (like the past, coherence, certainty, etc) which really haven’t, and significance makes things seem to appear, but also significance increases the quality of ‘thingness’ beyond the thing. You could say that entropy masks presence to the point of near absence, and significance stretches near-absence to the point of re-presence.