The nature of number

[Categories+Sheaves]

I was wondering if the number could in some way be analogues to the electron in that the act of observation affected it, that was why I was trying to observe the actions of numbers through an outside medium geometry.
If you use a fixed point to define a number, then the number can only be a fixed point, but I thought if we examine a series then we might be able to see if the number is fixed or not.

1. We use numbers to model the things we observe. So once we start talking about the ways we "observe" the model... too meta. Should we model our model? Model our model of our model? Reminds me of an Achilles/tortoise dialogue. Ever read G.E.B.?
2. If 'number blarg' is one thing at one moment and a completely different object at another moment, mathematicians would probably say 'number blarg' isn't well-defined.
3. I mean, mathematical objects exist through their behavior/intelligibility and because of it. There's nothing to really say about "a point" on its own--and I'm not even sure what we should mean by that. But a point in a plane, a point on a torus, a point in the prime spectrum of a ring... these
make sense.

Otherwise: still interested in that geometry stuff?