AlexW wrote: ↑Wed Apr 18, 2018 1:10 am
Let me compress our discussion a little bit as otherwise we end up with posts that become impossible to manage.
Oh good, I'm glad you took the initiative
If you don't mind I would like to zoom in on your camera-monitor as well as the 2+2=4 examples.
Sure, I encourage you to refer to the tape as much as you like
You stated that the regression a camera looking at a monitor creates can be seen as the basis for the idea of infinity.
While this sounds reasonable you are overlooking that in a finite system - to which the camera and monitor obviously belong (otherwise infinity would already be present even before the regression) - everything is by definition finite. That includes the resolution of the camera as well as the screen. The regression as such cannot create infinity, but the regression will end when the resolution is exhausted. One single pixel of a certain color will thus be the end of the regression - infinity can as such never be reached from a limited system (and even the idea of infinity is wrong as it is based on the false assumption that an infinite regression can be created in a finite system).
Yes, that's the finite reality of it as there is no evidence of the infinite in reality, but theoretically or mathematically if X were to divide itself in half in order to inspect one half of itself at a time, then we'd have x/2 + x/4 + x/8 + x/16 + ..... forever, which converges, but never reaches X. Of course, as you pointed out, we can never reach either infinity nor a picture of X in totality because we'll eventually find a pixel (or quanti) that cannot be split. And that's why an object cannot observe itself.
Another way to look at the problem is to make an observation, but by doing so we affect what we are observing because, afterall, we are part of the same continuum. So we observe X, but because we are part of X, we actually observe X+N and in our efforts to account for N in order to observe X, we'll arrive at something like this: X + N - N/2 - N/4 - N/8 - .... forever, which converges on X, but never arrives.
The idea of infinity is born out of circularity. A circle with infinite diameter is an infinitely long straight line with zero curvature. All infinities are in fact loops that connect in reality. Actually, the circle doesn't need to be infinite, but merely big enough that curvature is zero as far as it's physically possible to determine from within the universe due to the planck scale (or whatever limiting factor exists on the infinitesimal). A few orders of dark numbers ought to suffice just fine.
I postulate that there are no such things as straight lines, but loops instead. I also postulate there are no such things as true circles, but polygons comprised of very minute segments which seem very much insignificant, but meaningful enough to make PI not infinite in reality.
Any time infinity pops up, you've either done something wrong or you're going in circles.
Positive integers range from 1 to infinity and thus the (idea of the) system itself is built in the foundation of infinity.
That's only true within the context of math. In reality, we cannot go beyond "dark numbers" which are numbers that are too big to be represented even when written on the planck scale within the universe.
To make a system based on the infinite applicable in duality (our way of thinking) we have to introduce a basic error - we have to cut up infinity into slices of ones.
Duality is what defines the number in the first place. 1 is 1 because it is not not-one (- -1 = +1). Every number has a pair (1-1, 2-2, 3-3) except zero, which is paired with infinity because what is infinitely big is not what is infinitely small (zero).
Further, when you say we have to cut infinity into pieces, that's a little ambiguous because which infinity do you mean? If you say 1 is distinct from 2 because we've dissected them from an infinite continuum, do you mean we've distinguished them from the infinite set (1,2,3,4,5...) or the infinite numbers that lie between 1 and 2? There are infinite numbers between 1 and 2 alone without needing to go higher. There are several orders of infinity within mathematics, so which infinity are you referring to?
Now we suddenly have an infinite system apparently containing an infinite number of discrete parts called one and we postulate that by adding up all available ones we reach infinity. Voila, the mistake has been made and from now on we conveniently ignore the far away destination of infinity and busy ourselves with adding up its (imaginary) parts.
But you could make the same argument with a finite line. Assuming 1 is a dimensionless point on the number line continuum, then any dimensionless point on any finite line will be a member of a set of infinite points. A finite line 1 inch long contains infinite zero-size points. Therefore the argument of splitting a continuum into bits does not necessitate infinity since a finite thing does not need to be infinitely big to have infinite zero-size parts.
This is why I do not understand how you jump from "no separate things" to "therefore infinity". Why not a finite continuum?
In infinity 1+1 can never be 2, it always has to be 1 due to the fact that, in an infinite system, all (apparent) parts are as well infinite.
I don't understand what "In infinity" means nor how 1+1=1