One can notice that “=” (the sign of equlity) preserves/protects quantity. Protection of another features (i.e. number of divisors) follows from the former, ie. 52=52 protects quantity as the main reason. Knowing what was the main reason for Poincare’s work on dynamic chaos systems integration (capability to integrate), one may see that the “quantity” might be defined in a different (there- based on probability) way.
Lets note one final and very interesting thing. Mathematics does not allow this “time” element. When adding 1+1, we simply write the result 2, and 1+1=2, because transformation of LHS results in the same value of quantity as in case of RHS.
What is the reason behind the time? If it is claimed ilussion, then why do we perceive it? Change of mass for high-speed objects and time dilation for high-speed objects, as well as Galileo’s proof of objects falling in the same time- directs us towards topology of “time”-lines, claimed by Goedel. But what would that mean? And what would be the reasoning behind this construction?
When You take a look at Riemann’s habilitation thesis (“Uber die Hypothesen welche der Geometrie zugrunde liegen”), You see that Riemann already didn’t think that Euclidean space is for sure the “physical one”. He then claimed that space is nonuniform with metric tensor “g” and fields depend on matter distribution. But what would be the reason behind the matter distribution?
After Poincare published his first small paper, Einstein published his major paper (not referring to Poincare), and then Poincare published his final paper on space. But then Minkowski, trying to explain theory of relativity, introduced his one with , which is just introduction of fourth variable. I don’t support that.
Then, in 1923, Weyl, shouts out that the world is more bustling and free, and cannot be described well in Euclid’s geometry. Just before that, G.Mie shows his work on matter theory, and just after Weyl’s work we have nonlinear electrodynamics from Born and Born-Infeld. Now, more in probability we go. And more in toplogy, where ie. Penrose claims timespace is holomorfic variety of complex dimension 2. This is all because we claim that timespace is 4-dimensional holomorfic variety that is two functions (at least meromorfic) that cover each other in arbirtrarily small circumvolution, must also cover each other in the whole holomorfic variety.
But this is all based on new and new assumptions, without real trials at answering fundamental questions behind the idea of time. Lets now claim that time is really just an ilussion. Lets assume the existence of those “timelines”, claimed by Goedel. Then, how can we find those lines? Another question is why would those lines exist? In mathematics we don’t perceive any time. How would those lines be seen in mathematics- as those functions in 4-dim holomorfic timespaces? If yes, what kind of functions?