Topology and reality

Topology stems from logical concepts and as such is disjoint in its origins to physicality. I have been looking at topology from its origin to its application and it suffers from the same problems that all logical concepts share. A mathematical system is founded in base principles and extended to be consistent. This does not mean it is consistent with reality, but only with its own rules. If I consider the Betti number of a graph it has a logical meaning in the number of cuts and holes, but where is the association to the physical world? Math is meant to model something and it can actually model nothing as a result. A system of scratches extended to a science suffers from the same problem that I always encounter. It assumes that there is something that exists that is ONE. The problem is that there is no such physical thing that exists in the universe. Everything is infinite in its effect.So, to separate some point as being object and effect it creates a paradoxical system.
It seems that topology has two intersects with the physical universe and each has different physical rules. If I were considering the nucleus of the atom, a black hole or field interaction it would be modeled one way, and if I am dealing with sets of particles or systems it operates another. The interaction of the infinities is different than the principles established. I personally do not see how everyone is enamored with a system that was created by a people who had no clue as to the nature and complexity of the universe. When the universe was considered a mixture of Air Earth Fire and Water, could you really assume that they have some perfect insight into a system that underlies all description of matter?
There is no doubt that mathematics has utility in its current form, but it is not the model that best fits the physical world.
I am taking topology apart, step by step and labeling those principles that relate to a purely logical operation and those that can be connected to physicality in some way. It is a very useful science and there are many things that remain true even in the physical world, so long as one realizes the limits of application. The numbers aren't magical and never have been. Euler was a very intelligent person by all accounts and there is no doubt that his skill with numbers was legendary. This does not mean it correlates to physical reality.
In the field of network topology there are many different methods that I use to graph, analyze, and understand its properties. This is another case where the rules do not always follow from one situation to another. The science of numbers is incomplete and perhaps it will always be that, but that is the sad fact about knowing, it is never complete.
In order to understand better it is necessary to make the problem more complex. I have set about reordering the rules of topology so that they can be consistent with the different applications and I hope I can devise rule sets that let me know which applications correlate to which rule sets. When it comes to the topology of higher spaces, that is where the greatest gain is achieved. The application of existing topology rules are not consistent enough to say for certain that X is the measure of Y and is then testable.
The entire system is more complex than the measure applied and that is obvious. In the lab when I am compounding some chemical, I can say at each step what I will have as a product and how that is determined. If I were to just mix chemicals at random and have no idea of which ensues then it would be similar to nuclear physics as it exists. It is as close to alchemy as one can get in the 21st century. The measure and characterization of the parts is obviously incomplete and as such it becomes a matter of adding 2 drams of animal tincture and hoping for the best. It doesn't have to be that way. The energy is there and the system is consistent. There universe never fails to calculate the proper direction that a planet will take in its orbit and that is the assumption, that the universe is a perfect calculator. Whether that is completely true in all circumstances is the subject of many opinions.
In the same way that chemistry required an under structure that was at least complete, nuclear physics requires that model that exists under the complexity. It requires that the methods be clean and appropriate to the system. As I said, topology is not a single coherent concept, but has more complex structure to model different aspects of the universe.
I don't think that science is anywhere near complete and consistent. It is no different than when Newton or Euler walked the Earth, each new understanding allows a closer approach to the complexity. It was not until the time of Rutherford in 1911 that the existence of the nucleus of the atom was measured in gross terms. That is less than 100 years ago. It is almost like a dark age in comparison, horse drawn carriages and telegraph. To assume that the present is the height of science is absurd. It has always been that way. In 1900 it was assumed that all secrets of science would be known in their lifetimes. In the 60's it was penicillin that would cure all disease, and now it is different projections and AI will exceed human intellect by 1980, oops, a little late, but maybe this year is the year of the AI desktop.
I discovered an interesting relationship between topology, matrices, calculus, and numbers. If this had been observed in ancient times, calculus would be several thousand years older. Oh well, it is cosmic soup and so I will add another dram of topology tincture and see if this cures my confusion.