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Scale Invariance

Updated: Dec 1, 2024

It is tough to think of one overarching law of physics describing the entire universe. Maybe there is some addition to the field axioms that is needed. Perhaps some particle will unify all of the laws of nature. However real these ideas may be, one architecture of the natural world seems to subsume many other linear ontological relations. Scale invariant systems are present in the coastlines of continents, the circuits of semiconductor devices, and the waves that travel through the universe. It is not tough to think that the laws that control the small world also control the large one. For example, the gravitational law of Newton is of nearly the exact same for as that of Coulomb's law for charges. This inverse squared relation might underline some more fundamental aspects of the universe's symmetry of dimension, but there is something to laws that are not bound by a scale. Emergent properties and entangled states are two parts of physics that have recently garnered some attention. In fact, a recent Nobel prize in physics was awarded to work on neural networks. There is a connection between the neurons in the brain, the scientists in the global scientific enterprise, and the protons in a stellar plasma. Emergence comes from topological affine networks. Any network can assemble. It is just the patterns, based in some scale invariant law in multiple dimensions, that present the researcher with a surface to convolute into a machine code of ones and zeroes to be interpreted by a computer or detector. It goes without saying that you have to modify the fundamental theorem of calculus to involve a time stamp of logical events that correspond to emergent consciousness. This is far too difficult. What it means is that there is extra stuff connected to scale invariant systems that is the same at many levels. So, in a way, the entire universe is a conscious scale invariant entity.




 
 
 

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