Hypercells
Am I nuts? Maybe. But I think I’ve come up with a true Explanation for Everything. Well, maybe not an “explanation” per-se, but a description. Something that would explain the Universe and everything in it, in mathematical terms. The name for it is “Transcendental Sets”, though I may eventually call it “Hypercells”. But here I will refer to it both ways, interchangeably.
Transcendental Sets is a “new” mathematical system I am creating. It hopes to be able do describe Emergence in a general way that has not, to the best of my knowledge, been done before. It encompasses the entire system from the elemental constituents up to the macro levels of ontology.
Let me explain before you decide I am a complete crank!
Consider, if you will, quarks. Quarks interact by exchanging gluons. 3 quarks comprise baryons, and 2 quarks comprise mesons. The grouping of quarks into baryons or mesons is what I refer to as a “hypercell” — which is a type of set in which its constituents interact in some way. Here, the quarks constantly exchange gluons amongst themselves.
Now, the next level of organization — for baryons, at least — is organization into nuclei of atoms as is the case for the neutrons and protons. These baryons do interact via the “strong nuclear force” (really just the quarks and gluons interacting). But clearly the nucleus is a different thing from quarks and from the baryons — nucleons — that constitute them. Thus, the nucleus represents a new order hypercell.
Now, the nucleus forms a hypercell with electrons to make an atom. Thusly, the atom is a hypercell. It is distinct from the electrons and the nucleus that comprises it. It has emergent properties of its own that its constituents does not possess apart.
So, now we have this ascending levels of order — quarks –> nucleons –> nucleus –> atom. Each level represents something distinctly different with emergent properties the parts do not possess alone. Also note that a level of order depends, in part at least, on the emergent properties of the levels beneath it. That is to say, emergence of one level sets the stage for emergence to take place on the higher levels.
And so, let’s continue. Atoms interact to form molecules. The details of those interactions has to do with the way the electrons, bound to the nucleus as a part of the atom hypercell, now has new emergent properties that allows them to interact with other atoms in such a fasion to form what is called “chemical bonds”. The chemical bonds are an emergent phenomenon of atoms — something electrons would not do on their own, and neither would the nuclei. And so now we have molecules — hypercells of a new order.
Needless to say we can continue. molecules can themselves group together to form higher levels of order, as do the amino acids group together to form polypeptide chains. Or the sub-units of DNA group together to form DNA. Polypeptide chains fold in ways that give them unique properties that we call proteins or enzymes. Groupings of these units form organelles. Organelle groupings form the biological cell. Biological cells form organs, and organs form organisms. For the human organism, humans group together to form families and clans/societies, and societies group together to form countries. Atoms and molecules organize in many other ways besides the biological path, such as forming planets and stars, and planets and stars form planetary/star systems, and those group together to form galaxies. Galaxies form galactic clusters, and those, of course, form the whole of the Universe.
And to trace this chain or order, we have quarks –> nucleons –> nucleus –> atoms –> molecules –> molecular chains –> organelles –> biological cells –> tissues –> organs –> organisms –> families –> societies –> countries. Or a different branch: molecules –> planets and stars –> stellar systems –> galaxies –> galactic clusters –> universe. (This is not perfect nor complete, of course, because stars are too hot for individual molecules to make much of a difference, for example. Also, there were many levels left out when we went from molecules to planets.)
At each new level of order, you have new hypercells or transcendental sets forming. The formations are dependent on emergent properties of the levels beneath, yet in most cases the emergence is “unexpected” — one would not be able to directly predict or infer the emergence from the basis of the properties of the lower levels.