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Originally Posted by rsl12
I disagree--there are too many dualities in physics that are really fundamental, compared to the trialities (?) or quadralities. Even the examples I gave for one-ness and three-ness were pretty tentative--the grouping of three quarks is not really a triality--each of the three quarks grouped together is not the opposite of the other two (2 of one type, one of another). In contrast, a positive electric charge is the opposite of a negative one, a wave can be considered the opposite of a particle, energy can be considered the opposite of time. A particle's opposite is the antiparticle.
At the moment, I can't think of any examples of true triality, quadrality, etc in physics (i.e., where each item can be considered an 'opposite' of the other items in the grouping) other than 3-dimensional space (without time) or 4-dimensional space (with time) or 5-dimensional space (with Kaluza-Klein theory) or even higher (with superstring theories--I've seen no superstring theory currently being considered that has less than 11 dimensions?). The question of the # of dimensions in the universe is still being debated--it's not that all of these are examples of opposition are fundamental--only one of these is bound to be correct.
In nature and chemistry, it's more commonplace to see this sort of thing happening--a chemical flip between different configurations (cyclohexane flips between about 3 of these), a flower may have pentalateral symmetry. Because of the ways our eyes work, there are three primary colors (red green blue or cyan magenta yellow) But as has already been mentioned, even in nature and chemisty, the overwhelming majority of structures show duality (or bilateral symmetry), if they show any such symmetry at all.
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I know what you're saying, but what i'm saying is that there is an infinite number of groupings that can be considered significant if one is willing to consider them significant. Each quadratic equation is defined by three variables, a, b and c. Each cubic can be defined by four numbers. Any plane can be broken up into four quadrants, just like any map can be broken up into four directions. A three dimensional euclidean space needs to be, at least implicitily, broken up into eight different areas in order to use it for anything, throw time into the mix and you then have sixteen different areas. Sure these areas are very unintuitive and impossible to visualize in the context of three dimensional space, but they are incredibly significant in the physics of ordinary objects. In any area not simply divided by a line, a dichotomy just won't do. The real numbers have as many different subsets as stars in the sky.
How many forces are there in the universe now? I'm not sure exactly, i want to say four, but i kind of feel like maybe they figured out how to merge a couple of them. In any case, if there just happens to be a way to express all the forces in the universe as one unified force, would this in fact destroy any kind of notion of duality?
There are a great many things whose characteristics can be broken down into opposites, but there are a great many things whose characteristics can't be broken down into two opposites. Certainly there are many things made significant by their opposites, but most things don't have opposites, and perhaps only a fraction of the sum of their characteristics that can be isolated and contrasted with other things.
If you're wondering about four dimensional superstring theories, look up a man named sylvester gates. He's at the university of maryland. I saw him speak on superstrings a few weeks ago. Much of it was over my head, but i do remember him mentioning the fact that he was a proponent of four dimensional string theory.