Hi Tim, and in answer to your desires for the Universe to have a fundamental absolute symmetry__just let me show you why this is impossible with absolutely simple math, and its simply extended permutations through even simpler addition, and the fundamental rules of addition or combinatorics, as the same...
Take any absolute fundamental you choose, time, motion, matter, FS, energy, charge__and use any method you choose to convert such fundamentals to real mathematical representations, as per 1, 2, 3, __ positive & negative __ true & false, 1’s & 0’s, etc. It matters not how you work out the permutations, you must first work out the most fundamental logic of the permutations, and that is to logically consider what exactly is required to build these fundamental permutations or combinatorics from absolute scratch(as it's scratch we are usually theorizing from, in these areas)__as per applies to symmetries and asymmetries. The easiest to see is most likely the positive and negative charges, of say the fundamental em forces of the most fundamental photon mechanics, i.e., it's polarization and double polarization potentials, as was actually proved by Huygens, over 300+ years ago. Iff you have only absolute symmetry as your most fundamental logic and physical action, your method can never produce the asymmetries__we absolutely know makes up just about half of the Universe, as the negative and irregular forces__we plainly see. In order for such asymmetries to exist, which we know they do, they must be just as fundamental as the symmetries, or they can't possibly exist__Due to this absolute fundamental dynamics:
1. If you start any math with perfect symmetries, such symmetries can only produce more symmetries...
2. Only asymmetries are possible of producing both symmetries and still other asymmetries...3. Simple example: 1+1=2_a symmetry... Only -1+1=0_an asymmetry... Yet, -1+-1=+2_a symmetry...
4. No matter how you set these fundamental charges up, only a fundamental -1+-1=+2 will create that first positive symmetry(two negatives produce a positive example), of a required combinatoric Universal permutation math, applied to Bose-Einstein Photonic Condensation__From An Absolute Fundamental Field...(thus the requirement of my 9 fundamental degrees of freedom)
5.The Absolute Fundamental Asymmetric and Symmetric Charges Are Necessitated to Primordially Exist, To Exist At All__Which we know, in the end result, they do...
6. No absolutely fundamental permutations exist, except as asymmetries/symmetries building symmetries/asymmetries, at the same time asymmetries are building more asymmetries, as it's the asymmetries which are responsible for either building All symmetries and asymmetries, due to the mechanical fact__symmetries can Never build asymmetries...(and herein lies the deep motion catch, to wrap one's mind around...)(this is probably better understood through Markov Chains... http://en.wikipedia.org/wiki/Markov_chain )
7. +1+1 only makes +2... 1+2 only makes a +3 charge, i.e., no negative asymmetric change possible from positive integers...
8. Only the asymmetric negatively charged numbers(photons or poles of photons) produce the required negative charges, to build any of the known to exist asymmetries...(asymmetries seem to be built into the fundamental photons, or FS-Field as such...)(Really, they'd have to be, wouldn't they Tim...?)(Seems as though that would be a basic necessity of any quantized field__No...?)
9. Combine the most fundamental permutations any way you wish, you can't possibly produce a fundamental asymmetry__unless your permutation maths and particle-waves include an 'absolute fundamental negative asymmetry'__no matter whether produced by colliding wave-particles or mathematical permutations, Markov Chains and/or any possible combinatorics...(you just can't get negatives outta positives, no matter how hard you try, but you can get positives outta two negatives__just mathematical, fs-motion and charge facts...)
'Absolute Asymmetry Is An Absolute Fundamental Necessity of FS-Motion'__By default of its fundamental necessity, which can not be divided or derived as any sort of smaller infinitesimal action of Reality__Possible...
Absolute divisions/differentiations within 'The Absolute Calculus' http://en.wikipedia.org/wiki/Tensor prevents any other possibilities...(Tim, imo people/scientists/logicians/mathematicians/physicists/whoever, just haven't looked deep enough into FS-Motions absolute necessities of fundamental actions...)
Tim, if you look at permutation math explanations, even here http://en.wikipedia.org/wiki/Permutation on Wiki, you'll see they've truly left out this most fundamental necessity, and probably due to a defunct logic, of not realizing, logic requires triadic proofs of all its actions, or it's simply invalid psychology, even as applied to the logic of math...
If you'll notice Tim, in the entire above Wiki article, there's no mention of the 'fundamental triadic necessity method' of the fundamental proofs needed... Logics and maths trying to prove themselves, within themselves, was proved by both Godel and Tarski to be impossible, back in the `30's, and the last half of the 20'th century, was spent trying to develop just such sound proofs, verifications and validities of fundamental logics. As far as my studies go, only the 'cross-product of triadic systems of proofs is valid'__to accomplish this very tickleish job__otherwise, you're left defending the impossibility of the purely psychological ego, which ain't valid in any logic and/or math systems' proofs, as it's simply a circular logic pertaining only to itself__a dis-allowed ego-logic, where any hard science is concerned...
The above 9 points have been worked out much better and more thoroughly by other mathematicians/logicians than myself, but I don't happen to have the information at my fingertips, as I take so many notes, it's too hard to find until I better organize my most recent notes, over the last 6 months__that's over 2000 pages long... Every time I try to use search, I come up with far too many links, until I better collate the notes into subject categories...(that's why category logic is oh so needed, but when I'm just research reading, I can't take the time to properly collate, on the fly, or I'd never finish my research... Btw, my research is finally coming to an end, and I'll be collating my notes over the winter__I've only about 10,000 pages of em... Last time I had about 50,000 pages of em__That took three years, to just collate...)
Tim, see if you can give me a 'mathematically changed system', that can be produced by only symmetries, which produce asymmetries__without such fundamental motions, already containing such fundamental asymmetries, to do so...(I don't think it possible...!!!)
That's my challenge to ya...
http://en.wikipedia.org/wiki/Andrey_Markov
http://en.wikipedia.org/wiki/Tullio_Levi-Civita
http://en.wikipedia.org/wiki/William_Kingdon_Clifford
http://en.wikipedia.org/wiki/Alexander_Bain
http://en.wikipedia.org/wiki/William_Rowan_Hamilton
http://en.wikipedia.org/wiki/Augustus_De_Morgan
http://en.wikipedia.org/wiki/Charles_Sanders_Peirce
P.s.
DeMorgan, Hamilton, Bain, Peirce and Clifford are excellent souces of the logic I draw from, as they be the founding fathers of the physics' logics and maths, more widely used in standard model physics, than all the others put together__and include the above logic discussions, at these most fundamental necessity levels...
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