Lubos,
a most interesting take on such matters. I find the discussion (probably based on Lie Groups) a little outside my Aristotelian finite math biases. But I get the feeling that me and those you talk about are the real disembodied Platonist's.
I very much agree with you concept of faulty logic as a matter of the formalism and non-physical generalizations, but science does not claim to discuss the reality of such things-we do not know or show there is something evolving there or not, breaking or not spontaneously the indexing arbitrary assertions of symmetry. Yet if our brains respond to physical law who is to say that we are not blind to the faulty logic of our own formalism of thought processes no matter how irreducible and comprehensive the compass of a theory?
I can quite imagine a deeper layer of symmetry where something like 384 is relavant physically (the rotations of a hypercube) and these in a sense the elements of some dimensional algebra where 390 is a false guess in the accounting, the counting.
It is not wrong to include the Lorentz ideas as a group such that it appeals to the physical reality and not the the theory or formalism itself- yet it may be at least Platonic that the mathematics of the formalism is more the reality than the physical matter itself. Physics then is in theory only as good as our symbolic math tools- and for that matter so is the logic of it.
It is not clear to me at all that things taken only on the continuous group idea level show we can with confidence predict different masses and expect them in experiment. In fact I see the current debate on the string theory as supersymmetry not one choice to what we may find from the recent cosmological data- both things have their contribution and I fear it can only be seen with some sort of higher idea of how the physics work. Surely more and more we see the need for new and more fundamental physics.
Let is start with some ideal assumptions to keep a vigil on before we fix our direction of possibilities so to limit them to our time and culture. We assume time cannot be measured or if so by some analogy to space that can be measured in steps. One truth is that neither space as the dimensional quantity nor time as a directed yet different in quality (of linear differentiation) can be measured in what we think of as a physical way- it is a matter of convention at this point. In fact if we choose one or the other as privileged we may have quite a different interpretation as to what is excluded as physical even for example in equivalent quantum theories.
This is not to say there is no objective reality (in that shallow sense of relativism) and yes there are no grey groups. But color can add a dimension beyond the black and white of simple two space to begin to extend the idea for proofs by a matter of parity. Just as we vaguely understand the uncertainty principle as a modern achievement in physics we should think of when it really makes a difference for what Leibniz called the discernible of indiscernible (in relation to chirality). That is to say in the spirit of non-necessity there can be in between groups and these extended by mathematical deduction to our design of systems of physics by dimension.
I am learning from you and you are a good teacher but I cannot say I am fluent yet in your language. Yet the things I posted today on my blog (I will included this as I do not have time to be so creative- a daily finite quantity I think) are a fine recreation that as simple as they seem to me and as tedious to label out by mechanical brute force calculation- I see them hauntingly similar to what I can glean of the system of the body of physics as your generation presents it- may it be of some use to you where at least there is a rather independent verification of conclusions - at least for what there may be of a unified truth of a possible higher direction of theory.
Thank you,
The PeSla
* * * July 9, 2010
Lubos has given me this wonderful reply: I suppose the communication of such a design of logic is a rather difficult thing to evaluate- in today's post on the reference frame (not the one on light Higgs particles- which if they exist I hope they exist that way for there seems to be an intuitive grain of sense in Lubos's idea regardless if there are rumors or not about some truth). I tried to express if read more carefully about at least the philosophic nature of reality that my position is not one of the hard Intelligent Design creationism- in fact I feel that the idea I am posting today rather supports evolution ideas in science in a way that may seem far fetched and radical (atoms evolving?) Again, I use intelligent design in the way Fred Hoyle thought of things and as a term the Creationist took for their own. I mean something like his Creation field.
The failure to communicate is perhaps my own or society's rather than the perfection of the Platonic ideals (if we have to live in a world of two substances) but roughly I imagine that of our two hardest philosophers, Spinoza and Leibniz, Aristotelian and rationalist, that these add a sort of super symmetry of dialectics to the usual Plato Aristotle influences. Of course Spinoza as an influence on Einstein is perhaps symbolic of a Platonic Paramendian perfect sphere. So again the issue here is perhaps how we fundamentally perceive the notions of the infinite and finite where such group are shown to correspond. Lubos, while 2 + 2 = 4 recall that 2 x 2 also equals four, or 3 + 1, or if you add the information of the digits 1 and 1 in 11 squared is 1 + 2 + 1. In any case it is not unintelligible universes that I am counting here even if we can imagine them and try to explain that by some sort of anthropocentric global explanation.
If we read my post today carefully and compare it to commentary today in the reference frame, especially about the logic and physicality of things such as even the idea of randomness and initial states and arrows of "time" and ideas on entropy then one might decode my metaphors to show that synchronously I am addressing the very issues Lubos is today- of course there is the possibility I am in some sort of deep error even in my own language (I do not merely substitute symbols nor create them to assert meaning- these are a dynamic and multi dimensional system and can be real although much is hidden- is dark matter real or some sort of ghostly phenomenon or maybe an error in our modern cosmology?) But we are scientist right- well at least Lubos is and I am quite honored by his objective commentary. By the way Lubos (if you read this) the flag on the right of the illustration is the flag of North Carolina without the date as the civil war rebellion. I was always struck by the similarity of our state flags, especially the current NC flag.
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