In physics, we have a number of "fundamental" variables: force, mass, velocity, acceleration, time, position, electric field, spin, charge, etc
How do we know that we have in fact got the most compact set of variables? If we were to examine the physics textbooks of an intelligent alien civilization, could it be they have cleverly set up their system of variables so that they don't need (say) "mass"? Maybe mass is accounted by everything else and is hence redundant? Maybe the aliens have factored mass out of their physics and it is not needed?
Bottom line question: how do we know that each of the physical variables we commonly use are fundamental and not, in fact, redundant?
Has anyone tried to formally prove we have a non-redundant compact set?
Is this even something that is possible to prove? Is it an unprovable question to start with? How do we set about trying to prove it?
Interesting question as ever Derek, which touches on the nature of reality rather than on mere physics. It is also ultimately what the search for a GUT (grand unified theory) is all about, so the question is not really new.
The bottom line is, I think, that we don't know.
Here a couple of possible pointers:
1- I would subsume the question in your last § (about whether we can prove) into the question as to whether there is a GUT in the first place.
Whereas most (Steven Weinberg et al.) believe there is, others (Marcelo Gleisner et al.) think that the belief in the existence of a GUT stems from cognitive bias (ultimately influenced by, or born of, our monotheistic cultures.)
2- Some physicists have already answered the question (Shing Yung Tau, Eugene Wigner, Max Tegmark, et al.) by saying that the observed physical world is consistent only with a purely mathematical underlying structure, and that this independent mathematical structure is the only reality - with the physical world demonstrably an (ultimately unstable and transient) epiphenomenon or set of epiphenomena. Not everyone agrees. This would make all physical variables non fundamental - only math remains.
Incidentally, one thing that baffles me is the number of thinkers or philosophers who draw some godhood or godhead into the question, and then blithely go on to reject 2) above. But if someone sees fit to bring a godhead into the mix, then surely that person believes in a Platonic, spiritual universe rather than in a material, Aristotelian universe, and hence should readily adopt view 2), shouldn't they?
Mathematically, a factorial analisys should be done in order to select the independent variables from those depedendent.
@Chris. Tegmark's position is an extreme form of Platonism and is what is called "mathematical monism." Problems with this position are nicely discussed here:
http://www.science20.com/rationally_speaking/mathematical_universe_i_ain%E2%80%99t_convinced-127841
Interestingly, if one studies theology, the mainstream is Aristotelian rather than Platonic. Platonic thought tends to lead to heresies such as Gnosticism.
Gnosticism downplays the material universe, and consequently downgrades our corporeal bodies. This kind of thinking has a role to play in wars, as our bodies tend to then be viewed as expendable. However, mainstream theology considers the spirit and material body to be in a holistic unity (called a "hypostasis"), and in fact shuns the dualisms that Platonic thought introduces.
So this explains the reason for your interesting observation above.
Thanks Derek,
Interesting, thanks for posting Massimo Pigliucci's piece - which I find quite unconvincing on very specific grounds, maybe this should be the object of a separate thread, as this would likely lead to a rather lengthy and elaborate debate.
As for some 'religious' thought - as exemplified in the hypostasis dogma you are citing here above - whereas I understand that this indeed constitutes at least part of the answer why some people take the view they do - I have a problem with it.
Oftentimes religious thought seems to demand blind leaps of faith and/or ready, unexamined acceptance of dogmas and concepts without any prior logical analysis, even when said dogmas seem to be self-contradictory. As such, such modes of thought cannot qualify as parts of scientific debates. Simply peremptorily dictating , for example, a 'holistic unity' - whatever that means - of material body and spirit does not begin to make it so - I'd rather read up on , say, Ramachandran, Evan Harris Walker, Hodgson, Lockwood, Penrose, et al. , even Henry Stapp or Russell Targ's 'Limitless Mind' if it comes to that.
Whereas we may certainly not agree with everything that is offered in the literature, at least this literature constitutes bids to understand and progress, rather than ukases as to what we should unthinkingly think.
@Chris Yes, it was a bit off-track from the theme of the original question...but I thought I'd explain your interesting observation that mainstream theology rejects Platonism, when one might think it should be the opposite. I was not suggesting we go into further debate on it, as this is a science forum.
You can try a adimesinal, number analsys like the one is done in fluid flow, in order to modelice, or prototype the esential parameter.
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