There is a fine dividing line between accepting that our intuition may be highly inadequate in many situations, and rejecting ideas that seem perfectly ridiculous. Our intuition developed over the course of evolution in dealing with things at the human scale in both space and time. Primitive people had no need and obtained no survival advantage in dealing with the submicroscopic or the galactic scales, nor with nanoseconds or billions of years. That's why, in my opinion, it's ok (for example) for aspects of quantum theory to violate intuition drastically. Of course at some point we must, after careful thinking, decide that a theory is permanently unacceptable to our entire way of thinking. Within acceptability for the past century or so are the violations of intuition in relativity. Outside of all reasonable thinking is that A and not-A can both be true at once. Somewhere in the middle may be the possibility that general relativity and QM may never be reconciled and that perhaps our view of reality will forever require two theories that aren't compatible; I don't think that's logically impossible. Disagreements are welcome (but wrong, of course :o). Steve Gray Fred lunnon wrote:
A personal response to "Mathematical structures of the universe" by Max Tegmark, New Scientist 14 September 2007.
I don't imagine that I am the only individual in the universe who is both fascinated, and almost invariably disappointed, by cosmological speculation. I should like to believe that the author of this article does indeed possess some genuine insight into these profound questions, which he is sincerely endeavouring to express within the severe constraints imposed by everyday discourse: I remain nevertheless disconsolately unenlightened. Rather than shoot fish in a barrel by holding up his inevitably inadequate similies to ridicule, I prefer to engage in further speculation --- concerning instead the putative mechanism generating my persistent dissatisfaction.
One fundamental factor must surely be the slippery nature of language: and to be fair, this elusiveness is perhaps also the actual topic of Tegmark's article. To take one example, like many other people no doubt, I feel perfectly comfortable with the notion of a point particle, but slightly less so with that of a wave: my primitive mental picture of the latter cannot manage without some continuous medium (composed presumably of particles) in which to undulate; and I am constantly somewhat aware of its more abstract, evanescent nature as a mathematical construct.
Yet a passing acquaintance with quantum theory and relativity obliges me to countenance the likelihood that my instinctive precedence may be completely misconceived: the familiar solid particle a convenient invention of my imagination; the wave, sternly stripped of any material aether, the more fundamental concept. Having once accepted that, I must proceed to question my intuition about particles: there is now a serious possibility that this too is no more than a comfortable illusion, induced by familiarity (and in particular by exposure at an early age). Perhaps all I really know about them is expressed in their geometry and physics, the rest being emotional moonshine which serves merely to frustrate my ambition to comprehend a broader reality.
In recent years my own researches have included a number of possibly quixotic attempts to improve on the current pedagogic framework of elementary analytical geometry, through the employment of Clifford algebra. The routine grind involved in demonstrating that some particular algebra represents (say) Euclidean geometry as traditionally understood soon exposed the alarmingly piecemeal ragbag of concepts underlying my apparently serviceable geometrical intuition: I came eventually to the conclusion that such "proofs" do no more than restate (usually at some length but casting little light) the new model in terms of the old (e.g. Cartesian coordinates).
Upon tiring of the procedure, instead simply declaring as an axiom that "this algebra works", I belatedly realised that this is what the traditional models effectively already do; and that such a declaration is a matter of engineering rather than mathematics. Somewhat to my surprise, I also discovered that some cosmologists are currently pursue a very similar approach towards their more lofty objectives, enabling me to adopt the conceit that I too am a somewhat humbler practitioner of that ethereal profession.
Browsing current cosmological papers on this theme, I have been struck by the manner in which their authors seem pefectly at home with the assumption that the universe actually _is_ the symmetry group, string geometry, Clifford algebra, or whatever construct is under discussion --- and that no further "reason" for why it should behave in this particular manner is necessary. My instinctive response that they are confusing the model and the reality may very well do no more than rationalise discomfort with unfamiliarity.
It seems I am faced with a difficult choice: must I put my faith in one cosmological model or another, and at least attempt to acquire sufficient familiarity with it in order to develop that precious illusion of reality, my only guidance in the choice being my admittedly inadequate intuition; or should I perhaps practise patience, postponing a decision until such time as experiment decides between their testable hypotheses? [No longer young, I shall most likely find such confirmation inconveniently delayed.]
Fred Lunnon, Maynooth 26 Sept 2007
On 9/26/07, Dan Asimov <dasimov@earthlink.net> wrote:
Er, I meant to send that to Rich first, but instead sent it directly to all of math-fun. Oh, well.
A friend sent me that Tegmark article from the Sept. 14 New Scientist magazine, and the idea that physics is ultimately nothing more than the underlying mathematics seemed worth sending on to math-fun.
I'd be very curious to learn people's reactions to that article.
--Dan
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