This was an interesting article revealing a bit of infighting among physicists wrt string theory.
IMHO, it points to an ideological difference which would stem from the priority given to pure mathematics in physics. Indeed we've seen similar disputes here on the forum between those of us who center on the mathematics (information theory, complexity, etc.) related to evolution and those who center on the sciences (biology, chemistry, genetics, paleontology) .
It is a philosophical difference which I believe we would all benefit from exploring.
Personally, I fall on the “math first” side of the debate – I put mathematics above all sciences - and physics at the top of the science heap because of its integration with the mathematics.
My reasoning is that mathematical structures are universals per se and thus their discovery sheds light on all the sciences. As an example I assert Einstein’s ability to pull Riemannian geometry off-the-shelf to describe relativity. Other examples include dualities and mirror images - the "unreasonable effectiveness of math".
An example related the subject of this article - some string theorists like Vafa (my personal favorite) treat the physical ramifications of their work as secondary, e.g. he was not troubled by the consequence of an additional time dimension in f-Theory though it caused quite a stir in the physics community at large. IOW, good mathematics may not be widely accepted or have an application at the moment, but will remain "on the shelf" - because they are universals, which may be relevant at some other opportunity.
Additionally, even if physicists were not pursing a "theory of everything" - the mathematicians would. As an example, here's a link to Jurgen Schmidhuber's Algorithmic Theory of Everything.
I’d love to hear any arguments for why mathematics should not be given a higher seat in our body of knowledge than science!
One last point - I do agree with everyone here who instinctively believe that mathematical truths ought to be conceptually simple. The Kaluza-Klein based compactified string theories are not without competition, e.g. the easy to comprehend non-compactified 5D higher dimensional dynamics.
Mathematics asks different questions from those in the sciences. In turn, the various sciences ask different questions among themselves.
There are limits, math theorems that cannot be proved within math. Ultimately we cannot know.
Well, just the opposite here...a vote for math and all the "wunnerful" things that it 'hath wrought.'(If explanation is needed, you just ain't gonna get it )
I guess the real question still centers about the nature of the "unreasonable effectiveness of math." Yes, math does seem to describe things unusually well.
But is that because math is in some sense intrinsically descriptive of the universe? Or is it the more like "Junkyard Wars" teams hunting around in a junk-pile for likely-looking parts? (I.e., I have an idea, and here's somebody's esoteric math thing that looks handy in describing it?)
I guess another way of putting it is: is math invented, or is it discovered?
I'm preparing the following label to be placed on all high school math textbooks. Kids need to be taught the controversy.
New sticker for math textbooks:
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Warning: this axiomatic system includes propositions whose truth is undecidable within that system and its consistency is, hence, not provable within that system |