I promised Thaddeus to write something about physics envy. The problem is, a simple Google search will lead to numerous good articles that are much more eloquent than any I could write, and probably better thought out as well. I myself am sitting on the fence with regards to this. While it is easy to bash pretentious economics papers replete in arcane mathematics, part of me suspects that the "mathematization" of the soft sciences may actually be fruitful eventually. We just need to recognize when not to take our mathematics too seriously.
Furthermore, I am also wondering why "physics envy" is not called "maths envy" instead. Perhaps physicists hide their intellectual insecurities rather better? But more pertinently, why does mathematics work so darned well in physical theories but not in economics or biology or sociology? Is the physicist who gorges on mathematical texts akin to the beefcake in the gym -- merely engaging in muscle-building of another kind?
Here's an excerpt from the famous paper "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", by physicist/mathematician Eugene Wigner, which I highly recommend.
- There is a story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. "How can you know that?" was his query. "And what is this symbol here?" "Oh," said the statistician, "this is pi." "What is that?" "The ratio of the circumference of the circle to its diameter." "Well, now you are pushing your joke too far," said the classmate, "surely the population has nothing to do with the circumference of the circle."
I also found this amusing drawing:
I have a mild mental block now, which suddenly brings me to a stark realization:
I have literary envy.
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ReplyDelete(grammar edit)
ReplyDelete"why does mathematics work so darned well in physical theories but not in economics or biology or sociology?"
my fresh-out-of-the-ass opinion is that the foundation of mathematics (as a concept) had beginnings in observable reality. take basic arabic numericals for example: the idea that '1' is '1' and '2' is '2' can be demonstrated easily (please don't prove that 1 is not 1 my brain will implode). mathematics, at that foundational level, is thus an abstract symbology and translation of physical phenomena.
this level of kinship between physics and mathematics cannot be found (at least not at that quintessential level) between, say, mathematics and literature. my guess is that any school of knowledge that features prominence in deriving or derived from human emotion (the widest definition of it) will have a hard time getting along with mathematics. because a literary '1', for example, may be '0' or '2', dependent on the thinker, and nobody can satisfactorily and without doubt prove that he is absolutely wrong.
then again, it's possible to maintain that physics (not quantum mumbo jumbo) is humanity's experience of reality, and therefore open to the same obstacles in aligning with mathematics.
in conclusion, i don't know; but intuitively math and physics just has more obvious synergy.
Mathematics is overrated. It used to be that eloquent verbal arguments could win people over, even if the tipping point was the sheer brilliance of the choice of words. Nowadays, "irrefutable" has become synonymous with numerical "proof", which is dangerous because a valid mathematical proof is still predicated on the underlying axioms, which are almost never closely inspected. Packaging an argument with some mathematics seems to lend it some degree of objective correctness. Does it really?
ReplyDeleteMathematics works brilliantly in quantum physics because the entire theory is built on axiomatic foundations, and the calculations and logical deductions are consistent with these mathematical structures. Yet it is precisely this apparent agreement between abstract mathematics and physical reality that is most puzzling, and deeply troubling. It's not just that... it is profoundly disturbing.
Thus underlying all the fantastic successes of quantum physics is this absurd notion that reality plays out in some mathematical arena. If you really do believe that my desire to own this or that item is a differentiable real-valued function of your persuasive skills, for example, then you can probably borrow the whole calculus apparatus and prove that I will buy your snake oil. So integrate me!
If you ask me, it is quite a burden to carry such a heavy load of mathematical machinery around, although it is also loads of fun.