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Science
In reply to the discussion: Quantum Biology and the Puzzle of Coherence [View all]physics is abstract noun as is category of physicists as whole, and so their "seriousnes" does not really concern me or the ideas I like to discuss, it is concern of those who like arguments from authority and expect those to be taken seriously. There are people with title "physicist" who have interesting and deep ideas about "Life, Universe and Everything" and many that don't have much to say.
That said, there are some physicists who have had close relation with Gödel and his ideas (Einstein) and think that his proof is relevant to the search for Final Theory version of TOE:
Freeman Dyson has stated that
Gödels theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. [...] Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them.
NYRB, May 13, 2004
Stephen Hawking was originally a believer in the Theory of Everything but, after considering Gödel's Theorem, concluded that one was not obtainable.
Some people will be very disappointed if there is not an ultimate theory, that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind.
Gödel and the end of physics, July 20, 2002
Jürgen Schmidhuber (1997) has argued against this view; he points out that Gödel's theorems are irrelevant for computable physics.[18] In 2000, Schmidhuber explicitly constructed limit-computable, deterministic universes whose pseudo-randomness based on undecidable, Gödel-like halting problems is extremely hard to detect but does not at all prevent formal TOEs describable by very few bits of information.[19]
http://en.wikipedia.org/wiki/Theory_of_everything#G.C3.B6del.27s_incompleteness_theorem
Also you are probably familiar with Wigner's classic article called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences.
http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
I would rather say that the Big Ego of some physicists think it is just using math, just as the Big Ego of English speakers makes them say and think that they are using English, forgetting that category of subject is internal to language and very small part of it.
Many sources say that most theoretical physicists support some form of platonism, as you can't do theoretical physics without math and number theory (I don't have any actual survey available so that hearsay can be wrong). And as for particulars, most famously there is close connection between Riemann hypothesis and quantum theory known as Hilbert-Pólya conjecture; there are p-adic descriptions of quantum theory, etc. See more:
http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/surprising.htm
Scientific realism "states that the universe contains just those properties that feature in a scientific description of it; not properties like colour per se but merely objects that reflect certain wavelengths owing to their microscopic surface texture." Scientific descriptions being mathematical descriptions, but mathematics itself not being scientifically described and in that sense "transcendental" or "supernatural" (instead real part of nature just as phenomena described by math) is very paradoxical and irrational position.
This is one of the main reasons why I consider "Scientific realism" a lá materialism and positivism and objectivism irrational belief systems and especially so when emotionally attached to.
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