GUEST BLOGGER BILL GASARCH TOPIC: How much is what we do influenced by non-scientific criteria? (BEFORE I START TODAYS BLOG- A REQUEST. EMAIL ME OTHER LUDDITE QUESTIONS- I WILL POST THE BEST ONES ON FRIDAY) I) AN INCOMPLETE SUMMARY OF Thomas Kuhn's book The Structure of Scientific Revolution: For long periods of time a field of science will agree on the basic terms and problems of the field and will all work with that worldview (also called a paradigm). This is called Normal Science. This is GOOD since if people were working with different paradigms progress would be hard. BUT there comes a time when some problems just cannot be solved using the usual techniques. There will be an effort to jam this problem and some approaches to it into the current paradigm, but eventually, the old paradigm will fall and a new one will take its place. The new one will help to answer some old questions, and pose new ones that could not have even been asked in the old one. Newtonian Phy vs Einstein is the usual example, though there are others on a much less cosmic scale. II) People after him have misconstrued his work to saying that science has NO objective truth, that it ALL depends on the Paradigm. This is, of course, hogwash. More so when they claim that its a tool by the elite to dominate the masses, or some such (look up SOKAL HOAX on google for one view of this view). III) But a fair question CAN be raised along these lines: How MUCH of what scientists do depends on political or personality or other factors VERSUS how much is driven by objective scientific principles? A few examples a) What if in response to Russell's paradox the math world essentially axiomized what set theorist now call V=L (every object is constructable). Then we would know LOTs more about L, we would KNOW that the Axiom of Choice is true, and we would know that Cont Hyp is true. We might know that there were these weird other models that are unnatural where CH is false, but we wouldn't care. (Some Set Theorists tell me this could never happen- that people would be interested in other models. They are wrong.) b) What if in response to the Banach Tarski paradox mathematicians rejected some version of the axiom of choice? This would have been quite possible before AC began being used in so many places. c) The people who believe in constructive methods only (e.g, Brouwer) are portrayed as cranky old men holding onto an old paradigm that no longer worked. But if they had won then people like Hilbert would be viewed as crazy rebels who fortunately were never taken seriously. (This one I am less sure of- nonconstructive techniques are SO powerful that I think they may be inevitable.) d) If Computing Devices were invented either earlier or later then they were would have a drastic effect on Theory. While we think that P vs NP is a natural problem, it only came out once the technology was in place. Was it inevitable that it arise? Probably Was it inevitable that it be considered important? Hard to say. e) There is ALOT of work in Quantum Computing because (i) Peter Shor proved FACTORING in Quantum P hence giving the problem new interest, or (ii) There is (or actually was) lots of Grant money in it. (of course these two are linked) f) Do schools like MIT have too big an influence on what gets studied? (They have less influence now than the used to.) MORE GENERALLY, if I had the time and the energy I would do research on history/phil of math asking the question HOW MUCH DO EXTERNAL FORCES EFFECT WHAT IS STUDIED ? and I would do it WITHOUT an ax to grind.