What does a field of study do if there are several competing theories?
- The Natural Sciences: I would like to think that the truth wins out... eventually. There may be struggles and politics and whatnot but in the very end experiments are performed and the more predictive theory wins out (I know its more complicated then that.) There are some fields where it is hard to do experiments (e.g., String Theory). Others where the theory gives great explanatory power but might be hard to do direct experiments (Evolution). Those cases may be hard to deal with, but they manage. Does String Theory have great explanatory power?
- Mathematics: Here the question is not WHAT IS TRUE since we can use proofs (Again, I know its more complicated than that) but WHAT IS WORTH STUDYING. Applied Math may still use the real world for a litmus test to some extend. More abstract kinds of math may be harder to test by looking at the real world. Do Large Cardinals exist? Is the Axiom of Determinacy true? Some people claim that they look for internal consistency and also intuitions. And some people live-and-let-live (you want to use AC, fine, I won't) (Again, I know its more complicated than that.)
- Astrology : What does a field do when its predictions are either vague or no better than chance? If there was a well designed experiment to test which theory has more predicative value then I suspect they would all be found wanting. (Then again, I'm a Sagittarius and we are known to be skeptical.) So what other criteria could they use? Internal Consistency and Intuition? Whichever one makes people feel better (some astrologers might claim that they are really psychologists, telling people what they want to hear to sooth them). Whichever sells more books? Makes more money? Is there some sort of aesthetics involved? I ask this nonrhetorically. (An idea for a scam: The old astrology doesn't work because they don't take into account relativistic effects on the planets. Use my Relativistic Astrology! For people who like what they believe in to have some buzz words from science thrown in!)
I think in the title you meant to write "How do legit fields of knowledge decide between competing theories?" as opposed to "between competing fields".
ReplyDeleteFeel free to fix the title and delete my comment.
When you say "astrology", do you mean the predictions on today's newspaper or do you mean the basic principle that heavenly bodies affect human behavior?
ReplyDeleteAs for the latter, I wouldn't be so dismissive. I can't have normal sex (or conversation) with my wife every four weeks, and I am pretty sure that's an astrological experiment that has been giving the same results for the past 50,000 years.
Suggested reading: Paul Feyerabend. Against Method, 1975.
On a resource-short, overheating planet with 7x10^9 people on it, increasing weight accrues to theoretical frameworks that are enabling for planetary-scale enterprises.
ReplyDeleteFrom this perspective, the vigorous ongoing debate between Gil Kalai and Aram Harrow on Gödel's Lost Letter and P=NP is only superficially about the debate's nominal topic: the feasibility (or not) of fault-tolerant quantum computing (FTQC) … a STEM-related thesis regarding which (in GASARCH's phrase) "it's hard or impossible to do experiments."
From a larger perspective — and in common with increasingly many STEM debates — the Kalai/Harrow FTQC debate provides us with a theatre in which advocates of minimal, moderate, and radical STEM skepticism show us which points-of-view are most likely to be productive of planetary-scale enterprises.
Thus, across a broad span of STEM debates ("Does P=NP?" "Is FTQC feasible?" "Is fusion power feasible?") the best outcome by far is "everybody wins."
Fortunately for mathematicians, evolving ideals of mathematical naturality are emerging as the single most powerful tool we have, for ensuring that everyone *does* win, as judged by the criterion of planetary-scale STEM enterprise creation.
Elevator summary: The results of these debates often have lesser lasting significance than the ideals of mathematical naturality, and the associated enterprise opportunities, that emerge from the debate process.
Note: a few minutes after the above was written, Gil Kalai addressed a pair of comments to John Preskill; comments whose outstanding thoughtfulness and respect are (to my mind) exemplary of how these STEM debates can and should be conducted.
ReplyDeleteWill this debate settle the question of FTQC's feasibility? Not likely. Yet does much good come of the debate? Absolutely. :)
It has attempted to show that complexity classes P and UP are different, making proving the existence of one-way functions and responding to the problem of P versus NP millennium. See it in post "P versus UP" at the address:
ReplyDeletehttp://the-point-of-view-of-frank.blogspot.com/
Interesting (popular, of course) article in the New Yorker about mathematical modeling in evolutionary biology and a debate over the theory of inclusive fitness: http://www.newyorker.com/reporting/2012/03/05/120305fa_fact_lehrer.
ReplyDeleteSince it's unfortunately behind a paywall, here is the summary of my outsider impression of the debate: there is a theory based on simple math with a clear conceptual interpretation which seems to go against more recent data (http://en.wikipedia.org/wiki/Inclusive_fitness); that theory is overwhelmingly more popular in the evolutionary biology community than alternatives which might give more satisfactory explanation of the data but are considerably more sophisticated mathematically (http://www.nature.com/nature/journal/v466/n7310/full/nature09205.html). The theories btw aim to explain social "altruistic" behavior (in insects and some birds for example) in evolutionary terms.
I imagine that this kind of debate can be pretty protracted and influenced by the politics of science more so than in fields where experimental results arrive quickly. Also seems like when experiments are scarce, Occam's razor becomes more significant in deciding between alternative theories. The problem is, except in computational learning theory, Occam's razor is pretty subjective.
In general, my observations are that knowledge is 'sticky'. That is most people go out and learn something (usually in school) and then from that time forward they are stuck to that piece of knowledge. It becomes really hard for them to switch to another one, even if there is evidence that it is correct.
ReplyDeleteSo, what seems to me to be happening with competing theories is that they flip-flop over generations. One generation learns something and they stick to it. But then a competing theory comes along, becomes popular and the new generation learns that. Then somehow, the old idea springs back again and the next generation latches on to it again.
If there isn't an ability to kill one of the theories, then this ebb and flow will continue to perpetuate. And sometimes if one of the theories is actually discredited or displaced by something more accurate, it still manages to creep back in, but just at a slower rate.
If you step back and get really really objective about what we actually know, and what we think we know, you seem a tonne of examples of this type of transmission.
Paul.
How about Religion? Is it like natural sciences, mathematics, or astrology ?
ReplyDeleteI would contend that among the three, it is most like astrology.
DeleteI wrote last month on a very similar question (sorry, in French):
ReplyDeletehttp://david.monniaux.free.fr/dotclear/index.php/post/2012/02/06/%C3%89valuation-des-domaines-scientifiques
Peer review and evaluation of scientists is usually done by scientists from the same field. This begs the question: how do we evaluate entire fields? Indeed, what mechanisms are there that prevent a coterie of pseudo-scientists from establishing journals, conferences etc. around some fuzzy concepts, and evaluate each other ?
The best answer we reached is that evaluation is usually not solely from people in the same field, but from people in neighbouring fields, so that science somehow forms a continuum.
Would the claim that researchers in biology and physics have made about the discovery of natural computational processes that have nothing to do with computers and Lance's outright rejection of this be an example of competing theories?
ReplyDeleteI think that the introduction of Kuhn's "The Structure of Scientific Revolutions" gives some answers to the question. In some social sciences and humanities, experiments are not always possible and we do not have data to prove/disprove different theories. So, in the period of "ignorance" the accepted truth is whatever the community accepts as truth. (Yes, the circularity is intentional.) Only when the accepted theory starts being problematic, for whatever reason, a new paradigm starts being formed, eventually leading to the demise of the old theories. Although it would be fun to look at people at humanities and social sciences and make fun of their approaches, Kuhn shows pretty convincingly that the same thing happens also in the hard sciences.
ReplyDeleteOne way to make sense of astrology is to embed it in the larger concept of >synchronicity< created by the Swiss psychologist C. G. Jung. This is also casually alluded to by R. Smullyan in his book >The Tao is silent<. Jung worked on that topic together with the physicist and Nobel laureate W. Pauly. Today it has moved to the fringes of science mostly championed by mystics of all sort.
ReplyDeleteThis is the most Gasarch-like post I've ever seen!
ReplyDelete