Kuhn vs Copernicus

February 21, 2012 § Leave a comment

With respect to both planetary position and to precession of the equinoxes, predictions made with Ptolemy’s system never quite conformed with the best available observations. Further reduction of those minor discrepancies constituted many of the principal problems of normal astronomical research for many of Ptolemy’s successors… Given a particular ¬†discrepancy, astronomers were invariably able to eliminate it by making some particular adjustment in Ptolemy’s system of compounded circles. But as time went on, a man looking at the net result of the normal research effort of many astronomers could observe that astronomy’s complexity was increasing far more rapidly than its accuracy and that a discrepancy corrected in one place was likely to show up in another.

Say you have a mathematical model that predicts some system you have no control over. All models and all measurements are wrong, so you’ll never get complete agreement between theory and observations. At some point, though, you’re sure enough about your measurements that you think the inaccuracy is in the model. You can always add ad hoc terms to a model. If you did regression, for example, you can add terms until you get a sufficiently good fit. Given enough degrees of freedom, you can fit to any finite number of observations, though I guess they didn’t have enough computing power to do this in the 15th century. Why is this kind of model complexity bad? It defeats the point of falsification, for one thing.

Even Copernicus’ more elaborate proposal was neither simpler nor more accurate than Ptolemy’s system. Available observational tests, as we shall see more clearly below, provided no basis for a choice between them. Under these circumstances, one of the factors that led astronomers to Copernicus… was the recognized crisis that had been responsible for innovation in the first place. Ptolemaic astronomy had failed to solve its problems; the time had come to give a competitor a chance.

The trouble with falsification is not just that every theory is false, it’s that just about every theory is demonstrably false. You can show that a particular method falls down and practitioners will no-sell this. Instead your burden is to show that the theory is no longer useful, which is a lot harder. On the other hand, falsification does win (usually, maybe) in the very long run: the eventual triumph of Copernicus over Ptolemy is because it fits observation better, even if that wasn’t clear in Copernicus’ time. Crisis generates theories, but in itself, it doesn’t determine which theory wins.

Kuhn: Rules and fouls

February 13, 2012 § Leave a comment

Often, viewing all [scientific] fields together, it seems instead a rather ramshackle structure with little coherence among its various parts… [S]ubstituting paradigms for rules should make the diversity of scientific fields and specialties easier to understand. Explicit rules, when they exist, are usually common to a very broad scientific group, but paradigms need not be.

Kuhn’s use of “rules” is broad, encompassing everything from Newton’s laws to standards for measurement. The idea that one has to show statistical significance at level 0.05 is a rule adopted by a disparate range of fields, but this doesn’t mean these fields share a paradigm. To ponder: in what ways are rules used to legitimise new paradigms?

The scientific enterprise as a whole does from time to time prove useful, open up new territory, display order, and test long-accepted belief. Nevertheless, the individual engaged on a normal research problem is almost never doing any one of these things… What then challenges him is the conviction that, if only he is skillful enough, he will succeed in solving a puzzle that no one before has solved or solved so well.

This again relies on a narrow definition of the “scientific enterprise”, excluding medicine, for instance, which is often useful. As for testing “long-accepted belief”, there’s a whole industry of contrarians, sometimes including me, that do this. While we would love for those within the paradigm to listen to us, we kind of doubt they will, and instead seek acclamation from those in other paradigms, or more perniciously, the media. Do we fall within Kuhn’s “scientific enterprise” or not?

Kuhn: Detours en route to normal science

February 10, 2012 § Leave a comment

In the sciences (though not in fields like medicine, technology, and law, of which the principal raison d’√™tre is an external social need), the formation of specialized journals, the foundation of specialized journals, the foundation of specialists’ societies, and the claim for a special place in the curriculum have usually been associated with a group’s first reception of a single paradigm.

The part of this that bears further thought is the parenthesised aside. Consider macroeconomics. There’s a bunch of journals that are incomprehensible to those who haven’t learned the math and the jargon. Yet instead of a dominant paradigm, there remain a number of competing candidates that are almost, but not quite, incomprehensible to adherents of their rivals. Has macro failed to elevate one paradigm because social science data doesn’t allow a definitive winner? Or is it because the policy stakes are high?

When the individual scientist can take a paradigm for granted, he need no longer, in his major works, attempt to build his field anew, starting from first principles and justifying the use of each concept introduced. That can be left to the writer of textbooks. Given a textbook, however, the creative scientist can begin his research where it leaves off and thus concentrate exclusively upon the subtlest and most esoteric aspects of the natural phenomena that concern his group.

Does this mean that if want to have influence on a field, you should write a text? Depends on the field. A textbook writer in physics doesn’t have much latitude as to what to prioritise and what to downplay — the paradigm is settled. A textbook writer in (frequentist) statistics has more room to manoeuvre. You have to talk about t-tests, because the field expects you to, but you can downplay them in a way you can’t downplay F = ma.

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