Kuhn 9: Examples versus Definitions
Feb. 20th, 2009 10:14 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
koganbotScientists solve puzzles by modeling them on previous puzzle-solutions, often with only minimal recourse to symbolic generalizations. Galileo found that a ball rolling down an incline acquires just enough velocity to return it to the same vertical height on a second incline of any slope, and he learned to see that experimental situation as like the pendulum with a point-mass for a bob. Huyghens then solved the problem of the center of oscillation of a physical pendulum by imagining that the extended body of the latter was composed of Galilean point-pendula, the bonds between which could be instantaneously released at any point in the swing. After the bonds were released, the individual point-pendula would swing freely, but their collective center of gravity when each attained its highest point would, like that of Galileo's pendulum, rise only to the height from which the center of gravity of the extended pendulum had begun to fall. Finally, Daniel Bernoulli discovered how to make the flow of water from an orifice resemble Huyghens' pendulum. Determine the descent of the center of gravity of the water in tank and jet during an infinitesimal interval of time. Next imagine that each particle of water afterward moves separately upward to the maximum height attainable with the velocity acquired during that interval. The ascent of the center of gravity of the individual particles must then equal the descent of the center of gravity of the water in tank and jet. From that view of the problem the long-sought speed of efflux followed at once.
--Thomas S. Kuhn, "Postscript - 1969" in The Structure of Scientific Revolutions, 2nd Edition, Enlarged, pp 189-190.
Now let's go back to where (and I've excerpted this before) Kuhn uses the term "paradigm" for the first time in any of his writing:
Except in their occasional introductions, science textbooks do not describe the sorts of problems that the professional may be asked to solve and the variety of techniques available for their solution. Rather, these books exhibit concrete problem solutions that the profession has come to accept as paradigms, and they then ask the student, either with a pencil and paper or in the laboratory, to solve for himself problems very closely related in both method and substance to those through which the textbook or the accompanying lecture has led him
--Thomas S. Kuhn "The Essential Tension" (1959), from the collection The Essential Tension, p. 229
In pure or basic science... the characteristic problems are almost always repetitions, with minor modifications, of problems that have been undertaken and partially resolved before. For example, much of the research undertaken within a scientific tradition is an attempt to adjust existing theory or existing observation in order to bring the two into closer and closer agreement... The attempt to make existing theory and observation conform more closely is not, of course, the only standard sort of research problem in the basic sciences. The development of chemical thermodynamics or the continuing attempts to unravel organic structure illustrate another type - the extension of existing theory to areas that it is expected to cover but in which it has never before been tried. In addition, to mention a third common sort of research problem, many scientists consistently collect the concrete data (e.g., atomic weights, nuclear moments) required for the application and extension of existing theory.
These are the normal research projects in the basic sciences, and they illustrate the sorts of work on which all scientists, even the greatest, spend most of their professional lives and on which many spend all... [T]he fascination of his work lies in the difficulties of elucidation rather than any surprises that the work is likely to produce. Under normal conditions the research scientist is not an innovator but a solver of puzzles, and the puzzles upon which he concentrates are just those which he believes can be both stated and solved within the existing scientific tradition.
--"The Essential Tension" pp 233-234
Here Kuhn is talking about how scientists are trained and what they do with their training. So (1) a paradigm is a concrete problem solution (a.k.a. puzzle solution). (2) Earlier in the paper Kuhn had pointed out that students within a discipline use identical or similar textbooks. So they're trained on identical or similar problems that they either run across in the text (along with the solution of the problems) or that appear at the end of chapters and that the students solve for themselves. For this reason scientists within a discipline almost literally share paradigms.
Kuhn at least implies that the scientists apply these textbook-learned paradigms throughout their career, seeing new puzzles as like old. And presumably they also model their work on puzzle solutions they find in the professional literature or that they work out for themselves and re-apply to a somewhat different problem, etc., though these puzzle-solutions haven't yet made it into the textbook.
What he doesn't discuss here is (i) scientists using paradigms before there were professional disciplines and textbooks (I don't think you get "scientist" as an occupation prior to the late 18th century, though obviously we can in retrospect see people doing science for thousands of years before then, and, says Kuhn, "in some fields, like mathematics and astronomy, the first firm consensus is prehistoric" [p. 231]); (ii) scientists modeling their work on paradigms during periods of scientific revolution (so, even if there are competing paradigms [in both the narrow and broad sense of the term "paradigm"] and a lot of modifying and rejiggering of paradigms, I can't imagine scientists not modeling a good deal of their work on previous work); (iii) one scientist using another scientist's concrete puzzle solution in his or her own work, whether or not other people in the discipline are also using it or noticing. It seems to me that "modeling" is going to be the same operation whether or not the model is widely accepted or widely shared.
But also, looking at the examples that Kuhn himself gives in the first passage, at least one of the scientists (Galileo) is practicing revolutionary not normal science but is nonetheless modeling one concrete puzzle solution (the pendulum) on a previous concrete puzzle solution (ball rolling down and up incline plane). And - correct me if I'm wrong, since I know almost zilch about the institutional development of the sciences - Huyghens and Bernoulli were working before there were textbooks and before "mechanics" was a distinct "profession" or "discipline" and before there was anything like modern-day specialization or standardized education. (What modern-day department would you place those guys in? You'd have the choice of physics, mathematics, astronomy, philosophy, statistics, maybe even some engineering.)
And also, in the example that appears in "What Are Scientific Revolutions?" - Planck trying to model his probabilistic derivation of his black-body radiation law on Boltzmann's probabilistic derivation of the entropy and velocity distribution of a gas - I don't know (though I have no idea, actually) if Boltzmann's derivation had been previously used as a paradigm by anybody or had made it into any textbooks.
Kuhn seems to be running together, in his various descriptions of "paradigm" (in the sense of "concrete puzzle solution") several different questions: (a) what's it like to use a paradigm, (b) what's it like to share paradigms, and, in the definition I quoted yesterday, (c) why do we need the notion of paradigm? So his definitions contain restrictions that can get in the way of his main idea.
--Thomas S. Kuhn, "Postscript - 1969" in The Structure of Scientific Revolutions, 2nd Edition, Enlarged, pp 189-190.
Now let's go back to where (and I've excerpted this before) Kuhn uses the term "paradigm" for the first time in any of his writing:
Except in their occasional introductions, science textbooks do not describe the sorts of problems that the professional may be asked to solve and the variety of techniques available for their solution. Rather, these books exhibit concrete problem solutions that the profession has come to accept as paradigms, and they then ask the student, either with a pencil and paper or in the laboratory, to solve for himself problems very closely related in both method and substance to those through which the textbook or the accompanying lecture has led him
--Thomas S. Kuhn "The Essential Tension" (1959), from the collection The Essential Tension, p. 229
In pure or basic science... the characteristic problems are almost always repetitions, with minor modifications, of problems that have been undertaken and partially resolved before. For example, much of the research undertaken within a scientific tradition is an attempt to adjust existing theory or existing observation in order to bring the two into closer and closer agreement... The attempt to make existing theory and observation conform more closely is not, of course, the only standard sort of research problem in the basic sciences. The development of chemical thermodynamics or the continuing attempts to unravel organic structure illustrate another type - the extension of existing theory to areas that it is expected to cover but in which it has never before been tried. In addition, to mention a third common sort of research problem, many scientists consistently collect the concrete data (e.g., atomic weights, nuclear moments) required for the application and extension of existing theory.
These are the normal research projects in the basic sciences, and they illustrate the sorts of work on which all scientists, even the greatest, spend most of their professional lives and on which many spend all... [T]he fascination of his work lies in the difficulties of elucidation rather than any surprises that the work is likely to produce. Under normal conditions the research scientist is not an innovator but a solver of puzzles, and the puzzles upon which he concentrates are just those which he believes can be both stated and solved within the existing scientific tradition.
--"The Essential Tension" pp 233-234
Here Kuhn is talking about how scientists are trained and what they do with their training. So (1) a paradigm is a concrete problem solution (a.k.a. puzzle solution). (2) Earlier in the paper Kuhn had pointed out that students within a discipline use identical or similar textbooks. So they're trained on identical or similar problems that they either run across in the text (along with the solution of the problems) or that appear at the end of chapters and that the students solve for themselves. For this reason scientists within a discipline almost literally share paradigms.
Kuhn at least implies that the scientists apply these textbook-learned paradigms throughout their career, seeing new puzzles as like old. And presumably they also model their work on puzzle solutions they find in the professional literature or that they work out for themselves and re-apply to a somewhat different problem, etc., though these puzzle-solutions haven't yet made it into the textbook.
What he doesn't discuss here is (i) scientists using paradigms before there were professional disciplines and textbooks (I don't think you get "scientist" as an occupation prior to the late 18th century, though obviously we can in retrospect see people doing science for thousands of years before then, and, says Kuhn, "in some fields, like mathematics and astronomy, the first firm consensus is prehistoric" [p. 231]); (ii) scientists modeling their work on paradigms during periods of scientific revolution (so, even if there are competing paradigms [in both the narrow and broad sense of the term "paradigm"] and a lot of modifying and rejiggering of paradigms, I can't imagine scientists not modeling a good deal of their work on previous work); (iii) one scientist using another scientist's concrete puzzle solution in his or her own work, whether or not other people in the discipline are also using it or noticing. It seems to me that "modeling" is going to be the same operation whether or not the model is widely accepted or widely shared.
But also, looking at the examples that Kuhn himself gives in the first passage, at least one of the scientists (Galileo) is practicing revolutionary not normal science but is nonetheless modeling one concrete puzzle solution (the pendulum) on a previous concrete puzzle solution (ball rolling down and up incline plane). And - correct me if I'm wrong, since I know almost zilch about the institutional development of the sciences - Huyghens and Bernoulli were working before there were textbooks and before "mechanics" was a distinct "profession" or "discipline" and before there was anything like modern-day specialization or standardized education. (What modern-day department would you place those guys in? You'd have the choice of physics, mathematics, astronomy, philosophy, statistics, maybe even some engineering.)
And also, in the example that appears in "What Are Scientific Revolutions?" - Planck trying to model his probabilistic derivation of his black-body radiation law on Boltzmann's probabilistic derivation of the entropy and velocity distribution of a gas - I don't know (though I have no idea, actually) if Boltzmann's derivation had been previously used as a paradigm by anybody or had made it into any textbooks.
Kuhn seems to be running together, in his various descriptions of "paradigm" (in the sense of "concrete puzzle solution") several different questions: (a) what's it like to use a paradigm, (b) what's it like to share paradigms, and, in the definition I quoted yesterday, (c) why do we need the notion of paradigm? So his definitions contain restrictions that can get in the way of his main idea.
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redux of bernoulli's wiki entry
Date: 2009-02-21 11:42 am (UTC)He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.
His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724... Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motions of rotation. His chief work is his Hydrodynamique (Hydrodynamica), published in 1738; it resembles Joseph Louis Lagrange's Méchanique Analytique in being arranged so that all the results are consequences of a single principle, namely, conservation of energy. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and Colin Maclaurin, a prize was awarded by the French Academy: these three memoirs contain all that was done on this subject between the publication of Isaac Newton's Philosophiae Naturalis Principia Mathematica and the investigations of Pierre-Simon Laplace.
so it rather depends what you mean by "text book"
Date: 2009-02-21 11:55 am (UTC)prior to the reformation and the renaissance, libraries were also monasteries, books were copies of the graeco-roman classic (plus a lot of arabic science and some hebrew works), and plus many religious tracts, some concerning the nature of the world
from round about the 15th century, control of some of these libraries began to shift to private citizens -- the politics of translation also shifted (political battles over the bible in english, the "vulgate", rather than just latin, greek and hebrew)
with the translations arrived a hugely new interest in finding out for yourself, rather than taking (say) aristotle as read
universities had long had secular departments -- for the study of law in particular -- these would have had codifications of laws and essays on law; mathematics departments would have had (ast a minimum) euclid in several languages; and lanuage departments would have been full of books of exercises in grammar -- probably the closest to what you mean by text books -- which were called things like "gradus ad parnassum" (step by step to the temple"), and from which the term paradigma is actually borrowed (being grammatical exemplars)
with the reformation, a a class of scholar started publishing their own works --- we're talking now about 1600-1750ish?, not quite the enlightement - and discussion of how to get sutdents to learn and think well was also increasingly explored (milton wrote a pamphlet on same during the civil war)
so shorter the above: text books already existed in other disciplines and were arriving in these ones (indeed, helping establish these ones); bernoulli and huyghens and etc were themselves writing proto-textbooks (note that bernoulli's first is called "exercises"!)
guilds existed pre-reformation and were proto-disciplinary, though the information and technique they nursed and transmitted was intended to stay WITHIN the guild, so the perocess of tranmission may not have been as handily alienable as exercise books written in the vulgate (today known as "teach yrself statistics for dummies" etcd)
no subject
Date: 2009-02-21 11:58 am (UTC)(disclaimer: may not actually have been tudors in charge -- but the Tudor-Stuart-Cromwellian era is the era of the start of the Brit Empire, and the establishment of many of these institutions were justified by and paid for by the requirements of the imperial state... )