Beauty and Revolution in Science

The book was delivered on time and in perfect condition. It's a nice edition with hard cover. The contents are mostly for philosophers and researchers

Outstanding; clear and profound.

McAllister needs to be credited with writing the only serious book on aesthetics in science. However, there are several working assumption in play throughout the work that need further elaboration, and his rationalism appears more in the end like an empiricism. Moreover, McAllister's historical case studies form science require critique by someone qualified in that area before I would consider them more.Whatever false arguments the work might have made, it is a worthwhile read and purchase. I would sooner take seriously Goodman's ways of worldmaking.

Dr McAllister has written a wonderful piece of work which deserves to be read by all with a passing interest in aesthetics and science. The writing is superb, the argument clear and revealing, the connections sometimes quite stunning. I look forward to a sequel!

Kuhn’s Structure of Scientific Revolutions is still, after almost sixty years, a centerpiece of controversy about what scientists do, and what they should or should not do. Scientists in particular sometimes seem to react as if what Kuhn says devalues science, making the progress of science, through revolutionary theory, less rational and less in compliance with scientific method than they believe it to be.McAllister’s book is an attempt to turn Kuhn’s Structure of Scientific Revolutions on its head. While accepting the role of aesthetic factors in the evaluation of scientific theories, McAllister builds a framework for understanding revolutions within a rationalist theory of science and theory evaluation.The core of McAllister’s framework is his claim that theories are evaluated on empirical criteria and aesthetic crieteria, and on the relationship between those two sets of criteria. Empirical evaluation is as we would expect — confirmation and disconfirmation by empirical test. Aesthetic criteria take up the greater part of the discussion. They are laid out in Chapter 3 — as four “classes” — form of symmetry, invocation of a model, visualizability/abstractness, and metaphysical allegiance. He also discusses simplicity as a class of aesthetic properties, although simplicity proves to be a slippery type of criterion. Actually, all those types of aesthetic criteria are interpretable — it’s important to keep in mind that they are classes of aesthetic properties, not cut and dried properties or criteria in and of themselves.Aesthetic criteria change over time — what models scientists accept, what symmetries they strive after (or do not), whether or not theories should lend themselves to visualization, and what metaphysical allegiances the scientific community holds. For example, the mechanistic worldview of pre-20th century physics is no longer a requirement for contemporary physics, as neither is determinism. Visualizability is likewise diminished in importance for many quantum physicists, and abstraction may be held out as a virtue.Empirical criteria, though, do not change, according to McAllister. The test of a theory against observation is a constant.Revolutions happen when the aesthetic criteria that characterize a scientific community’s evaluations of theories — termed the “aesthetic canon” — become increasingly stressed and violated by theories that outperform aesthetically compliant theories on empirical grounds. Thus, despite its damage to metaphysical tenets concerning determinism, visualizability, and the mechanistic view of the universe, quantum theory’s empirical superiority to classical physics carried the day. The aesthetic canon had to change in response. The revolution occurs when the aesthetic canon is overthrown in favor of a new or radically changed one.Aesthetic factors are thus a conservative force, contrary to Kuhn, for whom it is what McAllister terms aesthetic factors that actually push revolutions forward against empirically superior established theory.Having presented his framework, McAllister then analyzes two sets of case studies in its light. One is the pair of candidate astronomical revolutions — Copernicus’s heliocentric theory and Kepler’s theory of elliptical orbits — and the other is the pair of 20th century landmarks in physics — relativity theory and quantum theory.McAllister’s analysis leads him to claim that relativity theory and Copernican theory were not true revolutions. Neither, in his view, constituted an overthrow of existing aesthetic criteria for theory evaluation. Copernican theory, for example, retained from traditional, Aristotelian theory, requirements of circular and uniform motion for celestial bodies, even re-affirming those principles against Ptolemy’s use of the equant point to anchor the orbits of those bodies. Kepler, by contrast, abandoned circular and uniform motion in his theory of elliptical orbits.He also claims that Copernican theory and relativity did not constitute the kind of stress on aesthetic criteria by virtue of empirical superiority that he believes characterizes true revolutions. Again, in the case of Copernican theory, it’s famously not clear that Copernican theory outperformed Ptolemaic in terms of predicting the positions of objects in the sky. It fails to fit the framework McAllister has argued for.As against Kuhn, McAllister is claiming that the roles of aesthetic criteria and empirical criteria are reversed. In revolutionary science, empirical superiority stresses accepted aesthetic criteria to the breaking point, rather than Kuhn’s less rationalistic model, in which aesthetic criteria take the lead.What is called “normal science” for Kuhn, is for McAllister a period of time in which both empirical and aesthetic criteria remain in place, as McAllister claims was the case during the Copernican period. Revolutions happen when theories’ empirical performance outpace the scientific community’s adherence to a current aesthetic canon.McAllister develops his framework primarily through analytical means, using thoughts and anecdotes from the practices of scientists more to illustrate points than to inspire his theory. In the case studies, he then holds the resulting framework up against scientific practices during real and supposed revolutionary times, to confirm his theory.But the order in which he develops his framework is from the analytical and abstract to the test against facts, now interpreted within the framework itself. He doesn’t motivate the framework by showing inadequacies in Kuhnian thinking for accounting for the facts — the facts about scientific practices instead come after the framework.He also uses his theory to interpret those scientific practices. For example, enlightened by his theoretical framework, Copernican theory fails to be a true revolution.If we were trying to understand why Copernican theory was not a revolution, that’s great. But if we are determining whether or not it was a revolution, where that is still an open question, I think that McAllister’s arguments aren’t quite so strong.A different story could be told, emphasizing Copernicus’s rejection of geocentrism (and other metaphysical principles of the Ptolemaic universe), rather than the conservation of circular and uniform motion, and claiming that in fact, it was this rejection that carried the day in spite of the theory’s lack of empirical superiority.Further, what counts as a “revolution” in science is certainly debatable. There’s no fact of the matter about that — it’s a judgment, I think, far more than a fact. Thus a theory of scientific revolution that explains that one instance — the Copernican — was not really a revolution and another — the Keplerian — was, can’t really be said to be thereby “confirmed.” It is hard to say that the theory is “true” when its confirmation follows from facts being viewed through its lens rather than in some way neutrally.The theory may of course still be “enlightening” as a coherent interpretation, and I think McAllister’s is enlightening within the large mix of thinking about what scientists do.I will mention one potential advantage of Kuhn’s framework that I think is important. In a Kuhnian world, scientific revolutions may not be entirely autonomous within science — political, artistic, philosophical, . . . all sorts of factors may influence aesthetic criteria independently of anything contained within science itself and become important factors in fomenting revolution. For McAliister, certainly there can be such extra-scientific factors at work in helping revolutions along, but the driving force for him is superior empirical validation of new theories.Reading McAllister’s theory of revolution, and contrasting it with Kuhn’s, raises, to me anyway, an overarching question: What is the purpose of a theory of scientific revolutions (or of a theory of scientific practice in general)? Is it to better understand what scientists do, or is it to prescribe how science ought to be done, or both?I’m not sure that McAllister wants to change anything that scientists do, or even influence them to think about what they do differently. Kuhn, I’m not sure of. He certainly has upset a lot of scientists, especially with his more radical claims about incommensurability and discontinuity in science.I think it is also interesting to contrast both McAllister and Kuhn with Feyerabend on this question — I don’t think that Feyerabend, despite his reputation as a radical thinker, wants to change what scientists do, so much as prevent them (or philosophers of science) from constraining what they do with a theory of what they do.I’ll stop there. I think I just opened a big can of worms.

McAllister "aims to defuse the threat posed to the rationalist image of science" (p. 9) by scientists' talk of beauty, such as Weyl's remark that he "always tried to unite the truth with the beautiful: but when I had to choose one or the other, I usually chose the beautiful" (p. 91). To defend the rationalist view McAllister offers the following _thesis of aesthetic induction_: "[S]cientists attach to each aesthetic property a weighting roughly proportional to the degree of empirical adequacy that they attribute to theories exhibiting that property. The table of weightings constructed in this way constitutes the scientists' aesthetic canon, used thereafter to evaluate theories" (p. 203).The thesis may be separated into two claims:(1) Whenever a scientist expresses _positive_ (i.e., appreciative) aesthetic judgement of a theory, this is due to his identifying properties of the theory that have been correlated with empirical success in past theories.(2) Whenever a scientist expresses _negative_ aesthetic judgement of a theory, his evaluation will be reversed if the theory proves empirically successful.In other words, these theses show, respectively, why neither _pursuing_ nor _rejecting_ theories on aesthetic grounds is a serious violation of rationality. McAllister's evidence for his thesis consists in two pairs of case studies, corresponding to these two claims; namely, Copernicus' astronomical theory and Einstein's relativity theory for the first; and Kepler's law of ellipses and quantum mechanics for the second.Let us consider McAllister's evidence for (1). McAllister notes that Copernicus adhered to the Platonic emphasis on uniform circular motion and criticised Ptolemy for violating this principle in his use of the equant (i.e., in allowing circular motion to be uniform only with respect to a point other than its centre). Let us allow for the sake of argument that these were aesthetic judgements (though I do not think that McAllister has any good evidence for this). Then, sure enough, these aesthetic judgements were a form of conservatism. But (1) is not supported but rather flatly contradicted. According to McAllister's theory, the empirical success of Ptolemy's theory should have led scientists to induce aesthetic _appreciation_ for the equant, which is precisely the opposite of what happened. McAllister skirts this point and instead offers the following explanation."The sixteenth century's strong preference for theories that attribute uniform circular motion to celestial bodies is easily explained by the aesthetic induction. To Copernicus and his contemporaries it would have seemed that Aristotelian natural philosophy had built up an impressive empirical track record. This appraisal was largely justified: ... everyday experience accords well with Aristotelian theories in mechanics and biology. Through the operation of the aesthetic induction, the community came to attach great weight to the requirement that theories in the various sciences should show allegiance to the metaphysical claims of Aristotelianism." (p. 174)Copernicus theory had many virtues, but "allegiance to the metaphysical claims of Aristotelianism" was most emphatically not among them. The absurdity of this claim should be obvious enough that it need not be documented here. Suffice it to note that _even if_ Copernicus had been impressed by Aristotelianism, McAllister's account would still be arbitrary and ad hoc. For why would Copernicus induce the beauty of the principle of circularity rather than, say, the theory of the four elements (which would of course have precluded heliocentrism)? In fact, the latter would make much more sense since McAllister brings up "everyday mechanics" as the empirical support for Aristotle's theory. (Of course, in Aristotle's cosmology, the natural motions of the four elements govern the "everyday" terrestrial realm, whereas circular motion belongs to the ethereal element of the heavens only.)The second case of positive aesthetic judgement discussed by McAllister is Einstein's relativity theory. Einstein was not motivated by empirical concerns but by aesthetics, as McAllister notes. In particular, "Einstein held strongly to a relationist view of space and motion that had originated in a criticism made of Newton by Leibniz," which "motivated [Einstein] in his work on both the special and the general theory of relativity" (p. 184). McAllister notes with approval that this "reveals what Abraham Pais sees as 'relativity's aesthetic origins'" (p. 186). Again this is not a confirming instance of (1) but rather a clear counterexample to it. Like Copernicus, Einstein held a view precisely opposite to that which should have been favoured by McAllister's aesthetic induction. Why had he not induced aesthetic appreciation for absolute space, in light of the empirical success of classical physics? McAllister has no answer. He simply presses the point about conservatism and avoids mentioning the aesthetic induction altogether.These two cases, Copernicus and Einstein, are McAllister's examples of scientists motivated by aesthetics rather than empiricism, in the manner of the Weyl quotation. McAllister's thesis is that the rationality of such cases is secured by (1). But in these case studies McAllister downplays this crucial part of his thesis, focusing instead on his more general claim that aesthetics is a form of conservatism. He argues explicitly for (1) only in the former case, and then very unconvincingly; in fact, both cases seem to directly contradict (1).Now let us consider McAllister's evidence for (2). As examples of innovations initially criticised as aesthetically displeasing McAllister points to Kepler's law of ellipses and indeterminism in quantum mechanics. These innovations were resisted, to be sure, but was this for aesthetic reasons? McAllister is able to say yes only by construing aesthetics very broadly. In the case of Kepler, McAllister is unable to quote anyone calling ellipses aesthetically displeasing or ugly. Instead, the criticism of Kepler was formulated in terms of circles being more befitting or apt to describe celestial motions. But, says McAllister, judgement of aptness is a form of aesthetic judgement: "a property is aesthetic if, in virtue of possessing that property, a scientific theory is liable to strike beholders as having a high degree of aptness" (p. 37). It is quite the same with quantum mechanics. Einstein and others disliked its indeterministic element, which McAllister turns into an aesthetic judgement by the same trick as before, namely by extending the concept of aesthetics: "I propose to regard the allegiances that scientific theories have to metaphysical world views as aesthetic properties of them" (p. 55).It seems to me that McAllister's broadening of the concept of aesthetics makes his claim about aesthetic conservatism loose virtually all its counterfactual force. Could there be _any_ conservatism that is not aesthetic by McAllister's definition? Non-aesthetic conservatism would have to be such that it could not be explicated neither in traditional aesthetic terms, nor in terms of "aptness," nor in terms of "metaphysics" (of which McAllister gives no definition). And the fact that the two last criteria are so conveniently fitted to McAllister's two case studies makes one wonder whether the list is complete even at this.This is a sly trick indeed: since any case of conservatism is now aesthetic, any case of conservatism being overcome by empirical success becomes a confirmation of McAllister's theory. Of course no one would deny that there are plenty of such cases in the history of science. So Q.E.D., McAllister's theory fits historical data.McAllister's two case studies are indeed of this form: first establish that the conservatism was aesthetic, then that it was overcome by empirical data. In the case of the law of ellipses, for example, McAllister quotes Crüger writing in 1629 that "I am no longer repelled by the elliptical form of the planetary orbits" (p. 179). This after he had become convinced of the value of the Rudolphine Tables based on Kepler's theory. No further evidence is provided that the repulsion in question was aesthetic in nature, even though one can surely be "repelled" by many other things besides, such as, for example, mathematical intractability.But even if we set aside the problem of the delineation of aesthetics a no less serious problem remains. Let us say that a particular astronomer once found circles particularly aesthetically pleasing, and placed great emphasis on this fact. Suppose that he then realised that circles are empirically inadequate and that it is necessary to use ellipses instead; and that he subsequently stopped talking about the beauty of circles. I say: nothing in this indicates that he has changed his aesthetic preferences. It may be that he still hold the exact same aesthetic views, but that he choses not to keep expressing them since there would be no point in doing so.To state this last point in more general terms: no one doubts that conservatism, including aesthetic conservatism, has often been overcome by empirical data; the novel part of (2) is that the aesthetic standards themselves change in the process. McAllister presents no evidence for this in the case of the law of ellipses. In the quantum mechanics case, his supposed historical evidence has the following form. Initially, some people found the theory aesthetically displeasing. Later, _other_ people found the theory aesthetically pleasing on _different_ grounds. Such evidence quite clearly says nothing about aesthetic induction.Now let us consider in more detail McAllister's evidence for induced aesthetic appreciation in the case of quantum theory. The first piece of evidence McAllister offers for induced aesthetic appreciation is a quotation by Gribbin, written in 1984:"[W]ave mechanics gives an _illusion_ of something familiar and comfortable. ... Several generations of students, who have now grown up to become professors themselves, might have achieved a much deeper understanding of quantum theory if they had been forced to come to grips with the abstract nature of Dirac's approach, rather than being able to imagine that what they knew about the behavior of waves in the everyday world gave picture of the way atoms behave." (p. 195)From this McAllister concludes:"The change in attitude illustrates how, in the wake of a revolution, scientists reassess the merits of their aesthetic commitments. As the empirical track record of quantum theory improved, its aesthetic properties reshaped the aesthetic canon of physicists. ... Gribbin's denunciation of the requirement of visualization, which would have been unthinkable in the 1920s, shows how far this amendment of aesthetic canons has proceeded." (p. 195)The conclusion is unwarranted for the simple reason that the quotation in question has nothing to do with aesthetics. Rather, it merely makes a purely _factual_ claim (i.e., that wave mechanics is misleading). McAllister's conclusion follows only if one _assumes_ that factual claims go hand in hand with aesthetic commitments. But of course this assumption is precisely the thesis that McAllister is trying to justify.McAllister's second piece of evidence for his thesis consists in two casual and inconclusive quotations from Heisenberg and Jammer (from 1970 and 1966 respectively) expressing aesthetic appreciation of quantum theory (p. 201). Actually, Heisenberg does not even go that far. He merely notes that "the beauty and completeness of old physics seemed destroyed" in the early 20th century, but that later research "has again restored exact science ... to the state of harmonious completeness." As for Jammer, McAllister's allusion to him reads in full: "Max Jammer felt able to appraise quantum theory as 'an imposing intellectual structure of great beauty.'" McAllister then asserts, without any further argument or discussion, that "The discrepancy between these statements and Planck's and Einstein's declarations of revulsion at quantum theory is a demonstration of the power of the aesthetic induction for foster aesthetic appreciation for empirically successful theories" (p. 201). The discrepancy shows nothing of the sort, for, as I argued above, the fact that a theory is considered ugly is some respects does not preclude it from being (especially at a later stage) beautiful in other respects. Therefore the quotations in question fail to establish any discrepancy at all in aesthetic standards. Even this objection aside, these quotations would still have nothing to do with aesthetic induction. For suppose that there was a discrepancy in aesthetic standards between Planck and Einstein on the one hand and Heisenberg and Jammer on the other hand. Then this proves merely that some people like quantum theory and some people don't, which does nothing to support McAllister's thesis. What McAllister needs is for Heisenberg's and Jammer's aesthetic standards to have changed into that form by induction from empirical data. But for this there is no evidence. Only the Heisenberg quotation hints at a change in aesthetic evaluation, but this change could just as well (not to say more naturally) be interpreted as being due to improvements in the theory rather than a change in aesthetic standards.We have now seen that McAllister's own evidence for his thesis of aesthetic induction is exceedingly weak. I now want to add a further point of criticism to highlight McAllister's opportunism in dealing with historical evidence. My argument consists in inverting two of McAllister's own prototypical examples. I shall show how, by using McAllister's own criteria, one can derive the exact opposite of his conclusions; namely that Copernicus theory was ugly and Kepler's beautiful.As regards Copernicus, McAllister's argument is based, as we saw above, on the claim that Copernicus's theory, by virtue of his elimination of the equant, is in better accord than Ptolemy's with the ancient requirement of perfect circular motion. But Copernicus managed to remove the equant only at the cost of making the centre of the orbit non-stationary. Thus the centre of the epicycle does not trace out a circle in space, as it does in Ptolemy's theory. Whence one could claim with good reason, as Kepler in fact did, that it is Ptolemy's theory and not Copernicus's that is in better accord with the requirement of perfect circular motion.Next I wish to show that although McAllister uses Kepler's law of ellipses as a prototypical instance of a counter-aesthetic revolution, Kepler's theory must in fact be considered highly beautiful by McAllister's own standards. In a preliminary discussion (chapters 3 and 7), McAllister identifies an number of aesthetic properties which "have profoundly influenced theory choice in the sciences since at least the Renaissance" (p. 41). I say that _all of them_ apply to Kepler's astronomical theory.First a short summary of Kepler's theory. The sun is magnetic. As it rotates on its axis it creates a circular force field that pushes the planets around their orbits. The planets deviate from circular orbits and make ellipses because they themselves are magnetic. It is as if, Kepler says, the sun generates a circular stream in which the planets float like boats, only their magnetic axes act as a rudder of sorts, causing the elliptical orbit.Already this short sketch shows clearly how well Kepler's theory satisfies two of McAllister's aesthetic properties: invocation of a model, and visualisation. As a complement to visualisation, McAllister takes abstractness (the property of transcending the particular visualisation used) to be an aesthetic property. Kepler's law are examples of this.The further aesthetic properties discussed by McAllister are the following.Simplicity. A great simplification introduced by Kepler's theory was the explanation of variations in latitudes by the fact that the planetary orbits are in somewhat differently inclined planes all passing through the sun. The latitudes had previously been treated by very cumbersome and _ad hoc_ means.Symmetry. One form of symmetry admitted by McAllister is that of "offer[ing] explanations of the the same form for events deemed physically equivalent" (p. 43). This is precisely what Kepler's theory does: it subsumes all planets under one unified physical model, whereas previously each planet had its own epicyclical model, differing from the others not only in terms of parameter values but also qualitatively (e.g., number of circles employed, treatment of latitude, etc.).Metaphysical allegiance. Kepler himself specifically spoke of metaphysical arguments for his theory (e.g., Astronomia Nova, Donahue trans., p. 53). In particular, he found it appropriate that the sun should be the cause of all motion, in light of the "worthiness of eminence of the sun" and the fact that "the source of the world's life ... is the same as the source of the light which forms the adornment of the entire machine, and which is also the source of the heat by which everything grows."