Wednesday, December 22, 2010

Whewell on Epochs of Induction

When William Whewell set out to write his history of the inductive sciences, he was writing at a time at which it was not uncommon to see history in terms of the actions of 'Great Men'. The temptation to do this in the context of a history of science was perhaps even greater: names like Galileo, Kepler, and Newton were still, one might say, ringing in people's ears. Whewell considered such great names important. At the same time, however, he did not want to write a history of geniuses doing things: he wanted to write a history of knowledge. The evidence of history shows, however, that progress in knowledge does not consist of big, individual jumps, but, as Whewell put it, of "a long-continued advance; a series of changes; a repeated progress from one principle to another, different and often apparently contradictory" (p. 9), in which new facts are discovered or reinterpreted and old ideas are refined or rejected on the basis of evidence. The history of science is a long story, one that develops very slowly; and, despite the brisk pace of scientific change in Whewell's day, Whewell had no illusions about the ease with which nature opened up her secrets. It had taken millenia, and centuries full of great minds, to make knowledge of the natural world progress to the level it had in the nineteenth century.

Recognizing the complexity of the story of science raises a serious problem for the historian: how does one organize one's account in order to make sense of this complexity? How one does this will to some extent depend on one's view of science itself. On Whewell's view, scientific progress consists of the "superinduction" of ever more refined Ideas on ever more massive bodies of discovered Fact, and the resulting progress, which is scientific progress, is improvement in generalization: the things we say about the world become increasingly universal and bring more and more phenomena under their scope. It is this that is involved in Whewell's famous proposal of consilience, or the "jumping together" of phenomena that previously seemed distinct so that they are now seen as distinct manifestations of the same principles, as a mark of scientific progress. In order to describe this progress on a massive scale, Whewell proposed a theory of scientific history based on a triadic structure of Prelude, Epoch, and Sequel, each of which had its essential role to play in the course of scientific history.

The Epochs, of course, are characterized by the epoch-making discovery. As Whewell notes, most of the major scientific figures that all people recognize as having contributed on a major scale to civilization are associated with scientific Epochs. And, of course, precisely the temptation is to make one's history of science a history of Epochs, of great leaps forward.

But, says, Whewell, a closer look at the historical evidence always shows that these Epochs did not arise out of nothing. There was a long, slow history of preparation, "during which the ideas and facts on which they turned were called into action;--were gradually evolved into clearness and connection, permanency and certainty" (p. 12). This period Whewell calls the Prelude. The Prelude builds up both Fact and Idea; this reaches a sort of critical mass, at which point Fact has been developed enough and Idea refined enough that some scientist or other finally sees the last steps that lead to a major innovation in our understanding of the world. It's interesting how Whewell manages to walk a very fine line here: the build-up of the Prelude is necessary for the Epoch, and in some sense makes it inevitable. But this inevitability does not eliminate the importance of the great scientific geniuses of history: they are the people who saw before anyone else where things were heading, and therefore first formulated the basic ideas of a new age of scientific knowledge.

Once the geniuses have done their Epochal work, though, there is still much left to do: further evidence has to be found, the ramifications of the theories have to be pursued, and finer points that have not yet been settled have to be argued out. The amount of time and labor this requires more or less guarantees that one person, or even a small group of people cannot do it alone. This gives us the Sequel of the Epoch, in which "the discovery has acquired a more perfect certainty and a more complete development among the leaders of the advance; has been diffused to the wider throng of the secondary cultivators of such knowledge, and traced into its distant consequences" (p. 13).

Having this account of the overall structure of scientific discovery in hand, Whewell set out in his History of the Inductive Sciences with the ambition of making the history of science -- and therefore science itself as represented by its actual course -- intelligible to a degree it had never been before.

It's useful to see how this works in the case of the most developed science of Whewell's time -- the only science that had been in development long enough that it had undergone not only an Epoch but three of them, by Whewell's reckoning: formal astronomy (the 'formal' indicating that we are not here considering the subject matter of astronomy in light of physical Ideas, like cause and force, but in purely formal terms: the explanation of the phenomena of the heavens in terms of the formal Ideas of time and space).

The earliest inductive epoch in formal astronomy Whewell calls the Inductive Epoch of Hipparchus. The scientific problem with which it dealt was the problem of the wandering bodies, i.e., planets, which appeared to defy the otherwise rigid order of the heavens. Slowly people had begun to develop rules for describing their motions, tracing over long years the various cycles that the various planets undergo, but this does not get one very far; as the saying goes, it gives you Bradshaw, not the train. By thinking about the planets on analogy with wheels, the ancient Greeks were able to come up with the notion of an epicycle. This was a very important development, one that immediately handled a number of otherwise puzzling problems, like retrograde motion. And astronomers were forced to extend it by further anomalies uncovered by close examination of the data, such as the peculiarities involved in the paths taken by the moon and the sun across the sky. It doesn't take much to see that the notion of an epicycle can easily handle this sort of problem; so it was extended. Thus we have a progress in conceptions of the epicycle going with progress in acquaintance with facts. All these were prerequisites for the first great theory of astronomy, that of Hipparchus.

The scientific problem as developed in the Prelude to the Epoch, then, was to reconcile the celestial phenomena by means of equable (i.e., uniform) circular motions. Whewell noted that, while we tend to dismiss this problem as involving a kind of obsession with circles, as a part of the prelude it not only made sense, it was perhaps the most reasonable thing to try, since, if it panned out, a model consisting entirely of circles would give you the phenomena by way of the simplest and most manageable conjecture, since a great deal had been done on the geometry of circles. Even in Whewell's assessment, for all that he has some very nineteenth-century views about scientific progress, the bad name epicycles had received was due not to the work done in the Prelude, nor Hipparchus's advance in constructing a fully successful theory of epicycles and eccentrics, but to the bitter disputes that unfolded in the Sequel to the Epoch, in which the circularity condition was held with great tenacity even in the face of mounting evidence against it. And the tenacity, of course, was due precisely to the fact that had made it such an important part of the Prelude, namely, that it was such a simple and elegant supposition. There's an ambivalence to it that Whewell appreciates; and he puts it forward as an example of how the love for simplicity both drives scientific progress and creates impediments to it.

In any case, Whewell identifies Hipparchus as the cardinal point in astronomical progress during this Epoch, on the basis (he says) of the maxim that he who proves, discovers. The epicycle was nothing new when Hipparchus came along, of course; it had already been in use for the purposes of explaining anomalies in the wandering bodies. Similarly with the eccentric. To have a genuine theory of epicycles and eccentrics, however, you need to be precise: you need to identify the magnitudes, distances, and positions of the of the circles you are positing, in such a way that the circles capture the irregular and anomalous motions for which you are trying to account. One of the signs of Hipparchus's genius was his ability to come up with this on the basis of surprisingly limited data; the tables he constructed stood up to the test of predicting eclipses, the most serious and important test of any astronomical model at the time. By doing so, they showed that they were an adequate representation of the path of the sun to the level of precision required for tracking eclipses. Hipparchus did the same with the moon, to the same level of precision, on the basis of only six recorded eclipses. This formed a clear and definite basis for people to extend the same idea to the bodies of the planets. Hipparchus did not complete this task, but famously gathered together much of the material for it; according to Ptolemy the whole mass of astronomocial observations left to posterity by Hipparchus' time was dwarfed by the mass left to posterity by Hipparchus himself.

Again, we have a tendency to underrate the importance of this theory of eccentrics and epicycles; we now know that perhaps its key postulate is false, and we tend to think of the theory as inordinately complicated and tangled. And again, this is in great degree an illusion of hindsight, attributable to the fact that we are separated from Hipparchus's actual Epoch of discovery by a long and complicated Sequel. As Whewell notes, the value of a true part of a theory may far outweigh its error; and the usefulness of a rule does not always depend on its simplicity. As he notes, "The first steps of our progress do not lose their importance because they are not the last; and the outset of the journey may require no less vigor and vitality than the close" (p. 181).

On Whewell's view we can situate Hipparchus in the history of scientific progress because Hipparchus really did discover something true, and, what is more, true for all time. What is true about the theory of Hipparchus is its resolution of the phenomena into circles; and it is as true today that they can be so resolvedas it was then. For instance, this resolution allows us to construct precise tables, in principle as precise as you please, by which we can clearly determine the position of the planets at any time. The underlying assumption about the world that made this resolution possible, and thus the precise predictions, was perhaps false; but at least a basic assumption of how motion works is needed for any theory of motions, and it was a simple and straightforward assumption to make. Eccentrics and epicycles were perfectly capable of representing the quantity of the inequalities in planetary motion; and this was not a small discovery. So well does it do so, in fact, that for the convenience of calculation of this inequality, the theory first put forward by Hipparchus was very difficult to beat; as Whewell notes, if we complain about the complexity of an unusually simple method of calculation for a given natural quantity, what we are really complaining about is nature, not the method of calculation. Moreover, we tend to assume that astronomers gave the same faith to epicycles and eccentrics that we do to Kepler's ellipses; when in fact they were much more ambivalent, and were usually quite explicit about its being simply the best hypothesis on hand. The precise representation of apparent motion provided by the theory, however, allows you to collect the data that is needed before you can identify the actual motion of the planets; without Hipparchus, there would be no Kepler.

After the Epoch of induction, we entered the Sequal, a period of development, verification, application, and extension. In Whewell's view, this period was started by Hipparchus himself, who developed a catalogue of stars for more accurate record-keeping, showed with greater precision the length of years and days. He also began discovering points that did not confirm the theory -- parallaxes, for instance -- but which astronomers at the time did not have sufficiently refined Ideas to handle. One of the problems parallax shows in the theory, for instance, is that while it can accurately chart apparent position, it has serious trouble getting the distances correct.

The most famous person in the Sequel, however, is naturally Ptolemy, whose development, extension, and popularization of the Hipparchian theory is what became dominant, and is, in fact, our primary source for knowing anything about Hipparchus at all. One of Ptolemy's several contributions was the discovery of yet another celestial inequality, the evection of the moon, and his accounting for it by the theory of epicycles. This discovery was quite crucial to astronomy, or would become so much later on, because it suggested that there might be numerous inequalities that were yet remaining to be discovered, and that the confirmation of the theory lay in its power to explain such residual phenomena. It was also one of the first in a long line of discoveries of inequalities in the moon's motion that are due to the pull of the sun; and the importance of those for the later Newtonian discovery of universal gravitation can hardly be underestimated. From Ptolemy the Sequel extends through very long years, until the rise of a new inductive Epoch: the Epoch of Copernicus, followed (after a short but extraordinarily contentious Sequel) by the Epoch of Kepler. Such was the view of the history of formal astronomy Whewell had as he looked back at it with his triadic template for scientific progress, in any case. The Hipparchian era was in such a view a stage in astronomical progress, involving a Prelude of preparation, an Epoch of induction, and a Sequel of development.

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All quotations are from the 1837 edition of the first volume of the History of the Inductive Sciences, which I have used here primarily because it seems to be the edition most easily accessible by Google Book, for those who can access it.

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