Archive: History of Science
The soul of man pictured
The illustration above is from Jan Comenius’ celebrated, oft-reprinted school-book. The Orbis sensualium pictus presents, in words and in pictures, “all the fundamental things in the world and all the acts of life”. In pictures (an expensive novelty at the time) because, after all, “in Intellectu autem nihil est, nisi priùs fuerit in Sensu” (a famous Aristotelian slogan), and so one must exercise the senses, perceiving by their means the differences of things, so as to lay the foundations of wisdom and right action.
Two new theorems in number theory
In grade school we learn how to divide one whole number by another. Sometimes nothing is left over, but often the division leaves a “remainder”. One learns to say “Eleven divided by five is two remainder one”. Numbers that always leave a remainder when divided by another number other than themselves or 1 are called prime. All other numbers are called composite (except 1, which is neither prime nor composite).
The BEHGHK particle
In advance of the big announcement from LHC, here are some links to information about the Higgs boson.
John Conway explains, in “Higgs 101” at Cosmic Variance, why physicists think there has to be a Higgs field and a corresponding particle (the “carrier” of the field, as the photon is the carrier of electromagnetic fields, and the hypothetical graviton of gravitational fields). This is not for the totally naïve, but if you have a decent impressionistic grasp of high-energy physics, Conway’s piece will give you a good account of the importance of the Higgs particle to the so-called “Standard Model” in fundamental physics. Were it not to exist, that model would have to be radically revised.
See also the video at PhD Comics. The viXra.org blog has a nice list of papers on electroweak symmetry and symmetry breaking, from Heisenberg in 1928 to Ellis, Gaillard, and Nanopoulos in 1976, which initiated discussion of ways to detect the Higgs particle.
Skulls in the Stars notes that the hypothesis of the existence of the symmetry-breaking mechanism was put forward almost simultaneously by six physicists in three groups, all of whom published their work in Physical Review Letters in 1964. One of the six, Carl Richard Hagan, was among the teachers of the author of Skulls, whose account of the graduate students’ relative ignorance of their teachers’ eminence, and of their consuming interest in gossip about those same teachers, sounds very familiar.
All six co-discoverers of the Higgs mechanism were awarded the Sakurai Prize in 2010. But only Higgs’s name is used to designate the particle (on the controversy surrounding the naming of the Higgs, see Alasdair Wilkins’ piece at io9)—this even though the paper by Robert Brout and François Englert, which also put forward the hypothesis of a symmetry-breaking mechanism responsible for creating mass, was published several months earlier. It did not, however, explicitly mention the particle.
Another group of three physicists, Tom Kibble, Gerald Guralnik and Carl Hagen, finished their paper on the symmetry-breaking mechanism just as the other papers were being published (see Guralnik’s history of his group’s contribution; also Guralnik 2009). In his detailed analysis of the three papers, Guralnik holds that only his group had a complete solution to the problem of explaining spontaneous symmetry-breaking; the earlier papers did not (2009:19–20). The moral, perhaps, is that the best presentation of a hypothesis need not be the best-known: celebrity, like grace, tracks works only imprecisely.
“Une trace impérissable de ces fugitives mélodies”
The earliest known recording of the human voice from which intelligible sound has been recovered was made by the French scientist Édouard-Léon Scott de Martinville on 9 April 1860—seventeen years before Edison’s first phonograph recording. It is a bit of “Au clair de la lune”.
On 20 April another recording, longer and with better fidelity, was made. Earlier recordings exist, but for lack of calibration they have not been converted. Scott calibrated his later recordings with a tuning fork of known pitch.
The recovery was carried out by First Sounds, a group devoted to preserving, recovering, and publishing old recordings.
Below is a sketch from Scott’s patent application (“brevet d’invention”), dated 25 Mar 1857.
The truth about infinitesimals
In what follows I am not pushing any conclusions; I’m offering an extended example with which to think about questions of truth and historical interpretation.
Russell knew how things stood with infinitesimals. Weierstrass and Cantor have solved the problem of placing the calculus on a rigorous basis. The infinitesimals of an earlier age are banished; the contradictions entailed by their use can now safely be ignored because it has been shown we can do without them. (NB: My guide in this discussion is John Bell’s The continuous and the infinitesimal, esp. ch. 4.)
Leibniz in particular is censured for having given a “wrong direction to speculation as to the Calculus”.
His belief in the actual infinitesimal hindered him from discovering that the calculus rests on the doctrine of limits, and made him regard his dx and dy as neither zero, nor finite, nor mathematical fictions, but as really representing the units to which, in his philosophy, infinite division was supposed to lead (Russell, The Principles of mathematics 325).
Leibniz’s—and his successors’—attempts to save infinitesimals were bound to come to naught, because “infinitesimals as explaining continuity must be regarded as unnecessary, erroneous, and self-contradictory” (Principles 345: his verdict on Hermann Cohen’s Neo-Kantian interpretation of the calculus).
Celebrating the accomplishments of Weierstrass, Russell makes his work a fulfillment of Zeno’s:
After two thousand years of continual refutation, these sophisms [Zeno’s paradoxes] were reinstated, and made the foundation of a mathematical renaissance, by a German professor, who probably never dreams of any connection between himself and Zeno. Weierstrass, by strictly banishing all infinitesimals, has at least shown that we live in an unchanging world, and that the arrow, at every moment of its flight, is truly at rest (347).
What Russell knows is that the key notion of the calculus—that of limit—has been defined by nineteenth-century mathematicians in terms that make no reference to other than “normal” finite quantities. In the classical ε, δ definition of convergence, those variables range over ordinary numbers like .01 or 1/π. The dx and dy of Leibniz’s calculus are thus eliminated; every proposition containing such symbols can be replaced, salve veritate and also salve deductive relations, by a proposition not containing them. Elimination by definition became a familiar strategy in analytic philosophy, carried forward in extremis by “nominalists” whose aim was to eliminate by similar means all abstracta, including the sets or classes to which, in the late nineteenth century, all other mathematical entities then conceived had been reduced. The model and origin of all such reductions was, directly or indirectly, that of Weierstrass.
The importance of that model would be difficult to exaggerate. It was seen to be the successful solution, ending all dispute, to a longstanding philosophical and mathematical problem, the problem of infinitesimals. It was Progress with a capital P.
Higgitt’s historical heifer
[Cross-post from New APPS.] I want to recommend and to comment on a post by Rebekah Higgitt at her new venue Teleskopos.
She starts with a wonderful quotation from Augustus de Morgan (yes, that de Morgan), on the difficulty that ordinary readers may have in understanding the “merit of any new step in the advancement of a system”. In his biography of Newton (see also Essays on Newton p51), he writes:
Unless he be acquainted with the history of preceding efforts, he comes to the consideration of that merit from the wrong direction; for he reads the history from the end. He goes to the mail-coach, back from the railroad instead of forward from the old strings of pack-horses: from a macadamized road lighted with gas to the rough stones and the oil-lamps, instead of beginning with the mud and the link-boys.
We all come in at the wrong end; the difficulty is that of having a beginning, of not being there all along. The ranks of the famous, for example, appear differently to each cohort. For anyone under thirty-five, John Lennon has always been dead; he is dead, of course, but for me he is also—not just by hearsay but in experience—the twenty-something Beatle who told the rich folks in Albert Hall to rattle their jewelry, the promoter of peace, the artist felled by bullets in 1980. So too the student of physics approaches its great discoveries from the wrong end, when they are completed, established, no longer at the quickening edge of science.
As Higgitt says, the ordinary reader lacks context (other than what is part of “general knowledge”): the “small guys surrounding the big ones”, the textbooks we no longer read, the decor taken for granted as de Morgan takes for granted lamps lighted with gas (rather new in the 1840s!), as Einstein took for granted synchronized clocks (his father designed them: see Peter Galison, Einstein’s clocks). To the mathematician Hamilton in 1853 De Morgan writes:
In reading an old mathematician you will not read his riddle unless you plough with his heifer;* you must see with his light if you want to know how much he saw [quoted by Higgitt].
Higgitt goes on to quote De Morgan’s review of Whewell’s History of the inductive sciences (1847; the review was published in 1849). Whewell, says De Morgan, “appears to have considered foreign to his purpose” inquiries into the when and even the by whom of scientific discovery. But
it is of great importance in the history of philosophy to show, that the germs of brilliant discoveries have often been long in the hands of mankind, unappreciated and little thought of, till some accidental association with a fertile principle or abstract truth, developed their nature, and gave them new value. The more we apply ourselves, with antiquarian industry, to examine the history of the human mind, the more apparent it will be, that the present accumulation of science, however massive, has grown particle by particle, and has never really experienced any sudden increase.
Is this, Higgitt asks, a plea for the cultural history of science avant la lettre?
Feyerabend: heathen, yes, anti-science, no, at least not until Farewell to Reason (but really what he opposed was the employment or diversion of science to authoritarian, anti-democratic ends: invoking “expertise” so as to shut off debate and exclude “laypeople” from decision-making). Certainly not a nut-job; he disliked academic stuffiness and professorial anxieties about respectability and stuck many a pin in many an inflated ego (read “New Clothes from the Emperor’s Bargain Basement” to see him take apart Larry Laudan).
I once read all of the reviews of Against Method I could find. Very few of them took the trouble to understand his arguments. They mostly got stuck at his announced “anarchism” and the slogan “anything goes”, and thereupon stopped reading. Feyerabend quite understandably became angry at his treatment by the reviewers. Admittedly he was given to boxing the ears of those he thought were deliberately obtuse, but he also with some care reiterated the points he thought they had missed.
Professional philosophy has since his heyday gotten even more stuffy and respectable. I can’t think of a single figure who even begins to approach Feyerabend (or crazy old Popper, for that matter, the High Priest of Objectivity from whom F. and several other well-known philosophers of science were apostates) in their willingness to question everything rather than sticking safely to some well-trodden terrain of “problems” and “solutions”.
On contingency in history
ES: Daston’s response to this situation is to promote an agenda to chart the growth and transmutation of reason and the accompanying techniques and epistemic virtues through the ages. (One sees some of this in her book with Galison on objectivity.) While this (Foucault-lite genealogy) is certainly a philosophic project in so far as philosophy is the science that also reflects on itself and its (historical) presuppositions (one can say that reason is partial without historical self-understanding), the philosophy to be found here is skin-deep. Its results will provide a lot of information, and, perhaps, a healthy skepticism about the nature and sources of science’s self-image.
But it lacks philosophic ambition because it has fully embraced the cult of contingency. It can’t even bring itself to use this historical knowledge to ask what the necessary conceptual, social, mathematical or technical pre-conditions are or may be for the way (scientific) reason develops in society. That project, first hinted at by David Hume (in his treatment of justice) and widened by Adam Smith, Hegel, and Marx, was revived and transformed by the early Foucault in The Order of Things (original title: Les Mots et les choses), while Kuhn, Popper, Feyerabend, and Lakatos were having their epic debates during the 1960s. The problem with Foucault’s archeology is that he never appears to have seriously engaged with the citadel of science: physics. Now a half century later there appear to be few ambitious historically informed projects left.
“Cult of contingency” [a phrase used by ES to denote the position he opposes] is a nice bit of rhetorical icing. But where’s the cake? In response to comments pointing out that some historians regard their work as having provided evidence for contingency, you reply that their methods make it impossible to see anything but contingency.
The structure of your argument so far is: those who hold that the history of science exhibits no regularities (that, I gather, is what you mean by the “contingency” part of “cult of contingency”; you seem to agree that no-one has discovered “laws of development” in the history of science: but in your view there are or may be regularities of some weaker sort?) do not have sufficient evidence for their claim because they have not looked for evidence for the counterclaim that there are regularities.
Whether that is deserving of the propaganda label “cult”, I don’t know. Sounds like garden-variety confirmation bias to me. (How many providentialist historians devoted serious effort to disproving contrary hypotheses?) I suspect the original impetus behind the predilection for contingency that many historians of science do exhibit was owing to a reaction against presentist progressivist history (rather than against Marxist theories of history, say). Writing the history of old science as the slow but inevitable march from darkness and ignorance to our present condition of enlightenment and knowledge resulted quite often in lousy history.
I agree that to force a choice between historical laws and mere chance is fallacious. But it seems to be very difficult to find grounds—even when you do look for them (and I think you need a lot more evidence to support your claim that people have not)—to deny contingency over the long run, because events like the publication of The Origin of Species depend on a whole host of earlier developments such that if you remove one or some of them, it’s not at all clear what “would” have happened subsequently.
Imagine 18th-century natural history in the absence of discoveries from the New World, Asia, and Africa; consider whether Darwin would have had models for the transformation of species had there not already been a lot of thinking about “development” in the late 18th and early 19th century, in cosmology and geology especially; or to what degree his evidence-gathering relied upon extensive worldwide networks of correspondence such that the existence of the technologies supporting then was contingent with respect to the character of biological thought in the period.
In short: changes in the sciences (and a fortiori in philosophy) tend to depend on complexes of active causes (e.g. the agencies behind the Human Genome Project) and causal conditions (knowledge concerning polymerase chain reactions?) that seem to be contingent (or “chance” in the Aristotelian sense of logically contingent meetings of causal sequences which taken in themselves are owing to the natures of the objects involved in them, and are therefore not “chance”). That, and not some supposed “cult of contingency”, would be the grounds for denying that strong global regularities are likely to be found in the history of science (or philosophy: but perhaps philosophy is a special case? if so, how?).
ES: “I am not against the claim that history is contingent; I am against a methodology that enshrines contingency into its ideological core, so that very different understandings (note the plural) of history are ruled out in advance. (Ones in which history has a meaning, a function, a political craft, a regulative ideal, etc.)”.
It seems to me that several quite different issues are conflated here. One is whether history—i.e. the past, considered as the object of the discipline of history—is contingent, i.e. devoid of regularities of its own (that is, not already belonging to psychology, biology, etc.). That is a matter to be settled by the evidence. Does science do better in free-market societies? How are scientific disputes brought to an end—by crucial experiments, or what? Those are perfectly sensible empirical questions. [Added here: And if they were answered in the affirmative, then the history of science would have regularities of its own.]
Another is whether there are long-term narrative “arcs” in the history of science or the history of philosophy. I think there are, but I think it takes tremendous work to (i) formulate reasonable claims while
In an ideal world I would be working on a long-term arc concerning authority and authorities—the breakdown of the system we see in the late Middle Ages and even into the early seventeenth century, a system in which each discipline was based around a few authoritative texts, teaching took the form of commentary on those texts, and innovation occurred within what was ostensibly an exposition or extension of authoritative, authorized opinion; followed by a sort of interregnum (the 17th century, more or less), followed by a reconstitution of authority. That’s an arc that, if I included some account of the rise of the older system (taking off from H. I. Marrou and others on knowledge-systems in antiquity), would extend over 1500 years or more. It wouldn’t be a story of progress, necessarily; nor do I know in advance whether the succession of systems of authority has an explanation of the sort that would exhibit it as other than contingent—as perhaps a progression rather than a mere succession. It doesn’t seem to me that I’m ruling that out. (Or that in Physiologia I was ruling out the insertion of its story into some larger story about the rise of modern science. But I did want to make that larger story harder, or ideally impossible, to tell without taking late Scholasticism seriously, which does eliminate certain triumphalist narratives resting largely upon ignorance of those sources.)(ii) avoiding partiality and the “déformations professionelles” that result from knowing some sciences better than others, and (iii) satisfying that good old Hempelian total evidence requirement.
A third issue concerns the function of historical narratives (I think we can agree that the history we have in mind is mostly narrative history, which by its form alone—even if you don’t go so far as Hayden White—is already conducive to attributing intentionality or purposiveness to historical change). History as political craft, I take it, would be a sort of Mirror for Magistrates: it would use accounts of the past as a basis for practical advice. Nothing wrong with that.
History as a regulative ideal? I don’t know what you mean, unless you’re thinking of e.g. the progress of humanity toward universal peace as a sort of lens through which to examine historical change. History as propaganda, I suppose, is what it amounts to: the sort of reading that certain Christians engage in to show that the eschatology of Revelations has been realized through the ages and is being realized in the present. I have my doubts as to whether historians of that sort are likely to satisfy the rather strict requirements you place on the contingentists: are they required to refute contrary hypotheses too? I don’t deny that good history—and perhaps the most memorable sort of history—can be written under the guidance of an ideal; but I’m not sure that we need more of it.
It was bound to happen, I suppose. Cornell has remaindered my books. You can get them cheap at Labyrinth. Elsewhere too, no doubt. All under $15.
- Physiologia. In paper. ISBN: 0801486874
- Life’s form. In hardcover. ISBN: 0801437636
- Spirits and clocks. ISBN: 0801437644
I’d rather the books were read than sitting in a warehouse. In case you’re wondering, remainder sales don’t pay royalties. In that respect I’m entirely disinterested.
*See The Panda’s Thumb for details on the decision by the Kansas Board of Education. Pat Robertson has told the good citizens of Dover not to bother praying if a disaster comes. I’m glad somebody knows what God’s up to. His ways, of late, have been yet more mysterious than usual.
†Missouri, by the way, has eight neighbors. Only one other state has as many.