Occasional reflections on Life, the World, and Mathematics

Posts tagged ‘history of science’

Montaigne on random controlled experiments

In the past I’ve read a few individual individual essays by Montaigne, but lately I’ve been really enjoying reading them systematically — partly listening to the English-language audiobook, partly reading the lovely annotated French edition by Jean Céard et al. It’s fascinating to see the blend of inaccessibly foreign worldview with ideas that seem at times astoundingly modern. For example, in the essay titled “On the resemblence of children to their fathers” (which seems to have almost nothing at all to say about the resemblence of children to their fathers), in the course of disparaging contemporary medicine Montaigne suddenly anticipates the need for random controlled trials — while at the same time despairing of such a daunting intellectual project. After acknowledging a few minor cases in which physicians seem to have learned something from experience he continues

Mais en la plus part des autres experiences, à quoy ils disent avoir esté conduis par la fortune, et n’avoir eu autre guide que le hazard, je trouve le progrez de cette information incroyable. J’imagine l’homme, regardant au tour de luy le nombre infiny des choses, plantes, animaux, metaulx. Je ne sçay par où luy faire commencer son essay : et quand sa premiere fantasie se jettera sur la corne d’un elan, à quoy il faut prester une creance bien molle et aisée : il se trouve encore autant empesché en sa seconde operation. Il luy est proposé tant de maladies, et tant de circonstances, qu’avant qu’il soit venu à la certitude de ce poinct, où doit joindre la perfection de son experience, le sens humain y perd son Latin : et avant qu’il ait trouvé parmy cette infinité de choses, que c’est cette corne : parmy cette infinité de maladies, l’epilepsie : tant de complexions, au melancholique : tant de saisons, en hyver : tant de nations, au François : tant d’aages, en la vieillesse : tant de mutations celestes, en la conjonction de Venus et de Saturne : tant de parties du corps au doigt. A tout cela n’estant guidé ny d’argument, ny de conjecture, ny d’exemple, ny d’inspiration divine, ains du seul mouvement de la fortune, il faudroit que ce fust par une fortune, parfaictement artificielle, reglée et methodique Et puis, quand la guerison fut faicte, comment se peut il asseurer, que ce ne fust, que le mal estoit arrivé à sa periode ; ou un effect du hazard ? ou l’operation de quelque autre chose, qu’il eust ou mangé, ou beu, ou touché ce jour là ? ou le merite des prieres de sa mere-grand ? Davantage, quand cette preuve auroit esté parfaicte, combien de fois fut elle reiterée ? et cette longue cordée de fortunes et de rencontres, r’enfilée, pour en conclure une regle.

But in most other experiences, where they claim to have been led by accidents, having no other guide than chance, I find the progress of this information hard to believe. I imagine a man looking about him at the infinite number of things, plants, animals, metals. I don’t where he would start. And when his first whim took him to an elk horn, which might be easy to believe in, he would find his second step blocked: There are so many diseases, so many individual circumstances, that before he could arrive at any certainty on this point, he will have arrived at the end of human sense: before he could find, among this infinity of things, that it is this horn; among the infinity of diseases, epilepsy; among the individual conditions, the melancholic temperament; among all the ages, the elderly; among all the astrological conditions, the conjunction of Venus and Saturn; among all the parts of the body, the finger. And all of this, being led by no argument, by no prior examples, by no divine inspiration, but purely by chance, it must be achieved by the most completely artificial, methodical and regulated turn of chance. And suppose the cure has been accomplished, how could you tell whether the disease might not have simply run its course, or the improvement occurred purely by chance? Or if it might not have been the effect of some other factor, something he ate, or drank, or touched on that day? Or the merit of his grandmother’s prayers? And if you could provide complete proof in one case, how many times would you need to repeat the trial, and this long series of random encounters, before you could conclusively determine the rule.

Annie Get Your Prior

I was reading Sharon McGrayne’s wonderful popular (no, really!) book on the history of Bayesian statistics. At one point it is mentioned that George Box wrote a song for a departmental Christmas party

There’s no theorem like Bayes’ Theorem
Like no theorem I know…

A bit later we read of Howard Raiffa and Robert Schlaifer singing

Anything frequentists can do, Bayesians do better

(More or less… the exact text is not reproduced.) So it seems the underappreciated role of Irving Berlin in the development of Bayesian thought has yet to be adumbrated. Perhaps researchers will some day uncover such hits manqués as “How High is the Bayes Factor?”, “I’m Dreaming of a Conjugate Prior”, or even “Bayes Bless America”.

The Pope’s Shluchim

I’ve just been reading Amir Alexander’s book Infinitesimal, about the intellectual struggle over the concepts of infinitesimals and the continuum in mathematics and science (and theology) in the 17th century. The early part of the book is a history of the Society of Jesus, presented as a ruthless and intellectually daring force for religious conservatism, strictly hierarchical, devoted to its holy founder, a thoroughly mystical movement that built its reputation and influence on educational outreach. And then it struck me: The Jesuits were just like Chabad-Lubavitch!

The patron saint of cranks and charlatans

I can’t remember who it was who referred to Galileo that way. Ted Cruz, the right-wing US senator, presidential candidate, and one-time Ivy League super-elitist has invoked the protection of this saint to defend his position on climate change, in opposition to the overwhelming consensus of the experts:

Today the global warming alarmists are the equivalent of the flat-earthers. You know it used to be: ‘It is accepted scientific wisdom the Earth is flat.’ And this heretic named Galileo was branded a denier.

This is standard crank-Galileo stuff, impressive for the number of misconceptions it builds into such a small space. Of course, Galileo’s critics didn’t think the Earth is flat. It was certainly not “accepted scientific wisdom” in his day. (Beyond any theoretical or cultural understanding, it was nearly a century since Portuguese sailors had circumnavigated the globe.) Galileo was not dismissed by the scientific experts of his day. His theories and discoveries were controversial, but he was generally acclaimed by scientific authorities. He was punished for contradicting the Church’s entrenched philosophical commitments, by a panel that, while not completely devoid of expertise in astronomy and Aristotelian physics, was chosen for its institutional commitment to the Church. It’s not really the most felicitous comparison for a climate-change denier to bring up.

Logical fallacies aside — “They laughed at the Wright brothers. They also laughed at the Marx brothers.” — there aren’t many cases of new ideas being dismissed as ridiculous by the scientific community, and later proved right. There is often entrenched conservative resistance (as there should be) to radical new ideas, but almost never is a single thinker so far beyond everyone else that his ideas don’t elicit significant support. Perhaps the best exception is Alfred Wegener, with his obviously crackpot theory of continental drift. For some reason Galileo, who was very much respected and mainstream, gets called into service to defend the crazies, and not Wegener. I imagine that Cruz’s backers would be almost as uncomfortable with plate tectonics as they are with evolution, if they knew anything about it. At that point the USGS would be banned from using plate tectonics to predict earthquakes.

In any case, Wegener wasn’t sitting in a Senate office reading Heritage Foundation talking points; he learned everything that was known about geophysics (which wasn’t much at the time) conducting expeditions to Greenland to collect evidence.

Hippie science

There are two books I’ve read sort of recently, From Counterculture to Cyberculture by Fred Turner and How the Hippies Saved Physics by David Kaiser, that supplement each other as a picture of how antimaterialistic culture of the SF Bay area in the late 1960s through mid-1970s produced a lot of nonsense, but also hugely important new impulses in hard technical fields. Silicon Valley grew out of an ethos of DIY back-to-the-earth-ism (hence the “Homebrew Computer Club”), while the Fundamental Fysiks Group at Lawrence Berkeley Lab, took the energy of enthusiasm for parapsychology and mysticism, and channeled it into revival of an inquisitive style of physics that rediscovered entanglement and Bell’s Theorem, and laid the groundwork for quantum cryptography and quantum information science.

Einstein and the Quantum

I just saw an ad (in Blackwell’s Books) for a book titled Einstein and the Quantum, with a text that began

Einstein himself famously rejected quantum mechanics with his God does not play dice theory…

Putting aside the fact that “God does not play dice with the universe” is a quip, not a theory, I’m fascinated by this extreme statement of a calumny on Einstein that I knew as standard when I first learned about quantum mechanics from popular science in the 1970s, that the old man, despite his revolutionary past (and he was only in his late 40s) simply lacked the intellectual flexibility to keep up, rejected the new science, and was proved wrong by the march of progress.

In fact, that famous remark (from a 1926 letter to Max Born) acknowledged up front that the emerging probabilistic view of quantum mechanics was proving very useful. He simply rejected the willingness to deny a micro-level interpretation. (And the so-called Copenhagen “Interpretation” of quantum mechanics is really an anti-interpretation, a programmatic refusal to interpret. For more comments on the pedagogical function, see here.) The fact that this approach went from strength to strength as a calculating tool does not mean that its interpretive framework, the one that said that probabilities are the fundamental objects and there is no use going deeper, has been proved, any more than the success of Maxwell’s equations proved the existence of molecular vortices in the luminiferous aether. In particular, proponents of the Copenhagen Interpretation have tended to ignore the fact that they are helping themselves to a supposedly primitive concept, probability, that is actually complex, strange, and sorely in need of physical foundations.

Certainly one powerful strain of modern work on the foundations of physics — in particular, the Everett interpretation of quantum mechanics (cf. David Wallace’s The Emergent Multiverse) also rejects the notion that there is some randomness at the core of quantum mechanics, and takes as a point of departure the entanglement theory first proposed in the Einstein-Podolsky-Rosen thought experiment.

* Einstein wrote, “Die Theorie liefert viel, aber dem Geheimnis des Alten bringt sie uns kaum näher. Jedenfalls bin ich überzeugt, daß der nicht würfelt.“ Literally: “The theory gives us much, but it hardly brings us nearer to the Ancient One’s secret. In any case, I am convinced that he does not throw dice.”

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