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Category Archives: Science history

Christine Ladd-Franklin:

It is not possible that what is common to several classes should have any quality which is excluded from one of them. If, for example, no bankers are poor and no lawyers are honest, it is impossible that lawyers who are bankers should be either poor or honest.

From “On the Algebra of Logic” in Studies in Logic, Charles Sanders Peirce, editor, pp. 17–71 (1883).

Dear Gentlemen,

Betcha people at Science and PLOS are giggling fit to burst right about now.

Yours,
Blake

While looking through old physics books for alternate takes on my quals problems, I found a copy of Sir James Jeans’ Electricity and Magnetism (5th edition, 1925). It’s a fascinating time capsule of early views on relativity and what we know call the “old quantum theory,” that is, the attempt to understand atomic and molecular phenomena by adding some constraints to fundamentally classical physics. Jeans builds up Maxwellian electromagnetism starting from the assumption of the aether. Then, in chapter 20, which was added in the fourth edition (1919), he goes into special relativity, beginning with the Michelson–Morley experiment. Only after discussing many examples in detail does he, near the end of the chapter, say

If, then, we continue to believe in the existence of an ether we are compelled to believe not only that all electromagnetic phenomena are in a
conspiracy to conceal from us the speed of our motion through the ether, but also that gravitational phenomena, which so far as is known have nothing to do with the ether, are parties to the same conspiracy. The simpler view seems to be that there is no ether. If we accept this view, there is no conspiracy of concealment for the simple reason that there is no longer anything to conceal.

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A post today by PZ Myers nicely expresses something which has been frustrating me about people who, in arguing over what can be a legitimate subject of “scientific” study, play the “untestable claim” card.

Their ideal is the experiment that, in one session, shoots down a claim cleanly and neatly. So let’s bring in dowsers who claim to be able to detect water flowing underground, set up control pipes and water-filled pipes, run them through their paces, and see if they meet reasonable statistical criteria. That’s science, it works, it effectively addresses an individual’s very specific claim, and I’m not saying that’s wrong; that’s a perfectly legitimate scientific experiment.

I’m saying that’s not the whole operating paradigm of all of science.

Plenty of scientific ideas are not immediately testable, or directly testable, or testable in isolation. For example: the planets in our solar system aren’t moving the way Newton’s laws say they should. Are Newton’s laws of gravity wrong, or are there other gravitational influences which satisfy the Newtonian equations but which we don’t know about? Once, it turned out to be the latter (the discovery of Neptune), and once, it turned out to be the former (the precession of Mercury’s orbit, which required Einstein’s general relativity to explain).

There are different mathematical formulations of the same subject which give the same predictions for the outcomes of experiments, but which suggest different new ideas for directions to explore. (E.g., Newtonian, Lagrangian and Hamiltonian mechanics; or density matrices and SIC-POVMs.) There are ideas which are proposed for good reason but hang around for decades awaiting a direct experimental test—perhaps one which could barely have been imagined when the idea first came up. Take directed percolation: a simple conceptual model for fluid flow through a randomized porous medium. It was first proposed in 1957. The mathematics necessary to treat it cleverly was invented (or, rather, adapted from a different area of physics) in the 1970s…and then forgotten…and then rediscovered by somebody else…connections with other subjects were made… Experiments were carried out on systems which almost behaved like the idealization, but always turned out to differ in some way… until 2007, when the behaviour was finally caught in the wild. And the experiment which finally observed a directed-percolation-class phase transition with quantitative exactness used a liquid crystal substance which wasn’t synthesized until 1969.

You don’t need to go dashing off to quantum gravity to find examples of ideas which are hard to test in the laboratory, or where mathematics long preceded experiment. (And if you do, don’t forget the other applications being developed for the mathematics invented in that search.) Just think very hard about the water dripping through coffee grounds to make your breakfast.

“This room smells of mathematics!
Go out and fetch a disinfectant spray!”

A.H. Trelawney Ross, Alan Turing’s form master

It’s been a while since I’ve felt riled enough to blog. But now, the spirit moves within me once more.

First, I encourage you to read Andrew Hacker’s op-ed in The New York Times,Is Algebra Necessary?” Then, sample a few reactions:
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Now and then, one hears physicist stories of uncertain origin. Take the case of Niels Bohr and his horseshoe. A short version goes like the following:

It is a bit like the story of Niels Bohr’s horseshoe. Upon seeing it hanging over a doorway someone said, “But Niels, I thought you didn’t believe horseshoes could bring good luck.” Bohr replied, “They say it works even if you don’t believe.” [source]

I find it interesting that nobody seems to know where this story comes from. The place where I first read it was a jokebook: Asimov’s Treasury of Humor (1971), which happens to be three years older than the earliest appearance Wikiquote knows about. In this book, Isaac Asimov tells a lot of jokes and offers advice on how to deliver them. The Bohr horseshoe, told at slightly greater length, is joke #80. Asimov’s commentary points out a difficulty with telling it:

To a general audience, even one that is highly educated in the humanities, Bohr must be defined — and yet he was one of the greatest physicists of all time and died no longer ago than 1962. But defining Bohr isn’t that easy; if it isn’t done carefully, it will sound condescending, and even the suspicion of condescension will cool the laugh drastically.

Note the light dusting of C. P. Snow. Asimov proposes the following solution.

If you despair of getting the joke across by using Bohr, use Einstein. Everyone has heard of Einstein and anything can be attributed to him. Nevertheless, if you think you can get away with using Bohr, then by all means do so, for all things being equal, the joke will then sound more literate and more authentic. Unlike Einstein, Bohr hasn’t been overused.

I find this, except for the last sentence, strangely appropriate in the context of quantum-foundations arguments.

The question came up while discussing the grand canonical ensemble the other day of just where the word fugacity came from. Having a couple people in the room who received the “benefits of a classical education” (Gruber 1988), we guessed that the root was the Latin fugere, “to flee” — the same verb which appears in the saying tempus fugit. Turns out, the Oxford English Dictionary sides with us, stating that fugacity was formed from fugacious plus the common +ty suffix, and that fugacious (meaning “apt to flee away”) goes back to the Latin root we’d guessed.

Gilbert N. Lewis appears to have introduced the word in “The Law of Physico-Chemical Change”, which appeared in the Proceedings of the American Academy of Arts and Sciences 37 (received 6 April 1901).
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REVIEW: Gregory J. Gbur (2011), Mathematical Methods for Optical Physics and Engineering. Cambridge University Press. [Post also available in PDF.]

By golly, I wish I’d had this book as an undergrad.

As it was, I had to wait until this past January, at the ScienceOnline 2011 conference. These annual meetings in Durham, North Carolina feature scientists, journalists, teachers and students, all blurring the lines between one specialization and another, trying to figure out how the Internet can help us do and talk science. Lots of the attendees had books recently published or soon forthcoming, and the organizers arranged a drawing. We could each pick a book from the table, with all the books anonymized in brown paper wrapping. Greg “Dr. Skyskull” Gbur had brought fresh review copies of his textbook. Talking it over, we realized that if somebody who wasn’t a physics person got a mathematical methods textbook, they’d probably be sad. So, we went to the table and hefted the offerings until we found one which weighed enough to be full of equations, and everyone walked away happy.

MMfOPE is, as the kids say, exactly what it says on the tin. It begins with vector calculus and concludes with asymptotic analysis, passing through matrices, infinite series, complex analysis, Fourierology and ordinary and partial differential equations along the way. Each subject is treated in a way which physicists will appreciate: mathematical rigour mortis is not stressed, but when more careful or Philadelphia-lawyerly treatments are possible, they are indicated, and the ways in which their subtleties can become relevant are pointed out. In addition, issues like the running time and convergence of numerical algorithms are, where appropriate, addressed.
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On occasion, somebody voices the idea that in year [tex]N[/tex], physicists thought they had everything basically figured out, and that all they had to do was compute more decimal digits. I won’t pretend to know whether this is actually true for any values of [tex]N[/tex] — when did one old man’s grumpiness become the definitive statement about a scientific age? — but it’s interesting that not every physicist with an interest in history has supported the claim.

One classic illustration of how the old guys with the beards knew their understanding of physics was incomplete involves the specific heats of gases. How much does a gas warm up when a given amount of energy is poured into it? The physics of the 1890s was unable to resolve this problem. The solution, achieved in the next century, required quantum mechanics, but the problem was far from unknown in the years before 1900. Quoting Richard Feynman’s Lectures on Physics (1964), volume 1, chapter 40, with hyperlinks added by me:
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In network science, one can study the dynamics of a network — nodes being added or removed, edges being rewired — or the dynamics on the network — spins flipping from up to down in an Ising model, traffic flow along subway routes, an infection spreading through a susceptible population, etc. These have often been studied separately, on the rationale that they occur at different timescales. For example, the traffic load on the different lines of the Boston subway network changes on an hourly basis, but the plans to extend the Green Line into Medford have been deliberated since World War II.

In the past few years, increasing attention has been focused on adaptive networks, in which the dynamics of and the dynamics on can occur at comparable timescales and feed back on one another. Useful references:
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Consider the Lagrangian density

\[ \mathcal{L} (\tilde{\phi},\phi) = \tilde{\phi}\left((\partial_t + D_A(r_A - \nabla^2)\right)\phi - u\tilde{\phi}(\tilde{\phi} - \phi)\phi + \tau \tilde{\phi}^2\phi^2. \]

Particle physicists of the 1970s would recognize this as the Lagrangian for a Reggeon field theory with triple- and quadruple-Pomeron interaction vertices. In the modern literature on theoretical ecology, it encodes the behaviour of a spatially distributed predator-prey system near the predator extinction threshold.

Such is the perplexing unity of mathematical science: formula X appears in widely separated fields A and Z. Sometimes, this is a sign that a common effect is at work in the phenomena of A and those of Z; or, it could just mean that scientists couldn’t think of anything new and kept doing whatever worked the first time. Wisdom lies in knowing which is the case on any particular day.

[Reposted from the archives, in the light of John Baez's recent writings.]

Meanwhile, our long cybernetic nightmare continues. Thoughtlessness abounds. Things fall apart; the ice sheets cannot hold. Bloggers demand their due from a system which is ill-prepared to provide it. Satirists strive mightily to invent new jokes about Twilight.

Some things I’ve enjoyed reading recently:
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By the way, what I have just outlined is what I call a “physicist’s history of physics,” which is never correct. What I am telling you is a sort of conventionalized myth-story that the physicists tell to their students, and those students tell to their students, and is not necessarily related to the actual historical development, which I do not really know!

Richard Feynman

Back when Brian Switek was a college student, he took on the unenviable task of pointing out when his professors were indulging in “scientist’s history of science”: attributing discoveries to the wrong person, oversimplifying the development of an idea, retelling anecdotes which are more amusing than true, and generally chewing on the textbook cardboard. The typical response? “That’s interesting, but I’m still right.”

Now, he’s a palaeontology person, and I’m a physics boffin, so you’d think I could get away with pretending that we don’t have that problem in this Department, but I started this note by quoting Feynman’s QED: The Strange Theory of Light and Matter (1986), so that’s not really a pretence worth keeping up. When it comes to formal education, I only have systematic experience with one field; oh, I took classes in pure mathematics and neuroscience and environmental politics and literature and film studies, but I won’t presume to speak in depth about how those subjects are taught.

So, with all those caveats stated, I can at least sketch what I suspect to be a contributing factor (which other sciences might encounter to a lesser extent or in a different way).

Suppose I want to teach a classful of college sophomores the fundamentals of quantum mechanics. There’s a standard “physicist’s history” which goes along with this, which touches on a familiar litany of famous names: Max Planck, Albert Einstein, Niels Bohr, Louis de Broglie, Werner Heisenberg, Ernst Schrödinger. We like to go back to the early days and follow the development forward, because the science was simpler when it got started, right?

The problem is that all of these men were highly trained, professional physicists who were thoroughly conversant with the knowledge of their time — well, naturally! But this means that any one of them knew more classical physics than a modern college sophomore. They would have known Hamiltonian and Lagrangian mechanics, for example, in addition to techniques of statistical physics (calculating entropy and such). Unless you know what they knew, you can’t really follow their thought processes, and we don’t teach big chunks of what they knew until after we’ve tried to teach what they figured out! For example, if you don’t know thermodynamics and statistical mechanics pretty well, you won’t be able to follow why Max Planck proposed the blackbody radiation law he did, which was a key step in the development of quantum theory.

Consequently, any “historical” treatment at the introductory level will probably end up “conventionalized.” One has to step extremely carefully! Strip the history down to the point that students just starting to learn the science can follow it, and you might not be portraying the way the people actually did their work. That’s not so bad, as far as learning the facts and formulæ is concerned, but you open yourself up to all sorts of troubles when you get to talking about the process of science. Are we doing physics differently than folks did N or 2N years ago? If we are, or if we aren’t, is that a problem? Well, we sure aren’t doing it like they did in chapter 1 of this textbook here. . . .