A few weeks ago, I found an old physics book on a colleague’s “miscellaneous” shelf: University of Chicago Graduate Problems in Physics, by Cronin, Greenberg and Telegdi (Addison-Wesley, 1967). It looked like fun, so I started working through some of it.
Physics problems age irregularly. Topics fall out of vogue as the frontier of knowledge moves on, and sometimes, the cultural milieu of the time when the problem was written pokes through. Take the first problem in the “statistical physics” chapter. It begins, “A young man, who lives at location $A$ of the city street plan shown in the figure, walks daily to the home of his fiancee…”
No, no, no, that just won’t do any more. Let us set up the problem properly:
Asami is meeting Korra for lunch downtown. Korra is $E$ blocks east and $N$ blocks north of Asami, on the rectangular street grid of downtown Republic City. Because Asami is eager to meet Korra, her path never doubles back. That is, each move Asami takes must bring her closer to Korra on the street grid. How many different routes can Asami take to meet Korra?
Solution below the fold.
Continue reading Less Heteronormative Homework
This is, apparently, a time for reflection. What have I been up to?
And so this is Korrasmas
Things have been Done
Kuvira is fallen
A new ‘ship just begun
We all knew it
Well, other than watching cartoons?
At the very beginning of 2014, I posted a substantial revision of “Eco-Evolutionary Feedback in Host–Pathogen Spatial Dynamics,” which we first put online in 2011 (late in the lonesome October of my most immemorial year, etc.).
In January, Chris Fuchs and I finished up an edited lecture transcript, “Some Negative Remarks on Operational Approaches to Quantum Theory.” My next posting was a solo effort, “SIC-POVMs and Compatibility among Quantum States,” which made for a pretty good follow-on, and picked up a pleasantly decent number of scites.
Then, we stress-tested the arXiv.
By mid-September, Ben Allen, Yaneer Bar-Yam and I had completed “An Information-Theoretic Formalism for Multiscale Structure in Complex Systems,” a work very long in the cooking.
Finally, I rang in December with “Von Neumann was Not a Quantum Bayesian,” which demonstrates conclusively that I can write 24 pages with 107 references in response to one sentence on Wikipedia.
Shimer College: the worst school in America?
Subhead: This tiny, eccentric institution in Chicago was just voted the worst place to study in America. But does Shimer, which shuns lectures and has no societies or clubs, deserve such an accolade? Jon Ronson went there to investigate.
In the body, we have a bit more detail:
This is a ‘great books’ college. The great books of the western tradition, not the professors, are the teachers: Da Vinci’s Notebooks and Aristotle’s Poetics and Homer’s Odyssey and de Beauvoir’s Ethics of Ambiguity and Kafka and Derrida and Nietzsche and Freud and Marx and Machiavelli and Shakespeare and the Bible.
Continue reading Concerning “Great Books”
Here is Paul Dirac in October 1927:
If we are honest — and scientists have to be — we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can’t for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards — in heaven if not on earth — all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins.
To which Wolfgang Pauli is said to have replied,
Continue reading Dirac, Pauli and You
For your edutainment:
Continue reading Links
One day, I’ll be able to explain the story behind how I got into this, but looking back on all the oddities of it, I’m not sure that a medium other than manga could do it justice.
My Struggles with the Block Universe [arXiv:1405.2390]
Christopher A. Fuchs, Maximilian Schlosshauer (foreword), Blake C. Stacey (editor)
This document is the second installment of three in the Cerro Grande Fire Series. Like its predecessor arXiv:quant-ph/0105039, “Notes on a Paulian Idea,” it is a collection of letters written to various friends and colleagues, most of whom regularly circuit this archive. The unifying theme of all the letters is that each has something to do with the quantum. Particularly, the collection chronicles the emergence of Quantum Bayesianism as a robust view of quantum theory, eventually evolving into the still-more-radical “QBism” (with the B standing for no particular designation anymore), as it took its most distinctive turn away from various Copenhagen Interpretations. Included are many anecdotes from the history of quantum information theory: for instance, the story of the origin of the terms “qubit” and “quantum information” from their originator’s own mouth, a copy of a rejection letter written by E. T. Jaynes for one of Rolf Landauer’s original erasure-cost principle papers, and much more. Specialized indices are devoted to historical, technical, and philosophical matters. More roundly, the document is an attempt to provide an essential ingredient, unavailable anywhere else, for turning QBism into a live option within the vast spectrum of quantum foundational thought.
As the comment field says, “CAUTION, do not unthinkingly print from a printer: 2,348 pages, 4 indices, 6 figures, with extensive hyperlinking.”
MSwtBU was originally submitted to the arXiv on 10 May 2014, the anniversary of the predecessor volume and before that of the Cerro Grande Fire, which started the whole business. To my knowledge, it is the longest item currently on the arXiv.
omg 2000+ pages. There goes my free time.
— Dave Bacon, via Twitter
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).
Betcha people at Science and PLOS are giggling fit to burst right about now.
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.
Continue reading Time Capsule
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:
Continue reading “Is Algebra Necessary?” Are You High?
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).
Continue reading Fugacity
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.
Continue reading Gbur’s Mathematical Methods
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:
Continue reading “More Decimal Digits”
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:
Continue reading Adaptive Networks