Studies in Logic

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).

“You’ll get so preoccupied with equations that you forget to eat!” #BadWaysToPromoteScienceToYoungWomen

Time Capsule

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.

“Seneca Cannot Be Too Heavy”

Reading today’s Saturday Morning Breakfast Cereal, I got all “someone is WRONG about HAMLET on the INTERNET!”

1. Hamlet couldn’t have said anything much before the play starts, because he was off at school in Wittenberg.

2. He sees the ghost on the night of the first day in the play where he appears. Not a long delay there. And his reaction to being told “The serpent that did sting thy father’s life now wears his crown” is, “O my prophetic soul!” Or, in a different idiom, “Called it!”

3. He has every reason not to act rashly, because (a) he wants to be King (Claudius “popp’d in between the election and my hopes”), and (b) he can’t trust that the ghost is really his father. “The devil hath power to assume a pleasing shape”, etc. Watch your Star Trek, people! Emo!Hamlet is a comparatively recent invention. Prior to the late 1700s, the standard was to play Hamlet as a chessmaster, a brilliant young man trying to turn a bad situation to his advantage, facing a shrewd opponent.

4. It’s the characters in the play who remark on Hamlet’s “transformation”. That’s why Claudius sends for Rosencrantz and Guildenstern.

Welcome, dear Rosencrantz and Guildenstern!
Moreover that we much did long to see you,
The need we have to use you did provoke
Our hasty sending. Something have you heard
Of Hamlet’s transformation; so call it,
Sith nor the exterior nor the inward man
Resembles that it was.

5. He’s so antisocial that he…has a girlfriend? And, as Claudius says, is beloved by the general populace of Denmark? Indeed, that’s a big part of why Claudius doesn’t have Hamlet killed for stabbing Polonius. As he tells Laertes, he doesn’t want to hurt Gertrude, and in addition…

The other motive,
Why to a public count I might not go,
Is the great love the general gender bear him;
Who, dipping all his faults in their affection,
Would, like the spring that turneth wood to stone,
Convert his gyves to graces; so that my arrows,
Too slightly timber’d for so loud a wind,
Would have reverted to my bow again,
And not where I had aim’d them.

6. He won’t kill his uncle first because he wants to be crowned, not executed; and second, because he wants Claudius damned, not just dead.
Continue reading “Seneca Cannot Be Too Heavy”

Precalculus -> Statistics

Now that 2.2 metric Ages of Internet Time have passed since Andrew Hacker’s ill-advised “math is hard!!” ramble, I figure it’s a good day to propose my own way of improving high-school mathematics education. Be advised: this is a suggestion about the curriculum, not about how to train teachers, buy books and all that un-TED-friendly stuff which reformers happily gloss over. And I’ll be talking about changes late in the game, which won’t address problems at the “why can’t Johnny add?” level.

When I was in high school—at a pretty well-supported public school, out in the ‘burbs at the comparatively unimpoverished end of town—I took a “precalculus” class my eleventh-grade year. Most of the advanced-track students I knew did the same thing. (If you’d gotten yourself on the even-more-advanced track back in eigth grade, you took precalculus in tenth.) This was supposed to prepare us for taking the AP Calculus class our senior year, which would allow us to get college credit. Instead, it was a thoroughgoing waste of time. The content was a repeat of Algebra II/Trigonometry, which we’d taken the year before, with two exceptions thrown in. The first, probability, was a topic our teacher didn’t know how to teach. In fact, she admitted as much: “I don’t know how to teach probability, so you’re all going to read the book today.” The second, limits, served no purpose. I’ll explain why in a moment.

I suggest the following: scrap “precalculus” and replace it with a year-long statistics course. This plan has several advantages:

Bohr’s Horseshoe

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.

Gbur’s Mathematical Methods

REVIEW: Gregory J. Gbur (2011), Mathematical Methods for Optical Physics and Engineering. Cambridge University Press. [Post also available in PDF.]

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.

Signature in the Cell (Repost)

The following is a list of debunkings of Stephen C. Meyer’s Signature in the Cell, arranged more or less in chronological order. I have not included every blog post I’ve seen on the topic; as I did for Behe’s The Edge of Evolution, I’ve focused on the most substantive remarks, rather than keeping track of every time somebody just quoted somebody else. (I’ve also probably overlooked, forgotten, mistakenly thought I’d already included or never been made aware of some worthwhile essays.) In some cases, additional relevant posts can be found by following links within the essays I have listed.
Continue reading Signature in the Cell (Repost)

OpenLab 2010

The 2010 edition of The Open Laboratory, the annual anthology of science blogging, is now available for purchase, as a handsome print volume or a PDF compatible with e-reader devices. Proceeds from book sales go to funding the ScienceOnline 2012 conference, which is currently in the planning stage.

Eventually, I’ll find/make the time to write about how we make blog posts into a book. First, Series Editor Bora Zivkovic chooses the guest editor for the year. Then, the two of them contact me and tell me it’s time to take the LaTeX templates out of their ceremonial encasements. Next, I draw a transmutation circle and start looking for sacrifices. . . .

In the wake of ScienceOnline2011, at which the two sessions I co-moderated went pleasingly well, my Blogohedron-related time and energy has largely gone to doing the LaTeXnical work for this year’s Open Laboratory anthology. I have also made a few small contributions to the Azimuth Project, including a Python implementation of a stochastic Hopf bifurcation model.

I continue to fall behind in writing the book reviews I have promised (to myself, if to nobody else). At ScienceOnline, I scored a free copy of Greg Gbur’s new textbook, Mathematical Methods for Optical Physics and Engineering. Truth be told, at the book-and-author shindig where they had the books written by people attending the conference all laid out and wrapped in anonymizing brown paper, I gauged which one had the proper size and weight for a mathematical-methods textbook and snarfed that. On the logic, you see, that if anyone who was not a physics person drew that book from the pile, they’d probably be sad. (The textbook author was somewhat complicit in this plan.) I am happy to report that I’ve found it a good textbook; it should be useful for advanced undergraduates, procrastinating graduate students and those seeking a clear introduction to techniques used in optics but not commonly addressed in broad-spectrum mathematical-methods books.

Compliments of the Season

Merry Christmas, everyone.

To our thinking, Reader, it was a sorrowful star, that star of Bethlehem. What good purpose for Jesus or for anyone it served we cannot discover. It stood over Bethlehem, however, with a dire meaning to the homes there. All the little children there, except the one that “fled” into Africa were soon to be little corpses. The star of Bethlehem has had some little tolerable poetry and a great deal of doggerel addressed to it; also a considerable quantity of religious and sentimental prose. It has, too, had a good deal of banter bestowed upon it, which yields less amusement however, than the laborious effort of some theologians to throw light upon it by semi-natural conjectures as to how it may have been produced. They seem to have been led into these ill-advised attempts to naturalize the Magi’s light from its being termed a star; forgetful of the fact that the Jews who did not know what or where the real stars are, but thought them to be little ornaments to our earth, would very naturally give that name to such an appearance.

[…]

There were, so it seems to us mortals, two ways open to Providence of shielding Jesus from harm. First, by staying the arm of Herod, and thus saving not only the life of Jesus, but also the lives of all his fellow little towns-children; or, as here given, flight on the part of the holy family, and abandonment, sauve que peut, for all the other little Bethlehemites. We are grieved to find that Providence chose the latter. And as we read this, we are compelled to say that our heart is not with the fugitives into Egypt, but entirely with the little victims and their parents thus left behind.

[…]

The visit of the Magi to Jerusalem proved to be a most calamitous occurrence. Their declaration in Jerusalem that a King of the Jews was just born excited Herod’s attention; led to the flight of Jesus and his parents from the country; and, worst of all, led to the dreadful massacre our author now proceeds to narrate. What useful, what conceivable purpose was served by this untoward announcement on the part of the Magi, is not discoverable. Jesus, for at least thirty years afterwards lived in seclusion up in Galilee, his very existence unknown in Jerusalem. And when he went there towards the end of his life, we shall look in vain for the slightest reference either by himself or by anyone else to what we here read. Anything more utterly purposeless than this visit to Jerusalem of the Magi and its pitiable consequences it would be difficult to imagine.

[…]

Were we told that Herod overtook these mischievous Magi and slaughtered them also, we think few readers would feel very much more grieved.

The first Christmas was not a festive one in Bethlehem. There was “lamentation and weeping and great mourning” there. Poor Bethlehem! The journey of Joseph and Mary from Nazareth for the special purpose that Jesus might be born in Bethlehem may have been an honour, but it was dearly bought.

[…]

With the amiable view, we suppose, of softening our pain at the narrative of this massacre, and its permission in such a connection, some commentators have ventured to offer us some considerations, intended, we gather, to be soothing to our hearts if not to our minds. These little victims were in reality favoured beings, we are told; they are now termed “the holy innocents,” though why more holy or more innocent than any other children dying young is not stated; they were by this means saved from the ills and trials of life; and they are now safely lodged in Heaven. Some doubt, however, seems to exist as to whether they continue babes in that happy land or no. We do not know what warrant there is for such assertions, nor do we know whether these commentators would like their own children to be favoured in a like way. From such a point of view it almost seems a matter of regret that the radius of the slaughter was not greatly extended. We know nothing in the world more truly sad than the wild arguments used by pious men in struggling with the ugly parts of their holy writ. For ourselves, we find a much more solid comfort as we think of this melancholy story. It is that it rests on the sole unsupported statement of our author. Of corroboration there is not a vestige. Learned Christian scholars have toiled zealously, not, as one might have hoped, to dispel this story, but we regret to say, to substantiate it. We are thankful to add without any success whatever.

From pages 12 ff. of A Plain Commentary on the First Gospel by an Agnostic, Williams and Norgate, 1891. http://books.google.com/books?id=cXpCAAAAIAAJ.

Goodnight, children, everywhere.

Synchronicity for Fun and Profit

So: Ryan North, Matthew Bennardo and David Malki ! organized a synchronized book-buying event which propelled their short-story anthology Machine Of Death to the #1 spot on Amazon.com’s bestseller list. Since any bestseller only actually moves a few hundred copies on a single day, they figured, why not get everybody to buy on the same day and push the book to the top of the list for just that long?

It worked. And then it got better:

American conservative talky guy Glenn Beck called us out on his show yesterday because it turned out that his book also had its official release date on October 26th, and he was upset that it was in third place to Keith Richard’s new autobio “Life” and our little book. He told his listeners that he’d worked on his book for over a year, and that his books always debut at #1, and that we (along with Keith) were part of a left-wing “culture of death” that “celebrates the things that have destroyed us” and that everyone should support life by buying his book instead of ours?

It’s basically amazing.

Every time you piss off Glenn Beck, a LOLcat gets its invisible bike.

In completely unrelated news, Brian Switek‘s Written In Stone is coming out next Monday, the first of November. (Free preview!) Written In Stone is about evolution. Glenn Beck is a creationist.

(Whatever you fellows do, I’m buying two copies. I promised my mother I’d get one autographed for her at ScienceOnline 2011.)

UPDATE (29 October): Ach! All my evil plans, they are ruined!

Blag Break

Lots of #!\$#% to get done. Will be away from the Blogohedron for a while. (That includes snarkfests in other people’s comment threads.) Will hopefully come back with upgraded software, a satisfactory comment system and all that, in the not-too-distant future.

Meanwhile, why not help science bloggers build something a little more lasting than usual, and support The Open Laboratory?

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Curses Curses Squared, Google Books Edition

And speaking of things which we couldn’t even have complained about a few short years ago, you know what bugs me? Reading through a chapter of something interesting — say, David Berenstein‘s “Large-N field theories and geometry” — and having pages missing from the middle, at the whim of Google Books. It’s like a game to test one’s knowledge: if page 260 ends with the Polyakov action in the conformal gauge, and page 263 has what looks to be a Virasoro constraint in light-cone coordinates, what could have gone between? Of course, this doesn’t work so well if the missing page has something new you’d like to learn . . . .

Vertices on the Blogohedron

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:
Continue reading Vertices on the Blogohedron

Calloo! Callay!

My copy of Quantum Mechanics and Path Integrals by Feynman and Hibbs just arrived! If, say, David Griffiths’ textbook epitomizes the ordinary “vernacular” treatment of quantum mechanics, QMaPI is a classic unorthodox approach. Intended for students who already have a bit of background in the subject, it builds up the Lagrangian alternative to the Hamiltonian method, a highly useful idea when one goes on to study field theory, string theory or advanced statistical physics.

For years, this book was only available in beat-up old library copies and illegal DJVU files from Lithuania, but now, Dover has brought forth a new edition. I’m not certain on this, but it appears as if the book was so heavily pre-ordered that Amazon.com sold out of it the day it became available for purchase.

EDIT TO ADD: One erratum — on p. 364, Thorber should be Thornber.