The soul of man pictured

Source: Jan Comenius, Orbis pictus
(Syracuse, NY: C. W. Bardeen, 1887).

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 infra-ordinary: Scholar, disassembled

I received a new shoulder-bag for my birthday. Here are the permanent residents of my old bag awaiting transfer to the new. And yes, every single one of these items (with the exception of the mysterious paper) has proved useful on at least one occasion in the last ten years…

Row 1 a :iPad to monitor adaptor b :lip balm c :wallet-sized Fresnel magnifier d :Altoids tin (contains 1 Ricola lozenge) e :Staedtler eraser f :weathered wood from the coast of BC Row 2 a :Cheshire Cat button b :fountain pen cartridges c :binder clip d :paper clip (“owl” style) e :tweezers f :mysterious paper wrapped in plastic g :AAA batteries, 3 rechargeable, 2 not Row 3: a :second pair of reading glasses b :magnifier with light c :paper for notes, bookmarks, etc. d :colored pens, mechanical pencils e :comb (freebie from Thai Airways)

Row 4: a :45° triangle b :bag for sunglasses c :hand-knit cloth (for cleaning glasses) d :Ministaff colored pencil kit e :rotary lead pointer Row 5: a :pill box b :eyedrops c :miniature portfolio d :notebook with strap Row 6: a :hairbrush (fine) b :hairbrush (coarse) c :shoehorn d :magnifier e :notebook f :notebook

The Emirate of El Paso and the Austin Free State

Our New Neighbor to the South!

A petition at whitehouse.gov urging that Texas should secede from the United States has gathered over 100,000 signatures. Following the iron logic of secession, El Paso and Austin have filed petitions to secede from Texas should it secede from the US, and no doubt certain neighborhoods of those cities will file petitions to secede from the secession from the secession.

Texans should really think twice about this. The United States has a tendency to turn the governments of small- to medium-sized oil-rich countries into unstable dictatorships, and then, when it tires of its new playthings, it bombs them. Texas, or rather Texans, would, of course, save a significant amount of money if they no longer paid Federal income tax. But even $389 million doesn’t go very far when one stealth bomber costs a billion.

Veterans Day Poppy

(In remembrance of, among others, Captain Beefheart.)

It may well be that the conception of well-marked generations got its impetus from the world wars, now usually called One and Two. The first, once simply The Great War, was the war of my grandparents; the second, that of my parents. That distinction was clear, easy to remember, soundly based in events.

Good enough is good enough: on the future of teaching

US Stamp: Mark Hopkins, 1940.
Source: Wikimedia.

There is or was in economics a so-called law known as Gresham’s: bad money drives out good. Another law, of broader application, would have it that good enough dominates best.

The web, and indeed Wikipedia—to which I just happily referred—, illustrates this point. Copying is easy, compiling is easy, finding new information is not so easy, even if that means simply reading journal articles and adding a bit to the existing common store. I have Fuch’s dystrophy, a hereditary disease of the cornea. Naturally I’d like to know all I can about it. I search online, diligently, repeatedly. What I find is the same information (some of it perhaps incorrect) repeated over and over again, often verbatim, from Wikipedia to the Mayo Clinic to NIH. As soon as one tries to investigate specific questions, e.g. about the risk of surgery, one discovers that the web has no answers. I would say that it is broad but shallow; yet even that conveys the wrong impression, since the “breadth” consists largely in repetition of a small core of fact and not obviously untrue speculation.

The information one gleans, with grains of salt for more dubious sources, is for many purposes good enough. Were you a journalist or a student needing two sentences on Fuch’s, you’d have them, quickly and without effort. But it is not much better than good enough. I think that that is a general tendency: the apparent wealth of the (publicly accessible) web belies a widespread poverty.

Good enough drives out best—and even better.

Apply this now to university teaching.

On bad anecdotes and good fun

My initial topic is the attractions of scandal, and an oft-told story: Diderot, humiliated at the court of Catherine by his inability to answer Euler’s supposed mathematical proof of the existence of God, limps back home to Paris.

The moral generally drawn from the story is: Learn your algebra! My moral will be an admonition to historians (but not only to historians).

I’ve read the Diderot anecdote many times—mathematicians seem to like it—and I’ve long been suspicious. Inspired by a colleague’s use of it in a talk last semester, I did some checking. Here’s what I found.

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 so-called “Higgs mechanism”, by which massive particles receive their mass, consists in the force of the field being “felt” by those particles as resisting their motion (as a ping-pong ball immersed in water “feels” the resistance of the water, and—in good Aristotelian fashion—therefore moves at finite speed). The Higgs mechanism “breaks” an original symmetry among fundamental particles, so that some, like the proton and electron, have mass and some, like the photon, don’t. Only massless particles can travel at the speed of light; all others must move more slowly.

(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,

Peter Higgs. Source: APS.

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.

Baron May of Oxford, Guralnik, Hagan (1961).
Source: Guralnik 2011.

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.