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 because, after all, “in... Continue reading

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. Source: Jan Comenius, Orbis sensualium pictus bilinguis. (Coronæ: Petrus Pfannenschmiedius, 1675). One could hardly find a better example of what philosophers often ridicule in “folk” conceptions of the soul: the soul presented in ghostly outline, as something that, being visible, could only be corporeal; and if it is corporeal, then to conceive it as spiritual is of course a mistake. Source: Jan Comenius, Orbis sensualium picti pars prima. (Noribergae: Martinus Endter, 1664). Comenius, or rather the illustrator of his text, has set himself the task... Continue reading

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). ▶ If you want to get to the new mathematics immediately, click here. If you want to take a more leisurely route, keep reading. The fascination of primes, as Emily Riehl notes, often draws people into mathematics. Oliver Sacks describes a pair of twins who, though quite incapable of calculating, could produce, and recognize, very large prime numbers. Sacks, when he understood that the numbers they murmured to each other were primes, joined in, contributing eight- and ten-digit primes. The twins, pleased at his comprehension, and delighted to find even larger primes to contemplate than their own six-figure numbers, soon were “swapping twenty-figure primes” (The Man who Mistook his Wife... Continue reading

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 things like “Eleven divided by five is two remainder one”. Numbers that always leave a remainder when divided by another number... Continue reading

As some of you may know, Niall Ferguson engaged in a bit of gay-bashing yesterday (links below), holding that Keynes wouldn’t have cared about future generations because he was gay (the point is apparently taken from Gertrude Himmelfarb: see the Delong item referred to below). Now he has apologized. In... Continue reading

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 Continue reading

Job-talk season will soon be upon us, and before that the formidable Eastern APA. Well-appointed philosophers now come equipped with sleek slide-shows in which years of toil have been reduced to bullet points and fuzzy photos of colleagues in their offices. Although the Dark Ages of Powerpoint have passed, some... Continue reading

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. Continue reading

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... Continue reading

(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... Continue reading

(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. Edward Lutyens, Thiepval Memorial to the Missing of the Somme (1932). Credit: calotype46 at Flickr (license). The first war seems not to have touched my family much. Both my grandfathers were too old to be conscripted, and my Swedish grandfather lived in a neutral country. The second war, on the other hand, touched everyone. All my uncles served; all my aunts contributed on the home front. My father, after receiving a BME courtesy of the Army, travelled to Japan just in time to see Macarthur accept the surrender of the Japanese at Tokyo Bay. Of his experiences he, like many veterans, said very little. It was not for them to speak of “the greatest generation”. That was someone else’s invention.... Continue reading

Number theory is notorious for producing conjectures that are easy to state but difficult to resolve. The Fermat theorem, stated in 1637—by Fermat, of course, in the margin of his copy of Diophantus’ Arithmetica—, requires nothing but a knowledge of basic arithmetic to comprehend fully. It was proved (by Andrew... Continue reading

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... Continue reading

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, including Wikipedia—to which I just happily referred—, illustrates this point. Copying... Continue reading

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. First of all, Diderot knew the calculus, and I’m quite sure Euler knew he knew it. So the story was unlikely to be true. I had little trouble tracking down its source (also here), which I translate: The empress [Catherine], struck by the usefulness, the necessity even, of imposing silence on Diderot in these matters [i.e. of religion], yet wishing nevertheless to appear to have no part in the means employed [to silence him], did not invoke her authority, but instead agreed that... Continue reading

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... Continue reading