Essentials

Albert Einstein and Kurt Gödel used to walk home together from the Institute for Advanced Study in Princeton. In Incompleteness (2005), Rebecca Goldstein gives a sample of their conversation, broached by Gödel:

All of his thinking is governed by an ‘interesting axiom,’ as Ernst Gabor Straus, Einstein’s assistant from 1944 to 1947, once characterized it. For every fact, there exists an explanation as to why that fact is a fact; why it has to be a fact. This conviction amounts to the assertion that there is no brute contingency in the world, no givens that need not have been given. In other words, the world will never, not even once, speak to us in the way that an exasperated parent will speak to her fractious adolescent: ‘Why? I’ll tell you why. Because I said so!’ The world always has an explanation for itself, or as Einstein’s walking partner puts it, Die Welt is vernunftig, the world is intelligible. The conclusions that emanate from the rigorously consistent application of this ‘interesting axiom’ to every subject that crosses the logician’s mind — from the relationship between the body and the soul to global politics to the very local politics of the Institute for Avanced Study itself — often and radically diverge from the opinions of common sense. Such divergence, however, counts as nothing for him. It is as if one of the unwritten laws of his thought processes is: If reasoning and common sense should diverge, then… so much the worse for common sense! What, in the long run, is common sense, other than common?

Somewhat related: Richard Feynman’s sense of “social irresponsibility.”

| Science & Math · Society

Unpaired Words

In his 1987 book The Game of Words, Willard R. Espy offered a poem of “forgotten positives”:

I dreamt of a corrigible, nocuous youth,
Gainly, gruntled, and kempt;
A mayed and a sidious fellow, forsooth —
Ordinate, effable, shevelled, ept, couth;
A delible fellow I dreamt.

Correspondingly, he pointed out, many common words ending in -less seem to have no opposites ending in -ful:

A tailful dog, one leaf-ful spring
Set out for toothful foraging,
And as he dug in rootful sod,
Paid voiceful tribute to his God.
At which, a feckful, loveful lass,
Whose strapful bodice charmed each pass-
Erby, cried out, “O timeful sound!
O ageful, lifeful, peerful hound!”

| Language

Summing Up

J. Horace Round’s 1895 book Feudal England contains a bitter invective against Oxford historian Edward Augustus Freeman — it’s hidden in the index:

Freeman, Professor: unacquainted with the Inc. Com. Cant., 4; ignores the Northamptonshire geld-roll 149; confuses the Inquisitio geldi 148; his contemptuous criticism 150, 337, 385, 434, 454; when himself in error 151; his charge against the Conqueror 152, 573; on Hugh d’Envermeu 159; on Hereward 160-4; his ‘certain’ history 323, 433; his ‘undoubted history’ 162, 476; his ‘facts’ 436; on Heming’s cartulary 169; on Mr. Waters 190; on the introduction of feudal tenures 227-31, 260, 267-72, 301, 306; on the knight’s fee 234; on Ranulf Flambard 288; on the evidence of Domesday 299-31; underrates feudal influence 247, 536-8; on scutage 268; overlooks the Worcester relief 308; influenced by words and names 317, 338; on Normans under Edward 318 sqq.; his bias 319, 394-7; on Richard’s castle 320 sqq.; confuses individuals 323-4, 386, 473; his assumptions 323; on the name Alfred 327; on the Sheriff Thorold 328-9; on the battle of Hastings 332 sqq.; his pedantry 334-9; his ‘palisade’ 340 sqq., 354, 370, 372, 387, 391, 403; misconstrues his Latin 343, 436; his use of Wace 344-7, 348, 352, 355, 375; on William of Malmesbury 346, 410-14, 440; his words suppressed 347, 393; on the Bayeux Tapestry 348-51; imagines facts 352, 370, 387, 432; his supposed accuracy 353, 354, 384, 436-7, 440, 446, 448; right as to the shield-wall 354-8; his guesses 359, 362, 366, 375, 378-9, 380, 387, 389, 433-5, 456, 462; his theory of Harold’s defeat 360, 380-1; his confused views 364-5, 403, 439, 446, 448; his dramatic tendency 365-6; evades difficulties 373, 454; his treatment of authorities 376-7, 449-51; on the relief of Argues 384; misunderstands tactics 381-3, 387; on Walter Giffard 385-6; his failure 388; his special weakness 388, 391; his splended narrative 389, 393; his Homeric power 391; on Harold and his Standard 402-3; on Wace 404-6, 409; on Regenbald 425; on Earl Ralf 428; on William Malet 430; on the Conqueror’s earldoms 429; his Domesday errors and confusion 151, 425, 428, 436-7, 445-8, 463; on the ‘Civic League’ 433-5; his wild dream 438; his special interest in Exeter 431; on legends 441; on Thierry 451, 458; his method 454-5; on Lisois 460; on Stigand 461; on Walter Tirel 476-7; on St. Hugh’s action [1197] 528; on the Winchester Assembly 535-8; distorts feudalism 537; on the king’s court 538; on Richard’s change of seal 540; necessity of criticising his work, xi., 353.

While we’re at it: Here’s a detail from the index to the Rectory Magazine, handwritten by Lewis Carroll for his family in 1848:

https://commons.wikimedia.org/wiki/File:Lewis_Carroll%27s_own_handwrtten_index.png

He would have been about 16.

(Thanks, Jim.)

| History · Literature · Society

Safety First

What’s the greatest number of times that players have castled in a single chess game? Surprisingly, the answer is three. From the Irish Chess Journal, November-December 1987:

An amusing incident occurred in this year’s Armstrong Cup between W. Heidenfeld and N. Kerins. Heidenfeld first castled Kingside and then, in face of a strong attack, moved his King back to its original square and then inadvertently castled on the Queen’s side. The incident was unnoticed by both players: the game continued and Kerins went on to win. Wolfgang does not lose many games in Irish chess but he has probably created some sort of a record, in Ireland at least if not elsewhere, by castling on both sides and still losing a tournament game!

Via Edward Winter. Here’s the game.

| Entertainment · Oddities

Of Thee I Sing

https://commons.wikimedia.org/wiki/File:Set_partitions_4;_Hasse;_circles.svg
Image: Wikimedia Commons

A set of 4 elements can be partitioned in 15 ways.

Pleasingly, this is also the number of rhyme schemes that a 4-line poem can take: AAAA, AAAB, AABA, AABB, AABC, ABAA, ABAB, ABAC, ABBA, ABBB, ABBC, ABCA, ABCB, ABCC, ABCD.

A poem with 5 lines has 52 possible schemes, corresponding to the partitions of a 5-element set, and so on. These are called Bell numbers.

| Science & Math

Shell Attack

Freud observed that people who have much in common can still fight bitterly because they grow overly sensitive to the disagreements remaining between them. He called this the “narcissism of small differences”: “It is precisely the minor differences in people who are otherwise alike that form the basis of feelings of hostility between them.”

In Gulliver’s Travels, 11,000 people die in a war between the Big-endians, who break their eggs at the big end, and the Little-endians, who break them at the little end. A Lilliputian admiral attacks Gulliver because “he had good reasons to think you were a Big-endian in your heart; and, as treason begins in the heart, before it appears in overt acts, so he accused you as a traitor on that account, and therefore insisted you should be put to death.”

| Society

Around the Block

https://commons.wikimedia.org/wiki/File:Cube_divided_into_eight_sub-cubes.jpg

From Arthur Engel’s excellent Problem-Solving Strategies (1998):

On a cube, mark all the vertices and all the midpoints of the faces. Can an enterprising ant visit all these points by walking only along face diagonals and never retracing its steps?

Click for Answer
| Puzzles

Young and Old

For a 1752 essay, Samuel Johnson compiled these notes on how a man’s outlook changes as he grows older:

Hope predom. in youth. Mind not willingly indulges unpleasing thoughts. The world lies all enameld before him, as a distant prospect sun-gilt — inequalities only found by coming to it. Love is to be all joy — children excellent — Fame to be constant — caresses of the great — applauses of the learned — smiles of Beauty.

Fear of disgrace — Bashfulness — Finds things of less importance. Miscarriages forgot like excellencies; — if remembered, of no import. Danger of sinking into negligence of reputation. Lest the fear of disgrace destroy activity.

Confidence in himself. Long tract of life before him. — No thought of sickness. — Embarrasment of affairs. — Distraction of family. — Publick calamities. — No sense of the prevalence of bad habits. — Negligent of time — ready to undertake — careless to pursue — all changed by time.

Confident of others — unsuspecting as unexperienced — imagining himself secure against neglect, never imagines they will venture to treat him ill. Ready to trust; expecting to be trusted. Convinced by time of the selfishness, the meanness, the cowardice, the treachery of men.

“Such is the condition of life, that something is always wanting to happiness,” Johnson wrote in the finished essay. “In youth, we have warm hopes, which are soon blasted by rashness and negligence, and great designs, which are defeated by inexperience. In age, we have knowledge and prudence without spirit to exert, or motives to prompt them; we are able to plan schemes and regulate measures, but have not time remaining to bring them to completion.”

| Society

Small World

A puzzle from the 1975-1976 issue of Eureka, the journal of the Cambridge University Mathematical Society:

A jet fighter on the surface of the Earth is being chased by two identical fighters, all with ample fuel. Can the pursuers get within shooting range, no matter how they start out?

Click for Answer
| Puzzles