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Advance Notice

In his 1966 book New Mathematical Diversions From Scientific American, Martin Gardner predicted that the millionth digit of π would be 5. (At the time the value was known only to about 10,000 decimal places.) He was reprinting a column on π from 1960 and included this in the addendum:

It will probably not be long until pi is known to a million decimals. In anticipation of this, Dr. Matrix, the famous numerologist, has sent me a letter asking that I put on record his prediction that the millionth digit of pi will be found to be 5. His calculation is based on the third book of the King James Bible, chapter 14, verse 16 (it mentions the number 7, and the seventh word has five letters), combined with some obscure calculation involving Euler’s constant and the transcendental number e.

He’d intended this as a hoax, but eight years later the computers discovered he was right.

| Science & Math

The Smithy Code

In deciding a plagiarism case against author Dan Brown in 2006, British justice Peter Smith handed down a peculiar judgment: Certain letters in the text had been italicized with no explanation. Apparently inspired by Brown’s book The Da Vinci Code, Smith had hidden a message in the text.

The judgment included the sentence “The key to solving the conundrum posed by this judgment is in reading HBHG and DVC.” In context, those abbreviations refer to The Holy Blood and the Holy Grail, the book that Brown had been accused of plagiarizing, and The Da Vinci Code.

“I can’t discuss the judgement, but I don’t see why a judgement should not be a matter of fun,” Smith had said in handing down the opinion, which found Brown not guilty. He promised to confirm any correct solution.

He offered enough hints to reporters that Guardian media journalist Daniel Tench eventually solved it: It was a polyalphabetic cipher using a keyword based on the Fibonacci sequence, yielding the plaintext “Jackie Fisher who are you? Dreadnought.” Jackie Fisher was a British admiral whom Smith admired. (The code is described here; Tench describes the solving here.)

The Court of Appeal later said that Smith “was prompted by the extensive use in [The Da Vinci Code] of codes, and no doubt by his own interest in such things, to incorporate a coded message in his judgment, on which nothing turns. The judgment is not easy to read or to understand. It might have been preferable for him to have allowed himself more time for the preparation, checking and revision of the judgment.”

| Puzzles

Dear Sirs

Here’s a letter that might have been received by the Restormel County Council. What’s unusual about it?

Dear Sirs:

I shed no tears to learn that the hill in Mansion Road, close to most locals’ homesteads, is at last considered at least a minor threat to residents in the area. At times in the cold season the ice created on this road is a colossal attraction to the local children. Some slither and slide on the ice on sleds, tin sheets, etc, to their hearts’ content, and create concerns to motorists, and others in the area, in the colder months. It is nice to see that this matter is at last in hand, to note its consideration as an essential element in Restormel’s schemes to decrease the district’s road accidents.

A Contented Resident.

Click for Answer
| Language

A Planned And

Martin Gardner offered this curiosity in the August 1998 issue of Word Ways: Roll two six-sided dice. If they show a total of 6 or 8, roll them again. Otherwise, go to the chapter of Genesis (the King James version) that corresponds to the total on the dice. Now turn both dice upside down and go to the verse whose number is now displayed. The first word of that verse will always be And.

(Martin Gardner, “Mysterious Precognitions,” Word Ways 31:3 [August 1998], 175-177.)

| Literature · Oddities

Pangrammatic Loops

A marvelous variation on self-inventorying lists, from the inimitable Lee Sallows:

Recalling that a self-enumerating pangram corresponds to a closed loop of length 1, here follows a loop of length 2, which is to say, a pair of pangrams that enumerate each other. The pangrams are both minimal in the sense of containing none but essential letters with no “and”s or other devices openly or surreptitously added.

ONE A, ONE B, ONE C, ONE D, THIRTYONE E, FOUR F, ONE G, FIVE H, FIVE I, ONE J, ONE K, ONE L, ONE M, TWENTYTWO N, SEVENTEEN O, ONE P, ONE Q, SEVEN R, FOUR S, ELEVEN T, THREE U, FIVE V, FOUR W, ONE X, THREE Y, ONE Z.

ONE A, ONE B, ONE C, ONE D, THIRTYTWO E, SEVEN F, ONE G, FOUR H, FIVE I, ONE J, ONE K, TWO L, ONE M, TWENTY N, NINETEEN O, ONE P, ONE Q, SEVEN R, THREE S, NINE T, FOUR U, SEVEN V, THREE W, ONE X, THREE Y, ONE Z.

An alternative (non-minimal) pair includes plural s’s:

ONE A, ONE B, ONE C, ONE D, TWENTYSEVEN E’S, SIX F’S, ONE G, THREE H’S, SIX I’S, ONE L, TWENTY N’S, SIXTEEN O’S, ONE P, ONE Q, SIX R’S, NINETEEN S’S, TWELVE T’S, FOUR U’S, FOUR V’S, FIVE W’S, THREE X’S, FOUR Y’S, ONE Z.

ONE A, ONE B, ONE C, ONE D, TWENTYNINE E’S, FIVE F’S, ONE G, THREE H’S, SEVEN I’S, ONE J, ONE K, TWO L’S, ONE M, TWENTY N’S, SIXTEEN O’S, ONE P, ONE Q, SIX R’S, TWENTY S’S, TEN T’S, FOUR U’S, THREE V’S, FOUR W’S, FIVE X’S, THREE Y’S, ONE Z.

In similar vein, pangrammatic loops of length 3 follow, but now in shorthand, using arabic numerals to stand for number words, i.e. 1 = one, 2 = two, etc. The first list is enumerated by the second, the second by the third and the third by the first. The 1st loop contains minimal pangrams, the 2nd, pangrams with plural s’s:

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z
1  1  1  1 31  5  1  5  9  1  1  1  1 20 16  1  1  5  5 11  1  4  3  4  2  1
1  1  1  1 28  7  1  3  8  1  1  2  1 20 18  1  1  5  2  8  3  6  3  2  3  1
1  1  1  1 31  2  5  9  7  1  1  1  1 16 15  1  1  5  3 16  1  3  6  2  3  1

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z
1  1  1  1 32  5  2  3  7  1  1  1  1 22 18  1  1  3 19 14  2  6  7  2  3  1
1  1  1  1 32  3  2  6  6  1  1  1  1 20 18  1  1  6 19 16  2  4  7  2  3  1
1  1  1  1 27  2  2  5  8  1  1  1  1 19 17  1  1  5 21 14  2  2  6  5  3  1

Here also a minimal pangrammatic loop of length 4 (no equivalent using plural s’s exists):

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z
1  1  1  1 25  4  2  4  7  1  1  2  1 16 18  1  1  5  5 11  3  4  5  4  2  1
1  1  1  1 28  9  2  3  7  1  1  2  1 16 18  1  1  6  3  9  5  7  5  2  2  1
1  1  1  1 30  3  3  5  9  1  1  1  1 20 15  1  1  3  5 12  1  5  6  3  2  1
1  1  1  1 30  6  1  6  8  1  1  2  1 17 14  1  1  6  2 12  1  5  4  2  3  1

“There exist no minimal pangrammatic loops of length 5 or longer until we reach lengths 10, 33, and 55 (no plural s’s) and lengths 15, 22, 23, 207 and 312 (with plural s’s),” he adds. “This completes what I believe to be an exhaustive survey of all self-enumerating minimal pangrammatic loops.”

(Thanks, Lee.)

| Language · Science & Math

Podcast Episode 276: An Unlikely Confederate Spy

https://commons.wikimedia.org/wiki/File:Rose_O%27Neal_Greenhow.jpg

As the Civil War fractured Washington D.C., socialite Rose O’Neal Greenhow coordinated a vital spy ring to funnel information to the Confederates. In this week’s episode of the Futility Closet podcast we’ll describe one of the war’s most unlikely spies, and her determination to aid the South.

We’ll also fragment the queen’s birthday and puzzle over a paid game of pinball.

See full show notes …

| History · Podcast

First Friends

In 1978, archaeologists excavating a late Paleolithic tomb in northern Israel uncovered the skeletons of an elderly human and a 5-month-old puppy. They had lain there together for 12,000 years.

“The most striking thing about these remains was the fact that whoever presided over the original burial had carefully arranged the dead person’s left hand so that it rested, in a timeless and eloquent gesture of attachment, on the puppy’s shoulder,” writes James Serpell in In the Company of Animals (1996).

“The contents of this tomb not only provide us with some of the earliest solid evidence of animal domestication, they also strongly imply that man’s primordial relationship with this particular species was an affectionate one. In other words, prehistoric man may have loved his dogs and his other domestic animals as pets long before he made use of them for any other purpose.”

(Simon J.M. Davis and François R. Valla, “Evidence for Domestication of the Dog 12,000 Years Ago in the Natufian of Israel,” Nature 276:5688 [1978], 608.)

| Science & Math

Books

fc books

Just a reminder — Futility Closet books make great gifts for people who are impossible to buy gifts for. Both contain hundreds of hand-picked favorites from our archive of curiosities. Some reviews:

“A wild, wonderful, and educational romp through history, science, zany patents, math puzzles, wonderful words (like boanthropy, hallelujatic, and andabatarian), the Devil’s Game, self-contradicting words, and so much more. Buy this book and feed your mind!” — Clifford A. Pickover, author of The Mathematics Devotional

“Futility Closet delivers concentrated doses of weird, wonderful, brain-stimulating ideas and anecdotes, curated mainly from forgotten old books. I’m hooked — there’s nothing quite like it!” — Mark Frauenfelder, founder, Boing Boing

“Meant to be read in pieces, but impossible to put down.” — Gary Antonick, editor, New York Times Numberplay blog

“Futility Closet is a dusty museum back room where one can spend minutes or hours among seldom-seen curiosities, and feel that none of the time was wasted.” — Alan Bellows, DamnInteresting.com

Both books are available now on Amazon. Thanks for your support!

| Uncategorized