More Fortuitous Numbers

Two years ago I wrote about the number 84,672, which has a surprising property: When its name is written out in (American) English (EIGHTY FOUR THOUSAND SIX HUNDRED SEVENTY TWO) and the letter counts of those words are multiplied together (6 × 4 × 8 × 3 × 7 × 7 × 3), they yield the original number (84,672).

Such numbers are called fortuitous, and, not surprisingly, very few of them are known. When I wrote about them in 2019, the whole list ran 4, 24, 84672, 1852200, 829785600, 20910597120, 92215733299200. Now Jonathan Pappas has discovered two more:

1,239,789,303,244,800,000

ONE QUINTILLION TWO HUNDRED THIRTY NINE QUADRILLION SEVEN HUNDRED EIGHTY NINE TRILLION THREE HUNDRED THREE BILLION TWO HUNDRED FORTY FOUR MILLION EIGHT HUNDRED THOUSAND

3 × 11 × 3 × 7 × 6 × 4 × 11 × 5 × 7 × 6 × 4 × 8 × 5 × 7 × 5 × 7 × 3 × 7 × 5 × 4 × 7 × 5 × 7 × 8 = 1,239,789,303,244,800,000

887,165,996,513,213,819,259,682,435,576,627,200,000,000

EIGHT HUNDRED EIGHTY SEVEN DUODECILLION ONE HUNDRED SIXTY FIVE UNDECILLION NINE HUNDRED NINETY SIX DECILLION FIVE HUNDRED THIRTEEN NONILLION TWO HUNDRED THIRTEEN OCTILLION EIGHT HUNDRED NINETEEN SEPTILLION TWO HUNDRED FIFTY NINE SEXTILLION SIX HUNDRED EIGHTY TWO QUINTILLION FOUR HUNDRED THIRTY FIVE QUADRILLION FIVE HUNDRED SEVENTY SIX TRILLION SIX HUNDRED TWENTY SEVEN BILLION TWO HUNDRED MILLION

5 × 7 × 6 × 5 × 12 × 3 × 7 × 5 × 4 × 11 × 4 × 7 × 6 × 3 × 9 × 4 × 7 × 8 × 9 × 3 × 7 × 8 × 9 × 5 × 7 × 8 × 10 × 3 × 7 × 5 × 4 × 10 × 3 × 7 × 6 × 3 × 11 × 4 × 7 × 6 × 4 × 11 4 × 7 × 7 × 3 × 8 × 3 × 7 × 6 × 5 × 7 × 3 × 7 × 7 = 887,165,996,513,213,819,259,682,435,576,627,200,000,000

A 10th solution, if one exists, will be greater than 10138.

Details are here. Jonathan has also discovered some cyclic solutions (ONE HUNDRED SIXTY EIGHT -> FIVE HUNDRED TWENTY FIVE -> SIX HUNDRED SEVENTY TWO -> FOUR HUNDRED FORTY ONE -> FOUR HUNDRED TWENTY -> ONE HUNDRED SIXTY EIGHT) and the remarkable 195954154450774917120 -> 195954154450774917120000 -> 1959541544507749171200000.

(Thanks, Jonathan.)

Direction

Ancient Egypt was an essentially one-dimensional country strung out along the Nile, which flows from south to north. The winds were conveniently arranged to be predominantly northerly. To go north, a traveler could let his boat drift, while with a sail he could move south against the slow current. For this reason, in the writing of the ancient Egyptians, ‘go downstream (north)’ was represented by a boat without sails, and ‘go upstream (south)’ by a boat with sails. The words (and concepts) or north-south and up-downstream became merged. Since the Nile and its tributaries were the only rivers known to the ancient Egyptians, this caused no difficulties until they reached the Euphrates, which happened to flow from north to south. The resulting confusion in the ancient Egyptian mind is recorded for us to read today in their reference to ‘that inverted water which goes downstream (north) in going upstream (south).’

— P.L. Csonka, “Advanced Effects in Particle Physics,” Physical Review, April 1969, 1266-1281

Podcast Episode 335: Transporting Obelisks

https://commons.wikimedia.org/wiki/File:Cleopatra%27s_needle_being_brought_to_England,_1877_RMG_BHC0641.tiff

In the 19th century, France, England, and the United States each set out to bring home an Egyptian obelisk. But each obelisk weighed hundreds of tons, and the techniques of moving them had long been forgotten. In this week’s episode of the Futility Closet podcast we’ll follow the struggles of each nation to transport these massive monoliths using the technology of the 1800s.

We’ll also go on an Australian quest and puzzle over a cooling fire.

See full show notes …

Podcast Episode 334: Eugene Bullard

https://commons.wikimedia.org/wiki/File:Eugene_Bullard_in_Legionnaire_Uniform.jpg

Eugene Bullard ran away from home in 1907 to seek his fortune in a more racially accepting Europe. There he led a life of staggering accomplishment, becoming by turns a prizefighter, a combat pilot, a nightclub impresario, and a spy. In this week’s episode of the Futility Closet podcast we’ll tell Bullard’s impressive story, which won him resounding praise in his adopted France.

We’ll also accidentally go to Canada and puzzle over a deadly omission.

See full show notes …

Recall

http://en.wikipedia.org/wiki/File:Pillsbury2.jpg

Memory feats of chess master Harry Nelson Pillsbury:

  • On April 28, 1900, he played 20 opponents blindfold (sitting alone in a room without board or pieces while the moves were announced to him), playing 600 moves in six and a half hours. Afterward he corrected several mistakes that his opponents had made in recording their moves. Two opponents had not kept a record at all, but Pillsbury gave the moves of those games “without any serious effort.”
  • In tour spanning 1900 and 1901, he gave about 150 simultaneous displays, many blindfold. In one 16-game blindfold exhibition in Buffalo, in which he won 84.4 percent of the games, he correctly announced mate in eight in one of the games.
  • In Toledo, Ohio, he simultaneously played 12 games of chess and four games of checkers without sight of any board, while at the same time playing duplicate whist with other people.
  • He was prepared to interrupt a blindfold display at any point, have a portion of a deck of cards read out to him, name all the remaining cards, and then resume play.
  • Before one blindfold display in Philadelphia he studied a list of 29 unfamiliar words and phrases; after the exhibition and again the next day he recited the list, first forward and then backward.
  • Two and a half hours into one 12-board blindfold display he suggested a rest for the players. During this time he invited them as a group to compose a numbered list of 30 words and to read them to him. He was then asked, in jumbled fashion, to give the number of a given word or the word of a given number. All his responses were correct. Afterward he recited the whole list backward and then resumed the blindfold display.

“Philadelphia master and organizer William Ruth told Dale Brandreth that he once sat with Pillsbury at a railroad crossing and wrote down the fairly long and different numbers on each of a large group of passing boxcars while Pillsbury attempted to memorize them. Ruth reported to Brandreth that Pillsbury’s memory for the numbers was incredibly accurate and in the correct order.”

(Eliot Hearst and John Knott, Blindfold Chess: History, Psychology, Techniques, Champions, World Records, and Important Games, 2009.)

“A Bully Is Always a Coward”

English proverbs:

  • Give neither counsel nor salt till you are asked for it.
  • A hedge between keeps friendship green.
  • A fault confessed is half redressed.
  • A hungry man is an angry man.
  • Please your eye and plague your heart.
  • If you run after two hares you will catch neither.
  • A good lawyer makes a bad neighbor.
  • Speak fair and think what you will.
  • It is not the suffering but the cause which makes a martyr.
  • A fool will laugh when he is drowning.
  • A foe is better than a dissembling friend.
  • A disease known is half cured.
  • Let your purse be your master.
  • Short counsel is good counsel.

And “Whosoever draws his sword against the prince must throw the scabbard away.”

Back and Forth

In the autumn of 1947, Oxford mathematician John Henry Whitehead became fascinated with palindromes. He came up with STEP ON NO PETS but felt this could be surpassed. He put the problem to research student Peter Hilton, who suggested SEX AT NOON TAXES. Whitehead liked this but still felt that a longer sensible palindrome must be possible.

So Hilton spent an entire night working on the problem, writing nothing down, just lying in the dark. By morning he had:

DOC, NOTE, I DISSENT. A FAST NEVER PREVENTS A FATNESS. I DIET ON COD.

“Henry was delighted, and spread the word about my palindrome far and wide,” Hilton wrote later. Among those who heard about it were their former colleagues at Bletchley Park, where Whitehead and Hilton had helped to decrypt German ciphers during the war, and from there Hilton’s composition found its way into The Codebreakers, F.H. Hinsley and Alan Stripp’s account of that effort.

Robert Harris quoted the palindrome in his review of that book, “to indicate what sort of people the codebreakers were,” Hilton wrote. “But he also quoted the remark, attributed to Churchill, on the priority to be given to recruiting suitable people for this work: ‘When I told them to leave no stone unturned, I did not intend to be taken so literally.'”

(“Miscellanea,” College Mathematics Journal 30:5 [November 1999], 422-424.)

One World

In 1922, Baltic German teacher and linguist Edgar de Wahl offered a new language to facilitate communication between people from different nations. He called it Occidental, and designed it so that many of its words will be recognizable by those who already know a Romance language:

Li material civilisation, li scientie, e mem li arte unifica se plu e plu. Li cultivat europano senti se quasi in hem in omni landes queles have europan civilisation, it es, plu e plu, in li tot munde. Hodie presc omni states guerrea per li sam armes. Sin cessa li medies de intercomunication ameliora se, e in consequentie de to li terra sembla diminuer se. Un Parisano es nu plu proxim a un angleso o a un germano quam il esset ante cent annus a un paisano frances.

“Material civilization, science, and even art unify themselves more and more. The educated European feels himself almost at home in all lands that have European civilization, that is, more and more, in the entire world. Today almost all states war with the same armaments. Without pause the modes of intercommunication improve, and in consequence from that the world seems to decrease. A Parisian is now closer to an Englishman or a German than he was a hundred years before to a French peasant.”

It gained a small community of speakers in the 1920s and 1930s and had largely died out by the 1980s — but in recent years it’s seen a resurgence on the Internet as Interlingue.

Podcast Episode 331: The Starvation Doctor

https://commons.wikimedia.org/wiki/File:Linda_Burfield_Hazzard,_FS,_DO.png

In 1911 English sisters Claire and Dora Williamson began consulting a Seattle “fasting specialist” named Linda Burfield Hazzard. As they underwent her brutal treatments, the sisters found themselves caught in a web of manipulation and deceit. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Williamsons’ ordeal and the scheme it brought to light.

We’ll also catch a criminal by the ear and puzzle over a prohibited pig.

See full show notes …