Young American

Thomas Jefferson received the following letter on July 31, 1806:

To his Excelency Thomas Jefferson Esq.

Sir.

It is A Boy of 15 years Old Address to You the following lines. I feel A Strong regard for my Country’s welfair.

I think if I had A been Presendent at the time them opposen Set of People (I allude to the Brittish) appeared before Newyork I Should A been for rasing all the Naval force in the United States and opposed thire proceeding’s. My Father is an Englishman Born. Ever Sence I had an knowledge of Nation affaires I dispised them tirents as there are. I often read of the American War. I fear they Never will Come hear Again. I think if they Should I take up armes boy as I am in my Country’s Defence. If every one was as true to thier Country as me I think the Contest last war would not of been of so long Duration. Conquer or Die is my Wash Word.

A True American though a Youth

Huza to the Constetuon
Huza to the Repubeck
Huza Fredom Independence
Huza to all America.
PS. Sir Excuse the spelling.

“Opus 34″

A magic square by Lee Sallows. The 16 pieces progress in area from 1 to 16, and those in each row, column, and long diagonal can be assembled to form the same target shape with area 34.

Science, Fiction

Inspired by Jules Verne’s Twenty Thousand Leagues Under the Sea, marine engineer Simon Lake devoted himself to making a working practical submarine. In 1898, when his company built the first sub to operate successfully in the open sea, Verne sent a congratulatory telegram:

WHILE MY BOOK ‘TWENTY THOUSAND LEAGUES UNDER THE SEA’ IS ENTIRELY A WORK OF IMAGINATION, MY CONVICTION IS THAT ALL I SAID IN IT WILL COME TO PASS. A THOUSAND MILE VOYAGE IN THE BALTIMORE SUBMARINE BOAT IS EVIDENCE OF THIS. THIS CONSPICUOUS SUCCESS OF SUBMARINE NAVIGATION IN THE UNITED STATES WILL PUSH ON UNDER-WATER NAVIGATION ALL OVER THE WORLD. IF SUCH A SUCCESSFUL TEST HAD COME A FEW MONTHS EARLIER IT MIGHT HAVE PLAYED A GREAT PART IN THE WAR JUST CLOSED. THE NEXT GREAT WAR MAY BE LARGELY A CONTEST BETWEEN SUBMARINE BOATS.

Bonus fact: The “20,000 leagues” in Verne’s title refers to the distance of the Nautilus’ voyage, not its depth. The sea is only about 2 miles deep; 20,000 leagues is nearly 70,000 miles.

In a Word

http://commons.wikimedia.org/wiki/File:Otterness_CR022.jpg

immiserization
n. the act of making or becoming progressively more miserable

luctiferous
adj. bringing sorrow, mournful, gloomy

The Road Coloring Problem

http://commons.wikimedia.org/wiki/File:Road_coloring_conjecture.svg

Every road in this little town is a one-way street, and each street is colored either red or blue. This has a helpful effect: If you start at any house in town and follow the sequence blue-red-red three times in a row, you’ll always arrive at the yellow house.

If you follow blue-blue-red three times, you’ll always arrive at the green one.

In 1970 Roy Adler and Benjamin Weiss asked whether it’s always possible to create such a coloring in a given network; in 2009 Avraham Trahtman proved that, within certain constraints, it is.

Carry On

Letter to the Times, Feb. 6, 1946:

Sir,

I have just written you a long letter.

On reading it over, I have thrown it into the waste paper basket.

Hoping this will meet with your approval,

I am, Sir,

Your obedient Servant,

A.D. Wintle

Passing Through

http://commons.wikimedia.org/wiki/File:Mystery_airship_SFCall_Nov_19_1896.jpg

November 1896 saw the start of a strange wave of airship sightings across the United States — the San Francisco Call published the image above on Nov. 19, claiming that the craft had passed over eastern Sacramento the previous night, where hundreds had seen “its brilliant searchlight traveling over the city, and who will also swear that they heard the voices of its occupants and distinguished their merry song and laughter.”

In the frenzy that followed, the San Francisco Chronicle published an interview with attorney George D. Collins, who claimed that he represented the airship’s inventor, a wealthy Maine man who had spent 17 years and $100,000 perfecting the craft. “The reports from Sacramento the other night were quite true. It was my client’s ship that inhabitants saw. It started from Oroville, in Butte County, and flew in a straight line for sixty miles directly over Sacramento. After running up and down once or twice over the capital, my friend came on a distance of another seventy miles and landed on a spot on the Oakland side of the bay, where the ship now lies guarded by six men. In another six days several defects will be done away with and it is then his intention to fly right over San Francisco.”

That never happened, and Collins was quickly forgotten, but it’s interesting to note that 10 years earlier, in 1886, inventor Moses Cole had patented a strikingly similar “new and improved aerial vessel” (below). “It consists of two semi-spheroidal balloons,” Scientific American had reported, “between which are situated the cabins for the passengers and crew, these being fitted with windows and surrounded by a circular balcony.” Possibly the Call’s artist had used Cole’s patent for inspiration. Or possibly Collins was telling the truth. Or possibly Martians had adopted Cole’s design as a disguise. We’ll never know.

http://commons.wikimedia.org/wiki/File:Cole_Air_Vessel_1897.jpg

See Just Visiting.

The Suicidal King

Imagine a 1000 x 1000 chessboard on which a white king and 499 black rooks are placed at random such that no rook threatens the king. And suppose the king goes bonkers and wants to kill himself. Can he reach a threatened square in a finite number of moves if Black is trying actively to avoid this?

Click for Answer

Cameo

http://commons.wikimedia.org/wiki/File:Gioacchino_Pagliei_-_The_Naiads,_1881.JPG

The last canto of Dante’s Purgatorio contains this perplexing sentence:

And if perchance
My saying, dark as Themis or as Sphinx,
Fail to persuade thee, (since like them it foils
The intellect with blindness) yet ere long
Events shall be the Naiads, that will solve
This knotty riddle, and no damage light
On flock or field.

When did water nymphs solve the riddle of the Sphinx? It turns out that Dante was relying on a flawed medieval edition of Ovid’s Metamorphoses that rendered Laïades (meaning Oedipus, the son of Laius) as Naïades, or naiads. He believed that water nymphs had ridden their sea monsters across the desert to solve the Sphinx’s riddle.

The version of the story that we know, in which Oedipus solves the riddle, comes from Sophocles’ Oedipus, which, being written in Greek, was unavailable to Dante. And he cast his own version in such exquisite language that it’s now immortal — one classic work misquoting another.

(Thanks, Jim.)

Pi Without Circles

The sum of the squares of the reciprocals of the positive integers is π2/6.

The sum of their fourth powers is π4/90.

The sum of their sixth powers is π6/945.

The area of the region under the Gaussian curve y = e-x2 is the square root of π.

The probability that two integers chosen at random will have no prime factor in common is 6/π2.

The integer 8 can be written as the sum of two squares of integers, m2 + n2, in four ways, when (m, n) is (2, 2), (2, -2), (-2, 2), or (-2, -2). The integer 7 can’t be written at all as the sum of such squares. Over a very large collection of integers from 1 to n, the average number of ways an integer can be written as the sum of two squares approaches π. Why?

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