Computer science legend Donald Knuth offered this puzzle at the 29th International Puzzle Party in San Francisco in August 2009. It’s a partially completed Latin square: The challenge is to place letters in the remaining cells so that each row and column contains the same five letters and in the bottom row these spell a common English word. The solution is unique.
Draw a triangle and color its vertices red, green, and blue. Then divide it into as many smaller triangles as you like (the smaller triangles must meet edge to edge and vertex to vertex). Now color the vertices of these smaller triangles using the same three colors. You can do this however you like, with one proviso: The vertices that lie on a side of the large triangle must take the color of either of its ends (so, for instance, the point at the bottom center of the triangle above must be colored either green or blue, not red).
No matter how this is done, there will always exist a small triangle with vertices of three colors. In fact, there will always be an odd number of such triangles.
“Every honest researcher I know admits he’s just a professional amateur. He’s doing whatever he’s doing for the first time. That makes him an amateur. He has enough sense to know that he’s going to have a lot of trouble, so that makes him a professional.” — Charles F. Kettering
Thomas Edison proposed to his second wife, Mina, in Morse code.
“My later courtship was carried on by telegraph,” he wrote in his diary. “I taught the lady of my heart the Morse code, and when she could both send and receive we got along much better than we could have with spoken words by tapping out our remarks to one another on our hands. Presently I asked her thus, in Morse code, if she would marry me. The word ‘Yes’ is an easy one to send by telegraphic signals, and she sent it. If she had been obliged to speak of it, she might have found it harder.”
After the Battle of Gettysburg, a dead Union soldier was found near the center of town. He bore no identification, but in his hands he held a photograph of three children. In this week’s episode of the Futility Closet podcast we’ll follow the efforts of one Philadelphia physician to track down the lost man’s family using only the image of his children.
We’ll also sample a 9-year-old’s comedy of manners and puzzle over a letter that copies itself.
German scientist Otto von Guericke conducted a memorable experiment on May 8, 1654: He connected two hemispheres, sealed their rims together, and drew out the air between them using a pump of his own devising. The resulting vacuum was so strong that 30 horses could not pull them apart.
At the time the experiment was seen as a strike against Aristotle’s dictum that nature abhors a vacuum. It’s repeated today as a dramatic demonstration of the power of atmospheric pressure.
In the early 1970s, Alan Berry and Ronald Morehead visited the Sierra Nevada of eastern California and emerged with “the Sierra Sounds recordings,” 90 minutes of vocalizations and wood knockings that they attributed to Bigfoot. In studying these and other recordings, “Bigfoot language expert” R. Scott Nelson has devised a Sasquatch Phonetic Alphabet to record the utterances:
0:4.5 (W) (W)
0:8.62 (W) (W) (W)
0:15.11 RAM HO BÄ RÜ KHÄ HÜ
0:16.70 WAM VO HÜ KHÖ KHU’
0:17.52 NÖ U PLÄ MEN TI KHU
0:18.82 NÄR LÄ
0:20.21 NA GÖ KÜ STEP GÄ KÜ BLEM
0:21.25 Ü KÜ DZJÄ
0:21.76 FRrÄP E KHÜK LE
(A fuller transcription, and Nelson’s notating conventions, are here.)
What should we make of this? Nelson claims that “the creatures mentally process information at a much higher rate than humans do, or at least they are able to communicate their ideas much faster,” which makes their speech impossible for humans to understand, but “we have verified that these creatures use language, by the human definition of it.”
“No, we haven’t,” answers linguist Karen Stollznow in Language Myths, Mysteries and Magic (2014). “Before creating a transcription of this ‘Bigfoot language’, Nelson first needed to demonstrate that this is language. He has tried to authenticate the recordings, rather than analyze them in an unbiased way. Unknown sounds don’t immediately qualify as ‘language’, any more than an Unidentified Flying Object must be extraterrestrial.”
“There is no solid physical evidence to support the existence of Bigfoot. Before we establish the existence of Bigfoot language, we need to establish the existence of Bigfoot.”
Advertisements in the Sing Sing inmate newspaper Star of Hope, May 19, 1900:
WANTED — A home-like home. Present one, not what it is cracked up to be. Address Clinton 4,320.
WANTED — A good night’s rest. Gallery shouters and instrumentalists take note. Nemo, Star Office.
WANTED — An eraser, (must be mighty sharp) to blot out the past. A stock of experience, (fringed and threadbare) given in exchange. For particulars, Auburn 20,101.
WANTED — That rara avis, the con who does not think he is better able to manage the Star than the present Editor. Applications solicited by Sing Sing 51,094.
WANTED — A few blank pages in the Book of Life, wherein we desire to make some new entries — on the Cr. side. Address Summa Summarum, New York State Prisons.
WANTED — Immediately — an Opportunity. Price no object if goods are fair and in good working order. Anxious, Clinton 4,298.
WANTED — Anno Domini 1902. Will give in exchange one and a quarter yards of warranted genuine, homemade Spring po’ms — just too lovely for every day wear. Samantha, Auburn 595 (W. P.)
LOST — Five days’ ‘short time.’ Finder can have same by arranging with the Powers That Be. Address Nostalgic, Auburn 20,210.
(From Karel Weiss, The Prison Experience, 1976.)
Princeton scholar Thomas P. Roche Jr. calls this “an astounding piece of ingenuity,” one of “the most elaborately numerological poems I have found in the Renaissance.” Poet Henry Lok created it in 1597, in honor of Elizabeth I. It can be read as a conventional 10-line poem, but there are fully eight other ways to read it:
“1. A Saint George’s crosse [+] of two collumbs, in discription of her Maiestie, beginning at A, and B, in the middle to be read downward, and crossing at C and D to be read either singly or double.”
Rare Queen, fair, mild, wise
Shows you proof
For heavens have upheld
Just world’s praise sure.
Here Grace in that Prince
Of earth’s race, who
There shields thus God
Whom choice (rich Isle, stay!) builds.
“2. A S[aint] Andrew’s crosse [X], beginning at E and read thwartwaies, and ending with F, containing the description of our happie age, by her highnesse.”
God crowned this time, wise choice of all the Rest,
And so truth, joy of just kings’ known, God blest.
“3. Two Pillars in the right and left side of the square, in verse reaching from E and F perpenddicularly, containing the sum of the whole, the latter columbe hauing the words placed counterchangeably to rime to the whole square.”
God makes kings rule for heauens; your state hold blest
And still stand will their shields; fear yields best rest.
“4. The first and last two verses or the third and fourth, with seuenth and eighth, are sense in them selues, containing also sense of the whole.”
“5. The whole square of 100, containing in it self fiue squares, the angles of each of them are sense particularly, and vnited depend each on other, beginning at the center.”
1 Just, wise of choice
2 Joy of kings’ time
3 This truth all known
4 So crowned the God
5 Blessed God and rest.
“6. The out-angles are to be read 8 seuerall waies in sense and verse.”
“7. The eight words placed also in the ends of the St. George’s crosse, are sense and verse, alluding to the whole crosse.”
Rare grace here builds
There shields for heaven.
Rare Grace there shields
For heaven here builds.
“8. The two third words in the bend dexeter of the St. Andrew’s crosse, being the middle from the angles to the center, haue in their first letters T. and A. for the Author, and H.L. in their second, for his name, which to be true, the words of the angles in that square confirme.”
THis ALl
T[he]H[enry]is A[uthor]L[ok]l
“9. The direction to her Maiestie in prose aboue, containeth onely of numerall letters, the yeare and day of the composition, as thus, DD. C. LL. LL. LL. LL. VV. VV. VV. IIIIIIIIIIIII. For, 1593. June V.”
The whole square is intended to demonstrate the powers of language to accommodate the queen’s praises in God’s providential order. Further, the arrangement of the words forms a comment on the political situation at the time: St. George is the patron saint of England, St. Andrew is the patron saint of Scotland, and the pillars may represent Elizabeth’s chosen emblem, the Pillars of Hercules. “The fact that the words of the square can be forced to yield meaning within the imposed specifications is amazing in itself.”
(Thomas P. Roche Jr., Petrarch and the English Sonnet Sequences, 1989.)
synodite
n. a traveling companion
dépaysé
adj. removed from one’s usual surroundings
credenda
n. things to be believed; matters of faith
David Livingstone reaches the Atlantic, May 31, 1854:
The plains adjacent to Loanda are somewhat elevated and comparatively sterile. On coming across these we first beheld the sea: my companions looked upon the boundless ocean with awe. On describing their feelings afterwards, they remarked that ‘we marched along with our father, believing that what the ancients had always told us was true, that the world has no end; but all at once the world said to us, “I am finished; there is no more of me!”‘ They had always imagined that the world was one extended plain without limit.
(From his Missionary Travels and Researches in South Africa, 1857.)
