Blades of Glory

I don’t know why this never caught on — in 1959 Klara Karwowska invented little windshield wipers for eyeglasses:

The present invention is directed to a wiper means for maintaining the lenses clean or clear of steam, rain, snow, or other foreign matter, and the wiper mechanism of the present invention includes a source of electrical energy such as the battery which may be secured to the frame in any suitable manner.

The battery would make them a little bulky, but that’s a small price to pay for clear vision. I could wear these in the shower!

In a Word

n. cessation of labor

v. to extend hospitality to

adj. disposed to follow a leader

adj. brought back to one’s senses

I spent an evening at the house of the president of Harvard University. The party was waited on at tea by a domestic of the president’s, who is also Major of the Horse. On cavalry days, when guests are invited to dine with the regiment, the major, in his regimentals, takes the head of the table, and has the president on his right hand. He plays the host as freely as if no other relation existed between them. The toasts being all transacted, he goes home, doffs his regimentals, and waits on the president’s guests at tea.

— Harriet Martineau, Society in America, 1837


In 1960, British researcher Donald Michie combined his loves of computation and biology to consider whether a machine might learn — whether by consulting its record of past experience it could perform tasks with progressively greater success.

To investigate this he designed a machine to play noughts and crosses (or tic-tac-toe). He called it the Machine Educable Noughts And Crosses Engine, which gives it the pleasingly intimidating acronym MENACE. MENACE consists of 304 matchboxes, each of which represents a board position. Each box contains a collection of beads representing available moves in that position, and after each game these collections are adjusted in light of the outcome (as described here). In this way the engine learns from its experience — over time it becomes less likely to play losing moves, and more likely to play winning (or drawing) ones, and it becomes a more successful player as a result.

University College London mathematician Matthew Scroggs describes the engine above, and he’s built an online version that you can try out for yourself — it really does get noticeably better as it plays.

Near and Far

Designed by Baroque architect Francesco Borromini in 1632, this gallery in Rome’s Palazzo Spada is a masterpiece of forced perspective — though it appears to be 37 meters long, in fact it’s only 8. The effect is produced by diminishing columns and a rising floor; the sculpture at the end, which Borromini contrived to appear life size, is only 60 centimeters high.
Image: Wikimedia Commons


A famous artist once painted an angel with six toes.

‘Who ever saw an angel with six toes?’ people inquired.

‘Who ever saw one with less?’ was the counter-question.

Life, June 12, 1890

That Settles That

The famous mathematician Stanislaw Ulam thought of the following paradox, which is now known as the Ulam Paradox: When President Richard Nixon was appointed to office, on the first day he met his cabinet he said to them: ‘None of you are yes-men, are you?’ And they all said, ‘NO!’

— Raymond Smullyan, A Mixed Bag, 2016

The Grapevine

A problem from the British Columbia Colleges Senior High School Mathematics Contest, 2000:

Not all of the nine members on the student council are on speaking terms. This table shows their relationships — 1 means two members are speaking to each other, and 0 means they’re not:

  A B C D E F G H I
A - 0 0 1 0 0 1 0 0
B 0 - 1 1 1 1 1 1 1
C 0 1 - 0 0 0 1 1 0
D 1 1 0 - 1 0 1 0 1
E 0 1 0 1 - 0 1 0 0
F 0 1 0 0 0 - 0 0 1
G 1 1 1 1 1 0 - 0 0
H 0 1 1 0 0 0 0 - 0
I 0 1 0 1 0 1 0 0 -

Recently councilor A started a rumor, and it was heard by each councilor once and only once. Each councilor heard it from, and passed it to, another councilor with whom she was on speaking terms. If we count councilor A as zero, then councilor E was the eighth and last councilor to hear the rumor. Who was the fourth?

Click for Answer

An Orderly Alphabet
Image: Wikimedia Commons

In the early days of typewriting, this was usually the first thing typed on each new typewriter after it rolled off the production line:

Amaranath sasesusos Oronoco initiation secedes Uruguay Philadelphia

A worker known as an aligner typed it to check that the resulting letters were aligned correctly on the platen.

How does it work? ‘Amaranath,’ the misspelled name of an imaginary flower, checks the alignment of the vowel ‘a’ between a number of common consonants. ‘Oronoco’ checks the ‘o’ key, while ‘secedes,’ ‘initiation’ and ‘Uruguay’ check three vowels that are among the most commonly used of all letters, ‘e,’ ‘i,’ and ‘u.’ ‘Sasesusos’ not only compares four of the five vowels in the same word against the baseline of the letter ‘s,’ but also ‘includes several of the most common letter combinations in twentieth-century business English.’ ‘Philadelphia’ checks the horizontal alignment of ‘i’ and ‘l,’ the narrowest letters on the keyboard.

What does “Amaranath sasesusos Oronoco initiation secedes Uruguay Philadelphia” actually mean? “Unlike most sentences, it was rarely spoken, and no one particularly cared what it might mean in the conventional sense.” (The “quick brown fox” came later.)

(From Darren Wershler-Henry, The Iron Whim, 2005.)

Character Building

“It is astonishing the influence foolish apothegms have upon the mass of mankind, though they are not unfrequently fallacies,” wrote Sydney Smith. He used to amuse himself by collecting them; the first was Because I have gone through it, my son shall go through it also:

A man gets well pummelled at a public school; is subject to every misery and every indignity which seventeen years of age can inflict upon nine and ten; has his eye nearly knocked out, and his clothes stolen and cut to pieces; and twenty years afterwards, when he is a chrysalis, and has forgotten the miseries of his grub state, is determined to act a manly part in life, and says, ‘I passed through all that myself, and I am determined my son shall pass through it as I have done;’ and away goes his bleating progeny to the tyranny and servitude of the long chamber or the large dormitory. It would surely be much more rational to say, ‘Because I have passed through it, I am determined my son shall not pass through it; because I was kicked for nothing, and cuffed for nothing, and fagged for everything, I will spare all these miseries to my child.’ It is not for any good which may be derived from this rough usage; that has not been weighed and considered; few persons are capable of weighing its effects upon character; but there is a sort of compensatory and consolatory notion, that the present generation (whether useful or not, no matter) are not to come off scot-free, but are to have their share of ill-usage; as if the black eye and bloody nose which Master John Jackson received in 1800, are less black and bloody by the application of similar violence to similar parts of Master Thomas Jackson, the son, in 1830. This is not only sad nonsense, but cruel nonsense. The only use to be derived from the recollection of what we have suffered in youth, is a fixed determination to screen those we educate from every evil and inconvenience, from subjection to which there are not cogent reasons for submitting. Can anything be more stupid and preposterous than this concealed revenge upon the rising generation, and latent envy lest they should avail themselves of the improvements time has made, and pass a happier youth than their fathers have done?

(From his memoir.)