How many people are in this group?
“Immune”
There is, in fact, nothing about religious opinions that entitles them to any more respect than other opinions get. On the contrary, they tend to be noticeably silly. If you doubt it, then ask any pious fellow of your acquaintance to put what he believes into the form of an affidavit, and see how it reads. … ‘I, John Doe, being duly sworn, do say that I believe that, at death, I shall turn into a vertebrate without substance, having neither weight, extent or mass, but with all the intellectual powers and bodily sensations of an ordinary mammal; … and that, for the high crime and misdemeanor of having kissed my sister-in-law behind the door, with evil intent, I shall be boiled in molten sulphur for one billion calendar years.’ Or, ‘I, Mary Roe, having the fear of Hell before me, do solemnly affirm and declare that I believe it was right, just, lawful and decent for the Lord God Jehovah, seeing certain little children of Beth-el laugh at Elisha’s bald head, to send a she-bear from the wood, and to instruct, incite, induce and command it to tear forty-two of them to pieces.’ Or, ‘I, the Right Rev. ————-, Bishop of ————, D.D., LL.D., do honestly, faithfully and on my honor as a man and a priest, declare that I believe that Jonah swallowed the whale,’ or vice versa, as the case may be.
— H.L. Mencken, American Mercury, March 1930
Good Works
“Pins have been the means of saving many lives, through people not swallowing them.” — Theo Johnson, Personal Recollections of the Zoo, 1891
Parfit’s Hitchhiker
Suppose that I am driving at midnight through some desert. My car breaks down. You are a stranger, and the only other driver in this desert. I manage to stop you, and I offer you a great reward if you drive me to my home. I cannot pay you now, but I promise to do so when we reach my home. … If you drive me to my home, it would be worse for me if I pay you the promised reward. Since I know that I never do what will be worse for me, I know that I would break my promise. Given my inability to lie convincingly, you know this too. You do not believe my promise. I am stranded in the desert throughout the night.
— Derek Parfit, Reasons and Persons, 1984
The Tonnetz
In 1739, Leonhard Euler devised a “tone net” to represent graphically the traditional harmonic relationships in European classical music. In the version above, the dark blue triangle at the center is an A minor triad; the red triangle to its right is the relative major, C; and the red triangle below it is the parallel major, A. Every such pattern is mirrored in all the other keys. The tones are numbered from 0 (A♭) to 11 (G). Major triads are red, and minor are blue. The thinnest lines denote minor thirds, thicker are major thirds, and the thickest horizontal lines are fifths. See this page for further relationships.
The heart of the figure, shown in somewhat darker colors in the diagram, is a parallelogram composed of 24 triangles. The top edge of this parallelogram can be joined to the bottom, which lists the same notes in their enharmonic equivalents, and if the resulting cylinder is twisted slightly then its ends can be joined in the same way, forming a torus.
Sea Battle
This is a tug-of-war on the water at Healy’s Lake, Ontario, Canada. The boat is a punt used for ‘cadging’ baggage in the wilderness; the idea of a tug-of-war on the water was the suggestion of Dr. Joel M. Ingersoll, of Rochester, New York. … The left-enders ‘walked away’ with those on the right.
— T.J. Wilstach of New York, in the Strand, October 1903
Math Notes
Multiply 92 by 8, then multiply that product by 8, and so on. List the products, indenting them successively as shown and continuing indefinitely:
92 736 5888 47104 376832 3014656 24117248 192937984 9999999...
The sum converges to a string of 9s.
From Archimedes’ Lab’s Zoo of Numbers.
Limerick
Said a logical linguist named Rolles,
“As we always call Polish folk Poles,
For better precision
(I am a logician)
We ought to call Dutch people Holes.”
A Show of Hands
I think this is from the 1976 Soviet mathematical olympiad:
Fifty accurate watches lie on a table. Prove that there exists a moment in time when the sum of the distances from the center of the table to the ends of the minute hands is greater than the sum of the distances from the center of the table to the centers of the watches.
Brainstorm
In 2015, Canadian politician Sheldon Bergson changed his name to Above Znoneofthe, so that it would appear on electoral ballots as “Znoneofthe, Above.” (The Z, which is silent, ensures that the name will appear last in a list of candidates.)
He ran in an Ontario provincial by-election the following year, winning 0.43 percent of the vote, and has participated in several races since. Amazingly, he’s not the first person to try this.
(Thanks, Alessia.)