Stargazing

https://commons.wikimedia.org/wiki/File:Dipper.jpg
Image: Wikimedia Commons

The second star in the Big Dipper’s handle is actually two stars, Mizar and Alcor. Distinguishing the two with the naked eye has been used as a test of vision for hundreds of years. Arabic tradition held that only those with the sharpest eyesight could see Mizar’s companion, and the 13th-century Persian astronomy writer Zakariya al-Qazwini wrote that “people tested their eyesight by this star.” In Japan, it was said that being unable to see Alcor with the naked eye foretold an impending death of old age, and Alexander von Humboldt and François Arago both noted that Alcor can be seen only with difficulty.

In The Herschels and Modern Astronomy (1901), Irish astronomer Agnes Mary Clerke wrote, “The Arabs in the desert regarded it as a test of penetrating vision; … Vidit Alcor, at non lunam plenam (Latin for ‘he saw Alcor, but not the full moon’), came to be a proverbial description of one keenly alive to trifles, but dull of apprehension for broad facts.”

(Thanks, Sharon.)

| Science & Math

“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

| Religion

Parfit’s Hitchhiker

https://www.flickr.com/photos/mypubliclands/16358796247
Image: Flickr

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

| Oddities · Society

The Tonnetz

https://commons.wikimedia.org/wiki/File:Neo-Riemannian_Tonnetz.svg

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.

| Art · Science & Math

Sea Battle

https://archive.org/details/the-strand/The%20Strand%20v26%201903/page/478/mode/2up

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

| Entertainment · Oddities

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.

| Science & Math

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.

Click for Answer
| Puzzles