Misc

  • The telephone number 266-8687 spells both AMOUNTS and CONTOUR.
  • 38856 = (38 – 85) × 6
  • CARTHORSE is an anagram of ORCHESTRA.
  • The French for paper clip is trombone.
  • “The oldest books are only just out to those who have not read them.” — Samuel Butler

Gilbreath’s Conjecture

Doodling on a napkin in 1958, mathematician Norman L. Gilbreath noticed something odd. First he wrote down the first few prime numbers in a row. Then, on each succeeding row, he recorded the (unsigned) difference between each pair of numbers in the row above:

gilbreath's conjecture

The first digit in each row (except the first) is 1. Will this always be true, no matter how many prime numbers we start with? It’s been borne out in computer searches extending to hundreds of billions of rows. But no one knows for sure.

Person to Person

Suppose that you enter a cubicle in which, when you press a button, a scanner records the states of all the cells in your brain and body, destroying both while doing so. This information is then transmitted at the speed of light to some other planet, where a replicator produces a perfect organic copy of you. Since the brain of your Replica is exactly like yours, it will seem to remember living your life up to the moment when you pressed the button, its character will be just like yours, and it will be in every other way psychologically continuous with you. Is it you?

— Derek Parfit, “Divided Minds and the Nature of Persons,” in Mindwaves, 1987

Cast of Thought

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

Suppose, therefore, a person to have enjoyed his sight for thirty years, and to have become perfectly acquainted with colours of all kinds, except one particular shade of blue, for instance, which it never has been his fortune to meet with. Let all the different shades of that colour, except that single one, be placed before him, descending gradually from the deepest to the lightest; it is plain, that he will perceive a blank, where that shade is wanting, and will be sensible, that there is a greater distance in that place between the contiguous colours than in any other. Now I ask, whether it be possible for him, from his own imagination, to supply this deficiency, and raise up to himself the idea of that particular shade, though it had never been conveyed to him by his senses?

— David Hume, An Enquiry Concerning Human Understanding, 1748

A Penny Saved

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

When German physicist Walther Nernst learned that his cowshed was warm because of the cows’ metabolic activity, he resolved to sell them and invest in carp.

A thinking man, he said, cultivates animals that are in thermodynamic equilibrium with their surroundings and does not waste his money in heating the universe.

“Plane Geometry”

‘Twas Euclid, and the theorem pi
Did plane and solid in the text,
All parallel were the radii,
And the ang-gulls convex’d.

“Beware the Wentworth-Smith, my son,
And the Loci that vacillate;
Beware the Axiom, and shun
The faithless Postulate.”

He took his Waterman in hand;
Long time the proper proof he sought;
Then rested he by the XYZ
And sat awhile in thought.

And as in inverse thought he sat
A brilliant proof, in lines of flame,
All neat and trim, it came to him,
Tangenting as it came.

“AB, CD,” reflected he–
The Waterman went snicker-snack–
He Q.E.D.-ed, and, proud indeed,
He trapezoided back.

“And hast thou proved the 29th?
Come to my arms, my radius boy!
O good for you! O one point two!”
He rhombused in his joy.

‘Twas Euclid, and the theorem pi
Did plane and solid in the text;
All parallel were the radii,
And the ang-gulls convex’d.

— Emma Rounds