From Lee Sallows, a grid that inventories its own contents:
Science & Math
Good News
Suppose 10 percent of the population has a disease. Everyone is tested, and your test comes back positive. The test is 80 percent accurate. What is the chance that you have the disease?
Surprisingly, it’s little more than 30 percent. If the population is 100, then 10 people have the disease. Eight of them will get a correct positive result, 2 will get a false negative, and 18 of the remaining 90 will get a false positive. That’s 26 positives, of which only 8 are correct, or 30.8 percent.
Ghost Quiz
In 1885, Cecilia Garrett Smith and a friend were experimenting with automatic writing using a primitive Ouija board on which a planchette was guided by a visiting “spirit.”
“We got all sorts of nonsense out of it, sometimes long doggerel rhymes with several verses,” but the prophecies they asked for were rarely answered. When they asked who the guiding spirit was, the planchette wrote that his name was Jim and that he had been Senior Wrangler at Cambridge. Intrigued, they asked Jim to write the equation describing the heart-shaped planchette they were using, and they received this response:
This they interpreted as 
, which J.W. Sharpe later graphed thus:
“I am quite sure that I had never seen the curve before, and therefore the production of the equation could not have been an act of unconscious memory on my part,” Smith wrote later. “Also I most certainly did not know enough mathematics to know how to form an equation which would represent such a curve, or to know even of what type the equation must be.”
One wonders what Jim thought of all this. They never got any further math out of him.
The Problem of Future Contingents
If there will be a sea battle tomorrow, then that fact is true today and has always been true. Our future is thus inevitable. What freedom is left to us?
On the other hand, if statements about the future are neither true nor false today, then how can God have perfect foreknowledge of the future?
Misc
- Can a symbol symbolize itself?
- OVERPLAY and UNDERPLAY are Pig Latin for PLOVER and PLUNDER.
- 11264 = 11 × 26+4
- Could the universe be moved one mile to the right?
- “The art of living is more like wrestling than dancing.” — Marcus Aurelius
Proof That 10 Is Even
Cash and Carry
A favorite problem of Lewis Carroll involves a customer trying to complete a purchase using pre-decimal currency. He wants to buy 7s. 3d. worth of goods, but he has only a half-sovereign (10s.), a florin (2s.), and a sixpence. The shopkeeper can’t give him change, as he himself has only a crown (5s.), a shilling, and a penny. As they’re puzzling over this a friend enters the shop with a double-florin (4s.), a half-crown (2s. 6d.), a fourpenny-bit, and a threepenny-bit. Can the three of them negotiate the transaction?
Happily, they can. They pool their money on the counter, and the shopkeeper takes the half-sovereign, the sixpence, the half-crown, and the fourpenny-bit; the customer takes the double-florin, the shilling, and threepenny-bit as change; and the friend takes the florin, the crown, and the penny.
“There are other combinations,” writes John Fisher in The Magic of Lewis Carroll, “but this is the most logistically pleasing, as it will be seen that not one of the three persons retains any one of his own coins.”
Related: From Henry Dudeney, a magic square:
(Strand, December 1896)
“The Archaeologist’s Nightmare”
From Lee Sallows, a geometric magic square:
The shards in each row and column produce a complete plate.
So do the diagonals!
Bank Balance
‘Well, then, good fellow, holy father, or whatever thou art,’ quoth Robin, ‘I would know whether this same Friar is to be found upon this side of the river or the other.’
‘Truly, the river hath no side but the other,’ said the Friar.
‘How dost thou prove that?’ asked Robin.
‘Why, thus,’ said the Friar, noting the points upon his fingers. ‘The other side of the river is the other, thou grantest?’
‘Yea, truly.’
‘Yet the other side is but one side, thou dost mark?’
‘No man could gainsay that,’ said Robin.
‘Then if the other side is one side, this side is the other side. But the other side is the other side, therefore both sides of the river are the other side. Q.E.D.’
”Tis well and pleasantly argued,’ quoth Robin, ‘yet I am still in the dark as to whether this same Curtal Friar is upon the side of the river on which we stand or upon the side of the river on which we do not stand.’
‘That,’ quoth the Friar, ‘is a practical question upon which the cunning rules appertaining to logic touch not. I do advise thee to find that out by the aid of thine own five senses; sight, feeling, and what not.’
— Howard Pyle, The Merry Adventures of Robin Hood, 1883
The Thinker Unthought
If materialism is true, all our thoughts are produced by purely material antecedents. These are quite blind, and are just as likely to produce falsehood as truth. We thus have no reason for believing any of our conclusions — including the truth of materialism, which is therefore a self-contradictory hypothesis.
— J.E. McTaggart, Philosophical Studies, 1934