A Mysterious Windfall

A riddle by Isaac Newton:

Four people sat down at a table to play;
They play’d all that night, and some part of next day;
This one thing observ’d, that when all were seated,
Nobody play’d with them, and nobody betted;
Yet, when they got up, each was winner a guinea;
Who tells me this riddle I’m sure is no ninny.

Who are the players?

Click for Answer
| Puzzles

Benardete’s Book Paradox

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Here is a book lying on a table. Open it. Look at the first page. Measure its thickness. It is very thick indeed for a single sheet of paper — one half inch thick. Now turn to the second page of the book. How thick is this second sheet of paper? One fourth inch thick. And the third page of the book, how thick is this third sheet of paper? One eighth inch thick, etc. ad infinitum. We are to posit not only that each page of the book is followed by an immediate successor the thickness of which is one half that of the immediately preceding page but also (and this is not unimportant) that each page is separated from page 1 by a finite number of pages. These two conditions are logically compatible: there is no certifiable contradiction in their joint assertion. But they mutually entail that there is no last page in the book. Close the book. Turn it over so that the front cover of the book is now lying face down upon the table. Now, slowly lift the back cover of the book with the aim of exposing to view the stack of pages lying beneath it. There is nothing to see. For there is no last page in the book to meet our gaze.

— Patrick Hughes and George Brecht, Vicious Circles and Infinity, 1978

| Oddities · Science & Math

Flung Fire

A remarkable phenomenon was observed at Kattenau, near Trakehnen (Germany), and in the surrounding district, on March 22. About half an hour before sunrise an enormous number of luminous bodies rose from the horizon and passed in a horizontal direction from east to west. Some of them seemed of the size of a walnut, others resembled the sparks flying from a chimney. They moved through space like a string of beads, and shone with a remarkably brilliant light. The belt containing them appeared about 3 metres in length and 2/3 metre in breadth.

— Nature, May 20, 1880

| Oddities

Bedtime Reading

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In a 1952 survey of 200 traditional nursery rhymes, Geoffrey Handley-Taylor found that about half were “glorious and ideal for the child.” The others contained:

  • 8 allusions to murder (unclassified)
  • 2 cases of choking to death
  • 1 case of death by devouring
  • 1 case of cutting a human being in half
  • 1 case of decapitation
  • 1 case of death by squeezing
  • 1 case of death by shriveling
  • 1 case of death by starvation
  • 1 case of boiling to death
  • 1 case of death by hanging
  • 3 cases of death by drowning
  • 4 cases of killing domestic animals
  • 1 case of body snatching
  • 21 cases of death (unclassified)
  • 7 cases relating to the severing of limbs
  • 1 case of the desire to have a limb severed
  • 4 cases relating to the breaking of limbs
  • 1 allusion to a bleeding heart
  • 1 case of devouring human flesh
  • 9 threats of death
  • 1 case of kidnapping
  • 12 cases of torment and cruelty to human beings and animals
  • 8 cases of whipping and lashing
  • 3 allusions to blood
  • 14 cases of stealing and general dishonesty
  • 15 allusions to maimed human beings and animals
  • 2 allusions to graves
  • 23 cases of physical violence (unclassified)
  • 1 case of lunacy
  • 16 allusions to misery and sorrow
  • 1 case of drunkenness
  • 4 cases of cursing
  • 1 allusion to marriage as a form of death
  • 1 case of scorning the blind
  • 1 case of scorning prayer
  • 9 cases of children being lost or abandoned
  • 2 cases of house burning
  • 9 allusions to poverty and want
  • 5 allusions to quarreling
  • 2 cases of unlawful imprisonment
  • 2 cases of racial discrimination

“Expressions of fear, weeping, moans of anguish, biting, pain and evidence of supreme selfishness may be found in almost every other page.”

| Literature

“That”

I’ll prove the word that I have made my theme
Is that that may be doubled without blame,
And that that that thus trebled I may use
And that that that that critics may abuse
May be correct. Yet more–the dons to bother–
Five thats may closely follow one another:
For well ’tis known that we may safely write
That that that that that man writ was right.
Nay, e’en that that that that that that followed
Through six repeats the grammar’s rule has hallowed,
And that that that (that that that that began)
Repeated seven times is right! Deny’t who can.

— Anonymous

| Language