You and I spot a $20 bill on the street. To divide it, we agree to an auction: Each of us will write down a bid, and the high bidder will keep the $20 but pay the amount of his own bid to the other player. If we submit the same bid then we’ll split the $20. What should you bid?
Evidently a lover of broccoli, Elmer Walter of Pennsylvania saw a need for special tableware in 1907:
The primary object of the invention is to provide a table implement, such as a knife, fork, or other device with a mirror suitably secured in the handle of the implement, so that the user of the implement may have ready at hand a mirror for the purpose of inspecting the teeth in the mouth or the mouth or other portions of the face generally, at any time desired by the user of the implement.
“Oftentimes a patron of a restaurant or cafe finds the need of a mirror to discover a substance which has become lodged in the teeth,” he writes. A mirrored knife “may be used by him or her for the purpose indicated above substantially without attracting any attention.”
I was seriously tormented by the thought of the exhaustibility of musical combinations. The octave consists only of five tones and two semitones, which can be put together in only a limited number of ways, of which but a small proportion are beautiful: most of these, it seemed to me, must have been already discovered, and there could not be room for a long succession of Mozarts and Webers, to strike out, as these had done, entirely new and surpassingly rich veins of musical beauty. This source of anxiety may, perhaps, be thought to resemble that of the philosophers of Laputa, who feared lest the sun should be burnt out.
— John Stuart Mill, Autobiography, 1873
The Martian Census Bureau compiled the marital history of every male and female Martian, living and dead:
What’s wrong with these figures?
Wry haiku:
Having given his opinion
he returns home to
his wife’s opinion
— Yachō (1882-1960)
“Every woman”
he starts to say,
then looks around
— Anonymous
One umbrella —
the person more in love
gets wet
— Keisanjin (dates unknown)
By saying not to worry
he says something
worrisome
— Anonymous
At the ticket window
our child becomes
one year younger
— Seiun (dates unknown)
Ted Pauker devised the limeraiku, which compresses the rhymes of a limerick into the form of a haiku. Like limericks, they’re usually off-color:
There’s a vile old man
Of Japan who roars at whores:
“Where’s your bloody fan?”
Another, by W.S. Brownlee:
Said Little Boy Blue:
“Same to you. You scorn my horn?
You know what to do.”
See Lament.
Given a particular input, will a computer program eventually finish running, or will it continue forever?
That sounds straightforward, but in 1936 Alan Turing showed that it’s undecidable: It’s impossible to devise a general algorithm that can answer this question for every possible program and input.
The most charming proof of this was published in 2000 by University of Edinburgh linguist Geoffrey Pullum — he did it in the style of Dr. Seuss:
No program can say what another will do.
Now, I won’t just assert that, I’ll prove it to you:
I will prove that although you might work til you drop,
You can’t predict whether a program will stop.
Imagine we have a procedure called P
That will snoop in the source code of programs to see
There aren’t infinite loops that go round and around;
And P prints the word “Fine!” if no looping is found.
You feed in your code, and the input it needs,
And then P takes them both and it studies and reads
And computes whether things will all end as they should
(As opposed to going loopy the way that they could).
Well, the truth is that P cannot possibly be,
Because if you wrote it and gave it to me,
I could use it to set up a logical bind
That would shatter your reason and scramble your mind.
Here’s the trick I would use — and it’s simple to do.
I’d define a procedure — we’ll name the thing Q —
That would take any program and call P (of course!)
To tell if it looped, by reading the source;
And if so, Q would simply print “Loop!” and then stop;
But if no, Q would go right back to the top,
And start off again, looping endlessly back,
Til the universe dies and is frozen and black.
And this program called Q wouldn’t stay on the shelf;
I would run it, and (fiendishly) feed it itself.
What behaviour results when I do this with Q?
When it reads its own source, just what will it do?
If P warns of loops, Q will print “Loop!” and quit;
Yet P is supposed to speak truly of it.
So if Q’s going to quit, then P should say, “Fine!” —
Which will make Q go back to its very first line!
No matter what P would have done, Q will scoop it:
Q uses P’s output to make P look stupid.
If P gets things right then it lies in its tooth;
And if it speaks falsely, it’s telling the truth!
I’ve created a paradox, neat as can be —
And simply by using your putative P.
When you assumed P you stepped into a snare;
Your assumptions have led you right into my lair.
So, how to escape from this logical mess?
I don’t have to tell you; I’m sure you can guess.
By reductio, there cannot possibly be
A procedure that acts like the mythical P.
You can never discover mechanical means
For predicting the acts of computing machines.
It’s something that cannot be done. So we users
Must find our own bugs; our computers are losers!
Pullum, Geoffrey K. (2000) “Scooping the loop snooper: An elementary proof of the undecidability of the halting problem.” Mathematics Magazine 73.4 (October 2000), 319-320.
(Thanks, Pål.)
(Thanks, Eric.)
French science fiction writer Albert Robida has been lost in the shadow of Jules Verne, but in the 1880s he was widely popular for a trilogy of illustrated novels imagining life in the 20th century. He predicted social upheavals around the time of our two world wars and foresaw transatlantic air travel, home shopping, video telephones, and a feminist revolution. But his greatest innovation was one we haven’t reached yet — a president made of wood:
And he is really well made. See the hand that’s holding the pen? It is secured in position. You can try pushing and pulling it all you want, it won’t budge! There is a secret lock. Absolute security! The mechanism is extremely complex; there are three locks and three keys. The prime minister has one, the president of the chamber has another one, and the president of the senate has the third. A minimum of two keys is requested to activate the mechanism. In case of conflict between the prime minister and the president of the chamber, the president of the senate is summoned with his key. He stands with one side or the other and introduces his key into one of the locks. The mechanism is activated, and the automatic president signs away!
“He shall reign, but not govern,” explains a citizen. “The power will remain in the hands of the nation’s representatives. … The monarchists’ main objection to democracy has always been its inherent instability. With this wooden president, democracy equals stability!”
“Civilization is a stream with banks. The stream is sometimes filled with blood from people killing, stealing, shouting and doing the things historians usually record, while on the banks, unnoticed, people build homes, make love, raise children, sing songs, write poetry and even whittle statues. The story of civilization is the story of what happened on the banks. Historians are pessimists because they ignore the banks for the river.” — Will Durant, Life, Oct. 18, 1963
Written by German composer Peter Cornelius in 1854, “Ein Ton” has a single note for a melody — the note B is repeated 80 times in 42 bars.
I hear a tone so wondrous sweet
In heart and spirit of repeat.
Is it that breath that from thee fled,
The last faint breath e’er thou wert dead?
Nicolas Slonimsky writes, “Of course, there are constant modulations so that harmonic changes make up for monotony.”