In a Word

adj. pleasant to embrace

adj. fit to be embraced

Math Notes

1/473684210526315789 = 0.0000000000000000021111111111111111132222222222222
88888888888888891000000000000000002111111111111111113222222222222222224 ...

(Thanks, William.)

A Modest Proposal

In 1936, after his first wife had left him, Evelyn Waugh sent a letter to her cousin Laura Herbert, asking whether “you could bear the idea of marrying me.”

“I can’t advise you in my favour because I think it would be beastly for you,” he wrote, “but think how nice it would be for me. I am restless & moody and misanthropic & lazy & have no money except what I earn and if I got ill you would starve. In fact it’s a lousy proposition. On the other hand I think I could do a Grant and reform & become quite strict about not getting drunk and I am pretty sure I should be faithful. Also there is always a fair chance that there will be another bigger economic crash in which case if you had married a nobleman with a great house you might find yourself starving, while I am very clever and could probably earn a living of some sort somewhere.”

He added, “All these are very small advantages compared with the awfulness of my character. I have always tried to be nice to you and you may have got it into your head that I am nice really, but that is all rot. It is only to you & for you. I am jealous & impatient — but there is no point in going into a whole list of my vices. You are a critical girl and I’ve no doubt that you know them all and a great many I don’t know myself.”

They were wed the following spring.

“Feminine Correspondence”

From the Annual Register, 1840: “The following civilities between two ladies lately appeared in the public papers”:

Lady Seymour presents her compliments to lady Shuckburgh, and would be obliged to her for the character of Mary Stedman, who states that she has lived twelvemonths, and still is in lady Shuckburgh’s establishment. Can Mary Stedman cook plain dishes well? make bread? and is she honest, good tempered, sober, willing, and cleanly? Lady Seymour would also like to know the reason why she leaves lady Shuckburgh’s service? Direct, under cover, to lord Seymour, Maiden Bradley.

Lady Shuckburgh presents her compliments to lady Seymour. Her ladyship’s note, dated Oct. 28, only reached her yesterday, Nov. 3. Lady Shuckburgh was unacquainted with the name of the kitchen-maid, until mentioned by lady Seymour, as it is her custom neither to apply for or give characters to any of the under servants, this being always done by the housekeeper, Mrs. Couch — and this was well known to the young woman; therefore lady Shuckburgh is surprised at her referring any lady to her for a character. Lady Shuckburgh having a professed cook, as well as a housekeeper, in her establishment, it is not very likely she herself should know anything of the abilities or merits of the under servants; therefore, she is unable to answer lady Seymour’s note. Lady Shuckburgh cannot imagine Mary Stedman to be capable of cooking for any except the servants’ hall table. — November 4, Pavilion, Hans-place.

Lady Seymour presents her compliments to lady Shuckburgh, and begs she will order her housekeeper, Mrs. Pouch, to send the girl’s character without delay; otherwise another young woman will be sought for elsewhere, as lady Seymour’s children cannot remain without their dinners because lady Shuckburgh, keeping a ‘professed cook and a housekeeper,’ thinks a knowledge of the details of her establishment beneath her notice. Lady Seymour understood from Stedman that, in addition to her other talents, she was actually capable of dressing food fit for the little Shuckburghs to partake of when hungry.

(“To this note was appended a clever pen and ink vignette, by the Queen of Beauty, representing the three little Shuckburghs, with large turnip-looking heads and cauliflower wigs, sitting at a round table, eating and voraciously scrambling for mutton chops, dressed by Mary Stedman, who is seen looking on with supreme satisfaction, while lady Shuckburgh appears in the distance in evident dismay.”)

Madam, — Lady Shuckburgh has directed me to acquaint you that she declines answering your note, the vulgarity of which is beneath contempt; and although it may be the characteristic of the Sheridans, to be vulgar, coarse, and witty, it is not that of ‘a lady,’ unless she happens to have been born in a garret and bred in a kitchen. Mary Stedman informs me that your ladyship does not keep either a cook or a housekeeper, and that you only require a girl who can cook a mutton chop. If so, I apprehend that Mary Stedman, or any other scullion, will be found fully equal to cook for, or manage the establishment of, the Queen of Beauty. I am, your ladyship’s, &c., Elizabeth Couch (not Pouch).’

Jackson Strive$20_Series_2006_Obverse.jpg

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?

Click for Answer


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.”

A Niente

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

Green Ties

The Martian Census Bureau compiled the marital history of every male and female Martian, living and dead:

  • Never married: 6,823,041
  • Married once: 7,354,016
  • Married twice: 1,600,897
  • Married three times: 171,013
  • Married four times: 2,682

What’s wrong with these figures?

Click for Answer

Eastern Views

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

— 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.

“Scooping the Loop Snooper”

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.)