The Paradox of the Second Ace

http://commons.wikimedia.org/wiki/File:Bertall_-_Le_whist_3.jpg

You’re watching four statisticians play bridge. After a hand is dealt, you choose a player and ask, “Do you have at least one ace?” If she answers yes, the chance that she’s holding more than one ace is 5359/14498, which is less than 37 percent.

On a later hand, you choose a player and ask, “Do you have the ace of spades?” Strangely, if she says yes now the chance that she has more than one ace is 11686/20825, which is more than 56 percent.

Why does specifying the suit of her ace improve the odds that she’s holding more than one ace? Because, though a smaller number of potential hands contain that particular ace, a greater proportion of those hands contain a second ace. It’s counterintuitive, but it’s true.

| Science & Math

Modern Convenience

http://www.google.com/patents/US156282

For the stylish farmer, Jefferson Darby patented this plow attachment in 1874. The canopy can be adjusted both horizontally and vertically, “thus affording a complex and ample range of adjustment by which the shade may be shifted about as the plow changes direction and the sun moves along its course.”

“The attachment may also be attached to other agricultural implements, also upon wagons and other carriages.”

| Technology

The Vision Thing

http://en.wikipedia.org/wiki/File:John_Logie_Baird,_1st_Image.jpg

Diary entry by journalist Sydney Moseley, Aug. 1, 1928:

… I met a pale young man named Bartlett who is Secretary to the new Baird Television Company. Television! Anxious to see what it is all about … He invited me to go along to Long Acre where the new invention is installed. Now that’s something! Television!

Met John Logie Baird; a charming man — a shy, quietly spoken Scot. He could serve as a model for the schoolboy’s picture of a shock-haired, modest, dreamy, absent-minded inventor. Nevertheless shrewd. We sat and chatted. He told me he is having a bad time with the scoffers and skeptics — including the BBC and part of the technical press — who are trying to ridicule and kill his invention of television at its inception. I told him that if he would let me see what he has actually achieved — well, he would have to risk my damning it — or praising it! If I were convinced — I would battle for him. We got on well together and I have arranged to test his remarkable claim.

(Later) Saw television! Baird’s partner, a tall, good-looking but highly temperamental Irishman, Captain Oliver George Hutchinson, was nice but very nervous of chancing it with me. He was terribly anxious that I should be impressed. Liked the pair of them, especially Baird, and decided to give my support … I think we really have what is called television. And so, once more into the fray!

| Technology

The Lodging-House Difficulty

A puzzle by Henry Dudeney:

dudeney lodging-house difficulty

The Dobsons secured apartments at Slocomb-on-Sea. There were six rooms on the same floor, all communicating, as shown in the diagram. The rooms they took were numbers 4, 5, and 6, all facing the sea.

But a little difficulty arose. Mr. Dobson insisted that the piano and the bookcase should change rooms. This was wily, for the Dobsons were not musical, but they wanted to prevent any one else playing the instrument.

Now, the rooms were very small and the pieces of furniture indicated were very big, so that no two of these articles could be got into any room at the same time. How was the exchange to be made with the least possible labour? Suppose, for example, you first move the wardrobe into No. 2; then you can move the bookcase to No. 5 and the piano to No. 6, and so on.

It is a fascinating puzzle, but the landlady had reasons for not appreciating it. Try to solve her difficulty in the fewest possible removals with counters on a sheet of paper.

Click for Answer
| Puzzles

Long Time Coming

One day I was out milking the cows. Mr. Dave come down into the field, and he had a paper in his hand. ‘Listen to me, Tom,’ he said, ‘listen to what I reads you.’ And he read from a paper all about how I was free. You can’t tell how I felt. ‘You’re jokin’ me.’ I says. ‘No, I ain’t,’ says he. ‘You’re free.’ ‘No,’ says I, ‘it’s a joke.’ ‘No,’ says he, ‘it’s a law that I got to read this paper to you. Now listen while I read it again.’

But still I wouldn’t believe him. ‘Just go up to the house,’ says he, ‘and ask Mrs. Robinson. She’ll tell you.’ So I went. ‘It’s a joke,’ I says to her. ‘Did you ever know your master to tell you a lie?’ she says. ‘No,’ says I, ‘I ain’t.’ ‘Well,’ she says, ‘the war’s over and you’re free.’

By that time I thought maybe she was telling me what was right. ‘Miss Robinson,’ says I, ‘can I go over to see the Smiths?’ — they was a colored family that lived nearby. ‘Don’t you understand,’ says she, ‘you’re free. You don’t have to ask me what you can do. Run along, child.’

And so I went. And do you know why I was a-going? I wanted to find out if they was free too. I just couldn’t take it all in. I couldn’t believe we was all free alike.

Was I happy? Law, miss. You can take anything. No matter how good you treat it — it wants to be free. You can treat it good and feed it good and give it everything it seems to want — but if you open the cage — it’s happy.

— Former slave Tom Robinson, 88, of Hot Springs, Ark., interviewed by the Federal Writers’ Project for the Slave Narrative Collection of 1936-38

| History

The Troll

This litigious humour is bad enough: but there is one character still worse — that of a person who goes into company, not to contradict, but to talk at you. This is the greatest nuisance in civilised society. Such a person does not come armed to defend himself at all points, but to unsettle, if he can, and throw a slur on all your favourite opinions. If he has a notion that anyone in the room is fond of poetry, he immediately volunteers a contemptuous tirade against the idle jingle of verse. If he suspects you have a delight in pictures, he endeavours, not by fair argument, but by a side-wind, to put you out of conceit with so frivolous an art. If you have a taste for music, he does not think much good is to be done by this tickling of the ears. If you speak in praise of a comedy, he does not see the use of wit: if you say you have been to a tragedy, he shakes his head at this mockery of human misery, and thinks it ought to be prohibited. He tries to find out beforehand whatever it is that you take a particular pride or pleasure in, that he may annoy your self-love in the tenderest point (as if he were probing a wound) and make you dissatisfied with yourself and your pursuits for several days afterwards. A person might as well make a practice of throwing out scandalous aspersions against your dearest friends or nearest relations, by way of ingratiating himself into your favour. Such ill-timed impertinence is ‘villainous, and shows a pitiful ambition in the fool that uses it.’

— William Hazlitt, “On the Conversation of Authors,” 1820

| Literature · Society