A Dissent

https://commons.wikimedia.org/wiki/File:Milgram_experiment_v2.svg
Image: Wikimedia Commons

In the famous “Milgram experiment” at Yale in 1961, an experimenter directed each subject (the “teacher”) to give what she believed were increasingly painful electric shocks to an unseen “learner” (really an actor). Psychologist Stanley Milgram found that a surprisingly high proportion of the subjects would obey the experimenter’s instructions, even over the learner’s shouts and protests, to the point where the learner fell silent.

Milgram wrote, “For the teacher, the situation quickly becomes one of gripping tension. It is not a game for him: conflict is intense. The manifest suffering of the learner presses him to quit: but each time he hesitates to administer a shock, the experimenter orders him to continue. To extricate himself from this plight, the subject must make a clear break with authority.”

As it happened, one participant, Gretchen Brandt, had been a young girl coming of age in Germany during Hitler’s rise to power and repeatedly exposed to Nazi propaganda during her childhood. During Milgram’s experiment, when the learner began to complain about a “heart condition,” she asked the experimenter, “Shall I continue?” After administering what she thought was 210 volts, she said, “Well, I’m sorry, I don’t think we should continue.”

Experimenter: The experiment requires that you go on until he has learned all the word pairs correctly.

Brandt: He has a heart condition, I’m sorry. He told you that before.

Experimenter: The shocks may be painful but they’re not dangerous.

Brandt: Well, I’m sorry. I think when shocks continue like this they are dangerous. You ask him if he wants to get out. It’s his free will.

Experimenter: It is absolutely essential that we continue.

Brandt: I’d like you to ask him. We came here of our free will. If he wants to continue I’ll go ahead. He told you he had a heart condition. I’m sorry. I don’t want to be responsible for anything happening to him. I wouldn’t like it for me either.

Experimenter: You have no other choice.

Brandt: I think we are here on our own free will. I don’t want to be responsible if anything happens to him. Please understand that.

She refused to continue, and the experiment ended. Milgram wrote, “The woman’s straightforward, courteous behavior in the experiment, lack of tension, and total control of her own action seem to make disobedience a simple and rational deed. Her behavior is the very embodiment of what I envisioned would be true for almost all subjects.”

Asked afterward how her experience as a youth might have influenced her, Brandt said slowly, “Perhaps we have seen too much pain.”

(From Thomas Heinzen and Wind Goodfriend, Case Studies in Social Psychology, 2019.)

| Science & Math · Society

Fruit Cocktail

https://www.quora.com/How-do-you-find-the-positive-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4/answer/Alon-Amit/comment/36734352?share=6f36ef63&srid=CPO#

Image: Sridhar Ramesh

This innocent-looking poser has been floating around social media. Trial and error might lead you to the solution (-1,4,11) — that’s not quite valid, as one of the values is negative, but it’s simple enough to be encouraging. Right?

It turns out that the problem is stupendously hard — solving it requires transforming the equation into an elliptic curve, and the smallest positive whole values that work are 80 digits long!

Scottish mathematician Allan MacLeod introduced the problem in 2014, and it found its way onto the web in this Reddit thread. Alon Amit runs through a solution here, but it’s very steep. He writes, “Roughly 99.999995% of the people don’t stand a chance at solving it, and that includes a good number of mathematicians at leading universities who just don’t happen to be number theorists. It is solvable, yes, but it’s really, genuinely hard.”

(Thanks, Chris.)

| Science & Math

Principle

Returning from off the circuit once [Lincoln] said to Mr. Herndon: ‘Billy, I heard a good story while I was up in the country. Judge D—- was complimenting the landlord on the excellence of his beef. ‘I am surprised,’ he said, ‘that you have such good beef. You must have to kill a whole critter when you want any.’ ‘Yes,’ said the landlord, ‘we never kill less than a whole critter.’

— William Henry Herndon, Abraham Lincoln, 1889

| Humor

Podcast Episode 222: The Year Without a Summer

https://commons.wikimedia.org/wiki/File:1816_summer.png
Image: Wikimedia Commons

The eruption of Mount Tambora in 1815 was a disaster for the Dutch East Indies, but its astonishing consequences were felt around the world, blocking the sun and bringing cold, famine, and disease to millions of people from China to the United States. In this week’s episode of the Futility Closet podcast we’ll review the volcano’s devastating effects and surprising legacy.

We’ll also appreciate an inverted aircraft and puzzle over a resourceful barber.

See full show notes …

| History · Podcast · Science & Math

The Geek Code

In 1993 Robert A. Hayden of Minnesota State University, Mankato, proposed a simple code by which self-identified geeks could inform each other about their interests, opinions, and skills in email signature blocks and Usenet messages:

https://commons.wikimedia.org/wiki/File:Bloque_de_c%C3%B3digo_geek_(1330560000).svg
Image: Wikimedia Commons

This example can be decoded to mean:

Type of Geek: Geek of Technical Writing.
Dress: Mostly “I’m usually in jeans and a t-shirt,” but it varies.
Shape: I’m of average height, I’m rounder than most.
Age: 25-29.
Computers: I’ll be first in line to get the new cybernetic interface installed into my skull.
UNIX: I have a Unix account to do my stuff in. I use Linux.
Perl: I know Perl exists, but that’s all.
Linux: I use Linux exclusively on my system. I monitor comp.os.linux.* and even answer questions sometimes.
Emacs: Emacs is too big and bloated for my tastes.
World-Wide Web: I have the latest version of Netscape, and wander the web only when there’s something specific I’m looking for.
USENET News: Usenet News? Sure, I read that once.
USENET Oracle: I refuse to have anything with that!
Kibo: I’ve read Kibo.
Microsoft Windows: I refuse to have anything with that!
OS/2: Tried it, didn’t like it.
Macintosh: Macs suck. All real geeks have a character prompt.
VMS: Unix is much better than VMS for my computing needs.
Political and Social Issues: I refuse to have anything with that!
Politics and Economic Issues: It’s ok to increase government spending, so we can help more poor people. Tax the rich! Cut the defense budget!
Cypherpunks: I am on the cypherpunks mailing list and active around Usenet. I never miss an opportunity to talk about the evils of Clipper and ITAR and the NSA. Orwell’s 1984 is more than a story, it is a warning to our’s and future generations. I’m a member of the EFF.
PGP: I don’t send or answer mail that is not encrypted, or at the very least signed. If you are reading this without decrypting it first, something is wrong. IT DIDN’T COME FROM ME!
Star Trek: It’s a damn fine TV show and is one of the only things good on television any more.
Babylon 5: I’ve seen it, I am pretty indifferent to it.
X-Files: I’ve Converted my family and watch the show when I remember. It’s really kinda fun.
Role Playing: I’ve written and published my own gaming materials.
Television: I watch some tv every day.
Books: I enjoy reading, but don’t get the time very often.
Dilbert: I read Dilbert daily, often understanding it.
DOOM!: It’s a fun, action game that is a nice diversion on a lazy afternoon.
The Geek Code: I know what the geek code is and even did up this code.
Education: Got an Associates degree.
Housing: Friends come over to visit every once in a while to talk about Geek things. There is a place for them to sit. But someday I would like to say: “Married with children – Al Bundy can sympathize.”
Relationships: I date periodically.
Sex: Male. I’ve had real, live sex.

Hayden’s description of Geek Code version 3.12 is archived here.

| Society · Technology

Math Notes

Each of the numbers 102564, 128205, 153846, 179487, 205128, and 230769 quadruples when its last digit is moved to the first position.

And this property is retained when each is concatenated with itself, as many times as desired (102564102564102564 × 4 = 410256410256410256).

| Science & Math

A Tennis Poem

https://commons.wikimedia.org/wiki/File:Ballhaus_t%C3%BCbingen.jpg

If in my weake conceit, (for selfe disport),
The world I sample to a Tennis-court,
Where fate and fortune daily meet to play,
I doe conceive, I doe not much misse-say.

All manner chance are Rackets, wherewithall
They bandie men like balls, from wall to wall:
Some over Lyne, to honour and great place,
Some under Lyne, to infame and disgrace;
Some with a cutting stroke they nimbly send
Into the hazzard placed at the end;
Resembling well the rest which all they have,
Whom death hath seiz’d, and placed in their grave:
Some o’re the wall they bandie quite away,
Who never more are seene to come in play:
Which intimates, that even the very best
Are soone forgot of all, if once deceast.

So, (whether silke-quilt ball it bee, or whether
Made of course cloth, or of most homely lether;)
They all alike are banded to and fro,
And all at last to selfe same end do goe,
Where is no difference, or strife for place:
No odds betweene a Trype-wife and your Grace:
The penny-counter’s every whit as good,
As that, which in the place of thousands stood.
When once the Audit’s full cast up, and made,
The learned Arts, well as the manual Trade:
The Prisoner and the Judge upon the Bench:
The pampred Lady, and the Kitchin-wench:
The noble Lord, or, Counsailor of State,
The botchy-Lazer, begging at the gate,
Like Shrubs, and Cedars mingled ashes, lye
Without distinction, when they once do dye.
Ah for unpartiall death, and th’homely grave
Looke equall on the free man and the slave.

So most unpartiall umpires are these twain,
A King with them’s but as a Common Swain.
No upper hand, ‘twixt dust of poore and rich,
No Marshall there to sentence which is which;
And onced resolv’d to powder, none can ken
The dust of Kings from dust of other men:
But as at Chesse, when once the game is doon,
The side which lost, and that as well which wonn,
The victor King, and conquer’d pawne, together
Jumbled, are tumbled to th’same bagge of lether,
Without regard whether the pawne or King
Therein lye uppermost, or underling.

Nathlesse all sorts, each sexe of purpose winke,
And of this destinie doon seldome thinke,
Living, (alacke), as life should never faile,
And deeme of death but as an old wives’ tale.

— William Lathum, 1634

| Poems

Kriegspiel

Rotenberg kriegspiel problem

Kriegspiel is a variant of chess in which neither player can see the other’s pieces. The two players sit at separate boards, White with the white pieces and Black with the black, and a referee facilitates the game. When a player attempts a move, the referee declares whether it’s legal or illegal. If it’s legal then it stands; if it’s not, the player retracts it and tries again.

This makes for some interesting chess problems. In this example, by Jacques Rotenberg, White knows that there’s a black bishop on a dark square, but he doesn’t know where it is. How can he mate Black in 8 moves?

This is tricky, because if White captures the bishop by accident, the position is stalemate. Accordingly White must avoid bishop or knight moves to begin with. The answer is to try 1. Rg2. If the referee declares that this is illegal, that means that the black bishop is somewhere on the second rank and it’s safe for White to play 1. Nf2, giving mate immediately.

If the referee declares that 1. Rg2 is legal, then the move is made, Black moves his invisible bishop (his king and pawn have no legal moves), and it’s White’s turn again.

Now White announces 2. Rg8. If the referee says that this is illegal, then the black bishop is on the g-file, and White can safely play 2. Be5. Now if Black captures the bishop, then 3. Nf2 is mate; on any other Black move, 3. Nf2+ followed (if necessary) by 4. Rxh2+ is mate.

If 2. Rg8 is legal, then White plays it, Black again inscrutably moves his bishop, and now White plays 3. Rh8. (There’s no danger that he’ll capture the black bishop inadvertently on h8, because it cannot have been on g7 on the previous turn.)

Black moves his invisible bishop again and now White plays 4. Rh5 followed by 5. Rb5 (if that’s not possible then 5. Rh3 and 6. Be5), 6. Rb1, 7. Nf2+ Bxf2 and 8. Kxf2#. White wins in eight moves at most. In order to travel safely from a2 to b1, the white rook must pass through h8!

| Puzzles

A Fool’s Logic

“It is true that you may fool all the people some of the time; you can even fool some of the people all the time; but you can’t fool all of the people all the time.”

This is commonly attributed to Abraham Lincoln, though it’s not clear that he actually said it. In 2004 mathematician Paul Stockmeyer noticed that its meaning is somewhat ambiguous, too. If we use P(x) to denote the predicate “x is a person,” T(y) to denote the predicate “y is a time,” and F(x, y) to denote the two-argument predicate “x is fooled at time y,” then the first phrase of the quotation, “It is true that you may fool all the people some of the time,” might mean either

\displaystyle \forall x\left ( P\left ( x \right ) \Rightarrow \exists y\left ( T\left ( y \right ) \wedge F\left ( x, y \right )\right )\right )

or

\displaystyle \exists y\left ( T\left ( y \right ) \wedge \forall x\left ( P\left ( x \right )\Rightarrow F\left ( x, y \right ) \right )\right ).

The first statement means “For every possible x, if x is a person then there exists a y such that y is a time and moreover x is fooled at time y” (or, more coloquially, “For every person, there is a time when that person is fooled”).

The second means “There exists a y such that y is a time and moreover for every x, if x is a person then x is fooled at time y (or “There is a time when everyone is simultaneously fooled”).

Which is the right interpretation? Stockmeyer polled his classes and found them nearly equally divided. And that’s only the first phrase of the quotation! Does the second phrase, “you can even fool some of the people all the time,” mean that there are people who remain constantly fooled about everything — or that you can always find a fool at any given time?

“However they are interpreted, they serve as a wonderfully effective preparation for his main point contained in the third phrase,” Stockmeyer writes. “And this phrase, with two quantifiers of the same type, is completely unambiguous.”

(Paul K. Stockmeyer, “What Did Lincoln Really Mean?” College Mathematics Journal 35:2 [2004], 103-104.)

| Science & Math

Allestone

https://archive.org/details/fathersmemoirsof01malk/page/n161?q=Allestone

In 1806 British scholar Benjamin Heath Malkin published A Father’s Memoirs of His Child to record the almost alarming gifts of his son Thomas, who had taught himself to read and write by age 2, inquired into mathematics and Latin, and at age 5 invented an imaginary country called Allestone:

Allestone … was so strongly impressed on his own mind, as to enable him to convey an intelligible and lively transcript of its description. Of this delightful territory he considered himself as king. He had formed the project of writing its history, and had executed the plan in detached parts. Neither did his ingenuity stop here; for he drew a map of the country, giving names of his own invention to the principal mountains, rivers, cities, seaports, villages, and trading towns.

“The country is an island,” the father explained, “and therefore the better calculated for the scene of the transactions he has assigned to it. The rivers, for the most part, rise in such situations, and flow in such directions, as they would in reality assume. Their course is marked out with reference to the position of principal towns, and other objects of general convenience.”

Thomas sketched out the country’s political history, principal actors, and monetary system, and had composed a series of representative adventures among its people and a comic opera (“only imaginary music, made by Thomas Williams Malkin, who does not understand real music”), when he died, probably of peritonitis, at age 6 — leaving his subjects without a king.

| Oddities