Archive for November, 2011

Three views into mathematics

November 29, 2011

What better use for a lunch break than a bottle of cola and a blog post? Three books off the showing-off-how-mathematical-I-am bookshelf at my elbow. One semi-random sentence from each.

I

In 1924, reviewing reports on algebraic numbers issued by the National Research Council, he noted with pleasure the comparatively great amount of space that the authors had devoted to cyclotomy, a fact that he saw as an encouragement to beginners and proof that the “lusty” old subject was still very much alive.

(Constance Reid, The Search for E.T. Bell, also known as John Taine, Mathematical Association of America, 1993, p. 145)

An obscure book about a mathematician, a historian, a popularizer of mathematics (author of the justly famous and famously not always exact Men of Mathematics), a poet, and a science fiction writer, that was not always all that honest with his own personal history.

II

Pathological monsters! cried the terrified mathematician
Every one of them is a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set
And the Sierpinski Gasket makes me want to cry

(Sarah Glaz and JoAnne Growney, Strange Attractors: Poems of Love and Mathematics, A K Peters, 2008, p. 141; this bit is a Jonathan Coulton song lyric)

I guess this is what snotty types call “an eclectic collection”. I liked about half of the poems; the other half weren’t mathematical enough.

III

“No reason was ever given,” recalled Henriksen, “but his lawyer was permitted to examine a portion of the Erdös file and found recorded the facts that he corresponded with a Chinese number theorist named Hua who had left his position at the University of Illinois to return to Red China in 1949 (a typical Erdös letter would have begun: Dear Hua, let p be an odd prime…) and that he had blundered onto a radar installation in Long Island … while discussing mathematics with two other noncitizens.” The authorities apparently feared that the letters to Hua, filled with impenetrable mathematical symbols, might be coded messages.

(Paul Hoffman, The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth, Hyperion, 1998, p. 128)

One of two (!) Erdös biographies I have; the other is by My Brain Is Open by Bruce Schechter. Erdös (and I suppose that is not o-umlaut but some Hungarian doodle) was a real-life stereotypical mathematician. As can be glimpsed from the quote above.

Childish Finnish jokes

November 25, 2011

A Finnish boy is asked by his mother to go buy cucumber, eggs and liver. He goes, buys, and on the way back home skippety-skips to the path of a careless driver.

The driver rushes out of his car, yelling: “Boy! Are you okay?”

The boy stands up, sways, and answers: “Oh, oh, cucumber cut, eggs broke, the liver flown out there, but other than that I’m fine!”

* * *

This is a funny joke if you’re Finnish and about ten years old.

The necessary explanation is that kurkku, the Finnish word for cucumber, is a homonym for the word for throat; munat (eggs) is universal slang with the same anatomical meaning as “balls”; and maksa (liver) occurs in humans as well as in the foodshop.

Well, actually the eggs are sort of anatomically hazy. Eggs (plural) is balls (potku munille, a kick to the balls), but an egg (singular) can be the associated rod (ime munaa, suck a dick).

Also, to the best of my recall the saying about making omelettes and breaking eggs does not occur in Finnish except as a clumsy, children-amusing foreign import. Which could be interpreted to mean castrati make the best cooks. “You can’t get an omelette done without breaking a few balls, ey?”

Yes, this is not going to be a philosophically profound post. Let me tell you a few more youth jokes from a few decades ago.

* * *

Three generals, a Swedish, a Norwegian and a Finnish one, get into an argument over which of them has the bravest soldiers.

The Swede marches them to the base of a great big skyscraper, and tell a soldier of his: “Go to the top, and jump down!”

The soldier does this, and also splatters.

The Norwegian general admits this is a little bit brave, and then barks at one of his soldiers: “Get to the top of that tower, then jump down in parade salute, and don’t break it no matter what!”

The Norwegian soldier does this, and to the moment of impact maintains a perfect parade salute. After it, not so much.

The Finnish general agrees this is somewhat brave. Then he yells up one of his soldiers, and commands: “Get to the top of that building! Along the outer wall! Upside down! And then jump down and sing the national anthem as you do!”

And the soldier yells back: “You do the stupid fucking stunt yourself, sir!” — and walks away.

The Finn wins.

* * *

A third, too.

* * *

A Norwegian, a Swede and a Finn get into a competition over who is the toughest.

To decide this, they resolve to see which can stay in a sauna with a skunk the longest.

The skunk goes in; then, the Norwegian. After five minutes (and two ladlefuls of water) he comes out, crying, sobbing, saying “The smell! I can’t take it any longer!”

The Swede goes in next. Five minutes pass, and three ladlefuls. Then five minutes, and the sound of the entire ladle-bucket being poured. A great hiss of steam. Five more minutes. Then the Swede crawls out, gasping, choking, saying “The stench! The ungodly stench! I can’t take it any longer!”

Finally, the Finn goes in. Five minutes pass; then ten. Occasionally, the hiss of a ladleful of water on the stove is heard. Fifteen minutes, twenty. Sobbing is heard from the inside. Thirty. Gnashing of teeth, and dribbling water. Forty. Great wracking hopeless sobs. Fifty minutes.

Then the skunk staggers out, nose running, tears in its eyes, and moans: “The reek, the reek! I can’t take it any longer!”

* * *

And a fourth; this is a good one to stop with.

* * *

A little boy is staying with his grandparents.

One day in the middle of a dinner with the neighbors over, the boy blurts to the grandfather: “I need to go piss, pops!”

Later that shameful day the grandfather, being a delicate old sort, tells the boy: “Dear boy! Don’t use language like that ever again in this house! Never! If you need to go, just say ‘I feel like singing’ and you will be let to go.”

That night, the boy wakes up. He terribly needs to pee, but the house is dark and unfamiliar, so he creeps to the grandparents’ bedroom, shakes the grandmother awake, and whispers: “Gramma! Gramma! I… I feel like singing!”

To which she answers: “Oh? Don’t wake Grampa up, dear. Do it quietly and in my ear.”

Worth his weight in gold, eh?

November 23, 2011

According to Wolfram Alpha, the weight of your average human being is 70 kilos.

According to the same, 70 kilos of gold are worth some 3.6 million US dollars.

According to the EPA by the way of xkcd, the pencil-pusher estimate for the value of a human life is in the range of 8.4 million US dollars.

Hence, a human being is not only worth its weight in gold, but more! The average human being is worth a little bit more than twice its weight in gold!

(Note that if you weigh 160 kilos or more, you should be exchanged for a gold statue of similar weight post haste, before the sentimental types notice.)

Doctor KUKA

November 20, 2011

I’ve been watching Doctor Who for a couple of months now; I’ve gone through seasons one, two and three of the revival, and I have been well entertained. (If you ask me, Season One with Eccleston was brilliant. Season Two with Tennant was so-and-so with a terrible slump in the middle; and Season Three with Tennant was almost up to One. I’d hazard a guess that Davies or Moffat writing correlates strongly with not sucking.)

I don’t really have anything deep to say about Doctor Who — except that it is at its best when it gets as weird as it can be — but I just realized this autumn is not my first brush with the Doctor.

No, when I was thirteen or so, this would be 1995 maybe, I had a book out from the library bus that was a Doctor Who adventure.

This I know just because the name of the series has stuck in my mind. At the time, I didn’t who what Doctor Who was; indeed, I faintly recall being puzzled by the non-appearance of any Doctor called Who in the story. It felt like betrayal to a young, ignorant reader. There was some The Doctor, a character that just butted in into the story without bothering to explain just who he was and what he was doing there, much to the confusion of the plot characters and of the reader. It was all very confusing. Mostly because the old Who TV series had never been shown in Finland; the books weren’t published in any great numbers; and I had absolutely no idea what this thing was and which elements were supposed to be the recurring ones. With something like Transformers you knew it was big giant robots being destroyed by Megatron; with the Three Detectives it was, naturally, three detectives detecting; but Doctor Who? Not on the cultural radar of a Finnish boy circa 1995, and not a matter the original author had felt necessary to explain. (Then again, I was thirteen; not the age where you are interested in splicing a novel series into filling and staples.)

The story, now, I don’t remember anything about that. It had… maybe it was a near present-day Earth story, maybe it had monsters of some kind and a forest and er um.

Since as far as desultory googling can tell there have been just two Doctor Who book translations into Finnish before the new series, the book must have been either “Tohtori KUKA ja autonien hyökkäys” or “Tohtori KUKA ja luolahirviöt”, i.e. “Doctor Who and the Auton Invasion” (Terrance Dicks, 1974) or “Doctor Who and the Cave Monsters/Silurians” (Malcolm Hulke, 1974). Both were published by Weilin+Göös, a major-ish Finnish publisher, in 1976, as nice little hardbacks if I recall correctly.

Also, the Finnish titles are horrible. “Tohtori KUKA” is just “Doctor WHO”, but the dramatic capitalization is silly. And KUKA is, if possible, a word that sounds even more mundane and non-dramatic than WHO. You can yell “Who?” dramatically; I don’t really think a Finnish drama could do the same with “Kuka?” Especially since if you stretch the second consonant a touch too much you’re shouting “Kukka?”, that is, “A FLOWER?” (On the exchange, WHO couldn’t be capitalized in English. The UN would get mad.)

To finish with, here’s the cover of the Cave Monsters book. Can anyone tell me if Silurians are supposed to look like this?

Tohtori KUKA ja LuolahirviötYeah; those things are going to be in my dreams now.

A man and his too much free time

November 18, 2011

So I read the xkcd for today, and an idea hit me.

So I made a dummy page to make the lives of others a bit more surreal. Note the dates. Let people have that in their Google results, and wonder. (Well, once/if Google picks it up.)

(Note: not an actual functioning forum. A dummy page.)

Oh, the ideas

November 16, 2011

Had to write an e-mail to my department head today.

Our department not being all that formal — or so I hope — I began it with a “Hei.”, your basic Finnish version of the English “Hi.” with a crazy ethnic vowel added to it.

Then I fought myself for two terrible seconds, because I’m a horrible, inappropriate person, and managed to send the message without adding an L after the I. Because the likely outcomes would have been cold quiet outrage, or a message to the mailing list telling the head had a huge new retro idea for addressing him. (“Und fur ze Graduate Students, schnappy black Uniforms!”)

Because, you see, the Finnish word for your departmental head is “laitoksen johtaja”, or “the department’s leader”. And “leader” is what that German F-word means. Also “driver”, as in “Führerschein”, German for a driver’s license. Which I’m sure has caused plenty of horrible humor from young ones that’ve just got theirs.

Hans, to Gretel: “I’ve got the license! Let’s take a car and go invade Poland!”

Gretel, to Hans: “We are no longer friends.”

As you may gather, Finns are not that good with either respect or taste. And the head is actually a nice guy and not likely to become a fascistic dictator at the first opportunity; but to quote an old office proverb, illustrating the problem of orientation in hierarchy and its consequences in perception, “bosses look down and see shit; underlings look up and see assholes”.

* * *

In other, non-fecal news (though I could argue…), the NaNoWriMo novel is at about 40 000 words — which means, 4/5 of the required minimum after 1/2 of the time; woo hoo!) — and just had a climax in it. A sane, skilled writer would say “that’s it!” and write “the end”, but I am a) too interested in the fallout, b) not satisfied with the abruptness, and c) 10 000 words shy of victory.

Rock, paper, scissors, a mathematician ruining it

November 16, 2011

I

The obvious variation is to add more signs into the game: say “rock-paper-reviewer-editor-scissors”. It in inobvious, though, whether rock beats reviewer or the other way round. (Some of those reviewers are tough.)

One way is to draw a pentagram in a single line (making each segment an arrow pointing the way you draw it) and then to draw a circle round it (marking the direction you draw). Then you can treat the points of the pentagram as the five signs, with each point originating two arrows indicating two other points, and being indicated by two of the others; which gives two signs that submit, and two that conquer.

Also, probably the most Satanic game design in history.

This addition alone, though, doesn’t make the game more interesting, just more complicated.

One could say winning or losing by the circle is different from winning or losing by the pentagram: but how? (Through a pentagram loss, you forfeit your very soul?)

Ib

As for the simpler obvious variation: Rock-paper-plasticknife-scissors, the game with four sign(al)s/gestures, is a bit iffy. You tie with the same; you lose to one, win against one… but what about the fourth? If it is a tie, one half of games end in a tie. It can’t be a win or a loss, because that would make some signs better than others. If rock wins against against plasticknife, then plasticknife loses to both rock and scissors, wins against paper and ties against itself — it would always be better to play rock (WWLT) than to play plasticknife (WLLT).

Any odd number of gestures can be arranged to be equally good; no even number above two can be without increasing the number of ties.

Then again, with more gestures this just isn’t interesting. Who cares if Horned Goat loses to Hanged Man or Lone Dalek, if it’s the same loss either way?

Ic

Rock-paper-scissors doesn’t have the same kind of a hierarchical arrangement as playing cards do — there you don’t get to choose your cards, so you can have cards that are better than others, most of the time. In rock-paper-scissors, you need to have options that are somehow equal (by not knowing the other player’s choice, if in no other way), because why would you choose a sign that was less likely to win?

Consider the card game known as “Red”. Both players draw a card from a deck, face down. Both then reveal their card. A red always beats a black; below that, a bigger card always wins. Not a particularly interesting game, but perfect for high school students really tapped-out after an unwelcome lesson. If you could call the card you wanted in Red, you’d be screaming “Ace of Hearts!” all the time — and having a tie with your opponent, who would be shouting the same. (Or “Diamond Ace!” — it would be a pointless, melodramatic game either way.)

This illustrates that either your choices can’t matter, or you must have no choice at all… which is a depressing prospect, but rock-paper-scissors is not much of an intellectual game anyway, as far as its mechanics go. The psychology can of course be very interesting, especially when you keep playing it. (“Is she going for scissors again? Third time in a row? But what if she’s counting on me pulling rock, and intends to play paper? Then I should play scissors— unless—“, et cetera. Put two psychologists to work playing each other, and they’ll probably stare at each other for five minutes, and then one admits defeat.)

It would be ideal to make a game with mechanics just complex enough to generate interesting psychology. Rock-paper-scissors isn’t quite complex enough. (Then again, it’s better than tic-tac-toe, a game where any player smarter than your average calculator can always tie, and two such players will always tie.)

II

The obvious biological variation would be to play the game with both hands at the same time. But this too makes the game different — in this case quicker (two at the same time!) — but not more interesting.

Then again, this gives more scoring conditions: a double win, a small win (win one, tie one), a fighting tie (win one, lose one) and a full tie (tie both). (The first two are, from the other end, a double lose and a small lose.)

By crunching numbers, the likelihood these outcomes is, assuming the players are dumb automatons:

11% Double win (W/W)
22% Small win (W/T)

22% Fighting tie (W/L)
11% Full tie (T/T)

22% Small lose (L/T)
11% Double lose (L/L)

— one percent is lost in the rounding. (Use 1/9 and 2/9 if you want to be exact.) If you take the first two as “wins”, the middle as “ties” and the last two as “loses”, then the odds are the same as in a normal one-handed game of rock-paper-scissors; there’s just a bit more additional detail within each category. To make a sensible variant of the game, this added sensitivity should be utilized somehow. (Note the two ties aren’t different in any intuitive way; both players get the same result in each. Some new rule could distinguish them for some other new aspect of the game.)

Mind you, this could be a decision tool if you needed two exit conditions —

Double win : We’ll do what I want, all the way

Small win: We’ll do what I want, for the most part

Fighting tie: Fine, let’s do nothing; I’ll go home, this isn’t working!

Full tie: Let’s try to split everything evenly, okay?

— but I’m not sure anyone needs help for making decisions like that.

The mechanic is there; the game just needs an addition that uses it.

III

The third variation, a sort of obnoxious meta thing, would be to have three players, each with two hands, each playing a one-handed game with each of the other two at the same time.

Call the players A, B and C. Three games resolve at the same time, each with three possible results (win/lose, lose/win, tie); this gives twenty-seven different total outcomes. Those form four categories, the way I choose to group them.

I’ll write “A>B” for “A wins over B”, “A<B” for “A loses to B” and “A=B” for “A and B tie”.

1) A<B<C<A : a roundabout tie. A>B>C>A is the same thing: each player has one win, one loss, and there’s no assigning rank to them.

2) A=B=C, every game ties; everyone flashes the same sign. A great tie! Also, the appearance of a gang meet-up.

3) A>B(sthng)C<A — Strong ranking; One player wins both of his/her games: victory! (I’ll call it that to distinguish it from “wins”, which are the results of individual games.) The third game, between the two losers, either gives second and third places, or a divided second if they tie:

3a) Full rank: A>B>C<A. Player A takes first place (wins over B and C), Player B the second (wins over C, loses to A), Player C the third (loses to A and B). Alternately, A>B<C<A. (It’s probably sensible to say A>B>C=A and A<B<C=A belong here as well; one can’t argue for any different order than the obvious one.)

3b) Weaker rank: A>B=C<A. Player A is the winner; the other two both lose.

Note that there can’t be a case where two players win both their games: the game between them can have at most one winner. This three-player game produces either one victor (above) or less (below).

4) A>B(sthng)C=A — Weak ranking; No player can be ranked as the best of the three. (A>B>C=A is already included in 3a.)

4a) Weaker rank: A>B<C=A. There’s no victor, just two winners; but B sure loses.

4b) Weakest rank: A>B=C=A. There are two ties and one win-lose; thus, a winner, a loser, and one the game didn’t decide about. (Also, A<B=C=A.)

I think one has to think that a tie means “no decision”, because one can’t really interpret a tie as “are equal” because of situations like A>B=C>A. If B and C are equal, why is one strictly better than A and one strictly worse? Unless you interpret that as collapsing > into \geq into =; how you interpret the mechanics makes the game.

As for the improved version of rock-paper-scissors, I have no idea. I’m just throwing up mechanics.

Ruining the sequence game

November 10, 2011

This is an old puzzle-type question: “I give you three numbers, a, b, c. What is next?”

This is nice brain exercise, but as a mathematician I feel duty bound to tell you you can break this game in about five seconds, if you so wish. (Well, five seconds and a bit of calculation time.)

Let f be a function so that f(n) gives the n:th number in the sequence; in the above example,

f(1) = a,

f(2) = b

and

f(3) = c.

Suppose you want the next number to be d. That’s one more condition for f,

f(4) = d.

The trick now is that these are four fixed points for a function; and it is trivial to find any number of functions that give those four values, and thus are “the rule that gives the sequence”.

That is to say:

A+ Math Student: “The sequence starts 1, 2, 3. What’s the next one?”

Mathematician: “The next one is 666.”

A+MS: “What? Don’t be silly, the next one is 4!”

M: “Huh? What perverse logic is that? Your sequence consists obviously of the integer values of the function f(x) = \frac{331}{3}x^3 -662x^2 + \frac{3644}{3}x - 662. You’re just changing the answer because I got it right.”

Best of all, the trick can be used to go from any given number of sequence points into any further number of points you may want to insist on. It’s a bit prohibitively bothersome to calculate — but it is always possible.

* * *

Oh well, the calculation. Oi, the calculation. If you have four points, a third-degree (four-minus-one-th degree) polynomial is probably the easiest guess, that is, a function f,

f(x) = Ax^3 + Bx^2 + Cx + D

for some constants A, B, C and D, so that it holds that

A + B + C + D = a

8A + 4B + 2C + D = b

27A + 9B + 3C + D = c

64A + 16B + 4C + D = d.

Just run a Gauss-Jordan elimination in your head and… what?

Okay, just use the ready-made solution:

\displaystyle A = -\frac{1}{6}\,a+\frac{1}{2}\,b-\frac{1}{2}\,c+\frac{1}{6}\,d

\displaystyle B = \frac{3}{2}\,a-4b+\frac{7}{2}\,c-d

\displaystyle C = -\frac{13}{3}\,a+\frac{19}{2}\,b-7c+\frac{11}{6}\,d

\displaystyle D = 4a-6b+4c-d.

For a=1, b=2, c=3, d=666, that gives

\displaystyle f(x) = \frac{331}{3}\,x^3 -662x^2 + \frac{3644}{3}\,x - 662;

clearly and obviously the rule asked for.

That’s still a lot of numbers, but a person with quick wits (not me!) could easily memorize that, and answer any what-is-the-fourth question with a horribly misguided rules-lawyering technically correct answer.

And technically correct is for a mathematician the only kind of correct that matters.

* * *

It will be a tad easier to forget the fourth number, and just slap down the second-degree polynomial that fits the given three —

f(x) = Ax^2 + Bx + C

for

\displaystyle A + B + C = a

\displaystyle 4A + 2B + C = b

\displaystyle 9A + 3B + C = c

or

\displaystyle A = \frac{1}{2}\,a-b+\frac{1}{2}\,c

\displaystyle B = -\frac{5}{2}\,a+4b-\frac{3}{2}\,c

\displaystyle C = 3a-3b+c

— and proclaim: “Here’s your bloody rule; as for the fourth number calculate it yourself! I don’t have time for your silly games! Ha ha ha!”

Alternatively, proclaim: “Here you go. Trolled by maths.”

(As for that f giving the intended fourth point, that’s infinitesimally unlikely. Most clever sequences aren’t second-degree polynomials.)

* * *

Of course if one doesn’t feel bound to finding an explicit numerical rule, the possibilities are endless.

Less than 666 reasons the next number is 666

  • The rule is my rule. The next number is 666.
  • No, you’re doing it wrong. Trust me, I’ve heard this one before; the next one is 666.
  • No, it’s the medals that are awarded in Tour de France: gold, silver, bronze and hamstrung. One, two, three, six-six-six.
  • Obviously it is integers ordered according to the frequency of their appearances in Western literature. Those wacky Christian mystics, right? All about 666!
  • “The Beast comes, all of a sudden! One! Two! Three! Six hundred and sixty six, the Number of the Beast! In medias res, Lupus Magnus Innominandum, Lucifer Deovore Daalek Satanas!” is the rule.
  • What do you mean, the next one can’t be 666? What happened to respecting the other guy’s religion? Huh?
  • Four? I’m so quoting that on Facebook. (This does not actually produce a sense of conviction in the other party, but rather a sense of crippling self-doubt with pretty much the same results.)
  • Four? I never pegged you as a racist before.
  • What do you need a rule like that for? It’s as obvious as elementary, high, university and Satan on horseback!
  • “Wait, no.” (Repeat after each attempt to disagree. Each time increase the time between “wait” and “no”.)
  • No no, I got this. This is much more elegant than yours. See? “One, two, three, six hundred and sixty six, blood, blood, blood, blood, blood—” (repeat with slowly increasing volume until you win)
  • Is too! Look, I can point you at one guy on the Internet that agrees with me and not you—

Lemmata updating again, and apocalypse

November 9, 2011

For those (any?) that have been following my daily scribbley comic thingie, Lemmata: because of abysmal laziness and NaNoWriMo, I slipped with the updates.

I got better.

The daily bits for the 3rd to the 9th are going up hourly at the moment.

For those who don’t follow that, here’s an incredibly short story.

* * *

THE REASON WHY

In the year 2012, the apocalypse came. There was fire, and poison, and the whole Earth and all in it was contaminated and lost, and doomed to quickly perish. It was an unexpected disaster, and unavoidable: a noxious death a million years in the making.

While this all was going on, a spaceship appeared overhead.

That which guided it was willing to help; but not even that alien within did have the power to save the Earth.

No; though the alien within was one giant electric computer hivemind, and so ancient it had seen stars kindle and die, it knew just this: the Earth was lost. All of it was contaminated, and nothing of it could be touched save with a sword.

So the alien cast down great rays that killed many people; and in killing them performed the requisite brain scans to reconstruct their minds, their essences, inside the alien computer.

And it cast down great electric nets, and scooped in a great torrent up wholesale all that was in the great, various, glorious human electric distributed database called the Internet; and so in addition to a portion of humankind, a portion of its culture and history was saved.

And the alien hivemind moved away, leaving a lost and dead planet behind, and moving considered the sad plight of humankind, bereft of all its material possessions, reduced to a ghost in the machine, with the jumbled remains of the Internet as its scenery. No more Rome, or the pyramids — just pictures and words of them; holiday snaps and architects’ schematics.

No more cats; just pictures of them.

The alien saw this, and felt pity; and in its small power did what it could, and cast an electric ghost back in time.

That ghost came to the beginnings of the Internet, for an electric ghost could go nowhere else; and it was ever there calling until the day of doom and the day of the hivemind came again: and it called: “Preserve! Copy! Pirate! Torrent everything!

And that is why those things are done with such compulsion: why the book pirate will never read his whole library, and the pictures of cats overflow the Internet — for books and cats are precious, and one day will be no more.

Horrible mathematicians

November 7, 2011

Was talking to a friend, a mathematical like me, a frequent TA like me, and through subjects that you don’t want to know, it came to this:

“…which would be quite a web address to point the students at to get their copies of correct answers from! Ha ha ha!”

“Ha! Ha! Ha! I think we could think up something worse, though.”

“Like http://www.analanswers.com?&#8221;

After which, there was more laughter.

Explanation: Mathematical analysis is (a) a pretty good fraction of a math M.Sc., and (b) really abbreviated like that, pretty often.

The jokes for complex analysis and numerical analysis practically write themselves.

Eventually, one could slip the address into the contact details of an academic paper. Name, affiliation, snail mail, e-mail, booyah!

And a person ought to have a card — but because affiliations can fluctuate, it would just have

(your name here)
(phone number)
http://www.analanswers.com/

“Nice to meet you! Here’s my card; looking forward to working with you! Double-hand finger point, wink, leer!”

Though if the site had more than demonstration answers, maybe it should be http://www.analexplorations.com? Or http://www.realanalproblems.com, “Problems in Real Analysis”?

Or, if one had self-confidence and delusions of grandeur, http://www.analchampion.com?

And then there’s the old one, the real actual one I’ve seen on a blackboard for reals, of abbreviation in assuming f is an analytic function:

“but ass. f anal.”