Archive for March, 2013

The evolution of a solution

March 25, 2013

As a TA, I sometimes TA for a course whose coursework has no ready solutions. Then the following happens.

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Iteration 0: No solution. These problems are impossible. The lecturer is a sadist. These are his research problems.

Iteration 1: Death is the only solution.

Iteration 2: Hey, if we know “A” this problem is easily solved. Hooray!

Iteration 3: Oh, “A” follows from this problem. Dang.

Iteration 4: If we assume “B” is known, this is both easy and elegant!

Iteration 5: If we assume “B”, we’re assuming something not known or proven on this course!

Iteration 6: It’s one page if I hand-wave the hard part!

Iteration 7: It’s three pages and no hand-waving!

Iteration 8: It’s three pages, no hand-waving, and assuming $1 < 0$ holds!

Iteration 9: Hang on a minute, this is not a problem about “X”. That’s why no “X”-literature had a peep of it.

Iteration 10: This is about “Y”! And it’s an easy “Y”-problem!

Iteration 11: Three lines, easy peasy… aw crap, that inequality’s not strict.

Iteration 12: Three lines, plus eleven special cases, can this really be— (phone rings)

Iteration 13: “Misprint, Mr. Lecturer? The one in Problem 3, right? Right right. What? I meant the inequality… oh, that’s a different misprint?”

Iteration 14: It’s not an “Y”-problem. It’s an “X”-problem, and the zero was clever misdirection for infinity.

Iteration 15: I have… a solution? A skeleton anyway; let’s throw some meat on this pony!

Iteration 16: It’s a elephant. I can’t give this solution to the little ones. First thing, my wrist would break at the blackboard.

Iteration 17: I could use transparencies… Wait, no, I’d better try simplifying this. Get some jumping jacks, elephant solution!

Iteration 18: Right, I don’t need the special case where $r>1$ and $r<-1$; silly me.

Iteration 19, the homework meeting: “Mmh, yeah. You can prove it that way too.” (crushes paper, cries a silent tear, moves to the next problem)

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Iteration 19 can be averted by having a handout. (“Yeah, I guess you could use the obvious, elegant solution Mr. Poopypants put on the blackboard. If on the other hand you want a solution with pizazz and loxodromic Möbius transformations… well, one out of two ain’t too bad… here’s a handout… Aw, come on people, don’t you have saunas to set fire to or something?”)

Papal thoughts

March 13, 2013

The people below the balcony cheered at just the word that a new pope was chosen. How come? It could have been Pope Satan III the Trickster-Pope, for all that they knew. Unless they were sure God guaranteed the new pope was a good one and not a result of human error. In which case, why cheer at the word that he was chosen? He’s not some sun god whose absence puts the world in terrible peril.

And doesn’t it matter to the people who the new pope is? Are they that damned sure God will rig the vote? That God will rig the vote to support their own personal views in the important matters facing the Catholic Church?

Imagine American voters cheering the announcement that the presidential vote has been counted — I can’t imagine anyone, except the most PR-weary, cheering just the knowledge that either the Democrat or the Republican has won.

Or is the audience made of people who think it doesn’t change anything no matter who the pope is, and of people who think the Church isn’t in the business of changing anything?

The audience is pumped up, sure, but it feels to me like the actual person of the pope is almost incidental to them; they would have cheered anyone, would have cheered any speech not blatantly Satanic and un-Catholic. Because this is not the sort of irrational behavior that I get into, this all feels confusing, amusing and a little scary.

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Left the video stream I was watching open; it keeps showing the crowd from a distance, with its roaring, chanting and screaming on the audio channel. It could be some other religion or a soccer match just as well. If I knew more about crowds, I could probably say something incisive about pope-mobs and football crowds. (I wonder if it’s a pope-mob no-no to get falling down legless drunk after an evening like this? Wild premarital sex is probably not good; but where’s the line with celebrating a pope?)

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As for the guy the cardinals elected, Francis I of Argentina, well, I looked at his Wikipedia page and almost tweeted this:

Oh this modern world, that I can see in real time a doddering old man take up the stole of actual factual evil, discrimination and lie.

— but it would have needed an immediate footnote, something like:

Anybody that calls gay marriage “a machination of the Father of Lies that seeks to confuse and deceive the children of God” is evil. If you disagree, you are wrong.

Evil or horribly dumb, that is; and the new pope isn’t dumb.

Obviously it isn’t nice and ecumenical to call something “evil”, but I’m personally fairly certain that holding a fairly standard collection of modern humanistic values and opinions, held by people who think homophobia is bad and feminism is good, must lead, if followed, to appraising the Catholic Church as a great force for repression, discrimination, lie, and outright evil, with most of its peculiar features being better in perpetuating these bad things than in causing and upholding good ones.

Though obviously there’s room for argument over whether, say, accepting the miracles “caused” by would-be saints is lying for the sake of expediency, or some wilfully perverse and hopeful interpretation of natural probabilities, or something else — or whether treating the New Testament as basically a historical account instead of yielding to all the interesting better-understanding-of-humanity things Biblical scholars have found out really is better classified as fearful dishonesty (God’s wrath? angry crowds? neophobia? nobody asked, not interested?), or honesty out of obliviousness and unsound philosophical-historical methodology — lying after all implies that you know better.

Ah well; I seem to be getting into one-sentence-per-paragraph mode, so I’d better stop.

The mathematical life, part aleph

March 11, 2013

A harmonic function, for the purposes of this discussion, is a function $f$ for which $\Delta f = 0$. A superharmonic function is one for which $\Delta f \leq 0$, and a subharmonic one one for which $\Delta f \geq 0$. Consequently, a function is harmonic if and only if it is both superharmonic and subharmonic.

Thus, a superharmonic function is (generally speaking) not harmonic.

When I explained this to the teaching-of-mathematics studying fellow the next desk over, his comment was: “Are you telling me that Superman isn’t even a man?”

(To which I should have said, “He’s from Krypton, isn’t he? I don’t even know if we should call him a he! What the hell, he might have tentacles or nothing at all down there — wait, let me check, there must be fan fiction about this. Let me google for ‘superman duck penis’.”)

To which I answered, “Ja, but if ve take der Super-Man und der Sub-Man, they together make a Man!”

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A question, from the same discussion: As is well known, a topologist is a person who doesn’t know the difference between a donut and a coffee cup. This being so because in the topological sense they’re the same thing: if they were made of clay, you could morph one into the other without destroying or introducing any holes. (A donut has one, in the middle; a coffee cup has one, in the handle.)

The question now rises, how many holes should a donut have to be topologically equivalent to a human being?

Probably more than one, as the digestive pathway, mouth to fartmaker, is not the only one. But this quickly becomes a quest into the insides of the human being; it is not clear to me if even the male and the female of the species are topologically equivalent. (Either “Physiological gender as a topological concept” or “The topological equivalence of the sexes: Towards a mathematical feminism”, forthcoming once I get the funding.)

Research into this is on hiatus because the damn biologists, who surely have the requisite expertise, are far away across the frozen waste in a different building.

Discordianism is (not) a religion

March 6, 2013

And now, obscure pseudo-theology because I feel like it.

1. Discordianism is not a religion but a vaccine.
2. Discordianism is not a religion but a flower.
3. Discordianism is not a religion but the religion.
4. Discordianism is not a religion okay maybe it is.
5. Discordianism is not a religion butt.
6. Discordianism: I can’t believe it’s not religion!
7. Discordianism is not a religion but it will do.
8. Discordianism is not a religion but you’ll never prove it.
9. Discordianism is not a religion but neither is Christianity.
10. Discordianism is not a religion but you will still worship our Goddess in the end, I swear you will. Ha ha ha!
11. Discordianism is not a religion but don’t worry, be happy.