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Tuesday, June 23, 2009

Monday, June 22, 2009

Tarski and Hutch

Well, Wabulon and I are developing the screenplay for the pilot of a new TV series, based on Starsky and Hutch, but in which the character of Starsky is replaced by that of Alfred Tarski, the famed twentieth-century mathematician. Here is my first draft, awaiting Wabulon's comments:

Play Pen Night Club: Night.


(Inside people are dancing. Tarski and Hutch stand at the bar with Huggy.)

Huggy: How do you like this little gold mine I gotta take care of until my cousin Louie returns?

Tarski: Huggy Bear, you’re just an invariant transformation of Superfly.

Huggy: Funny, Tarski. But you know Superfly and me ain't never been in any sorta one-to-one correspondence! Anyway, my uncle got a big stake in frog futures. He had to leave for Venezuela to check out his new frog ranch. All this happened after the IRS read his latest tax returns. Really.

(Walks away. Hutch spots two girls sitting alone.)

Hutch: Would you look at that? (Hutch points at girls.)

Tarski: Look at that. (Tarski’s looking at a tiling pattern on the ceiling.)

Hutch: Look at that. (Points at girls.)

Tarski: Look at that. (Points. They both look and see the girls.)

Hutch: What are you gonna do, just stand here and stare? You gonna go over and talk to them.

Tarski: When you say “Go over and talk to them,” do you mean I should go over and talk to them?

Hutch: Yeah, that’s what I mean. (Sips his beer.)

Tarski: Okay. (Walks around Hutch in a hyperbolic curve while mumbling about wanting to establish a set-theoretic relation with “one of those babes.”)

Hutch: On second thought, maybe I’d better take control of this situation.

Tarski: Why?

Hutch: Hey, you restrict your attention to first-order logic, and let me handle the babes, OK? Watch the master at work, huh?

(Walks over to the girls’ table and leans down to talk to them. He sits down. Tarski comes over.)

Hutch: Oh, ladies, excuse me. Uh, this is, uh…

Tarski: Tarski. Alfred Tarski.

Hutch: Alfred Tarski, one of the four all-time greats in the history of formal logic.

(The girls squeal a little.)

Bobette: Hello. (Shakes hands.)

Tarski: Hi, uh…

Hutch: This is Barbette.

Tarski: Barbette?

Bobette: Bobette.

Tarski: Bobette.

Hutch: And this is Jane.

Tarski: Hi, Jane. (Moves to shake her hand and knocks the glass Hutch is holding out of his hand and onto Jane’s lap.) I’m sorry.

Hutch: You’ll have to excuse my friend.

Tarski: Uh, I guess I’m a little nervous. I just sent out a paper claiming that that much of Euclidian solid geometry can be recast as a first order theory whose individuals are spheres, a primitive notion, a single primitive binary relation "is contained in," and two axioms that, among other things, imply that containment partially orders the spheres.

Bobette: Oh, my, that’s impressive! I think you’re kinda foxy.

Tarski: Yeah? Would you like to see my cylindric algebra?

Bobette: Yeah, baby. (Licks her lips.)

(Tarski sits down and scribbles a number of formulae on a cocktail napkin, then holds it up for Bobette.)

Tarski: Foxy, huh?

Bobette: Yeah.

Tarski: Hey, you know something? The two of you look like twins. Did someone cut one of you into a finite number of pieces, and then re-assemble the pieces into the two of you?

(Huggy interrupts.)

Huggy: Hey, excuse me.

Hutch: What?

Huggy: Dobey’s on the phone.

Tarski: That sentence is true if and only if Dobey’s on the phone!

Huggy: Well, he IS on the phone, and he wants to speak to one of you. Says it’s urgent.

Tarski: Oh, no. (Hutch gets out a coin.)

Hutch: Heads or tails.

Tarski: What?

Hutch: Heads or tails.

Tarski: Heads.

Hutch: No, it’s tails. (Without looking.) Tough break, foxy.

Tarski: Terrific. (Leaves.)

Bobette: Do you guys come here a lot?

Hutch: No, no. As a matter of fact, we don’t.

(Tarski picks up the phone.)

Tarski: Yeah? What? But Captain, this is our night to work on binary relations. Yeah…Okay. Okay! (Hangs up and goes back to the table.)

Hutch: We really don’t have too much time off. We work 12 to 14 hour shifts.

Tarski: Hey, uh, the Captain says we gotta go.

Hutch: What? Ah.

Tarski: Sorry ladies. (Shakes their hands.)

Hutch: Well, it was nice to meet you.

Jane: Hey, are you guys really policemen?

Tarski: The sentence "We are policemen" is true if and only if we are policemen.

Hutch: Yep.

Bobette: That’s exciting.

Tarski: Yeah?

Bobette: Yeah.

Hutch: We should go. (Walks past Tarski.)

Tarski: Hey, I thought I proved to you that the question of whether or not we should go is formally undecideable.

Hutch: Yeah, whatever, Al. Let’s just get out of here.

Bobette: Bye. (They walk off. Tarski turns back.)

Tarski: Hey, hey, I didn’t get that cardinal number of yours. Do you commute here?

Hutch: Yeah, no…

Tarski: What?

Hutch: Get both of them, will you? (Tarski goes back and speaks to Bobette and then comes back.) You got them, huh?

Tarski: Yeah.

Hutch: Did you write them down?

Tarski: Tattooed on my brain.

Hutch: Oh. (They leave.)

Baby, Baby, Where Did That Post Go?

For those of you wondering where the Bruno and Ron Paul post went: it was a slug trap. I put it up, watched the comments build up, and once I had caught enough of the slimy little critters, I threw the thing out, without of course, looking inside.

Saturday, June 20, 2009

My Father's Limerick

I passed by "Man from Ravenna" again and was reminded of what I believe is my father's only limerick. I don't think I've posted it here before, but who really knows the future, or the past, or anything but this passing moment? Now what the ^&;$#!*$% was I trying to post? Oh, yeah, the limerick:

There was an old man of Rhode Island
Who was known as King William the Silent.
    When they bade him good morning,
    He replied without warning,
"Garunchnik!" and then he grew violent.

Saturday, June 13, 2009

Two Years from Now, What Will Be Happening?

Since pundits gain a great deal of fame from having correctly predicted the future, let me take a stab at saying what will being going on, say, two years from now, on June 13, 2011.

First of all, the stimulus programs will be seen to have fallen short of the mark. The Dow will stand at, say, 11,985, give or take a couple of points. Gold will be about $1515 an ounce, and oil at $97 per barrel. The yield on ten-year treasuries will be just under 3%. Unemployment claims will be stuck above 400,000.

In response, Paul Krugman and Brad DeLong will be saying "I told you so: the stimulus was too small." And in his response to their response, on June 13, 2011, Mario Rizzo will write a blog post pointing back to the blog post where he foresaw Krugman saying this, and claim that Hayekians have a right to say "I told you so" as well. And I predict Daniel Kuehn will come back with a note saying Mario's post has not proved anything. And Mario will agree!

Friday, June 12, 2009

Parting Shot

I had stopped by to peruse the recent messages and was just about to sign out when I for no particular reason remembered this, due to W. van O. Quine:

"Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation.

Keep up the good work.

Wednesday, June 10, 2009

Bad Book

So, I says to my daughter, 'Where's that bad book I was reading? I have to find it.'

She replied, 'If it's so bad, why do you want to find it?'

'If I find it and finish it, I've just read a bad book. But if I don't find it, I'll be in the middle of a bad book for the rest of my life!'

Tuesday, June 09, 2009

Passports

Yesterday I was at the Post Office ordering new passports for two of my children. The woman working the window, once again (it was the same woman I dealt with in January), lost track of several of the documents I handed her, despite the fact that it wasn't that huge a stack of paper, and they are the sort of things she deals with every day.

She told me the passports should arrive in 3-4 weeks. I told me wife, 'Well, that gives us two weeks [alveolar consonant][schwau]sp[long a]r'.

She said, 'That's good.'

I responded, 'Did you think I said "two weeks to spare"? What I said was "two weeks despair", after the four weeks have passed and we're despairing of ever getting the passports'.

Another Local Polar Axiom

When told that a post is 'very good', think 'very bad'.

Monday, June 08, 2009

OpenOffice Impress...

is a total piece of rubbish. It hangs on my Mac about once a day, losing all my work since my last save. It lets you work on outlines, but doesn't seem to let you print them. The printouts of your slides are crap. The help is pathetic. And just today, I worked on a presentation for a while in outline mode, and when I went back to slide view it turned out that working in outline view had trashed all of my slides -- formatting was ruined, photos and graphics moved to different slides, and more.

I'm going to go buy a real piece of software.

Sunday, June 07, 2009

Local Polar Axiom

When directed above, look below.

More on the Above "Proof"

The above "proof" adduces the square-free integers--a very interesting set. For all finite sets P of primes, Product P ordered by Sum P (and within each tranche by Size P) give a canonical ordering of the square-free integers:

2, 3, 5, 6, 7, 10, 15, 14, 21, 30, 11, 35, 42, 13, 22, 33, 70, 26, 105, 39, 55, 66, 17, 210, 65, 77, 78, 110, 19, 34, 165, 51, 91, 130, 154, 38, 195, 231, 330, 57, 85, 102, 182, 23, 273, 385, 390, 462, 95, 119, 143, 114, 170, 46, 255, 455, 546, 770, 69, 133, 190, 238, 286, 1155, 285, 357, 429, 510, 910, 115, 187, 138, 266, 1365, 29, 399, 595, 715, 570, 714, 858, ...

This uncomfortable order reflects the uncomfortable properties of primes in general, which is of course why I like it.

Like the primes themselves, the square-free integers may be isolated by the Sieve of Eratosthenes thus:

1) Write down the integers greater than 1.
2) Start with the first square greater than 1 (that's 4).
3) Strike it and all multiples.
4) Take the next square.
5) If it remains, strike it and all remaining multiples.
6) Goto (4).

Friday, June 05, 2009

Partnoy and Li on Derivatives

You've probably seen these already, but just in case...

Partnoy

Li

Li

The Number of Primes is Finite

The number of primes is finite. Proof: We know that the number of subsets of a set is incommensurably greater than the number of members: {a.b.c} has eight subsets; the integers have uncountably many subsets (maybe of the power of the continuum, maybe not, depending on your axiomatic taste). Consider the set of all finite subsets of the set of primes. The primes, being a subset of the integers, can be only countably infinite. If the number of primes is infinite, the number of finite subsets of primes is uncountably infinite. But to each finite subset of primes there corresponds uniquely an integer, namely the product of the members of the subset. The set of finite subsets of primes is in one-to-one correspondence with a subset of the integers, namely the “square-free” integers, those having no prime factor to a power higher than one. Thus the set of square-free integers and a fortiori the set of all integers is uncountably infinite. But we know that the set of all integers is not uncountably infinite. Thus our hypothesis is false: the number of primes is not infinite. Q.E.D.

New Obama Policy Stance

Here.

Yes, the newspapers were right:

snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead.

Wednesday, June 03, 2009

Tuesday, June 02, 2009

That Angel Guy Just Felt Me Up

First, this (you only need to watch if you don't remember the original here):


Next, this:


(Hat tip to Katie Reeves.)