### 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.

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.)

1. OK, well, here's a very brief first pass over your first pass. (Do you remember an early post about very large numbers--e.g., 1000000!--that you said was the longest post on record? I think you have surpassed it, or if not, you soon will.) More later.

"Tarski: When you say 'Go over and talk to them,' do you mean I should go over and talk to them?" Were you thinking explicitly of "'p' is true iff p"? If you were, that's subtle.

"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...Yeah? Would you like to see my cylindric algebra?" You've certainly managed to cover quite a bit of Tarskiana.

"Tarski: That sentence is true if and only if Dobey’s on the phone!" Now I know you were thinking of "'p' is true iff p."

"Tarski: Hey, I thought I proved to you that the question of whether or not we should go is formally undecideable." Reminds me of an exchange in Burton Dreben's seminar (I'm pretty sure I've told you this before). A student asked him if the question "Are there at least 777 consecutive 7s in the decimal expansion of pi?" was decidable. Dreben's reply (given with some amusement): Say you have two automata, one of which, when you start it, prints "Yes," and halts; the other prints "No," and halts. Clearly, one of them answers the question, even if I haven't the faintest idea which one. Yes, it's decidable.

2. Anonymous10:49 PM

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