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Back in the US...A

Greetings from sunny New Brunswick, New Jersey! Actually, it's not sunny because it's night. Ha, I'm funny.

My flight was, well, a flight. It was long (though at 7 hours, preferable to the 11-hour trans-Atlantic haul to the west coast), and there was a screaming baby. The guy next to me was reading about pediatric urology.

And I landed. Americans are so friendly. Random conversations with random strangers, because the train is slow or the kid is cute or the other passenger is stupid. I'd forgotten about that. A fashion designer seeing me struggling with my bags actually carried my 32.5 kilo suitcase all the way down the stairs for me at the train station and rolled it a block uphill, just to be nice.

I'm living in a Rutgers dorm in an apartment populated by two other AT&T interns. It's a dorm. The security is intense. The check-in bureaucracy doesn't know I exist, so I don't actually have a key yet, but the student on duty assured me with a mile-a-minute kwafee accent that it would be worked out tomorrow.

Target is a really big store.

Tonight, an IEEE awards dinner in Princeton, where I in all of my jet-lagged glory was both the youngest and the least well dressed. Highly amusing. The idea, apparently, was that I would get to meet some Princeton people, but none of the many old men and assorted wives there were actually from Princeton. I got to eat some nice catered appetizers and we escaped early.

Apparently New Brunswick has a big Hungarian-American population from '56. There's a Magyar Savings and Loan. Nearby was a hand-written sign in someone's window saying "Isten hozott!"

Already have things to think about. For a particular problem (recursively enumerable, say) you can make a Turing machine that computes it. If this machine has n states, it must accept before busy beaver(n) steps, which is a finite number. This, er, obvious observation that had never actually occurred to me before came about in a discussion of the complexity of problems based on the length of the program used to compute them, which is related to compression.

You can look for primes using the sieve of Eratosthenes. You can get a different sequence by applying successive iterations of your sieve not to all numbers but only to those that are left.

Tangentially related, does anybody know anything about making music from sequences of numbers? Such a thing reminded me of the description of Bach's Art of the Fugue in GEB and also gave me visions of generating sequences of tones of prime frequencies to torment experiment subjects in some evil psychologist's lab. There must be something between the two extremes.

Work tomorrow. Limos to ride, papers to sign. Perhaps I shall soon exist.

Comments

If you haven't read Dirk Gently's Holistic Detective Agency, there's a pretty good sub-plot involving music generated by numbers.

Otherwise, you may want to look into set theory as it relates to music. A friend of mine, who is a composition grad student at UCLA, mentioned that some modern pieces were structured and studied, not in terms of scales, but in terms of subsets of notes, and that the nomenclature was straight out of math class. I bet there is some sort of notation for the study, which would give you a way to go from numbers to set-theory-based modern music.

Unfortunately, the example I heard was about as structured as your prime-number psychological torment, so it may not be exactly what you're looking for.

Hey, thanks.

Musicians are weird.

I found a page of songs that seem to work pretty well: http://www.geocities.com/Vienna/9349/index.html

Dirk Gently's Holistic Detective Agency is worth it just for the couch subplot!

But can somebody explain how to parse "it must accept before busy beaver(n) steps"?

Presumably the TM accepting your r.e. element can take more than BB(n) steps since you start with a non-empty tape.

I suppose that's true. Ok, if the length of the input on the non-empty tape is m, make a modified TM that starts with an empty tape, uses m states to write the input to the tape, then computes using the n states of the original, and use BB(m+n) for your upper bound.

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