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Warrigal comments on Open Thread: January 2010 - Less Wrong
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"Imagine the human race gets wiped out. But you want to transmit the so far acquired knowledge to succeeding intelligent races (or aliens). How do you do?"
I got this question while reading a dystopia of a world after nuclear war.
Transmitting it to aliens ain't happening; we'd get them from radio to the present day, a couple hundred years' worth of technology, which is relatively little, and that's only if we manage to aim it right.
So, we want to communicate to future sapient species on Earth. I say take many, many plates of uranium glass and carve into it all of our most fundamental non-obvious knowledge: stuff like the periodic table, how to make electricity, how to make a microchip, some microchip designs, some software. And, of course, the scientific method, rationality, the non-exception convention (0 is a number, a square is a rectangle, the empty product is 1, . . .), and the function application motif (the way we construct mathematical expressions and natural-language phrases). Maybe tell them about Friendly AI, too.
Is there such a convention? We don't say that one is prime. e^x is often said to be the only function that is its own derivative, as if the zero function somehow didn't count.
One definition of a prime, of course, is "a number whose only factors are itself and 1, except for 1 itself". Another, however, is "a number with exactly two factors", which is probably the simpler than "a number whose only factors are itself and 1". And if 1 were prime, it would be a highly exceptional one, in that there would be many places to say "all prime numbers except 1".
The only functions defined over all real numbers that are their own derivatives are those of the form k*e^x for some real number k. These include not only e^x but 2e^x and 0e^x.
ke^x is its own derivative for any k, including 0. It's a lot more convenient for 1 not to be prime. But 0! = 1, for example.
Yes -- at least in the sense that I have found familiarity with (and sympathy toward) this practice to be an effective shibboleth for distinguishing the mathematically sophisticated.
(It's kind of like how it's a warning sign when someone doesn't think the word "dictionary" should be in the dictionary.)
Like Karl Pilkington?
Thank you. Sorry for the stupid question, then; do downvote the grandparent.
One is not prime. The zero function is a trivial function; it actually doesn't count (for reasons that are technical).
In what language or symbolic system would you do so? The Pioneer plaque and Voyager records both made an attempt in that direction, but I'm sure there's a better way.
In one of my classes in college, we were asked to try to decipher the supposedly universal language of the Pioneer plaque, which should have been relatively easy insofar as we shared a species (and thus a neural architecture) with the creators. We got some of it, though not all, which is apparently better than many of the NASA scientists on the project!
We humans can decipher ancient human languages given a large enough corpus. Non-humans shouldn't have too much trouble. The chief trouble I imagine is getting from idiomatic ways of saying things to what we're really trying to say, e.g. "I would be surprised if it were green" to "The sky is not green".
The second you talked about etching knowledge for the future, I immediately thought of The Long Now Foundation's Rosetta Project -- which intends to etch lots of linguistic information onto small metal discs, with lots of copies floating around for redundancy. They're apparently having production problems, though. I believe the Long Now book actually muses about how a "civilization start up guide" might be something handy to put in a similar format, but don't have it around at the moment.
Out of curiosity, why uranium glass?
And going off on a tangent, does the entire Long Now Foundation and its projects remind anyone else of Hanson's "Dreamtime" concept?