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Zack_M_Davis comments on Open Thread: January 2010 - Less Wrong
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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.
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.
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.
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).