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Suppose we wanted to transmit this knowledge, everything we had ever learned, to another world. First we would want to make the representation as compact as possible. By squeezing out redundancies we could compress the number so that it would occupy smaller and smaller spaces. In fact, if we are adept enough we can represent the number in a manner that requires almost no space whatsoever. We simply take the long string of digits and put a decimal point in front of it so that it becomes a fraction between 0 and 1, a mere point on a line. Then we choose a smooth stick and declare one end 0 and the other end 1. Measuring carefully, we make a notch in the stick -- a point on the continuum representing the number. All of our history, our philosophy, our music, our art, our science -- everything we know would be implicit in that single mark. To retrieve the world's knowledge, one would measure the distance of the notch from the end of the stick, then convert the number back into the books, the music, the images.
The success of the scheme would depend on the fineness of the mark and the exactness of the measurement. The slightest imprecision would cause whole Libraries of Alexandria to burn.
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Suppose the medicine men of Otowi had discovered this trick. Suppose, contrary to all evidence, that they had developed a written language, a number system, and tools of enough precision to encode a single book of sacred knowledge into the notch of a prayer stick -- the very book, perhaps, that explains what the symbols on the rock walls mean. And suppose a hiker, exploring one day in the caves above Otowi, found the stick. Could the knowledge be recovered?
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Aliens trying to decode our records might recognize what seemed to be deliberate patterns in the markings of ink on pages or the fluctuating magnetic fields of computer disks (though, again, if the information had been highly compressed, it would be harder and harder to distinguish from randomness). If they persisted, would they find truths to marvel at, signs of kindred minds? Or would they even recognize the books and tapes as things that might be worth analyzing? One can't go around measuring every notch on every stick.
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