
"Impossible for God"Cornell Chronicle: Sagan blogathon is Dec. 20 (full story)
Fans and bloggers are planning a worldwide
blogathon to commemorate
the life and legacy of Carl Sagan  consummate scientist, communicator and educator  on Dec. 20, the 10th anniversary of his death. Sagan was Cornell's David Duncan Professor of Astronomy and Space Sciences. Carl Sagan's famous book "Contact" has always had a special place in my cranial unit. As science fiction, it's good, if not my favorite. As a novel converted to a movie, it's better than most such attempts, and that's even before the prominent display of an Eventide DSP4000 Harmonizer^{®} brand special effects unit in a crucial scene. But my favorite scene from the book was this, almost at the very end: The Argus computer was so persistent and inventive in its attempts to contact Ellie Arroway that it almost conveyed a personal need to share the discovery. The anomaly showed up most starkly in Base 11 arithmetic, where it could be written out entirely as zeros and ones. Compared with what had been received from Vega, this could at best be a simple message, but its statistical significance was high. The program reassembled the digits into a square raster, an equal number across and down. The first line was an uninterrupted file of zeros, left to right. The second line showed a single numeral one, exactly in the middle, with zeros to the borders, left and right. After a few more lines, an unmistakable arc had formed, composed of ones. The simple geometrical figure had been quickly constructed, line by line, selfreflexive, rich with promise. The last line of the figure emerged, all zeros except for a single centered one. The subsequent line would be zeros only, part of the frame. Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts. The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle  another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn't matter what you look like, or what you're made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you'll find it. It's already here. It's inside everything. You don't have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist's signature. Standing over humans, gods, and demons, subsuming Caretakers and Tunnel builders, there is an intelligence that antedates the universe. The circle had closed. She found what she had been searching for. As written, the implication is that somehow the universe was designed with the transcendental value of pi so arranged that its digits were graphical as well as numerical. I was reading several comments about this in other blogs and one stated that actually constructing a universe and controlling the value of pi is "impossible for God." Without debating that question, I submit that if one searches long and hard enough, one will, indeed, find the "message" in the digits of pi. Consider: As far as anyone knows, pi is random and infinite. Should that not mean that any pattern, including the one above, will eventually appear? I did a little experiment. Sagan doesn't quantify just how good the resolution of the circle in the square was. I made a "real" circle that was 21 units in radius. This would probably look pretty good pixellated if I weren't too lazy to select the ones and zeros manually or write a program to calculate them. I also made the best circles I could in grids of 5, 7, 9, and 11 units. In a square of five units, seven if you count the frame, you would expect the pattern shown every 500 trillion possibilities. Pi has been calculated to millions of digits, and even the light blue pattern is expected once in 8*10^50 possibilities. But infinity means infinity! Who's to say that Sagan's message isn't already there! In fact, if we look long enough, we'll probably also find the circle in the frame, with SAGAN written in block letters, in English, right in the center. NP: "Tam Lin"  Fairport Convention 

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