"History, Stephen said…."

For a black widow —

See history in today's Boston.com
and Waldorf in this journal.

The New York Times  now offers a sequel to its philosophy series "The Stone"—

"a sword that heals."

From the Times  City Room this afternoon—

Click to enlarge

"One wild rhapsody a fake for another."

— Wallace Stevens, "Arrival at the Waldorf," in Parts of a World  (1942)

New from Miracle Pictures
– IF IT’S A HIT, IT’S A MIRACLE! –

Pi in the Sky
for Michaelmas 2002

“Fear not, maiden, your prayer is heard.
Michael am I, guardian of the highest Word.”

— A Michaelmas Play

Contact, by Carl Sagan:

Chapter 1 – Transcendental Numbers

  In the seventh grade they were studying “pi.” It was a Greek letter that looked like the architecture at Stonehenge, in England: two vertical pillars with a crossbar at the top. If you measured the circumference of a circle and then divided it by the diameter of the circle, that was pi. At home, Ellie took the top of a mayonnaise jar, wrapped a string around it, straightened the string out, and with a ruler measured the circle’s circumference. She did the same with the diameter, and by long division divided the one number by the other. She got 3.21. That seemed simple enough.

  No one had ever called Ellie stupid before and she found herself bursting into tears….

  After school she bicycled to the library at the nearby college to look through books on mathematics. As nearly as she could figure out from what she read, her question wasn’t all that stupid. According to the Bible, the ancient Hebrews had apparently thought that pi was exactly equal to three. The Greeks and Romans, who knew lots of things about mathematics, had no idea that the digits in pi went on forever without repeating. It was a fact that had been discovered only about 250 years ago. How was she expected to know if she couldn’t ask questions? But Mr. Weisbrod had been right about the first few digits. Pi wasn’t 3.21. Maybe the mayonnaise lid had been a little squashed, not a perfect circle. Or maybe she’d been sloppy in measuring the string. Even if she’d been much more careful, though, they couldn’t expect her to measure an infinite number of decimals.

  There was another possibility, though. You could calculate pi as accurately as you wanted. If you knew something called calculus, you could prove formulas for pi that would let you calculate it to as many decimals as you had time for. The book listed formulas for pi divided by four. Some of them she couldn’t understand at all. But there were some that dazzled her: pi/4, the book said, was the same as 1 – 1/3 + 1/5 – 1/7 + …, with the fractions continuing on forever. Quickly she tried to work it out, adding and subtracting the fractions alternately. The sum would bounce from being bigger than pi/4 to being smaller than pi/4, but after a while you could see that this series of numbers was on a beeline for the right answer. You could never get there exactly, but you could get as close as you wanted if you were very patient. It seemed to her

a miracle

 Cartoon by S.Harris

that the shape of every circle in the world was connected with this series of fractions. How could circles know about fractions? She was determined to learn

calculus.

  She had caught a glimpse of something majestic.

Chapter 24 – The Artist’s Signature

  The anomaly showed up most starkly in Base 2 arithmetic, where it could be written out entirely as zeros and ones. Her program reassembled the digits into a square raster, an equal number across and down. 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… there is an intelligence that antedates the universe. The circle had closed. She found what she had been searching for.

Song lyric not in Sagan’s book:

Will the circle be unbroken
by and by, Lord, by and by?
Is a better home a-waitin’
in the sky, Lord, in the sky?

“Contact,” the film: