Combinations
Only a few dozen lighting sequences were actually programmed into the sign's controller at any given time. Some online discussions of the sign reveal comments from individuals observant enough to have noted the repetition. Nonetheless, most of those familiar with the sign believed that it was slowly cycling through an essentially infinite number of possible lighting combinations.
If the only stipulation were that one element at a time would be lit, the number of possible sequences is simply:
90! = (90•89•88•87...3•2•1) ≈ 1.486 x 10138, or 1.486 quintoquadrogintillion. (The exact value is 1 485 715 964 481 761 497 309 522 733 620 825 737 885 569 961 284 688 766 942 216 863 704 985 393 094 065 876 545 992 131 370 884 059 645 617 234 469 978 112 000 000 000 000 000 000 000.)
Such a number may be incomprehensibly huge. If the Big Bang is reckoned to have occurred 13.8 billion years ago, there have been "only" about 4.35 x 1017 seconds since the birth of the universe. It is estimated that the Earth is made up of roughly 5.5 x 1050 atoms; the number of atoms in the Milky Way Galaxy is approximately 5 x 1068, and the number of atoms in the universe is estimated to be 3.5 x 1079.
However, the sequences programmed into the sign's controller suggested to some that the possible total was guided by one or more patterns (e.g., the same element--perhaps the bar below the W--would be lit in each of the nine units, working either left to right or right to left, followed by all nine instances of a second element, and so on, until all ten elements in all nine units were lit). It became a sort of mathematical puzzle to determine what the total number of sequences would be, given these (imagined) patterns.
For the smaller three-unit signs, the number of possible combinations under the "one at a time" scenario would have been:
30! ≈ 2.653 x 1032, or 265.3 nonillion. (The exact number is 265 252 859 812 191 058 636 308 480 000 000.)
This number may be quite small when compared to the figure for the nine-unit sign (it is 1.785 x 10-106 the size of the larger number—or 178 quintrigintillionths) but it nonetheless represents a number that may be well beyond a familiar human scale. One nonillion is approximately the number of bacteria living on Earth.
Read more about this topic: Westinghouse Sign
Famous quotes containing the word combinations:
“I had a quick grasp of the secret to sanity—it had become the ability to hold the maximum of impossible combinations in one’s mind.”
—Norman Mailer (b. 1923)
“Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.”
—Paul Valéry (1871–1945)
“...black women write differently from white women. This is the most marked difference of all those combinations of black and white, male and female. It’s not so much that women write differently from men, but that black women write differently from white women. Black men don’t write very differently from white men.”
—Toni Morrison (b. 1931)