Robust Analysis
Robust Analysis Vs Intuition
“Many of you still see mathematics as foreign and difficult”, Cooper said, beginning the afternoon
session. “So I’d like to depart from the syllabus for a few minutes to give you a practical
demonstration of the way mathematics can help you to think.” He put his chin in his hand and
peered at us. “If you took a single piece of paper,” he said, “folded it in half, folded it in half again,
and kept on folding it in half a total of thirty-two times, how thick would the sheet be?” He called on a
woman in the front row.
“Maybe two inches?” she said.
“Wrong!” Cooper called on others.
“Two feet thick?” “Three feet?”
Cooper shook his head. “The correct answer, ladies and gentlemen, is that one sheet of paper will
achieve a thickness of just over 271 miles. Observe”.
Turning to the chalkboard, Cooper took us through the mathematics. A ream of paper of 500 sheets
was about two inches thick, and each individual sheet was therefore about 2/500 or .004 of an inch
thick. After one fold, a sheet of paper took on the thickness of two sheets, after two folds, of four
sheets, and after three folds, of eight sheets. Two, four and eight could be expressed as two to the
power of one, two to the power of two, and two to the power of three.
“After 32 folds,” Cooper said, “the sheet has the thickness of two to the power of 32, or
4,294,967,296. That number times .004 equals 17,179,869 inches. Seventeen million one hundred
seventy-nine thousand eight hundred and sixty-nine inches equals 1,431,655 feet. And one million
four hundred thirty-one thousand six hundred and fifty-five feet equals approximately 271 miles.
“Ladies and gentlemen, there is no way intuition gets you there. But math gets you there in just a
brief series of calculations.”
Even I had to admit that Cooper had made his point. Math could provide a compact, powerful tool of
analysis. For a moment I was event struck with a kind of wonderment, a poet glimpsing the poetry of
math.
Extract from “Snapshots from Hell”
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