Did Ben Franklin Add Up?
SCOTT SIMON, host:
Benjamin Franklin was a brilliant, often vain man, who liked to play the role of the avuncular Everyman. He helped demonstrate that electricity could be captured and used. He devised bifocals. But despite his contributions to science, he's been viewed as a poor mathematician.
Paul Pasles, who teaches math at Villanova University in Pennsylvania, looks at Mr. Franklin's math skills in a new biography that's called "Benjamin Franklin's Numbers."
Of course, we outsourced the reading to our own math guy, Keith Devlin of Stanford University, who joins us from the studios there.
Keith, thanks for being with us.
Professor KEITH DEVLIN (Mathematics, Stanford University): Hi, Scott. Thanks for inviting me.
SIMON: Of course, he didn't spend much time in school, so his math had to be self-taught.
Prof. DEVLIN: Yeah. This I think is where this story came about that he wasn't good at mathematics because he actually, in his autobiography, he wrote about his schooling, and I quote, "I acquired fair writing pretty soon, but I failed in the arithmetic, and made no progress in it."
SIMON: As you read the words of Franklin or read this new biography called "Benjamin Franklin's Numbers," do you, Keith, reading this as a mathematician, apprehend some mathematical knowledge on Franklin's part?
Prof. DEVLIN: Yeah, absolutely. And I think there's a couple of great examples. Franklin had a lifelong interest in magic squares. Now, they are - they go back thousands of years but they were sort of numerical precursors to Sudoku. The idea is you enter numbers into a rectangle, into a square grid of 3-by-3 or of a 4-by-4 and you have to do them so that every row and every column and every major diagonal, all add up to the same number.
Now, to the outsider these look like just doodling with numbers but, in fact, to construct one of those things, you have to get deep into the mathematics and into the patterns. And Franklin did, in his lifetime, spent a lot of time constructing these things and you can only do that if you have a certain deep feeling for numbers.
The other example is what we find in his political and business writings. He is very early, much early than many other people in realizing that you could use what we would now call basic statistics in order to make political and business decisions.
SIMON: Of course, it's Jefferson who's usually adjudged to be the great ranking intellect among that group of men and women...
Prof. DEVLIN: Yeah.
SIMON: ...called the Founding Fathers.
Prof. DEVLIN: Right.
SIMON: I was figuring Dolley Madison in there too, and surely some others.
(Soundbite of laughter)
Prof. DEVLIN: Yeah.
SIMON: But people have suggested over the years that Franklin was perhaps the intellectual heavyweight of that group.
Prof. DEVLIN: Yeah. There's one or two examples of that one. Certainly, Franklin, he wrote an article in - let's see, I made a note of it here - in 1751 called Observations Concerning the Increase of Mankind and the Peopling of Countries. And that was really one of the first ever works in what we now call demographics, using mathematical techniques to look at how populations grow and how people move and how societies develop.
In fact, Franklin was the first person who speculated that populations probably increase exponentially. Now, we always associated that with Thomas Malthus, who was the one that demonstrated that. But, in fact, Malthus had already read Franklin's work and cited it when he did his work.
And now that you've mentioned Jefferson. The other example that I think is interesting - and this is somewhat speculative but Pasles makes this speculation in his book. We know that Franklin had a copy of Euclid's classic geometry textbook "Elements." Now, what Euclid did in "Elements," was show how you could develop mathematical truth starting with axioms, which mathematicians always describe as self-evident truths.
Now, if you look at Thomas Jefferson's first draft of the Declaration of Independence, what it says is we hold this truth to be sacred and undeniable that all men are created equal. Then along come Franklin and Adams and they work on it. And they redraft it. And that phrase, sacred and undeniable, has turned into self-evident. Now what Pasles speculates, and I think this is a reasonable speculation, is that, influenced by the way that mathematics builds sure truths on self-evidence assumptions, he thought it would be great if a nation was founded on axioms, i.e. self-evident truth.
SIMON: January 17th is his birthday, right?
Prof. DEVLIN: Absolutely. And as a mathematician, I now have an extra reason to celebrate his birthday.
SIMON: Keith, thanks so much.
Prof. DEVLIN: Okay. My pleasure, Scott.
SIMON: Keith Devlin, our master mathematician friend from Stanford University.