Posts Tagged ‘Pythagoras’
“All practical jokes, friendly, harmless or malevolent, involve deception, but not all deceptions are practical jokes”*…
When you think of the ancient Greeks, practical jokes might not be the first thing that comes to mind. But along with art, architecture, and philosophy, you can add trick cups to their list of accomplishments.
The Pythagorean cup is so-named because it was allegedly invented by Pythagoras of Samos (yes, the same guy who gave us theories about right triangles). It’s a small cup with a column in its center. It doesn’t look like much, but when an unsuspecting drinker fills it past a designated level, the liquid mysteriously drains out. Legend has it that Pythagoras used it as a way to punish greedy drinkers who poured themselves too much wine…
A timeless practical joke, brought to you by the ancient Greeks: more merriment at “Pythagorean Cup.”
* W. H. Auden, The Dyer’s Hand
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As we ponders pranks, we might send a “Alles Gute zum Geburtstag” to the polymathic Gottfried Wilhelm Leibniz, the philosopher, mathematician, and political adviser, who was important both as a metaphysician and as a logician, but who is probably best remembered for his independent invention of the calculus; he was born on this date in 1646. Leibniz independently discovered and developed differential and integral calculus, which he published in 1684; but he became involved in a bitter priority dispute with Isaac Newton, whose ideas on the calculus were developed earlier (1665), but published later (1687).
As it happens, Leibnitz was no mean humorist. Consider, e.g…
If geometry conflicted with our passions and our present concerns as much as morality does, we would dispute it and transgress it almost as much–in spite of all Euclid’s and Archimedes’ demonstrations, which would be treated as fantasies and deemed to be full of fallacies. [Leibniz, New Essays, p. 95]
This is cool, but I’m holding out for a disease…
Hankering for a little immortality? New Scientist has the answer:
While most mathematical theorems result from weeks of hard work and possibly a few broken pencils, mine comes courtesy of TheoryMine, a company selling personalised theorems as novelty gifts for £15 a pop.
Its automated theorem-proving software can churn out a theoretically infinite number of theorems for customers wishing to join the ranks of Pythagoras and Fermat. “We generate new theorems and let people name them after themselves, a friend, a loved one, or whoever they want to name it after,” explains Flaminia Cavallo, managing director of TheoryMine, based in Edinburgh, UK…
“We’re inventing totally novel theorems, and the tradition is you have the right to name these theorems,” explains Alan Bundy, professor of automated reasoning at the University of Edinburgh and another member of the TheoryMine team. “There are 10 star companies out there, and none of them have any affiliation to the International Astronomical Union.”
He’s got a point. Automated theorem proving is a well-respected mathematical field, used by manufacturers to guarantee that the algorithms in computer processors will work correctly. Bundy and his colleagues have worked in this area for a number of years, and Cavallo came up with the idea for TheoryMine during her final year of an undergraduate degree in artificial intelligence and mathematics at the University of Edinburgh, where she wrote a program to generate novel theorems for her dissertation.
From its library of mathematical knowledge, the program generates a set of mathematical axioms, then combines them in different ways to produce a series of conjectures. It then uses the library to discard a portion of these on the basis that there are already counter-examples, showing they can’t be true. Overly complex conjectures are also ignored. Then it applies a technique known as “rippling”, in which it tries out various sequences of logical statements until one of these sequences turns out to be a proof of the theorem…
“It’s a clever idea,” says Lawrence Paulson, a computational logician at the University of Cambridge and the creator of Isabelle, a theorem prover that Cavallo’s program uses. He is more interested in the theory behind the new program though, adding that “some of the technology here is quite impressive, and I would hope that it finds other applications apart from selling certificates”.
It may well do. Lucas Dixon, another TheoryMiner, is investigating the possibility of using the same techniques to elucidate the rules of algebra in quantum computing systems, which follow different mathematical rules to classical systems.
Don’t prepare your Fields medal acceptance speech just yet though, as TheoryMine’s theorems are unlikely to break drastically new ground. “We can’t say that we’ll never do that, but having looked at the things that come out, they’re not typically things that are going to change the world,” says Dixon.
Your correspondent just purchased “Eleanor’s Equation” for his daughter; reader’s can score their own mathematical monument at TheoryMine.
As we search for the “rum” in theorum,” we might wish a Buon Compleanno to Count Francesco Algarotti, the philosopher, critic, and popularizer of complex scientific ideas; he was born in Venice on this date in 1712– and wrote Neutonianismo per le dame (Newtonism for Ladies) when he was 21.
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