Tuesday, March 03, 2009

Marin Mersenne

Or we could call this "Priest, Piano, and Prime" - if you like alliteration.

Do you play the piano? Did you know that a Catholic priest worked out rules which are used in its construction? Yes... but let's try something a bit closer.

Do you worry about security on the INTERNET? Do you know that some of the best security measures rely on very large prime numbers, and the difficulties they pose to even powerful computers? A prime number, you may recall, is one that has no factors other than itself and one - no integer divides it evenly. (No, this is not a technical article, don't worry.) But because there is this odd connection between prime numbers and security, when I was in grad school we used to have a slogan: "Spies like big prime numbers." It was a bit of fun, hee hee.

Did you know that there are some very famous prime numbers named for a Catholic priest?

The Mersenne primes are those of the form
Mersenne thought that these numbers would be prime for certain values of p. It turned out that he was wrong in at least one case, when p is 67, but that wasn't discovered until 1903, when F. N. Cole blew away the American Mathematical Society by going up to the blackboard and working out 2-to-the-sixty-seventh by multiplying 2 x 2 x 2... (there are sixty-seven twos, but I won't write all of them). Then he went to another board and worked out
193,707,721 x 761,838,257,287
and the result was the same. He sat down, to vigorous applause, without having said a word. For more see here. Also see Eric Temple Bell's article, "The Queen of Mathematics" page 503 in The World of Mathematics Vol. 1.

Mersenne also formulated three laws of vibration:
1. When a string and its tension remain unaltered, but the length is varied, the period of vibration is proportional to its length. (The law of Pythagoras.)
2. When a string and its length remain unaltered, but the tension is varied, the frequency of vibration is proportional to the square root of the tension.
3. For different strings of the same length and tension, the period of vibration is prortional to the square root of the weight of the string.
[From Mersenne's Harmonie Universelle, quoted in The World of Mathematics Vol. 4.]
Which, if you've ever looked inside a piano, explains why the bass strings are so heavy. Now you know. (It's lots easier to look inside a piano than inside a computer, and often more interesting. I can never see the primes, even though they say there are some in there... Hee hee.)

The name of Father Marin Mersenne is still known by mathematicians, physicists, and historians of science. Father Jaki calls him "probably the best contemporary judge of what was good and bad in early 17th-century writings about science" [God and the Cosmologists, 86]

Mersenne was born in 1588 and studied at Le Mans and the Jesuit College of La Flèche. He entered the novitiate of the Minims - an order founded by St. Francis of Paula in the late 1400s. He was a life-long friend of Descartes, and Galileo and Gassendi (another scientist and Catholic) were also friends; he carried on correspondence with many scientists of that time.

Mersenne asked that, after his death, an autopsy be made on his body, so as to serve to the last the interests of science. He died in 1648.

Jaki tells us more about Mersenne:
...possibly the most selfless servant the scientific community had ever had. His disarming generosity, his tireless eagerness to learn and to communicate, earned him the trust, respect, and gratitude of most of those who played a part in ushering in, what Whitehead aptly called, the century of genius. Mersenne’s motivation in carrying for decades an almost superhuman workload of scientific correspondence and publications derived from that evangelical candor and zeal which his order, the Minimes, aimed to achieve. In Mersenne, there was the rare combination of theologian, scientist and, above all, of a virtuous Christian. It should not, therefore, be surprising that Mersenne wrote more extensively than others in his century about the relation of science and theology, and he did so with a consistently high level of judiciousness. In the clarity of the new mechanistic science he saw a powerful antidote to crude and refined forms of obscurantism alike. He fought with equal zeal the astrological tradition and the pantheistic animism of which in his time Robert Fludd, whom he used to call “the evil magician,” was the chief advocate. As Mersenne saw it correctly, the belief in the Creator was incompatible with both. In his monumental discussion of the biblical account of creation, the Quaestiones celeberrimae in Genesim, Mersenne delved into every possible ramification of the dogma of creation. He did so in the conviction, which he expressly stated, that no phrase of greater portent was ever formulated than the one declaring that "In the beginning God created the heaven and the earth."
[Science and Creation 284-5]
Here's another piece of detail about him, which you may find surprising:
Mersenne had high hopes that experimental and quantitative science would serve as a powerful antidote against magic, cabbala, and astrology, the natural allies of an animistic world view. No trained astronomer, Mersenne failed to see the importance of Kepler's Three Laws. He had shown greater sympathies for tracing out the harmonious proportions in music as well as in the physical world, as shown in his last major work, the Harmonie universelle (1636-7). Its inspiration was as scientific as it was Pythagorean. But Mersenne, whose first great work was a massive treatise on creation, was fully aware that an a priori approach to nature clashed with the utter contingency of the world, implied in the belief in the Creator. It was in that sense that he turned the table on Kepler by arguing that the actual measures in the world, in particular the sizes of planets, their distances and the like, were the actualisation of only one of infinitely numerous possibilities. Since those data could not be deduced from any known law of nature, they were to be viewed as being contingent on the sovereign act of the Creator. Mersenne's reasoning might in some specifics have gone too far, but it is useful to remember that those data about the planets to say nothing about data concerning the universe as a whole, are still waiting for a scientific explanation.
[Jaki, Planets and Planetarians, 26]
One more note from another source, which I had forgotten to explore, shows that Mersenne provided a service much like a blogg - or at least like e-mail:
Mersenne, who was said to have more in his head that all the universities together, acted as a clearinghouse for the various scientific works of his day. He took the place of the still nonexistent scientific journals, broadcasting through letters news of the latest achievements by Pascal, Descartes, Roberval, and others.
[Muir, Of Men and Numbers 60]

Footnote: I used information excerpted from here.


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