The Usefulness of Mathematical Learning - Part 2

Part 1

Continuing on the the second page, we find that

In all ages and countries where learning has prevailed, the mathematical sciences have been looked upon as the most considerable branch of it. The very name "Mathematician" implies no less, by which they were called either for their excellency or because of all the sciences they were first taught, or because they were judged to comprehend "all things mathematical". 

I'm no scholar of Greek, so I'm taking a bit of a liberty with what I think Arbuthnot was trying to say here. I do know that the original Greek word from which the term "mathematics" is derived has senses of meaning "what is learned." So it's not really surprising that he goes on to write

And amongst those that are commonly reckoned to be the seven Liberal Arts, four are mathematical, to wit, Arithmetic, Music, Astronomy, and Geometry.

He is referring here to the Quadrivium, which was the second course of study in the medieval university. The first was the Trivium, and consisted of Grammar, Logic and Rhetoric. Of course, contemporary people don't really think of music as a mathematical study, even though things like rhythm, pitch, tempo, and duration can all be quantified, and despite the explicitly mathematical origins of the art in the Western tradition starting with Pythagoras.

Not only that, logic actually is a branch of mathematics now, but wasn't in the 17th century. It started to be formalized as a mathematical study in a serious way by thinkers such as Boole, Pierce, and Russell.

In the next part, the author starts to describe why he thinks people don't learn math as much as they should.

But notwithstanding their excellency and reputation, they have not been taught nor studied so universally as some of the rest, which I take to have proceeded from the following causes:

The reasons he gives all sound very modern: people don't like to think so hard, they don't realize how useful math is, they think that only geniuses can learn it, it is not encouraged, and there aren't enough good teachers.

Spring Break: Alchemical Texts and Darwin Art

I went to new Haven for spring break.

The Beinecke Rare book and Manuscript Library has several interesting past, current, and future exhibitions dealing with the history of math and science. For example, "Trees in Fact and Fable" examines its subject from several disciplines, including botany. There is one about mathematics in early modern England, an International Year of Astronomy exhibition called "Starry Messenger", and some works on alchemy in the European imagination. (I got to see that one.)

Also at Yale, the Yale Center for British Art is hosting an exhibition called "Endless Forms": Charles Darwin, Natural Science, and the Visual Arts (site here). It deals with the effect the publication of Origin of Species had on the arts world. It includes scientific diagrams, paintings depicting prehistoric humans and other creatures, fanciful illustrations of past humanity, Romantic depictions of "the struggle for existence", and photographs of non-European people meant for the scientific study of race. Or I might say pseudo-scientific.

A long, detailed, and nuanced discussion of the affair between Galileo and the Church may be found here. Part of the interest is in the exposure of some of the "mythology" that surround this issue. Such as this:

According to one of these readings, Galileo knew the Earth to go round the Sun, as Copernicus had written, rather than the converse as implied in several Biblical passages. The Church would not allow science to disprove the revealed truth of Scripture, however, and hence threw Galileo to the Inquisition where he was forced under threat of torture to disclaim this opinion and never speak of it again. He was then imprisoned under house arrest for the remainder of his life, a clear example of the conflict between scientific investigation of the world around us and the presumed infallible authority of the Bible.

Which is a story often cited as the truth of history.

The Innumeracy of Intellectuals

Magnolia Sitter has linked to this very interesting article. The double standard of engineering students who don't like humanities versus humanities students who don't like math or science is especially interesting.

Also interesting to me is that in medieval education, the trivium and quadrivium consisted of grammar, logic, and rhetoric; and arithmetic, geometry, music, and astronomy, respectively. Of the seven courses in the original liberal arts curriculum, two were explicitly mathematical and three were closely related to mathematics.

To paraphrase Robert Anton Wilson, "Some people at the university specialized in manipulating mathematical symbols, others in verbal ones. Because the people who manipulated verbal symbols were better with language, they got to define themselves as the intellectuals."

The Most Important Image Ever Taken

According to this video, it is the Hubble Deep Field, and I'm inclined to agree. Whenever I look at it, I feel chills. This image, and the even higher resolution Ultra Deep Field, contain hundreds and hundreds of points, blobs, and smears of light. Each one is not a star, but an entire galaxy.

On the less inspired side of things, if you want to see something that manifests such intense stupidity and willful, possibly malevolent ignorance that it is capable of causing physical pain in those who watch it, go here.

The basic "idea", for those unwilling or unable to subject themselves to such gibbering imbecility, is staggeringly nonsensical, and incandescently moronic; a train wreck of epic cognitive ineptitude: Rainbows are a government conspiracy.

Or as the video says: "Everywhere we look, the visible spectrum, is rainbows. This cannot be natural." This is why we need math and science education with tough, rigorous, and reality-based curricula.

mathematics, astronomy, religion

I found something on the Library of Congress website: a collection of images from the Vatican Library of mathematical manuscripts from between the ninth and fifteenth centuries.

Saturday Comic:


The background is an ultra deep field photo taken by the Hubble Space Telescope and credit is due to ESA and NASA.

Pascal's quote is from the Pensées, numbers 205-206.