Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Sunday, July 17, 2011

Learning about Language & Understanding the Universe


When this video came across my desk a month or two ago, I sat up and paid attention. You should too. Give it a watch.


(For people reading this on Facebook, which doesn't like videos, click here.)

The notion that the arts and sciences are not at odds, but both ask fundamental questions about the most important things, is not news to me. But like hearing the Gospel once more and being born again for the 10,000th time, this hit me pretty heavy. Why? Two reasons.

First. I had not read any math lately. Or anything about math. Or numbers. There was a chapter about the Enigma machine I read a day or two before watching. It had quite a bit about combinations and numbers, but I glossed over that when I could have engaged it, and pressed on to the next bit of history. Now I have gone back and given Enigma a little more numerical consideration.

Second. I had been spending all day - indeed, about six weeks - deep in British archives, doing research. I was living the arts, you might say, being a good historian. But I realized that my history was often failing to ask the great questions of language and of the cosmos. Please, do not misunderstand: I was doing excellent history, with all kinds of primary sources and keen analysis. But my history was just that, and not more. And it should have been more.

One further thought comes to mind: When our video's narrator speaks of "math", what he really means is "pure math" or "philosophy of math," as opposed to "applied math". In some ways a minor detail, but oh so big. At most universities, though the Math Department is housed in a College of Liberal Arts and Sciences, it is engineers who take its classes and thereby pay its budget. So although said department may strive to consider numbers as language, as clues to the nature of the universe, it is usually reduced to calculating how heavy the truck can be before the bridge collapses. This is sad.

Friday, July 31, 2009

Athanasius Kircher: Patron of Polymathematical Nerds


On this feast of St. Ignatius of Loyola, I exhort all of you to read up on Athanasius Kircher, SJ, one of the greatest polymaths of the Jesuit order (and the 17th century, for that matter).

I first discovered Kircher through a contemporary polymath, Umberto Eco, who treats him in his excellent little volume Serendipities: Language and Lunacy. In his quest to translate the hieroglyphics on Roman obelisks, Kircher became an example of a brilliant man whose errors led to real discoveries:

"When Kircher set out to decipher hieroglyphs in the seventeenth century, there was no Rosetta stone to guide him. This explains his double mistake, namely, believing that hieroglyphs had only symbolic meaning and the absolutely fanciful way in which he identified their meaning . . . Kircher poured elements of his own fantasy into these reconstructions, frequently reportraying the stylized hieroglyphs in curvaceous baroque forms . . . in the third volume of the Oedypus there is long analysis of a cartouche that appears on the Lateran obelisk, where Kircher read a long argument concerning the necessity of attracting the benefits of divine Osiris and the Nile by means of sacred ceremonies activating the Chain of Genies, tied to the signs of the zodiac. Egyptologists today read it as simply the name of the pharaoh Apries. Kircher was then wildly wrong. Still, notwithstanding his eventual failure, he is the father of Egyptology, though in the same way as Ptolemy is the father of astronomy: in spite of the fact that his main hypothesis was mistaken. By following a false hypothesis he collected real archeological material, and Champollion (more than one hundred fifty years later), lacking an opportunity for direct observation, used Kircher's reconstructions for his study of the obelisk standing in Rome's Piazza Navona."

(Umberto Eco, Serendipities, 61, 62-63)

In addition to founding Egyptology, Kircher also contributed to Linguistics, Physics, Mathematics, Music, Engineering and many other disciplines, though some of his theories (like the composition of the "subterranean world") have since been rejected. Kircher was also a pioneer in the study of electromagnetism.

More information on Kircher can be found at the Catholic Encyclopedia and this fun fan site.

Here are Kircher's obelisks, his cosmology, one of his inventions, and his subterranean earth:

































Athanasius Kircher, ora pro nobis qui scientiae studemus.

Thursday, June 18, 2009

Pi, etc.


We recently lost the internet at my house for several days. One realizes just how much it has become a part of everyday life when it is gone. Rather than listing all the things I could not do, suffice it to say I found something I could: watch movies. So I did.

Darren Aronofsky’s Pi is a story about the search for meaning in the universe. It tells the tale of Max Cohen, a mathematician obsessed with finding patterns to explain phenomena around him. More to the point, he is interested in finding the pattern which will explain, well, everything. In the course of the story we encounter Wall Street types who are interested in such patterns primarily for the ability to predict the stock market, but we also meet kabbalists who seek to decode the Torah and find the long-lost name of God which will help usher in the messianic age.



The film reminded me of Eric Foner’s Story of American Freedom, a text I had to teach this past semester. Foner’s objective seems simple enough: to explain the changing definition of freedom from the time of the American Founding to the present day. However, as I tried to point out to my students, implicit in his presentation was another message. To help them tease that out, I gave a (very, very, very!) quick-and-dirty history of western philosophy, since such courses are not required at A&M.

Plato argued that there were such things as forms, things in heaven which embody ideas. Or rather, more to the point, are ideas, which are imperfectly embodied in particular occurrences. There is the form of the Tree, in which all trees participate, and by that participation they have something in common. There is the form of the Cat as well, along with abstract – but no less real – concepts such as Justice, Truth and Freedom.

Aristotle, though he spoke of substance and accidents, rather than forms, broadly agreed with Plato that there are fundamental categories at work in the cosmos, categories which transcend physical characteristics and abide in the very fiber of a thing’s being. But in the Middle Ages a fellow named William of Ockham denied that there were categories at all. Yes, he said, we can point to this fuzzy thing with whiskers and that fuzzy thing with whiskers, and we can call them both cats, because that would be a very useful thing to say. But in the end, Ockham argued, each is a unique object without anything fundamentally in common with the other. We apply labels for our convenience, but they do not correspond to any deeper meaning in reality.

Some centuries later Immanuel Kant tried to steer a middle course between these two positions, contending that there may be categories to the cosmos, but we cannot know them. Thus, in practice, he was an Ockhamite, arguing that the labels we affix may be handy, but may not actually correspond to the fundamental being of things. Finally, the nihilists – most famous among them being Friedrich Nietzsche – contended that there is no meaning to the cosmos at all, categorical or otherwise, a far cry from the ancients.

How did all this connect to Eric Foner and American history? While charting the changing meanings of “freedom” over the years, I would submit that Foner assumes – and implicitly argues – that there is no meaning to the term “freedom”; it does not really exist. Yes, Foner is willing to talk about it as a label we place on things, even a very convenient label, but in the end, does it correspond to anything in reality? Is there a right answer to the question, “What is freedom?” Foner demurs and – I would argue – ultimately denies.

Returning then to Mr. Aronofsky’s film and the pressing question it asks: Is there meaning to the cosmos? And if there is, what is it, and what does that meaning demand of me?

Agnosticism, exceedingly vogue in the ivory tower of academia, seeks to avoid these questions. Perhaps the answers simply are unknowable, though I doubt most have ever truly sought them. And if the point of all our academic endeavors is to know the truth, what does it say about us that we have abdicated any responsibility for knowing the highest truths?

This post first appeared yesterday on True. Good. Beautiful., a forum about entertainment and the film industry.