In case you haven’t noticed the absence of posting, this blog is on hiatus for a couple more weeks. I’m in the midst of moving across the country.
In the meantime, my favorite webcomic has a logic and math puzzles forum. Go play.
The best part, I think, of having a blog is that people read the blog. And then they read other cool things. And then they send you those cool things. And then you get to post them. And then more people read the blog. And they send more cool things. Repeat, ad infinitum, until all the cool things in the entire universe flow directly into your e-mail inbox.
To start off this victorious cycle, reader Matt sends in this article, which proves that the corporate media is good for something after all. Excerpts to follow:
The poet Jan Zwicky once wrote, “Those who think metaphorically are enabled to think truly because the shape of their thinking echoes the shape of the world.”
Zwicky, whose day job includes teaching philosophy at the University of Victoria in British Columbia and authoring books of lyric philosophy such as Metaphor & Wisdom, from which the above quotation was taken, has lately directed considerable attention to contemplating the intersection of “Mathematical Analogy and Metaphorical Insight,” giving numerous talks on the subject, including one scheduled at the European Graduate School in Switzerland next week.
Casual inquiry reveals that metaphor, and its more common cousin analogy, are tools that are just as important to scientists investigating truths of the physical world as they are to poets explaining existential conundrums through verse. A scientist, one might liken, is an empirical poet; and reciprocally, a poet is a scientist of more imaginative and creative hypotheses.
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“Mathematicians don’t talk a lot about analogy in mathematics,” says Simon Kochen, Henry Burchard Fine professor of mathematics at Princeton. “Not because it isn’t there, but just the opposite. It permeates all mathematics. It is pervasive. It’s a powerful engine for new mathematical advances.”
According to Kochen, the modern mathematical method is that of axiomatics — rooted abstraction and analogy. Indeed, mathematics has been called “the science of analogy.”
“Mathematics is often called abstract,” Kochen says. “People usually mean that it’s not concrete, it’s about abstract objects. But it is abstract in another related way. The whole mathematical method is to abstract from particular situations that might be analogous or similar (to another situation). That is the method of analog.”
This method originated with the Greeks, with the axiomatic method applied in geometry. It entailed abstracting from situations in the real world, such as farming, and deriving mathematical principles that were put to use elsewhere. Eratosthenes used geometry to measure the circumference of the Earth in 276 BC, and with impressive accuracy.
In the lexicon of cognitive science, this process of transferring knowledge from a known to unknown is called “mapping” from the “source” to the “target.” Keith Holyoak, a professor of cognitive psychology at UCLA, has dedicated much of his work to parsing this process. He discussed it in a recent essay, “Analogy,” published last year in The Cambridge Handbook of Thinking and Reasoning.
“The source,” Holyoak says, providing a synopsis, “is what you know already — familiar and well understood. The target is the new thing, the problem you’re working on or the new theory you are trying to develop. But the first big step in analogy is actually finding a source that is worth using at all. A lot of our research showed that that is the hard step. The big creative insight is figuring out what is it that’s analogous to this problem. Which of course depends on the person actually knowing such a thing, but also being able to find it in memory when it may not be that obviously related with any kind of superficial features.”
In an earlier book, Mental Leaps: Analogy in Creative Thought, Holyoak and co-author Paul Thagard, a professor of philosophy and director of the Cognitive Science Program at the University of Waterloo, argued that the cognitive mechanics underlying analogy and abstraction is what sets humans apart from all the other species, even the great apes.
Cool beans. Although I’m a little surprised that the author didn’t mention the classic math/science metaphor, Einstein’s beam of light. So this is where you, the reader, posts your favorite math/science metaphors in the comments. Or, if you disagree with the article, comment and say why. You know the drill.
“drag coefficient of a kitten”
(yes, this is a copout because I haven’t done anything interesting enough and math-related to blog about in a few days)
Apparently, there are html gizmos to produce some math symbols. And unicode! Yay to a cool person from another site who tipped me off.
Check this out: ∫ Oooh, yea, baby. Integrate with me.
August 12: Apparently, you can use numerical codes to produce many more math symbols in html.