“By removing the one size fits all lecture from the classroom and letting students have a self-paced lecture at home, and then when you go to the classroom, letting them do work, having the teacher walk around, having the peers actually be able to interact with each other, these teachers have used technology to humanize the classroom.”
~ Sal Khan, of Khan Academy
See also:
Duality
by Georges Whitesides, from No Small Matter: Science on the Nanoscale
We’re burdened by a curious conditioning that blinds us to one of the greatest — perhaps the greatest — of art forms. We live for poetry; we live in terror of equations.
We see a poem, and we try it on for size: we read a line or two; we roll it around in our mind; we see how it fits and tastes and sounds. We may not like it, and let it drop, but we enjoy the encounter and look forward to the next. We see an equation, and it is as if we’d glimpsed a tarantula in the baby’s crib. We panic.
An equation can be a thing of such beauty and subtlety that only a poem can equal it. As an evocation of reality — as the shortest of descriptions, but describing worlds — it is hard to beat the most artful of poems and, equally, of equations. They are the best our species can do.
Equations are the poetry that we use to describe the behavior of electrons and atoms, just as we use poems to describe ourselves. Equations may be all we have: sometimes word fail, since words best describe what we have experienced, and behaviors at the smallest scale are forever beyond our direct experience.
Consider Margaret Atwood:
You fit into me
Like a hook in an eyeA fish hook
An open eye
Consider Louis de Broglie (a twentieth-century physicist, and an architect of quantum mechanics):
λ = h/mv
Read the equation as if it were poetry — a condensed description of a reality we can only see from the corner of our eye. The “equals” sign is the equivalent of “is,” and makes the equation a sentence: “A moving object is a wave.” Huh? What did you just say? How can that be?
It’s an idea worth trying on for size. Poetry describes humanity with a human voice; equations describe a reality beyond the reach of words. Playing a fugue, and tasting fresh summer tomatoes, and writing poetry, and falling in love all ultimately devolve into molecules and electrons, but we cannot yet (and perhaps, ever) trace that path from one end (from molecules) to other (us). Not with poetry, nor with equations. But each guides us part way.
Of course, not all equations are things of beauty: some are porcupines, some are plumber’s helpers, and some are tarantulas.
* * * *
I’m a chemist. My universe is nuclei and electrons, and the almost endless ways they can assemble. Atoms are just at the border between ordinary, macroscopic matter and matter dominated by the Alice-in-Wonderland rules of quantum mechanics. Electrons, in particular, have the unnerving property of having mass and charge but no extent — no size. There’s no tiny BB down in their core, as there is a nucleus sitting at the center of an atom. “Ah,” you say, “that’s strange. If there’s nothing there, what is it that has a mass? And what’s charged?” Good question…
…As a chemist, I’ve come to uneasy terms with the weirdness of electrons and photons, and with their ability to meld into the ordinariness of macroscopic things. But sometimes, lying awake in a strange hotel room at 4 a.m., considering what I might say that I really understand about anything, I fret that the answer is: almost nothing.
“Can I ask you to please recall a time when you really loved something, a movie, an album, a song or a book, and you recommended it wholeheartedly to someone you also really liked, and you anticipated that reaction, you waited for it, and it came back, and the person hated it. So, by way of introduction, that is the exact same state in which I spent every working day of the last six years. I teach high school math. I sell a product to a market that doesn't want it, but is forced by law to buy it. I mean, that's kind of—it's just a losing proposition.”
~ Dan Meyer, from “Math Class Needs a Makeover,” TED Talks (May 2010)
“In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane to a generating straight line of that surface. Given a point (the focus) and a corresponding line (the directrix) on the plane, the locus of points in that plane that are equidistant from them is a parabola. The parabola has many important applications, from automobile headlight reflectors to the design of ballistic missiles.”
Excerpt from “Algebra in Wonderland,” by Melanie Bayley, New York Times (March 7, 2010):
Alice has slid down from a world governed by the logic of universal arithmetic to one where her size can vary from nine feet to three inches. She thinks this is the root of her problem: “Being so many different sizes in a day is very confusing.” No, it isn’t, replies the Caterpillar, who comes from the mad world of symbolic algebra. He advises Alice to “Keep your temper.”
In Dodgson’s day, intellectuals still understood “temper” to mean the proportions in which qualities were mixed — as in “tempered steel” — so the Caterpillar is telling Alice not to avoid getting angry but to stay in proportion, even if she can’t “keep the same size for 10 minutes together!” Proportion, rather than absolute length, was what mattered in Alice’s above-ground world of Euclidean geometry.
“I'm a composer, orchestrally-trained, and the inventor of the AlloSphere. With my visual artist colleagues, we map complex mathematical algorithms that unfold in time and space, visually and sonically. Our scientist colleagues are finding new patterns in the information. And our engineering colleagues are making one of the largest dynamically varying computers in the world for this kind of data exploration. I'm going to fly you into five research projects in the AlloSphere that are going to take you from biological macroscopic data all the way down to electron spin.”
~ Composer JoAnn Kuchera-Morin, founder of the Center for Research in Electronic Art Technology (CREATE)
Daron Larson
Freelance Contemplative
