Tagmath

Engineering professor Barbara Oakley explains how she rewired her brain for math at the age of 26:

When learning math and engineering as an adult, I began by using the same strategy I’d used to learn language. I’d look at an equation, to take a very simple example, Newton’s second law of f = ma. I practiced feeling what each of the letters meant—f for force was a push, m for mass was a kind of weighty resistance to my push, and a was the exhilarating feeling of acceleration. (The equivalent in Russian was learning to physically sound out the letters of the Cyrillic alphabet.) I memorized the equation so I could carry it around with me in my head and play with it. If m and a were big numbers, what did that do to f when I pushed it through the equation? If f was big and a was small, what did that do to m? How did the units match on each side? Playing with the equation was like conjugating a verb. I was beginning to intuit that the sparse outlines of the equation were like a metaphorical poem, with all sorts of beautiful symbolic representations embedded within it. Although I wouldn’t have put it that way at the time, the truth was that to learn math and science well, I had to slowly, day by day, build solid neural “chunked” subroutines—such as surrounding the simple equation f = ma—that I could easily call to mind from long term memory, much as I’d done with Russian.

Time after time, professors in mathematics and the sciences have told me that building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success. Understanding doesn’t build fluency; instead, fluency builds understanding. In fact, I believe that true understanding of a complex subject comes only from fluency.

For all intents and purposes, “the fifth line” was a code for asking whether one was Jewish or not. (People of other nationalities, like Tatars and Armenians, against whom there were prejudices and persecution—though not nearly on the same scale as against the Jews—were also picked up this way.) My “fifth line” said that I was Russian, but my last name—which was my father’s last name, and clearly sounded Jewish—gave me away.

Even if I hadn’t been using my father’s last name, my Jewish origin would have been picked up by the admissions committee anyway, because the application form specifically asked for the full names of both parents. Those full names included patronymic names, that is, the first names of the grandparents of the applicant. My father’s patronymic name was Joseph, clearly Jewish, so this was another way to find out (if his last name weren’t so obviously Jewish). The system was set up in such a way that it would pick up those who were at least one-quarter Jewish and everyone of those was classified as a Jew, much like it was in Nazi Germany.

Having established that by this definition I was a Jew, the woman said:

“Do you know that Jews are not accepted to Moscow University?”

“What do you mean?”

“What I mean is that you shouldn’t even bother to apply. Don’t waste your time. They won’t let you in.”

I didn’t know what to say.

“Is that why you sent me this letter?”

Tom Henderson, author of the forthcoming book Punk Mathematics, will keynote EsoZone Portland 2011 on November 18th at p:ear. Admission is free. Tom’s talk is tentatively titled “Time, Space, and the Self are Illusions – So Do ‘You’ Wanna Go ‘Out’ with ‘Me’ ‘Tonight’?” He’ll cover:

• Mining your history for strategy
• Virtual paranoia
• Using the howling void beyond your epsilon of consciousness for a good time

Tom has a masters in mathematics from Portland State University. According to the Kickstarter page for his book:

Punk Mathematics will be a series of mathematical stories. It is written for readers who are interested in having their minds expanded by the strange metaphors and implications of mathematics, even if they’re not always on friendly terms with equations. Better living through probability; the fractal dimension of cities and cancers; using orders of magnitude to detect bullshit; free will and quantum economics; and the mathematics of cooperation in a networked world on the brink of a No Future collapse.

For more on Tom, you can follow him on Twitter, read the Technoccult interview with him or listen to this interview on the Acme Science podcast Strongly Connected Components.

EsoZone Portland 2011 will take place over the course of November 18th and 19th. It will include a few pre-scheduled presentations, workshops and performances along with ample free space for ad-hoc “unconference” sessions in the style of BarCamp or Bird of a Feather.

Watch this space for more announcements.

There’s a new interview with Tom Henderson (aka Mathpunk) on the podcast Strongly Connected Components. Tom talks about numeracy, his teaching style and whatever happened to Math for Primates.

Strongly Connected Components: Tom Henderson

My interview with Tom is here.

What’s interesting is that this doesn’t seem to be a result of “swarm intelligence” – individual bees can somehow make these calculations:

Scientists at Queen Mary, University of London and Royal Holloway, University of London have discovered that bees learn to fly the shortest possible route between flowers even if they discover the flowers in a different order. Bees are effectively solving the ‘Travelling Salesman Problem’, and these are the first animals found to do this.

The Travelling Salesman must find the shortest route that allows him to visit all locations on his route. Computers solve it by comparing the length of all possible routes and choosing the shortest. However, bees solve it without computer assistance using a brain the size of grass seed. […]

Co-author and Queen Mary colleague, Dr. Mathieu Lihoreau adds: “There is a common perception that smaller brains constrain animals to be simple reflex machines. But our work with bees shows advanced cognitive capacities with very limited neuron numbers. There is an urgent need to understand the neuronal hardware underpinning animal intelligence, and relatively simple nervous systems such as those of insects make this mystery more tractable.”

PhysOrg: – Bumblebees can find the solution to a complex mathematical problem which keeps computers busy for days

Ken Keeler, the Futurama writer behind the theorem, actually has a PhD in math, so this was probably just a walk in the park for him. But for the rest of us non math geniuses, his theorem was used to explain a problem with an invention that let characters switch bodies. In the show, you can only switch bodies once with the same pair of people, so they needed an equation to prove that with enough switching bodies around, everyone will eventually end up as who they really are. Insert: funny jokes, robot humor and black comedy and mix accordingly.

Gizmodo: Futurama Writer Invented A New Math Theorem Just To Use In The Show

Tom Henderson, who I interviewed on his punk philosophy of mathematics, is writing a book and you can help fund it. He’s already surpassed his fund raising goal, but I’m sure he could always use more.

Punk Mathematics will be a series of mathematical stories. It is written for readers who are interested in having their minds expanded by the strange metaphors and implications of mathematics, even if they’re not always on friendly terms with equations. Better living through probability; the fractal dimension of cities and cancers; using orders of magnitude to detect bullshit; free will and quantum economics; and the mathematics of cooperation in a networked world on the brink of a No Future collapse.

Kickstarter: Punk Mathematics

I was going to post this last week as part of my post on Pi, but I forgot. So here it is now.

After I posted that article about technical analysis a couple people commented that it reminded them of the film Pi, about a renegade mathematician somehow using Pi to search for patters in the stock market with a homemade supercomputer in his crummy Manhatten apartment.

Technical analysis was probably the inspiration for the stock market portion of the film, but did you know that the part about renegade mathematicians building supercomputers in their living rooms to calculate Pi is actually based on a true story? Aronofsky almost certainly took the inspiration from this 1992 New Yorker story:

Gregory Volfovich Chudnovsky recently built a supercomputer in his apartment from mail-order parts. Gregory Chudnovsky is a number theorist. His apartment is situated near the top floor of a run-down building on the West Side of Manhattan, in a neighborhood near Columbia University. Not long ago, a human corpse was found dumped at the end of the block. The world’s most powerful supercomputers include the Cray Y-MP C90, the Thinking Machines CM-5, the Hitachi S-820/80, the nCube, the Fujitsu parallel machine, the Kendall Square Research parallel machine, the NEC SX-3, the Touchstone Delta, and Gregory Chudnovsky’s apartment. The apartment seems to be a kind of container for the supercomputer at least as much as it is a container for people.

Gregory Chudnovsky’s partner in the design and construction of the supercomputer was his older brother, David Volfovich Chudnovsky, who is also a mathematician, and who lives five blocks away from Gregory. The Chudnovsky brothers call their machine m zero. It occupies the former living room of Gregory’s apartment, and its tentacles reach into other rooms. The brothers claim that m zero is a “true, general-purpose supercomputer,” and that it is as fast and powerful as a somewhat older Cray Y-MP, but it is not as fast as the latest of the Y-MP machines, the C90, an advanced supercomputer made by Cray Research. A Cray Y-MP C90 costs more than thirty million dollars. It is a black monolith, seven feet tall and eight feet across, in the shape of a squat cylinder, and is cooled by liquid freon. So far, the brothers have spent around seventy thousand dollars on parts for their supercomputer, and much of the money has come out of their wives’ pockets. […]

Pi is by no means the only unexplored number in the Chudnovskys’ inventory, but it is one that interests them very much. They wonder whether the digits contain a hidden rule, an as yet unseen architecture, close to the mind of God. A subtle and fantastic order may appear in the digits of pi way out there somewhere; no one knows. No one has ever proved, for example, that pi does not turn into nothing but nines and zeros, spattered to infinity in some peculiar arrangement. If we were to explore the digits of pi far enough, they might resolve into a breathtaking numerical pattern, as knotty as “The Book of Kells,” and it might mean something. It might be a small but interesting message from God, hidden in the crypt of the circle, awaiting notice by a mathematician. On the other hand, the digits of pi may ramble forever in a hideous cacophony, which is a kind of absolute perfection to a mathematician like Gregory Chudnovsky. Pi looks “monstrous” to him. “We know absolutely nothing about pi,” he declared from his bed. “What the hell does it mean? The definition of pi is really very simple—it’s just the ratio of the circumference to the diameter—but the complexity of the sequence it spits out in digits is really unbelievable. We have a sequence of digits that looks like gibberish.”

New Yorker: Mountains of Pi

Since the publication of that story, the Brothers Chudnovsky have apparently turned their attentions to applying their expertise in supercomputing to other domains. Richard Preston, author of the original piece, wrote a follow-up for the New Yorker in 2005.

Reading all of this reminded me of a story I read earlier in the week about someone who claims to have “cracked the code” in Plato’s writings:

The hidden codes show that Plato anticipated the Scientific Revolution 2,000 years before Isaac Newton, discovering its most important idea – the book of nature is written in the language of mathematics. […]

However Plato did not design his secret patterns purely for pleasure – it was for his own safety. Plato’s ideas were a dangerous threat to Greek religion. He said that mathematical laws and not the gods controlled the universe. Plato’s own teacher had been executed for heresy. Secrecy was normal in ancient times, especially for esoteric and religious knowledge, but for Plato it was a matter of life and death. Encoding his ideas in secret patterns was the only way to be safe.

Manchester University: Science historian cracks “the Plato code”

(via Social Physicist)