Apr

7

I found this approach quite fascinating.

An M.I.T. professor wants his students to begin using educated guesses to come up with solutions to math problems in the real world.

"Why Math is Like Street Fighting":

Street fighting and math hardly seem like they would fit together.

But for Massachusetts Institute of Technology professor Sanjoy Mahajan, street fighting is a perfect analogy to encourage his students to use educated guesswork to solve math problems in the real world.

"In street fighting, the beautiful form of a kick doesn't matter," Mahajan said in a phone interview with the Star. "What really helps you is if you connect and get results you need and survive. You can think of problem-solving as being in a duel with nature. You want to get to the end. The beauty and the elegance of it doesn't matter."

In his course, the "Art of Approximation in Science and Engineering," Mahajan, associate director for teaching initiatives at MIT's Teaching and Learning Laboratory, wants his students to use a variety of principles or ways of reasoning - everything from analogical to pictorial - to come up with solutions.

Mahajan believes essentially the students have to lower their standards - a hard thing for any educator to utter and even harder thing for perfection-wired students to embrace.

"They have been trained that science and engineering is all about rigor and exactness. And yes, it is at the end. But at first you need a rough idea of where you are. You need to lower your standards and get something on paper."

Mahajan believes that if students focus on rigorous exact formulas of mathematics, they'll never come up with solutions. "Life comes at you with roughly stated problems," he said. And "you need rough answers."

He often encourages students to draw a picture of why something is true and then they can usually apply the answer to a harder issue. "Our brain is more developed visually than symbolically," he explains.

He also advises his students to find a simpler version of a problem they're trying to solve and try to solve that first. Once that's done, the student can apply the answer to the larger problem.

Another technique he said students can use is "the divide and conquer" form of reasoning. "If you have a hard problem, divide it into bits," said Mahajan. "Like the British ran their Empire."

Mahajan says the key to street-fighting math is to be intuitive and adept at understanding how equations work in the real world.

"You can use these techniques to explain interesting things about the physical world," said Mahajan, who was born in England, grew up in New Jersey. He went on to study physics at Stanford, then mathematics at Oxford University. He did his PhD in theoretical physics at the California Institute of Technology and post-doc work at Cambridge University in England.

"I wish everyone would learn math this way."

In an attempt to share his theories with the world, he has written a textbook for his students and anyone else who might be interested. Street Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem-Solving is published by MIT Press but is also available online, licensed under the Creative Commons Non-Commercial Share Alike. That means anyone who is interested can download it for free and distribute copies of it as long as they don't sell it.

Orson Terrill writes: 

I totally agree with this guy. Progress shouldn't be a prisoner of perfection. When I traded my first algorithmic "system" in currencies, I did not have the privileges to automate my trades with my currency "broker" (often they take the other side on paper), nor the funds to get a real intermediary (I was in college while supporting my teenage brother). Keeping two separate computers running, I had my right hand over my ten-key to an excel workbook, and my left middle finger on the key to take the bid or ask. Often, I would only get the initial figures into my excel sheet, and then "quick and dirty" my way forward for a few minutes. I was still able to put a large number of trades lasting less than a minute, and many that were only a few seconds (it depended on market volatility). The approach was to scalp after a relatively large move began to pause, and depending on the time of day, it could be unreasonable to expect scalping opportunities to remain for long (though they could before an important announcement, or as traders battle each other over the significance of whatever line in the sand has formed, or both).

It is true that much learning is sacrificed at the cost of the perfect learning of formulas that are usually only a model, or an impression, of what happens in the real world anyways. If you're hoping that a price model can be generalized, a holy grail, then it is almost certain that the conjecture will need be formulated with liberties taken.

Craig Mee replies: 

Point taken. But though you can win a scrappy dog fight, and the numbers are all quite correct in the excel spread sheet, for longevity in this game, I'm all for finding form and beauty. If you can fight day in and day out and keep your head above water and do ten years and kill it, good job, as in, job done. But to fight every day, and not suffer long term brain damage, I think, is tough to ask. 


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