Actually, yeah, that’s a pretty good description of what the course (and, I assume, the book) is all about.

]]>one rule of street fighting is to end it as fast as you can by attacking vulnerable areas.

so I should attack my math problem in the vulnerable areas and solve them as soon as possible?

]]>So what you have to do is take actions at random that have your goals as their strange attractor. ]]>

Anyway, the download is under “related links” in the left-hand column on the MIT Press page. Direct link to the PDF here: http://mitpress.mit.edu/books/full_pdfs/Street-Fighting_Mathematics.pdf

]]>You can’t go by pure logic because your opponent can do that too as well as deduce what you’ll be thinking. So everyone gets stuck in an infinite regression and nothing really happens. So what you have to do is take actions at random that have your goals as their strange attractor.

I’m reminded of a scene from *Smilla’s Sense of Snow* … about halfway into the novel (if memory serves), Smilla (who finds herself at the periphery of some murderous mystery) deliberately reveals herself to the bad guys … the narrative explains that sometimes, when you’re hunting reindeer (I think it was reindeer — Smilla’s mother was a native Greenlander), they won’t show themselves until you show yourself first.

It seems counter-intuitive, but apparently you can get the drop on your intended prey by confusing them with irrational behavior.

]]>People look at me as if I’m some kind of freak for being able to come up with even an approximate value for some weird-ass thing, like how thick a layer of rubber piles up on the side of the road due to tire wear.

]]>I majored in physics. I quickly realized that once you step outside those idealized, “neglect the mass of the pulley” physics problem sets, the math gets impossible very quickly. And I mean really impossible, not just hard — you can write the differential equation, but you can never get an exact solution.

But you can simplify things by looking at cases where something is very heavy or very light, or looking only at what happens in a very short or long time, and so forth. These are probably the “easy cases” that Mahajan talks about.

Then you can try to patch together these cases by figuring out what must be happening at the boundary between short and long time, or the boundary between heavy and light things, etc.

There are mathematically rigorous ways of doing this, using lots of calculus and infinite series and weird-looking Greek letters, so your work can look properly impressive to other scientists and mathematicians. But all you’re really doing is a more sophisticated back-of-the-envelope calculation, being a little more explicit about what you’re assuming and when your calculation applies.

It’s fun stuff. I love solving these kinds of problems, whether I’m doing it the formal way or the informal way.

]]>Spoken like a physicist rather than an engineer. :)

Mathematical precision is impossible, but in most of engineering the math and science lets you get REALLY damn close to predicting an outcome. All the fancy stuff serves a purpose beyond simply laying out the assumptions and looking impressive. It reduces your margin of error to a level where you can confidently say “good enough. now let’s make it twice as strong and we can be sure no one will die.”

]]>(a) Does doubling one variable halve the other? (constant product)

(b) Does doubling one variable double the other?(constant ratio)

(c) Does doubling one variable increase but not double the other?(constant difference)

(d) Does doubling one variable decrease but not halve the other? (constant sum)

This usually gives you equations you can solve. ]]>

how thick a layer of rubber piles up on the side of the road due to tire wear

So go on then, how much? Please show your working.

And while you’re at it, how many piano tuners are there in Chicago?

]]>I don’t think anyone should ever do a complicated problem without always having in mind what a reasonable answer will be.

Its also usually simple enough to do, even when you’re dunk and you stumble across a great deal on plastic balls on the internet and you quickly need to figure out how many you need to buy in order to fill up your friend’s apartment while he’s out of town.

]]>