Why math is cool, how it should be taught, and what programmers need to know about it.

[ Link: Math For Programmers ]

Here’s a list of 10 very interesting numbers.

The Beauty of the Diffie-Hellman Protocol

An exceedingly cool description of how various numbers are unique.

Fun With Numbers

Link: Math Pickup Lines

My love for you is a monotonically increasing unbounded function…

I don’t understand how you can take two moderately organized cords, drop them into a bag, and then extract them like a day later and have them be in absolute knots.

It doesn’t seem mathematically possible. Where does all the motion come from? Are these things snaking through each other while I sleep?

Puzzle: A Plane And a Conveyor Belt

Answer: Yes, it can. The wheels will roll freely at 100 knots, effectively leaving no force to counter the forward thrust created by the aircraft engines.

A few weeks ago a buddy of mine busted out the MHP on me. For those not familiar, it’s a now-famous mathematics puzzle named after the talk show host who hosted the show it’s associated with.

The idea is simple, and is covered in depth at Wikipedia, but for those looking for a simple rundown it’s basic concept is this: you’re given three doors and told one has a car behind it while the other two have goats. You are asked to pick a door. After your choice is made you’re then showed a goat behind one of the other two doors.

You are then asked if you want to switch to the remaining door or keep the one you chose initially.

The natural inclination is to think that since there are only two open doors remaining, and you already have one of them, that it’s precisely equal odds between them — and therefore not beneficial (or detremental) to your odds to change your choice.

That logic, however, is flawed.

It is, in fact, beneficial to change your choice. In reality, it takes you from a 33% chance to a 66% chance when you switch, or from 1/3 to 2/3.

If you doubt this go spend some time at Wikipedia. Anyway, I was so intruiged with the puzzle that I decided to write a bit of code to illustrate how this plays out in reality. There are many such programs out there already; I just wanted to do it for myself.

This code is rather crude, which it turns out is something of a signature of my little wannabe coding projects, but it was fun to write. I don’t have the time right now to write the decision process portion of the puzzle, and currently it just models the staying and leaving dynamic, but you get the idea.

(Here’s the code for anyone interested) And here are some results given four different sample sizes: daniel@marius mhp $ ./mhp.py 10 If you STAY you win 38 times. If you SWITCH you win 62 times. daniel@marius mhp $ ./mhp.py 1000 If you STAY you win 319 times. If you SWITCH you win 681 times.

daniel@marius mhp $ ./mhp.py 10000 If you STAY you win 3360 times. If you SWITCH you win 6640 times. 40

daniel@marius mhp $ ./mhp.py 100000 If you STAY you win 33319 times. If you SWITCH you win 66681 times. The results are quite clear: 1/3 vs. 2/3. If you make a choice and stay with it you win 1/3 of the time; if you switch from that initial choice you win 2/3 of the time.

And that's with completely random (as much as pseudo can be "completely") placement of both the car and the contestant's choice.

Very interesting indeed. It is, in fact, better to switch.

“Tonight, at one in the morning, it will be 01:02:03, 04/05/06″

A mathematical death.