Permutation Puzzle

Among the things I'm not good at are combinatorics and whatnot -- Let's say you have a fixed set of 18 numbers all in the range from 1 to 6 (so obviously a bunch of duplicates), and you need to put 3 of the numbers in each of 6 ordered bins. How many ways can the totals in all the bins come out?


On Corrupt Godless Programmers

There's a kerfuffle around Second Life at the moment and some shady antics of 3rd-party clients that are officially allowed to connect to the game. That I wouldn't care about, except that it motivated one of the fiercer critics to come up with this novel argument: computer programming (especially 3D) is inherently a godless and corrupt activity.

This completely short-circuits my usual "angry" filter. Is this a genuinely new idea in the world? Or is this the same as Dungeons & Dragons game religious criticism back in the 80's?

It's all about criminality.

And yes, I will say that coding as an activity does corrupt. I think it's because geeks as a class tend to be godless or agnostic. Sure, you will find the occasional self-professed believing Christian or Muslim or Jew, but by and large, coders do not recognize a Higher Power. They are not People of the Book, because they only recognize their own book, which is code. There are some that realize this manufactured, man-made thing is merely a creation, and not the Creator, and merely a bad imitation of the Creator's works in Nature. But most don't. Most think the coded artifacts are *better*.

This cult of the belief in code-as-law and coders as god particularly infects the virtual world industry, where people get to code not merely some word-processing application or processor of some function on the web, but get to control human beings very visibly, in the round, in 3-D. They love that.

I don't.

I think it's the beginning of their criminality, by which I mean their violations of the law and civilization norms to take, keep, and abuse power.


More Equals Signs

Previously I wrote about students not using equals signs properly. So apparently some guys at Texas A&M are getting papers published on this subject, and identifying it as a key way to distinguish between high-functioning and low-functioning math students and national education systems.

Reported is stuff like: "The two researchers suggest using mathematics manipulatives". I disagree. The problem is not lack of manipulatives. The problem is that nobody ever told students what the fucking equals sign means.

I'm semi-convinced that a greater emphasis needs to be paid on the physical syntax and grammar of writing (and as a result, reading) mathematics by students throughout the education system. But that's me.



Did you know -- Annualized inflation in Zimbabwe, late 2008, was estimated to be: 89.7 sextillion percent?



Godel's Naturalization

Back in college I heard this ridiculously awesome story of what happened when the mathematicians Morgenstern, Godel, and Einstein went for Godel's citizenship test. Just ran into a recollection of the event written by Morgenstern (type starts p. 2):

Read it here.



Laurie Santos giving a TEDTalk on the results of an economic experiment with a "monkey market":


The "Take home message of the talk" (as she says at 16:47) is that the choice to take risk differs on whether the situation is perceived as a gain or a loss -- regardless of the risk/reward being exactly the same in each case. When presented with the option of either (a) 2 grapes, or (b) 50/50 chances for either 1 or 3 grapes:

- Monkeys take the safe choice (a) in a gain situation, i.e., start with 1 grape and possibly add some more later,
- Monkeys take the risky choice (b) in a loss situation, i.e., start with 3 grapes and possibly take some away.

That being the same as humans tend to do on analogous tests. My personal interpretation is that this points out how negative numbers are actually a very sophisticated, hard thing to deal with for most people (and other organisms). Most of the time in a natural community you'd be taking actions to gain things -- the "loss" scenario is somewhat artificial and abusive, and we're not set up naturally to deal with that well (i.e., we don't have a natural built-in processor for negatives, and for most brains things just kind of go "kablooey" when forced to deal with them).