Week the Third

This week's most interesting activity was probably Friday's paper-folding puzzle (though, really, I doubt that's news for anyone taking the course. Who doesn't like spending 45 mins of a 1 hour lecture in Uni folding paper? It's awesome.) And of course, because it is Uni, also a bit mind-boggling at first. The puzzle is this: take a strip of paper, and fold it evenly over from left to right, and then continue doing so until you think you've amassed enough information on the art of paper folding, have found the meaning of life, cannot possibly fold it once more even if your entire future depended on it, or simply get bored (well, the last one not so much.) The point of this puzzle is to see if you can figure out the pattern in which the paper folds (whether, when unraveled, the folds are concave or converse) given the number of times it's been folded.

For example, assuming concave = 1 and converse = 0:
1 fold gets: 1
2 folds get: 011
3 folds get: 0011011
4 folds get: 001001110011011
and so on.

It took (I'm willing to admit) quite a few minutes to make sense of these observations. When I finally did, I noticed that (a.) the midpoint created by that first fold always stays the same and (b.) if you work outwards from that center, every new fold on one side is an inverse of the same-distanced fold on the other side! (genius, I know. You can do a mental 'facepalm' if you so desire.) Still, how can you get a pattern from that? Well, after looking at it a bit more in the hopes of prodding my brain into a state of usefulness, I garnered observation (c.) working again from the center, the left side is exactly the same as the pattern you get when folding it 1 time less, or: with n number of folds, the pattern on the left is the same as that of (n-1) folds. The pattern on the right is (as by observation (b.)), mirrored. Yay problem solving! Danny was right; using Polya's approach (outline the problem, concoct a few plans on how to solve it, and then attempt) is more successful than jumping headfirst into the folding.

Useful thing to remember:
A(antecedent) implies C(consequent) is false only if A is true and B is false.

Danny's quote of the week:
In talking about the usefulness of parentheses and variables: "We want to make sure there's still variables left for our grandchildren, but if we're just going from 2 variables to 4, I don't think that makes a huge difference on the store of variables in the world, so we'll probably be ok." And it's true; if ever in need, I'm sure we can move on to the greek alphabet or, who knows, maybe even use kanji.

Week the First! (and Second...and a bit of Third)

This....is harder than expected (no, not the course - we'll get to that later. Just this blog business.) It's not even that I don't like writing - for example, every November I somehow manage to delude myself into believing that it's a perfectly fine idea to write a novel in a month (yeah Nanowrimo!!). Needless to say, 3 days in I'm still staring at a blank word doc, 7 days in I've resigned myself to the fact that English is not my best friend, and by day 29 I'm thinking "What novel? Did I say I was gonna do that? No way..." (It does make one wonder why I don't succeed, considering the lengthy digressions I always make.) The point? I'm not a blogger, so sorry in advance.

So, we've finished 2 weeks of CSC165: Mathematical Expression and Reasoning for Computer Science, and started the 3rd today (we broke the rules of math! It was mind-boggling fun, especially at 11am.) I honestly don't know what to say about the course so far, so perhaps I'll just stick with a few insights that the prof, Danny Heap, so aptly stated himself:

- In week 1: Know that feeling you get when you've finally done something meaningful? That exhilarating head-rush of endorphins? (probably not.) Well you will soon! Apparently, solving problems is not only fun, but also the easiest way to get "a cheap, legal high"! Who knew math could be so exciting, and serve as a compelling substitute for drugs?! Well, now you know. Just make sure to write Danny in as a footnote on your road to success (especially if you ever solve that 'Streetcar Drama' puzzle.)

-In teaching about universal claims: "All females earn less than 55,000. To prove this claim false, you need to find just one counterexample. If we look at the table we'll see there's only one employee earning above 55,000. However, Al (60,000), is not a counterexample... because of chromosomes."

-In talking about equivalence: " If M 'belongs to' R, and R 'belongs to' M, that implies that R = M. Ok? Good, now let's avoid cheap jokes like 'same-set marriage' and move on with the lecture."

I doubt I'll ever be in a position to allot footnotes to people, but I'll keep that in mind, Danny.
Till next time, cheers.