Unexpected Consequences

At this time yesterday, I was merely excited to have finished my first self-designed sweater.

Today? Well today I have test knitters and patterns to write in different sizes. My little sweater got a really nice reception and other people want to make it. Imagine that!

I remember when I was in elementary school, the hot topic among educators was the achievement gulf in math and science between boys and girls. I went to a fairly stellar school that was both highly demanding and highly nurturing, but it was still apparent that, by the time students reached high school, math and science were a boy's club. And much as I wish I had been the exception to the rule, I wasn't. I made decent enough grades (ok, well maybe not in advanced chemistry, sorry Ms. N), but my heart wasn't in it. And it had been earlier on. Whether or not it was the style of teaching is something I don't feel fit to judge, I only know that if the choices were between Moby Dick and plotting something on a graph, I chose the former (even though I didn't actually like Moby Dick).

Fast forward to adulthood. An adulthood that did not have the benefit of a single math or hard science course in college. And where did I end up?

Computer programming. Soft, front-end computer programming, but computer programming nonetheless. Also confectionery, which any pastry chef will tell you depends more on science than creativity. And now, pattern design. While I'd like to believe that my shining prose will carry the pattern, the truth is that, provided the math is correct, no one will care about the flowery words.

This has gotten me thinking about math education because, in my wildest dreams, I would not have spent my adult life interacting in any way with math and science. I was going to edit books or magazines. Or write them. But logic loops, hygroscopy, and geometry? Please! Those things were for math people.

Now I deeply believe that applied math and science aren't worth a damn without the basics (I am a big believer in the basics: thou mayest not read Henry Miller if one has not read Chaucer first), but I wonder if my experience with math and science would have been different if the disciplines had been presented as not merely the precursors to careers in hard sciences. I'm not saying I might not have enjoyed the life of a nuclear physicist, I'm just saying it might have been a stretch. But I didn't know how big a part chemistry played in cooking until I had to start doing it.

And, forgive me, tenured English professors, but my brain has to work a lot harder with far more satisfactory results, when I challenge it with math and science. At this point I feel confident reading and understanding what I read, especially as much of that is subjective, but when faced with a problem that has a single solution? My mind delights.

The Ferry Crossing Problem

I first encountered this logic problem in a book, probably sci-fi, probably in 4th or 5th grade, which is why it has made such a lasting impression. The long and short of it is there are 6 people, 3 good guys and 3 bad guys, and a boat that seats 2 people. Bad guys can never outnumber good guys and all the good guys need to get to the other side without the bad guys. How do you do it. I've always liked this problem even when, like this morning, I frantically IM devoted partner asking him what it's called (doesn't actually have a name), and if you don't want to take the time to figure it out, at the end of the post and after some carriage returns, I'll print the answer.

Now I like math and I like logic and I like to be smug about my skills in both. Which is why the personal ferry crossing problem that I am struck by is so horribly humiliating. And it comes up a lot.

I cannot cannot cannot wrap my mind around the math associated with two cars and two drivers and catch myself almost weekly abandoning logic in my mind for reasons I cannot explain. For some reason I find myself thinking: if devoted partner and I go to a bar in separate cars and I get too drunk to drive, devoted partner can drive us both home and then go back to get my car. I think this, in one way or another, ALL THE TIME. Take our upcoming solo airplane trips. I have thought: ok, I'll drive my car to devoted partner's office, then he can drive me to the airport in his car, and then take my car back home. I simply cannot comprehend that devoted partner is unable to drive two cars simultaneously while also being unable to understand why the idea begins in my head as a good one.

And frankly it's starting to drive me a little crazy. I mean even the dullest crayon in the box figures out AFTER A YEAR that two cars require two drivers. But then there's me, happily plotting impossible itineraries.






Solution
G=good guy
B=bad guy

First crossing: G + B
Return trip: G
Second crossing: B + B
Return: B
Third: G + G
Return: G + B
Fourth: G + G
Return: B