Sometimes you’re just minding your own business, trying to get a little science done, and a little art pops out at you all unexpected.

What?!? You want to know where this comes from? All is revealed beneath the fold…

The dotted line is, not surprisingly, the sine function plotted from about -10 to +15. The dashed line is a crazy rational function evolved using genetic programming. The bold line shows where the test data came from that was used to evaluate the quality of the evolved solutions, and it’s clear that in that range the evolved function matches very closely.

It’s also clear that outside of that range (which was never part of the evolutionary training), the evolved function rapidly wanders off into its own happy place (including a nifty discontinuity at around x=10). This is in fact to be expected. The GP system was only allowed to use +, *, -, and /, i.e., all it could construct were rational functions. There are no rational functions that match sine across its entire range, so this is really about as good as we could do given those tools. If we’d given the GP system a periodic function (like cosine) in its toolkit, then it could potentially evolve something that would match sine everywhere. With rational functions, though, it just ain’t gonna happen.

But this graph looks a lot cooler than it would if they matched everywhere :-).

Oh?

The function that it actually evolved?

You sure you want to see that?

Well, OK…

where

• a = 2.76609789995
• b = 10.240744822
• c = 3.9532436939
• d = 3.20011637632
• e = 12.6508398844

I never promised it would make a lot of sense, did I? Evolution often doesn’t produce pretty. So much for intelligent design…

It actually took me a second to get it – how annoying that a web comic would actually be subtle enough to challenge a little :-).

A wonderfully nerdly performance of mental arithmetic. I found his use of word mnemonics to remember large numbers quite cool.

This wonderful little video (produced by some U of M Twin Cities mathematicians) has apparently been viewed over 1 million times now, which is a lot more views than it would ever get in class. I frequently run into faculty that are very intent on holding on to their teaching ideas and techniques, and certainly not sharing them openly with the world. They see those ideas as “their property”, to be guarded and controlled as much as possible. It’s a weird attitude, because almost none of them will ever see any money from those ideas, and the potential for wider viewing and usage is just so much greater if they open up (as in this case).

A good video like this takes a lot of time to produce, but faculty often put in huge hours on their lectures, labs, and demonstrations. Get it out there!

They don’t say anything about computing (but, sadly, most high schools don’t offer much in the way of meaningful computer science courses), but my experience suggests that much the same is true there: A solid math background is a definite win. Have some programming experience can help, but it can also get in the way if you end up needing to unlearn a lot. And any advantage one has from prior programming experience tends to wash out within the first yer (sometimes the first semester), while some solid math background continues to be an advantage all through the major.

The error bars are pretty huge, which isn’t entirely surprising given the variable quality of both instructor and student (both in high school and university). It would be interesting to better understand what role the quality of the high school instruction plays in the correlations. Does, for example, a bad science class actually have the potential to hurt you later on?

Both subjects [math and physics], which are traditionally seen as predominantly male, are far more popular among girls with names such as Abigail, Lauren and Ashley, which have been judged as less feminine in a linguistic test. The effect is so strong that parents can set twin daughters off on completely different career paths simply by calling them Isabella and Alex, names at either end of the spectrum. A study of 1,000 pairs of sisters in the US found that Alex was twice as likely as her twin to take maths or science at a higher level.

The (highly speculative) causalities are the reasonably obvious ones: Seeing names like “Barbie” or “Breeze” on the class list or application form brings beaucoup baggage to the party. This is hardly a win, especially since the patriarchy already ensures that females already have plenty of baggage when it comes to science and math. It’s also telling, if not entirely shocking, that giving boys certain names can have similar effects. Seeing “Bubba” on the football roster might elicit a snicker, but likely no surprise; seeing “Bubba” at the math league finals, on the other hand…

So it would seem that some parents have a fair bit to answer for:

‘A name is part of an impression package,’ said Mehrabian. ‘Parents who make up bizarre names for their children are ignorant, arrogant or just foolish.’

In the case of the Zappa family, I’m voting for “arrogant”; Frank certainly wasn’t ignorant.

1. I’ll start with something really random and meaningless: I have short pinkie fingers Actually, the fingers themselves are proportional to my other fingers, but there’s something a little off in the bones of the hand and both my pinkies start “too soon” and thus end about a joint short when compared to their neighbors. Its not exactly a big deal, as I didn’t even realize it until I was 13 or 14, when my piano teacher and I noticed it when I kept doing long reaches with my fourth finger insead my fifth. While I’m sharing trivial physical abnormalities, I also have a slightly curved spine, and smaller feet than expected for someone my height. My mother blames it all on smoking enthusiastically during both her pregnancies.
2. I’ve only considered leaving UMM once since coming here in 1991. As a Reed (math) grad, I had always dreamed of helping found the computing department at Reed. They weren’t kind enough to set something up just as I was coming out of graduate school :-), but did advertise for their first computing faculty a few years after I came here and I couldn’t resist the opportunity. I didn’t even make the interview, but I have no regrets. I’ve been (and continue to be) really happy here at UMM.
3. Like Bill, I read very slowly, although I think in different ways than Bill. I read slowly to begin with, and tend to do lots of daydreaming and thinking about what I’m reading on top of it. This is one of the reasons I’m a crap citizen of the blogsphere and related on-line worlds. There’s just way too much great stuff out there, and I’m way too slow a reader to stay on top of them. I suspect that’s one of the reasons I like Flickr; I can process a lot of images in the same time it would take me to read a fraction of PeeZed’s output.
4. Dr. Seuss (and my son) helped me learned to sing. I’d always enjoyed music, but only started singing with any regularity when Sub-Evil Boy was born; it was nice singing to an (infant) audience that was so wonderfully non-judgemental. Reading lots of Dr. Seuss at the same time also taught me volumes about timing and rhythm. While I don’t miss diapers, I definitely miss reading to him every night.
5. I have an Erdős number of 4. (Go to the Erdős Number Project for more info on how to compute your own Erdős Number.) The cool thing for me isn’t the number itself, but that it was lowered from 5 to 4 by a UMM alum (Nick Hopper) who I did research with when he was an undergraduate with. He went from here to CMU, where his advisor (and co-author) was Manuel Blum, who has an Erdős number of 1. Absolutely one of my highlights of my career at UMM, and I suspect this will be as low as my Erdős number ever goes. Rather remarkable it’s apparently the same as Bill Gates, but I suspect there are precious few other similarities between us.

I just stumbled across the fact that there’s a new Carnival of Mathematics, with their first edition up a bit over a week ago. The next edition is due to be posted on the 23rd on Good Math, Bad Math. Thanks to The Science Pundit for the pointer.

As far as I know there’s no carnival for computing – does anyone know different?

The situation in the U.S., where math and science requirements are often minimal at best, was contrasted to that in various parts of Europe and Russia, where everyone was expected to take math up to (and perhaps including) calculus, along with several years of science. The public school I attended in Montevideo, Uruguay, when I was an exchange student back in the late 70’s required everyone to take math (they were doing something like pre-calc), physics, and chemistry, whereas most of my classmates in Texas had stopped taking math and science courses a year or two earlier.

And while this obviously has the potential to hurt all kids, it particularly affects groups who are already stigmatized in this regard. 13 and 14 year-olds who are being bombarded with with idea that math/science is “hard”, that they (or their group) are “not good at it”, and that it’s “boring” or “nerdly” or irrelevant to their future, are then that much more likely to turn away and do other things.

So, do we require more math and science in junior high and high school in the U.S.? If we agree that it’s important, how do we make it happen effectively?