An Algebra Lecture that Chemists can Appreciate

Yesterday, my algebra professor spent some time discussing a fundamental topic in organic chemistry. Well, it appears in physics too, but who cares about that?

Background: we spent the past month talking about determinants. Everything from permutations to Laplacian expansions. And yes, evaluating them hurts...

Anyway, it's easy to see that any n linearly independent vectors in an n-dimensional space form a basis for the said space. Living in the very normal world of R^n, we can sort of say that n linearly independent vectors will form a "coordinate system" for R^n. This is easier to see in say, R^3.

Now, if we do take a look at R^3, we see that a given coordinate system has an orientation, "handed-ness" if you will. Aha! Chirality!

The mathematical notion of chirality is, shall we say, somewhat different than the run-of-the-mill organic chemistry explanation, and very, very interesting. It's a bit ironic that my algebra class covered chirality before my organic chemistry class, though.

Personally, I also found it hilarious that the two disciplines demonstrated chirality in such different ways...

Organic chemistry: Get a molecular modelling kit, and make a methane-like molecule with four distinct substituents. Make a model of its mirror image, and try to superimpose the two. Of course, there are other ways to get enantiomers, but this one is a classic. Price tag: however much a molecular modelling kit costs.

My algebra lecture: Make a coordinate system using the left hand, then the right hand (3 fingers each). Try to superimpose the two. Or, get 3 straws. Make them point in 3 different directions (not coplanar). Get another 3 straws and do the same thing. Try to deform one into the other by moving the straws around, without having the three straws being coplanar at any given point in time. Price tag: depends on whether you count the fingers or not.

What does all this have to do with determinants? I don't know. (Yet.) I'll post the actual material once my notes are complete...can't wait until Monday's lecture! Irony number 2: I have to skip an organic chemistry class to go to an algebra lecture talking about an organic chemistry concept. Technically, I should be going to the organic chemistry one...but...a lecture about chirality in mathematics beats a lecture about the conformations of substituted cyclohexanes. Sorry.

Meanwhile: prelabs, midterm preparation, and alot of assignments. Also known as: too many MSDS's to read...