I was grabbing lunch over at the student center before a big meeting today and saw a colleague from the math department carrying a sack that had e to the i pi, except using math symbols that I don't know how to reproduce in blogger or wordprocessors. (So, that's e, the symbol of the base of the natural logarithm thingy; i, the symbol of the imaginary square root of negative one; and pi, the ratio of any circle's circumference to its diameter--which has to be one of the coolest things to learn is a constant, no?)
Now, I pretty much understand the concept of i and pi, but e I just didn't get at all. I remembered from sixth grade math or something that it's the natural log, but what the heck does that mean?
So I asked! And it's SO COOL! My colleague started drawing stuff on the campus newspaper lying nearby, and it made sense! (My colleague's stuff looks much like these Wikipedia illustrations.)
What a very, very cool number! Why didn't they teach us that part in sixth grade?
I love that I can learn things in casual conversation that answer questions I never quite knew I had until the conversation starts.
Now I want to track down a chemistry colleague and ask why there are 6.02 x 10 to the 23 (10 superscript 23, however one does that on blogger) particles per mole. Why did ol' Avogadro choose that number? Because it always seemed to me so arbitrary, like a dozen, just an arbitrary extra name for a weird number that we had to learn. But, knowing chemists, there's some really great reason for that particular number.
There are lots of things in life that I semi-remember from grade or high school, and love to get a good explanation from my colleagues about. And the delightful thing is, my colleagues here are usually incredibly good at explaining things and helping me understand them, and willing to do so with a generous spirit and great kindness.
What questions would you line up?
Oh, I love conversations like that. I've always wondered, especially given the existence of constants like that, whether numbers have any independent existence outside humans, or if they're only a way we've invented of making sense of the world (with arbitrary things like a dozen). If there were other intelligent life forms on earth, would they come up with the same concept of numbers because there's something inherent about them? or would they come up with something entirely different? I finally got up the nerve to ask a mathematician that once, and he said it was about the biggest question in mathematics. :)
ReplyDeleteThe question I'd ask? Well, I asked it, about two years ago. After Derrida's passing the blogosphere was full of comments about his work. I'd never heard the term "deconstruction" before. (Or "literary theory," either, for that matter.)
ReplyDeleteAnd at a dinner conversation with a bunch of nerds (er, I mean, academics), I finally got to ask, and got a good answer. (Incidentally, the guy who gave me the answer? I married him!)
At that same dinner we proffies also talked about how an eclipse worked, why castrati could still have sex lives, and more. I love being able to ask questions -- without having to worry if the answer will be on a test! :)
BM fan -- do you seriously see any equivalence between feminism and male chauvanism? the latter seeks to keep women in their place, i.e., below regular humans. and feminism is essentially the belief that women are full humans.
ReplyDeleteI'm not a chemist, so will you believe a biologist instead?
ReplyDeleteAs you probably know, the mass of atoms and molecules is usually measured in Daltons. Roughly 1 proton = 1 neutron = 1 dalton of mass, although a proper chemist will tell you that isn't completely accurate. It's good enough for this explanation, though.
Avogadro's number is the product of a ratio used to convert between mass in daltons and mass in grams. It basically says that there are 6x10^23 daltons in a gram, e.g.:
Mass of Oxygen is 32 daltons.
If you take 6x10^23 oxygen atoms, their combined mass is [32 daltons/atom] x [6x10^23 atoms] / [6x10^23 daltons/gram] = 32 grams.
By extension, one mole of anything from carbon atoms to motorbikes with a mass of x daltons per item will have a combined mass of x grams.
So Avogadro's number is sort-of arbitrary, in that it's just a handy ratio used to convert between two convenient units of mass. The reason it's such a funny, non-round number is that the gram doesn't really make much sense as a unit: it's just the mass of 1 cubic cm of water, rather than being based on any fundamental physical constant. (Well, it's actually based on the mass of a lump of platinum kept in a special vault in France these days. Mass is the last thing we can't easily derive from other units, so that lump of platinum and its copies are the accepted definition of what a kilogram is. Every set of scales you've ever used was calibrated by a weight, which was calibrated by another weight... which can eventually be traced back to that single weight in the French vault. It has a fascinating story, read up if you can!)
Bit of a tangent, there.
So Avogadro started with one sensible unit (mass of an atom) and one rather arbitrary one (number of atoms/gram) then divided one by the other to get his number.
Ooo, thanks Bugs!
ReplyDeleteThis post is a bit old, perhaps, but still worth commenting on.
ReplyDeleteMy degree is in math, but my mother was an English teacher and I was very nearly an english major.
I share the same sentiment about topics from earlier education.
I only graduated in May, but can already think of classes which I want to revisit or study more. In fact, I plan on buying two textbooks I especially liked.
But the real reason I am posting this comment is about the math on your colleague's bag.
While s/he may have explained e to you, did s/he explain it in the context of what was printed on the bag?
It's quite a famous equation, in fact.
It's called Euler's Identity, and it's equal to -1.
Can you believe that?
Yes, that was part of the coolness of the bag! So very, very cool! Thanks for reminding me, though, and sharing it with everyone.
ReplyDelete