> Why all the long song and dance?
odd thing to say for someone can't get it together to trim the entire copy of my post out of your compose buffer.
but i'll take a stab at your question:
1.) because i see lots of people talking about science like they know all what it is, just from reading a few popular books on the subject, as if the content of those popular science books was gonna give you the full breadth and depth of science/math. for some reason, smart lefties can watch news coverage of the bombing campaign against the serbs, for example, and not be fooled by the vapidity of the coverage, yet i see perfectly smart people read a little popular science and suddenly feel convinced they been givin the whole story. unbelievable that people fall for the pulp science culture, to me that is. (popular science books from the fSoviet Union are much much better, have you ever noticed that?) and a lot of the sciency discussion i see on lbo has that superficial feel to it. i figured one way to stop grinding my teeth about it and start getting involved was to do a little song and a dance - who knows, i figured maybe some people would like to get down.
and after all, plenty of people (most) post to lbo WAY MORE than i ever do (have you ever even recognized a post from me before, ken?). all that singin and dancin turns you on? but one post on something as simply as 6/3 != 3/6 and the 'long song and dance' lecture gets trotted out.
fuck that dude....
2.) so i thought going into detail on a topic might be interesting to some people, get your hands dirty and all that, rather than just shooting your mouth off. i don't know about you, but there was so much chatter about minds and brains and is the mind in the brain or the brain in the mind, or the mind in the toe, etc etc i couldn't keep my head from spinning (which spun my brain which spun my mind). i needed to get down to something concrete. [maybe that'll bring out comments from the emptiness crowd].
3.) rotations and non-commutativity is a __hard__ subject. in practice i am talking about. have you ever worked on a project where you needed to deal with it? its NOT as simple as saying, uhh, duh, its just like 3 / 6 != 6 / 3....
i am working on a project right now with engineers and machinists who have worked in their field for 40 to 50 years each, really good capable people, and they constantly stumble on this bit about the order of rotations. its one of the few "theoretical" areas where i don't see people who are normally 'hands on, we don't need no stinkin math class' complain about the little lecture i give them on order of rotations. because everybody so far has seen they can't quite picture how it all comes together, but they look at the result of the machined part after they set up the milling machine by choosing the order of rotations arbitrarily: the part is all screwed up. i get a phone call and go down to the shop, and we all scratch our heads till i realize they messed up the order of rotation. not easy at all.
4.) and yet, if the article i posted about yesterday is at all true (which curiously, you didn't really comment on at all, cause you're busy telling us how __easy_ this is for you), then we have some kind of non-commutativity processing in the brain that can handle this kind of hard case. and more interesting is that we do it, yet when we theorize about it, its very hard to understand. and i thought that was an interesting thing to add to the discussion on brains and math and all that.
i eagerly await your reply (sans an entire copy of my post).
chow...
les schaffer