earlier i was tutoring a high school student in chemistry, and we were on the subject of isomers. interestingly enough, the section in her textbook read:
"an introduction to functional groups"
and i blinked.
of course, it had nothing to do with functional analysis or with groups from abstract algebra. odd, though, how these scientists use similar-sounding jargon.
i think maths have made me too paranoid for basic science. for one of her homework problems, it read:
"find all isomers of alkanes with 4 carbon atoms and with 5 carbon atoms."
really, this is a combinatorics problem, even though the student doesn't know what combinatorics means.
i asked her if she was sure that she addressed all the possibilities, and i think i made her paranoid about it. we went through some of the fine print -- e.g. double bonds between carbons are not allowed -- and then it came down to some innocent sounding questions, such as:
"how do you know that these two structures are really different?"
as an example, think of pentane and 2-methylbutane, pictured here. they are intuitively different, of course, but how do you explain the difference?
more to the point,
how do you explain this without anything hard,
like topology?
maybe it wasn't fair of me to ask her this. her teacher would probably not ask this. but i asked her anyway, and now i have to think of a simple answer.
so i tried to explain it in terms of cut points.
look: if you remove this atom from this first molecule, then it splits into three pieces. in this second molecule, if you remove any atom, there are always two pieces, not three. so they can't be the same, because we get different numbers of pieces.
so i reduced to the absurd. then again, it wasn't mathematics and it didn't require rigorous proof ..
.. still, the answer irks me. maybe i shouldn't have asked the question(s) in the first place. the student could have gone the rest of her life less worried, not having to worry about whether she got all the isomers or not.
maybe i should leave science to the scientists and science tutors.
2 comments:
I was taught to group the isomers by the length of the longest chain of carbon atoms. Then you attach "additional" atoms somewhere along the chain. For example, if there are 5 carbon atoms and the longest chain is 4 atoms long, it's easy to describe all isomers so that there is no doubt whether we found all of them.
huh: combinatorial, not topological. i knew there was a way of keeping count ..!
thanks, L.
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