biologists' worst enemy is mathematics

the title is a direct quote from my bioinformatics lecturer (i can't remember if i gave him a pseudonym, so let's call him DM, because he is a D&D enthusiast, and i can really picture him mastering a good game. apologies to the non-D&D fans who cannot relate). anyway. i think this applies to almost all non-mathematicians - from my friend base, i have yet to meet a non-mathmo who is a math enthusiast. so we'll work with this as an axiom (even though, by reading on, you'll see i, myself contradict this, so flawed logic ftl).

anywho. in a lecture, we are posed a question, as following. i post the entire question, for completeness, in the off-chance that someone amongst the readers is an avid mathmo, but if you are in the majority, feel free to skip the block-quoted portion, as its contents is irrelevant to the development of this post:

given a set of protein sequences, which are aligned:
N-FLS
N-F-S
NKYLS
N-YLS

we can construct a hidden markov model:


the question ensues: what is the probability of observing NKGYS?

ok so, the point of this all is, DM has glossed over the mathsy part for so many years and students have been able to answer the question.

but from a mathmos point of view, the question is far more complex than the 'expected answer' and from this i argue that,

the probability of observing any sequence in a HMM is the cumulative probability of each and every one of the possible ways of obtaining the sequence. whereas what DM wants is the single probability of the best possible path (also known as the viterbi path's probability).

hence, where the other students answered in one or two lines (and got full marks, mind you), i foolishly computed every single probability, and since the number of possible outcomes for a HMM increases exponentially, i pretty much calculated something to the n^5th degree. and even for the non-mathmos, that's a freaking huge number. i spent like the whole day doing one question (sheepishly, never questioning if i had done something wrong, because as we all know, when someone has the pre-conception that they're right, on go the blinkers!).

anyway, once he revealed his answer to us all in today's class, i was slightly pissed, but more than anything, i found this hillarious. sweet charlie chaplin jesus laughs at me, not with me.

so i confronted him at the end of the class, and he found it interesting that the wording of the question was so misleading, and yet caused so much confusion (where it had not to the others). not that i'm being condescending to 'non-mathmos' or anything. but you can probably see where i'm coming from when i could say that 'with great power (or knowledge) comes great responsibility (or overthinking + grief).

well yeah, sorry for returning to posting with a textwall of a ridiculously semantic insignificant issue. i promise to post something a bit more cheerful next time!

p/s: DM is the lecturer who offers chocolates if we can correct his slides or find mistakes. he owes me a bar for some other mistake, and by sam's hell i'm going to claim another one for all the grief that question put me through :p