this may be understatement, but mathematics can be confusing. i'd even say that it can be quite hard.
today over coffee i worked for a few hours, until my observations gradually suggested statements of an absurd inclination. i don't know how much logic everyone knows ..
(though i know that many of you do know enough logic, say, to be dangerous)
.. but i am referring to proofs by contradiction; colloquially speaking, they refer to verifying the validity of logical propositions to the absurdity of their negations.
to give a silly example, one might ask whether it is true or not that this morning, i killed a man in beijing with my bare hands.
well, suppose that i did; that would have meant that i was physically in beijing this morning, but that can't be true because i have an alibi: the barista at caribou coffee knows that i (or someone like me) had ordered a coffee and a cookie, and whittled away a morning, staring at pages of strange symbols while looking confused and frustrated.
so i couldn't have been in beijing, and so i couldn't have committed that murder. it's not rigorous proof, but then again, real life doesn't make a very good logical framework ..
.. so you'll just have to trust me: it wasn't me. (:
i still can't determine what, exactly, is wrong with a recent argument of mine. most of it seems right, if only because i've attempted to write a transparent, lazy argument which borrows most of its strength from the good results of others ..
.. but something remains amiss. i thought of an example which is inconveniently close to a counter-example to the conclusion of that argument.
in the last hour i worked, i resorted to troubleshooting and what computer programmers might recognise as 'debugging.' in other words, i narrowed down the errors to a few places in my argument-code, and now it's a matter of testing those places.
i'll input test data and look for valid output, but the data isn't numerical. instead i'll input a known metric measure space and the output will be a collection of geometric objects.
(the objects are metric currents, for those who know.)
so it's down to this: getting my hands dirty with the details of an example .. but isn't that what mathematical analysis is supposed to be? (:
3 comments:
What if you killed him at a distance, as in the Mandarin thought experiment from a Balzac's novel? [In case you don't know it: Imagine that you can get everything you want by killing some old Chinese Mandarin that you never met. You can kill him instantly and painlessly, without traveling to China or even rising from your chair. Would you?]
everything?
really? (:
out of curiosity, which balzac novel is that one? i've been looking for good reading, lately.
"Father Goriot" is the most common English translation of the title.
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