This is probably one of the craziest mathematical proofs I've written :-)
Hari made this statement in his latest post:
Is it worth to understand the meaning of this word from a lifeless sheet of paper in the dictionary..??I now have a theorem and a proof(?) :-D
Theorem: Certain feelings aren't expressible by words
Proof: We shall use a counting argument to prove this.OK, this is crap, but I truly enjoyed it :-D
Words are strings over a finite alphabet, and any expression corresponds to finite string. Thus the set of expressions is countable.
We shall now show that feelings are uncountable. Firstly, note that they are infinite since we have an infinite hierarchy of any emotion, happiness for example.
Define a metric over emotions with respect to a certain individual, such that the distance between two feelings f and g is just the difference in the total volume of hormones generated by both of them in the body.
This naturally defines a notion of a limit, and thus can now talk about the convergence of a sequence of feelings. Clearly, the limit of any such sequence is also a feeling and hence the set of feelings satisfy the completeness property that the set of real numbers do.
Hence the set of feelings contains atleast as many elements as real numbers, and hence is uncountable.
Thus certainly, a countable set of expressions cannot correspond to the uncountable set of feelings. Thus certain (infact most) feelings are not expressible by words. QED
RP
6 comments:
And you call ME weird?
:) but this actually makes sense. It is a proper meta-proof that words don't express everything.
Maybe if I had attended the lectures today I would have used quantum mechanics into this :-p
Doesn't prove anything...
It is not clear why we have "an infinite hierarchy of any emotion", but even assuming that it's infinite, suppose that feelings take only discrete values, like the integers. Maybe the volume of hormones is also discrete (something about quantisation). You can still have the metric, and... hey, is it true that integers have the completeness property while rationals don't?! Anyway, it's not a proof :p
But all this is unnecessary -- it is simpler to say that it is pointless to use more than (say) 1000 words to express a feeling, count the number of feelings expressible in so many words, and say that the number of possible feelings is more than that :-)
In any case, note that the saying about "certain feelings aren't expressible in words" usually doesn't refer to precisely specifying the degree/intensity of the feeling -- if two feelings are expressible, we wouldn't call a particular feeling in between them as inexpressible. So to hit the heart of the saying and not just the literal meaning, you must actually prove that there are feelings outside the convex hull of the set of expressible feelings :-)
:-))
My crap turned out to be more interesting that I thought.
I take back my last comment, I agree that this is no way a proof of anything :-)
And yes, integers do have the completeness property (limit of any converging set of integers is an integer) and the rationals don't (their closure is R).
And the convex hull thing is intriguing, of course the question is still crap but it would be nice to get a crap proof of it :-)
Damn crap is nice!!!
Explain in laymans terms...Math is too complex for this Engineer friend of yours...;))
forget the proof, it's crap :-D
But the point I wanted to make was that not all feelings can be expressed. And also, not even as "this is (blah) of a greater degree", there are lots of emotions that have absolutely no way of being 'puttable' by words.
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