Rainbows are love

Friday, June 19, 2009, 12:28 AM

I finally managed to catch Camp Rock yesterday! Fantastic!! I think it was a great movie just because it was a movie about music, and well, you know how much I love music! Tho I don't really have a specific type of genre that I like nor any artist that I adore very much, I just like music in general... and to have movie after movie related to music is just fantastic!!

Check out this MV by some person for the song This is Me by Demi Lovato feat. Nick Jonas!!

Tell ya one thing - I think this song is great!! Obviously, Demi should work on her dancing, but the song is absolutely great! No 2 ways about that!! Very expressive, and the way Nick and Demi sing together, they have such great chemistry...

By the way, notice Demi's smile? Look familiar? Maybe not to you, but I'd know that smile anywhere...

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WARNING: Mathematical post ahead!!! If you cannot bear it, please scroll down to the END OF MATHEMATICS part.

Field: Set theory.

I recently learned that the thought that music is subjective and different people enjoy different music is not exactly true. This means that there are some arrangements that sound nice and is appreciated by everyone, while other arrangements are regarded as lousy and not good.

Now this got me wondering, so if this is the case, how many "good music" can we possibly have? Finitely many? Countably infinitely many? Uncountably many?

First, we give a definition. An arrangement is a finite sequence of notes.

Consider this: There are, of course, countably many notes. Now let N denote the set of all notes. Therefore, if n denotes the number of notes in the arrangement, each arrangement is actually an element of N x N x ... x N (n times). Now we know that a finite product of countable sets is countable, and hence, there are countably infinite number of possible arrangements in this world.

Next, we give another definition. A good arrangement is an arrangement which the general public accepts as good, however "good" is defined.

Now, suppose A is a good arrangement, and B is another good arrangement. We denote AxB as the arrangement of A and B put together, and clearly AxB is not equal to BxA, so the operation x is not commutative. Note that neither AxB nor BxA may be a good arrangement, and hence, this operation x is not closed.

However, it is reasonable to accept that AxA is a good arrangement, since repeating the same arrangement twice still sounds reasonably good. In addition, nothing can stop us from repeating this a further 3 times, 4 times, and so on. This means that each good arrangement can be repeated a n times, where n is a positive integer.

This implies that there are countably infinitely many good arrangements!!

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Of course, you may ask, what significance did all this bring? Well, it turns out that there are infinitely many good arrangements in this world! That means that the music industry will go on forever since songwriters can keep producing different kinds of good arrangements! They just need to TRY and THINK HARDER!!!

Alright, that should be all for now.

~Falcon, OUT!!