Sunday, January 28, 2007

My reply to an email from one of my students

As for your question regarding tensors and why I chose that to be me email addy, there were several reasons for it. First, I wanted something that indicated, at least to some degree, my interests without necessarily providing information about my identity. I chose something from mathematics so as to be easily recognizeable by colleagues (I could think of little more humiliating or less usefel than sending a resume to the dean with an email addy of soldmysoultopopculture@whatever.com). Also, I like the concept of a tensor. It is a mathematical device which encodes within its structure information which is independent of the coordinate system used to describe a system. That is to say that a tensor is a device which communicates absolute information without the often confusing and usually pointless perspective of the system. In a more personal sense I chose it as an indicator of one of the aspects of my personality which I strive to perfect. It is my hope to be a servant of Truth and be bound less by something so trivial and random as human belief (at least those without justification). Belief is no end in itself, after all. Those beliefs which serve to help us grow justify
themselves in their benefit and thus ring of truth, but there are many beliefs which some people use maliciously as a tool to scare and intimidate. Those sort offend me to my very core and demean all of humanity with their pollution. (Quietly steps down from his ACME brand soap box and apologizes for his long winded nature).
   And now for one of my favourite topics, that of the infinite. Ah, there is just so much to say about infinity, it just seems I could keep going and going about it and never get any closer to being finished at all. The most important part, and in many ways hardest, of understanding infinity (if humans have the capacity for so arrogant a statement) is to accept that infinity is a concept more than a number, it does not have a value in the counting sense than the less transcendental numbers we use daily. Now this doesnt in any way restrict the infinite to being incomporable, for example there are infinities that are bigger and smaller than other infinities. Here is an example: There are an infinite number of integers (1,2,3,4,5,6,............rotated 8) but in between each one of those numbers is an infinite number of decimals. Thus, the total quantity of
numbers which have a value is bigger than the quantity of integers even though both of them are infinite. So if I were to try to count all the numbers (and I only count with integers) then I will run out of integers before I finish. (A mathematician named Cantor discovered this and introduced and named the first few infinite sets. The smallest infinity is the number of integers, called a countable infinity for obvious reasons. Next up is the infinity of ALL numbers, called Cantor 2, and has the quality of being uncountable. He then went on to show that Cantor 2 is a smaller infinity than Cantor 3, the quantity of ALL curves in the plane. After all, for every single one of those infinite values for x there are an infinite number of possible different lines which interesect it.) Now, in the traditional sense the infinite does not stop. After all, there is no wall at the end of it so if I reached it (even in the abstract) what is to stop me from simply taking one more step, then another, then another, right? But still we have come to understand that infinities have different sizes, and that does imply quite naturally the existence of a border of sorts. It strikes me with a sense of the spiritual, actually, because if I wanted to obtain the infinite and those greater things which stand beyond that veil requires no travel, no effort, just that I open my mind and recognize it. Though I've much more I could drone on about in this I think that I will give in to sleep and leave you with a favoured quote of mine, though I cant recall exactly who said it (who knows, it might have been me on a drunken evening).

I am but dust standing upon a stone, small beyond the insignificant,
but I close my eyes and on the inside, Ah! on the inside, I am infinite.



Hope that the rest of the weekend goes well and I'll see ya Monday, although there are an infinite number of instants between here and there so its a long way to travel.

The Thom