Written 4/22/2014
I am a wanderer.
Do not ask me, “Where did you come from?”
My homeland is far, far away, and words are weak.
How could you believe what I have done?
Understand what I have heard?
See what I have lived?
How could I translate from a language in which
every word has its own emotion,
every saying its own story,
And every idiom its own soul?
Do not ask me, “How was it back there?”
It is different here,
but everywhere I’ve been has been the same.
Everywhere I’ve been,
The sky had clouds and stars,
The hills had grass and birds and trees,
Roads had cars,
Schools had bells,
And humans were humans.
I have not seen war.
I have only seen small cruelties.
I have always lived near a river, near the sea.
And humans are humans.
Do not ask me, “How do you like it here?”
You are curious, but my mouth is tied,
for I cannot judge, cannot condemn
and every place was special when I lived there.
I loved the green mountains tinted gray behind the fog.
I relished the noise of energetic traffic
jostling and flowing in the streets.
I liked the bluish tint of driveways before sunset.
I marveled at the view in the backyard of
houses and trees across the glen.
Do not ask me, “How did you get here?”
The journey was not easy, yet it was not hard.
But as I go on living, a sorrow lingers below.
I am of this place now, but I have learned
That one can pretend that one will never leave
Yet the time of departure will come, regardless.
I can only walk so far before pausing,
Looking back, recollecting.
I will always remember where I’ve been,
but I’m afraid that I will forget.
Do not ask me, “Where are you going?”
For I think I know, but I know I’ll think differently.
I do not know what I need to know but don’t.
The world is wide; I have yet to find my way.
I am a wanderer.
Tuesday, June 17, 2014
Theory of Numbers
I wrote this essay as a class assignment. We are working on college essays, and I wrote this in response to a University of Chicago prompt asking for a theory that explains numbers.
Yet we use math everywhere. Even complex numbers, which might initially seem useless, find applications in electrical engineering and other branches of science. Constants like pi or e are ubiquitous. Still, this is only one system of math that happens to work for us. If we were to encounter an advanced alien civilization and compare our knowledge of physics and math with them, we would probably find some similarities and many differences.
Not all numbers are useful for describing the universe. With exponent towers, we can easily make a number so big or so small as to be meaningless, like the aforementioned 10^10^10^10^10^10. Mathematicians have created much larger numbers, like Graham’s number, but that deals with the abstract problem of coloring the edges of n-dimensional hypercubes.
Mathematics, for the most part, is self-consistent – but only because we made it so. We have number systems, like the set of rational numbers, and we can do arithmetic with them. But did we simply make all of this up? Mathematicians have “discovered” the ordinals, some of which are larger than any countable number – effectively infinite. Yet there are infinitely many infinite ordinals, and mathematicians have defined ways to add, subtract, multiply, and divide them. Both the rationals and the ordinals are self-consistent – under the established rules we cannot find a contradiction.
Ultimately, I say that numbers (besides the natural numbers) are only made up by humans. We can create new systems of numbers, as we like; we can play with our existing rules and make “discoveries” and theorems based on those rules. With the numbers we have, we can only approximate the behavior of the universe, and we cannot predict everything. Numbers are only a game – a game of our own making.
I propose that all numbers besides the counting numbers are completely subjective and do not exist except in human thought and imagination. Most numbers can only describe the universe approximately, and are thus not real. Natural numbers are useful, and rational and complex numbers might still find real world applications, but I can easily construct a whole number that dwarfs the size of the visible universe, like 10^10^10^10^10^10. There also exist surreal numbers and infinite ordinals, which are also numbers despite exhibiting some strange properties. Mathematics is a human endeavor, and though we have used it as a tool to describe the universe and advance technology and engineering, mathematics is only a tool of our own making, nothing more.
Numbers, when applied to the physical world, are simply imperfect labels of things. They are almost always approximations. One can never measure the mass of an object, like an apple, exactly, since there is always some error. Our world is not ideal: if we carefully made a square of side length 1 m and tried to measure the diagonal, it would not be exactly sqrt(2). Our theories for describing nature may not be perfect, either. The laws of Newtonian mechanics provide a very good approximation for how projectiles fly and galaxies twirl, but it is not exact, and it would be a bit arrogant for humans as a whole to presume that theories of quantum mechanics and relativity are the last, best description of the universe. (On the other hand, natural numbers, used for counting, seem to be fundamentally a property of the universe: if I say three electrons, I mean exactly three electrons.)
As it stands, numbers are limited in predicting things. Perhaps it is simple to describe the trajectory of small spherical frictionless cannonballs in a vacuum, but fully-fledged human beings are another thing. We cannot predict the actions of humans, except in a few isolated cases. The universe is effectively non-deterministic – there is much we do not know and cannot know.
Yet we use math everywhere. Even complex numbers, which might initially seem useless, find applications in electrical engineering and other branches of science. Constants like pi or e are ubiquitous. Still, this is only one system of math that happens to work for us. If we were to encounter an advanced alien civilization and compare our knowledge of physics and math with them, we would probably find some similarities and many differences.
Not all numbers are useful for describing the universe. With exponent towers, we can easily make a number so big or so small as to be meaningless, like the aforementioned 10^10^10^10^10^10. Mathematicians have created much larger numbers, like Graham’s number, but that deals with the abstract problem of coloring the edges of n-dimensional hypercubes.
Mathematics, for the most part, is self-consistent – but only because we made it so. We have number systems, like the set of rational numbers, and we can do arithmetic with them. But did we simply make all of this up? Mathematicians have “discovered” the ordinals, some of which are larger than any countable number – effectively infinite. Yet there are infinitely many infinite ordinals, and mathematicians have defined ways to add, subtract, multiply, and divide them. Both the rationals and the ordinals are self-consistent – under the established rules we cannot find a contradiction.
Ultimately, I say that numbers (besides the natural numbers) are only made up by humans. We can create new systems of numbers, as we like; we can play with our existing rules and make “discoveries” and theorems based on those rules. With the numbers we have, we can only approximate the behavior of the universe, and we cannot predict everything. Numbers are only a game – a game of our own making.
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