Chip Kendrick

Knowledge, Definition and Time

	Borges' story brings up the idea of an Aleph, a small globe through which 
everything, all perspectives, can be viewed.  The narrator of the story experiences this 
multiple view, and makes a very eloquent attempt at telling us what it must be like, but as 
he expects, it falls short.  I claim that this is because there are an infinite number of 
perspectives to be seen through the Aleph, or at the very least so many that the human 
eye could not view them all in the same field of vision, or even one at a time ( since the 
eye can only take in images at the rate of 10/second ), so that the Aleph must be 
communicating in some fashion that transcends time.
	One big assumption we must make to talk about the number of perspectives: that 
the Aleph is real, and is not a false Aleph as the narrator asserts, and that the experience 
really happened.
	Most would claim that the number of possible perspectives is infinite, either 
because space is infinite or has infinite detail.  If we deny this, we must claim that space 
is both limited and indivisible beyond a certain point in order to obtain a finite number of 
perspectives.  Even if we claim this, we must take into account the perspective within the 
Aleph of seeing the Aleph itself, and thus all perspectives within the Aleph and the Aleph 
again, and so onward to an infinite number of perspectives.  If we now claim that the 
same perspective cannot be shown twice, we for a moment see the way for a finite 
number of perspectives to exist, until we realize that a perspective seen through two 
Alephs differs from that seen through one.  We can make one final claim that the Aleph 
cannot show the perspective in which it will be viewed again ( despite the fact that the 
narrator claims to have viewed this perspective ), and making this claim, seem to arrive 
at a finite and therefore viewable number of perspectives.
	Until we consider just how many perspectives we are talking about.  The number 
of perspectives must be at least as large as the number of positions from which we can 
see a different array of photons, and there are at least as many such perspectives in the 
universe as there are positions for photons to hold, multiplied by the number of possible 
angles of view from the photon.  If the number of possible angles of view from a point 
the size of a photon is taken as finite, we still arrive at a minimum of pi times the radius 
of the known universe, squared, divided by the number of photons which can occupy a 
squared unit of whatever distance the known universe is measured by, all multiplied by 
the number of perspectives from a single point.  So many views could not be seen at once 
in a field of vision, and could not be seen sequentially in the amount of time the narrator 
appeared to spend looking at the Aleph.  Even if we claim a mix of these two methods, 
where a field of view is as subdivided as possible to allow the most possible views and 
fields of view are shuffled by at the maximum possible speed, we still arrive at far too 
large a time frame.
	One final possibility is that the Aleph is showing a finite number of perspectives 
and communicating them directly to the brain, in order to transcend the speed limitation 
of the eye.
	Yet we know enough of the brain to say that it is something like a computer, and 
is not capable of anything close to the required speed.
	So the Aleph must transcend time, finite or infinite number of images.
	The Aleph is outside of time in some way, whether this means it is at the end of 
time, the beginning, or is running parallel.  Some of the properties of the Aleph suggest 
that it is time, itself, or a small portion of time.  The knowledge given by the Aleph 
would allow one to predict and perhaps in some way form the future.  Does this 
knowledge of all things occurring at once simulate time?  Many philosophers have said 
that a being seeing all things and knowing how all things interact would be capable of 
seeing both past and future by simple extrapolation.  The most obvious paradox here is 
that a being seeing the future thus should see his own role in the future and be able to 
change his own actions.  A being at this junction must be God, and must be creating the 
universe as he understands or dreams its future existence, in much the way that a man 
creates another man in Borges' "The Dreamer".  Such a being would seem to coexist and 
coexperience the universe both for us and with us, and in both directions in time instead 
of the one direction we view.  Thus the universe for this being may have started at some 
unimportant moment, and diverged in both directions.  This may be the famed 'parallel 
universe', running back through time, where beings experience everything in reverse, and 
understand cause and effect in reverse.  To journey here, perhaps we must surpass the 
speed of light, since this is the threshold in physics relativity equations where effect 
begins to precede cause.
	All this is only to draw connections between time, godhood and knowledge ( with 
small references to speed and dreaming ).
	In Italo's story "The Light Years", the narrator of the story spends the entire story 
trying out various methods of boosting himself in the galactic opinion polls.  Finally, as 
he begins to become depressed about the unpredictability of his existence, and his 
inability to express his view of himself to others, he finds a kind of peace in deciding that 
at the end of the universe there will be truth.  Here time is equated with knowledge once 
again.  Things can only be really defined at the end of time and it is useless to try to see 
something's true nature in the middle of it's own definition, whether we be talking about a 
person, an object or a number.
	Or is it?  If we can extrapolate what will happen to something, if we can 
understand the trend that must be followed, we can conceive of an object without ending 
it's definition.  Here I am really referring only to numbers and to the idea of limits.  We 
can easily predict what will happen to, for instance, the sum of the infinite series 
represented by  .  Because we are dealing with a simple number, not an object 
whose path we cannot predict without knowing the layout of the entire universe, we can 
define a value.  In the same way we can call .99999 repeating equal to 1, if we make in 
the implicit assumption that the number has happened.  By this I mean only that while we 
can always say that a number can get infinitely close to another number, by calling it 
equal to that number we are saying that it has become infinitely close to that other 
number, and is either at the end of or outside time.
	These numbers, the decimal and the series, have an infinite detail to them, but an 
infinite detail that can be spoken of as a trend.  Now we must consider numbers unlike 
this, like e.
	e has that same infinite detail that .9999 repeating demonstrated, but e is not 
predictable.  We can say that .999 repeating is one, but we can never write the value of e.  
e and other non-repeating numbers are like the object whose path we cannot predict, they 
are like the immortal narrator of 'The Light Years', and their definition seems only 
possible at the end of time.
	The universe seems built of irrational numbers, and created by a God who is no 
more in control than we ourselves, and can only watch us define ourselves.  Perhaps all 
we can do is to wait for truth, and in the meantime, wander in the one realm where time 
is not necessary for definition, mathematics.