It's natural to ask which is better, and I believe most people would say "perfect" looks better on paper. So why approximate anything? Don't we have calculators and computers that can crunch the numbers for us and give us perfect answers for everything? The answer, actually, is no.
Probably the most famous example is of our friend pi. Nobody has ever perfectly evaluated pi in decimal form and no one ever will. My TI-83 can evaluate pi to about the ninth digit place. Better equipped computers and computational engines can provide even more. As many as you want so long as you a.) have the time to wait for the computer to calculate pi that far and b.) don't want all of the digits of pi. It would take an infinite amount of time to calculate the infinitely many unique decimal place values.
In a way, this is as close as we'll ever get to our friend:
And as handsome and perfect as the Greek vision of our friend is, it's rather useless; we measure everything in decimal. We compute (with computers) in binary. We encode in hexadecimal. Pi, in it's perfectly evaluated state, is worthless for purposes other than observation and pontification.
My first analogy relates evaluation to moral perfection and approximation as effort to be morally good. Specifically within certain divisions of Christianity, there sometimes seems to be a belief that even if you don't try to be the best you can, if you just reach the point of "good/holy enough" then that's okay. It's okay specifically because you can never be perfect anyways. So really evaluation becomes worthless yet again. A perfect person is not something we can all objectively agree upon. Approximation then becomes of great importance.
My second analogy relates evaluation to Truth and approximation to mere observation. I've talked to friends and peers and there seems to be a common discomfort with the possibility that we may never reach an absolute Truth no matter how far Science or Philosophy advances. "How can we even define progress? How can anything mean anything?" And on a larger level I'm, indeed, not sure if anything has meaning. But if we choose to assume that anything has any significance, then we can start making meaningful observations. Just because we can't reach infinity, it doesn't make the whole number line insignificant.
Finally I present a more concrete example of the significance of approximation. As we all may have noticed, the lifespan of a storage medium is finite. As a culture, we have moved quite rapidly from 8-tracks to cassettes to CDs, DVDs, Blu-Ray, etc. If we assume the lifespan of the CD as a popular medium is 20 years, then how long should we spend on making CD's better? Should we perfect the CD as a medium? Of course not, 20 years would pass before we make the CD able to fit an infinite amount of data (and that would be a perfect CD!). So let's just spend 3 months designing our medium, the CD. Well then we can use this medium for 19 years and 9 months, but it may only be possible to store 100 MB on this poorly designed medium. Very unfortunate given how expensive plastic is these days. Perhaps you can see that there is a point somewhere between 0 and 20 years that we should spend designing the CD for maximum efficiency. In order to achieve the maximum--and therefore perfect amount of efficiency--we must design our medium to be less than perfect.
I read this poem in the NY Times this morning, I think it relates.
ReplyDeleteThanks for the post!
Parable
First divesting ourselves of worldly goods, as St. Francis teaches,
in order that our souls not be distracted
by gain and loss, and in order also
that our bodies be free to move
easily at the mountain passes, we had then to discuss
whither or where we might travel, with the second question being
should we have a purpose, against which
many of us argued fiercely that such purpose
corresponded to worldly goods, meaning a limitation or constriction,
whereas others said it was by this word we were consecrated
pilgrims rather than wanderers: in our minds, the word translated as
a dream, a something-sought, so that by concentrating we might see it
glimmering among the stones, and not
pass blindly by; each
further issue we debated equally fully, the arguments going back and forth,
so that we grew, some said, less flexible and more resigned,
like soldiers in a useless war. And snow fell upon us, and wind blew,
which in time abated — where the snow had been, many flowers appeared,
and where the stars had shone, the sun rose over the tree line
so that we had shadows again; many times this happened.
Also rain, also flooding sometimes, also avalanches, in which
some of us were lost, and periodically we would seem
to have achieved an agreement; our canteens
hoisted upon our shoulders, but always that moment passed, so
(after many years) we were still at that first stage, still
preparing to begin a journey, but we were changed nevertheless;
we could see this in one another; we had changed although
we never moved, and one said, ah, behold how we have aged, traveling
from day to night only, neither forward nor sideward, and this seemed
in a strange way miraculous. And those who believed we should have a purpose
believed this was the purpose, and those who felt we must remain free
in order to encounter truth, felt it had been revealed.
— LOUISE GLÜCK, winner of the Pulitzer Prize and author, most recently, of “A Village Life”
That's a neat poem. I agree that it does relate. It's almost like time is the fourth dimension. Even if you stay put in three dimensions, you're constantly moving in the fourth (time).
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