Friday, May 7, 2010

A Piece of the Pi

I was doing a bit of early morning reading today (a fun work of fiction called "Cobweb", if you really must know), when I ran across the phrase, "the elegant perfection that mathematicians achieved in calculating the digits of pi". And it got me thinking.

Pi, I thought to myself, is an irrational number. It can never truly be calculated. It is infinite and non-repeating. That is the definition of an irrational number, which is just a bit different from an irrational neighbour, but still shares some similarities.

Rather than trying to capture the fullness and complexity of the number, we just refer to it simply as "pi". By reducing it to two letters, we feel that we have captured some of the elegence of it, and believe that we understand it. This is not the case. We know its effects, the ratio it maintains between a circle and its diameter, but we do not truly know it in its fullness. We can't. If those ancient Greeks who first noticed this ratio tried to write it down in its entirety, they'd still be writing. And they'd have a long way to go. It is infinite. Unending.

Douglas Adams once wrote that a significantly large room conveys infinity better than infinity itself, and you know, I think he was right. A few dozen digits of pi conveys its infinitude better than pages and pages of numbers that make no sense to most of us.

As this miniscule thought was going through my mind, another popped in, and I'm sure that some of you out there will correct me, but this is what I thought. I thought about Godel's Incompleteness Theorem.

"Godel's what?" I hear you. I had the same thought when I first heard about it way back in the days of university.

Kurt Godel was a mathematician who proved that all sets have inherent limitations imposed upon them by the nature of being sets. Or, as I summed it up in university, he proved that all infinite systems are either incomplete or inconsistent (they could also be both, but then they're really useless). For example, the set of positive numbers is incomplete, because it doesn't include those numbers that are the result of taking away a larger number from a smaller one, otherwise known as a negative number. If it wasn't incomplete, there would have to be something within it that would make it inconsistent, and then it wouldn't be much good as a system. If you really want to know more about it, just read the Wikipedia article. I'm not going to go into it more here.

Let me just say that I think this goes a long way to explaining some realities about religion. You see, quite often, we try to explain God, which is, fundamentally, an unknowable. In fact, He is THE Unknowable.

When I think about language, it is, in a sense, an infinite system. Some would say that it is not infinite, given that there are only so many words, but given the many combinations of words and sentences, I think it is infinite.

Aside - Some have postulated (boy, I must be thinking in math terms today) that an infinite number of monkeys typing at an infinite number of computers would eventually produce the works of Shakespeare. I lovingly disagree, and cite the internet as an example. Aside ended.

Where was I? Oh yes, language. I think we can fairly easily look at language as a math-type system, randomly assigning each word a number value. In fact, that seems to be what some Semitic languages have done, but I'm no expert there. If that is the case, then the singular word "God", or "Allah", would suffice to make the system incomplete, and therefore not necessarily inconsistent, by Godel's proof.

But this is often misleading, as we use a simple three-letter word, in English at least, to denote what is, in the end, the most complex concept we can try to imagine: God.

Some people would try to reduce this concept to something approachable, or attainable, but really, that just destroys the concept altogether. Any God that we can conceive of is, by definition not God.

In countless passages Baha'u'llah, Himself, testifies to His own ignorance concerning the true nature of God. One of my favorite passages, one that actually got me to take a second look at His claim when I was investigating, is found in Prayers and Meditations, number 75 (or LXXV, as they have it in Roman numerals for some reason).

"I know not how to sing Thy praise, how to describe Thy glory, how to call upon Thy Name. If I call upon Thee by Thy Name, the All-Possessing, I am compelled to recognize that He Who holdeth in His hand the immediate destinies of all created things is but a vassal dependent upon Thee, and is the creation of but a word proceeding from Thy mouth. And if I proclaim Thee by the name of Him Who is the All-Compelling, I readily discover that He is but a suppliant fallen upon the dust, awe-stricken by Thy dreadful might, Thy sovereignty and power. And if I attempt to describe Thee by glorifying the oneness of Thy Being, I soon realize that such a conception is but a notion which mine own fancy hath woven, and that Thou hast ever been immeasurably exalted above the vain imaginations which the hearts of men have devised."
He goes on to say , "Whoso claimeth to have known Thee hath, by virtue of such a claim, testified to his own ignorance..."

I truly love the reality of that statement, and the utter humility in His admission of it. But what else could He say? What else could He have done? And this from a culture in which many ask their teachers, if they admit to not knowing something, "Why should I study under you?"

No. I do not believe that Baha'u'llah could have ever claimed to have known God, for that would be obviously untrue. But He does know things about God which we do not, and He is also a clear channel for His guidance. That is why I believe He is a Messenger of God and follow Him. This example of His saying, effectively, "I don't know", also rings true with me. Perhaps that is why I feel so comfortable in admitting my ignorance (hmm, I sure have plenty to admit).

At the same time, He could not reduce the concept of God to a mere simplistic platitude.

Here I am reminded of those legislators in one particular state who decided to try and make pi equal to 3.2, or something very close to that, depending on the news report at the time. (It was Indiana in the late 19th century, but I don't want to mention it by name.) Today we laugh at the absurdity of it, but it was real. They really thought that they could do this in some silly attempt to either make math easier for the students, or to conform with some odd notion of what they thought the Bible said. Who knows why they tried, but try they did.

You see, in the end, I think it comes down to a simple concept: you cannot reduce the infinte and still be faithful to it.

Mathematics is a pure examination of reality, and we cannot mess around with it. One plus one will always equal two (please don't talk about mixing chemicals and having one litre plus one litre making only 1.8 liters in some reactions), and in geometry, the circumference of the circle is always 2 pi r.

But then again, I had a teacher who once told me, "Pi r squared". My response was, "No. Cake are square. Pi are round."

1 comment:

  1. Hi there!

    I have been reading your blog for a few weeks now and I am absolutely loving it. I wanted to write to you and tell you to keep the posts coming, because they are very encouraging for me (and other Baha'is, I'm sure!), but I wasn't sure which post to comment on. As an Engineering student, I decided I'd post on this one.

    I love the Pi analogy (I myself have memorized the first 100 digits of pi. I am 100/infinity of the way to understanding it!!!)

    Anyways, love the blog, love the insights, keep the posts coming!