Science & New Perspectives
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The Victoria Day weekend brought a number of events that alerted the peoples of the world to our fragile environment and small minds. Predictions, floods and tornados abound. Is a weatherman not another seer like a prophet preacher?
One happening concerned all the hype over the end of the world or what is known as the Rapture. It was sad to see some people spend their savings trying to get the world to take note of the predictions of an 89 year old preacher. The preacher was attempting to understand the infinite by looking for codes and signs. If asked if he was trying to understand the infinite, he would say yes. If asked if he was a man of faith, he would again say yes.
We should remember other times and other preachers predicting things by searching for secret codes in the Bible. These are people of faith, but somehow their faith is not good enough and they try to reason to some end by looking for signals and portents much like ancient seers.
Science has seers too!
The Large Hadron Collider is now working to find the secrets of the Big Bang and the Higgs Boson, which is the 'God Particle'. Long planned experiments are aimed at understanding the first few milliseconds of the known universe and what resulted. These long sought after secrets have scientists all over the world waiting in 'rapt' attention for results which are starting to come out of the LHC at a steady pace. They are dealing with finite things, however. What about the infinite?
This duality of religion and science has existed since records have been kept. The study of mysteries is inherent in both of them. The waxing and waning of the weight placed on observation and reason has been the tipping point of science. The nexus of faith and reason is the riddle of religion. Can we believe our senses? What is the extent of reason?
We take note of the life of the famous mathematician Georg Cantor. He was brought up in a very religious family and remained spiritual all his life, but he was troubled by fits of depression and instability.
His search in mathematics was to understand the infinite in a mathematical sense. This search for meaning took on an almost religious fervor. Some say that his mental breakdowns were the result of this quest.
He looked at the infinite in a way nobody else had ever contemplated. The first thing he did was to examine things called sets. Sets of things can have a finite or an infinite number of members. For example, the set of all letters of the alphabet is finite as is the set of all residents of Bruce County Ontario. These are finite sets and we can count them. Other sets are not so easy. For example, the set of all possible sets.
He extended his thoughts to countable infinite sets like the positive integers. This does not mean that we can sit on a stool and recite numbers for an infinite amount of time An infinite set is countable, if it can be put in one to one correspondence with the positive integers, which are clearly an infinite set.
Strangely he noted that you can take a subset of the integers like all the even ones and put them into 1 to 1 correspondence with all the positive integers. This means that infinite sets can have subsets that are also countable and infinite too.
What he discovered too was that there are some infinite sets that are not countable. For example, the number line from 0 to 1 containing real numbers is not countable at all although it is infinite too. It's another kind of infinity, somehow 'larger' than the set of all whole numbers.
He was able to prove this, which astounded the scientific community and produced a number of strange questions about the infinite. He extended his study to other sets that are not countable too like transcendental numbers (π is an example) Far from being rare these numbers abound and are not countable
The results of his study showed that there are different types of infinity. To sort this all out was an amazing feat and put him at odds with his peers for a time. In a way Cantor who lived in the 19th century produced the most important new branch of mathematics and it has extended into science. Could theology be left out?
There is a lesson here for 89 year old preachers. If you think you understand the Infinite by examining codes hidden from all but your eyes, you better take a look at Cantor's work. The infinite is inscrutable. It does not contain itself in the mind of man.
Cantor came to the conclusion that the Absolute was beyond man's reach, and identified this concept with God. Subsequently, he believed that he was doing theology by introducing transfinite numbers into mathematics.
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Monday, May 23, 2011