Saturday, May 07, 2011

What’s It All About?

In October I will be turning 60 years old and heading in for the homestretch. As one advances in age, one tries to put life into perspective and figure out what is important and what is not. I have always been a very curious individual, so about a dozen years or so ago, I figured that it would be a real shame to have gone through all of life without ever having figured out what’s it all about or understanding where I had been or how I had gotten there, so I assigned to myself the task of reading at least one book per week on science, philosophy or religion to help find out. Given my fondness for science, I must admit that most of these books were scientific in nature. At this point in life, I am greatly dismayed by the high levels of non-critical thinking that one finds in the “real” world of human affairs, and of all the needless anguish that it causes, so I have come to have little confidence in those forms of human thought that are not scientific in nature. With that said, the purpose of this posting will be to share my current working hypothesis of what’s it all about. As I pointed out in How To Think Like A Scientist, this will be an effective theory of what’s it all about, that I know is wrong from the onset, but for me, is still a good working hypothesis just the same. In truth, I don’t think anybody will ever really figure out what’s it all about.

As we saw in Self-Replicating Information, and in many of the other postings in this blog on softwarephysics, an ongoing theme throughout has been that, at least from the perspective of the “real” world of human affairs, it’s all about self-replicating information in the form of genes, memes and software that are all trying to survive in a nonlinear universe that is subject to the second law of thermodynamics. But in a much larger sense, my current working hypothesis is that it’s really all about mathematical information self-replicating at a cosmological level. As we saw in The Foundations of Quantum Computing, thanks to 20th century physics, there really is not much tangible stuff left in our physical Universe, as all of the “real” tangible things about us have dissolved into the pure mathematics of quantum field theories, with their arcane reliance upon the bizarre internal symmetries of 19th century group theory, or if the string theorists are correct, into the pure mathematics of vibrating strings and membranes that is so difficult, that even today, nobody can fully deal with them. Furthermore, as we saw in Some Reflections on nothingness, our universe may have begun as a quantum fluctuation, forming a universe that is made of “nothing”, with no net momentum, angular momentum, mass-energy, electrical charge or color charge to speak of. It’s like adding up the infinite set of all real numbers, both positive and negative, and ending up with exactly zero. In Is the Universe Fine-Tuned for Self-Replicating Information? and CyberCosmology, we also saw that our Universe might just be one instance within an infinitely large multiverse of universes and that our Big Bang might just be one of an infinite number of Big Bangs of mathematical information exploding into a new universe. We just happen to be one of the lucky lottery ticket holders to a universe that is capable of sustaining conscious intelligent beings that are able to appreciate the mathematics of a universe, in keeping with Brandon Carter’s Weak Anthropic Principle (1973).

In Model-Dependent Realism - A Positivistic Approach to Realism, we alluded to Eugene Wigner’s oft-cited paper The Unreasonable Effectiveness of Mathematics in the Natural Sciences (1960), which is available at:

This short, but fascinating, paper begins with:

There is a story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. "How can you know that?" was his query. "And what is this symbol here?" "Oh," said the statistician, "this is pi." "What is that?" "The ratio of the circumference of the circle to its diameter." "Well, now you are pushing your joke too far," said the classmate, "surely the population has nothing to do with the circumference of the circle."

Wigner then goes on with:

The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it.

….it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.

It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind's capacity to divine them.

The reason that such a situation is conceivable is that, fundamentally, we do not know why our theories work so well.

Wigner finishes the article up with:

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

My working hypothesis for the reason that mathematics is so effective at describing our Universe is that our Universe, and the whole multiverse for that matter, is itself just a form of self-replicating mathematical information. I realize that this working hypothesis is only an approximation of reality, if absolute reality even exists, but for me, it still is the best working hypothesis that I can come up with given my limited abilities. Human beings tend to take what they are familiar with and project it upon those things with which they are not. For example, many of the Middle Eastern monotheistic religions produced deities that took on the form of a supernatural Middle Eastern warlord, with all of the human shortcomings that have plagued mankind throughout history, such as jealousy, anger, vengeance, and the taking of sides in the petty disputes amongst the nations of the world. However, such a model would certainly be reasonable for a Middle Eastern population to adopt hundreds or thousands of years ago because it simply reflected the experiences of their times. They simply took what they were familiar with, and projected it upon that with which they were not. So, in a similar manner, as a pantheist with a background in mathematics and physics, I may simply be projecting my familiarity with mathematics upon what I call the Fundamental Essence of the Universe - the FEU. But for me, mathematics is the best model for the FEU that I can currently come up with because mathematics is both perfect and beautiful at the same time, and exists all on its own, even if there is nobody around to ponder it.

By the way, π really does have nothing to do with the statistics of a population, or with any of the other thousands of equations in physics in which it appears, not even the equation about being the ratio of the circumference of a circle to its diameter, because π really is just the sum of an infinite series of fractions with odd integer denominators:

π/4 = 1/1 – 1/3 + 1/5 - 1/7 + 1/9 – 1/11 + 1/13 – 1/15 + 1/17 ……

and where 4 is the first even integer raised to the first even power 22.

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Steve Johnston