FROM CHAPTER 6, BOOK 1 "THE END OF PROBABILITY"


The Law of Average and the future of science

The ultimate dream of science is the unification of all scientific principles under one roof. Some of us must have heard of "The Grand Unified Theory" of physics (GUT) which is in existence today. As it turns out, GUT is more a promising name than a reality. It is believed that there are four major forces in the universe: The force of gravity that we are all familiar with; the electro-magnetic force that governs the actions of electricity, magnets, and photons; the strong force that explains nuclear reactions; and the weak force that explains nuclear radiation. GUT claims to have unified the last three and is on its way to "bring gravity home", so to speak. A careful examination, however, reveals that the partial unification claimed by GUT still have many loose ends. In addition, even the most optimistic GUT proponent would agree that the theory might never have a satisfactory solution for gravity.

Superstring, the newest fashion of science at the time of this writing, believes it will beat GUT to the finish line in the unification marathon because gravity is built in with its first principles. At the same time superstring specialists complain that the existing mathematical techniques are not ready to solve the extremely complex equations that arise from the theory. This means it will take a long time before Superstring has any verifiable result of significance to share with the scientific community.

Lets assume for arguments sake that some day either GUT or Superstrings, or both, are successful in achieving their goal. Would their success complete the unification of physics? No! Because neither GUT nor Superstring has room for the very important class of so-called random phenomena, which require separate treatments by Chaotic theory, Catastrophe theory, etc.

We have not even mentioned the humanity sciences such as psychology, sociology, and economics where fuzzy logic is waiting for its heyday. It is impossible to see how these sciences would blend in with any theory in physics today.

Facing such enormous difficulties, many have argued that the unification of science would forever be an elusive dream. Specifically, they stress that it is theoretically impossible to ever bring natural sciences and humanity sciences together. The logic goes like this: Natural science is based on logic and mechanical principles, which are predictable; humanity science is based on emotions and reactions, which are unpredictable. The contrasts are simply too big to overcome.

As it turns out, the two branches of sciences do share a very important first principle. There is one old "law" that has been around for as long as anyone can remember. It is the celebrated "Law of Average". We heard it once in a while in daily conversation (and borrowed its name in an earlier chapter.) It is our consolation when things do not go our way or some bad person has done something wrong to us. We would say "I believe in the law of average. Things will get better," or would curse "The law of average will take care of him". We all have moments when we feel the law of average must be an important governing force in life, although we cannot prove it.

But what is the "Law of Average"? The reader can guess the answer from several chapters ago: The Central Limit Theorem averaging process. Thus, with the Central Limit Theorem science has in its hand a powerful tool that is equally applicable to both natural science and humanity science. It just didnt know how to use this powerful tool for three hundred years.

Although it is still too early, the writer will go ahead and make the prediction that the ultimate unification of science, and this of course means all of sciences, natural as well as humanity, will soon be possible. That is because the missing link has been re-discovered, and it is the celebrated Law of Average disguised under the name of the Central Limit Theorem.

The Central Limit Theorem will rise from obscurity, and it will do so in a big way. Not only that it will stand side by side with the great deterministic laws of Newton and Einstein, it should even surpass them. Because while Newton-Einstein laws and the Central Limit Theorem are equals in the world of innate matter and energy, only the Central Limit Theorem holds the key to the ultimate goal of science, which is a clear understanding of the heart and mind of the human race and its destiny in the universe.




FROM CHAPTER 4, BOOK 2 "THE NEW MEANING OF QUANTUM PHYSICS"
The deterministic nature of the wave equations

The fact that wave equations are classical picture of collective behavior of quantum events means that they have nothing to do with individual probabilities. Rather, they are long-term distributions of many quantum events. Thus, the probability interpretation by Max Born is invalid. Max Born has repeated the mistake committed earlier by the Probability theory by erroneously interpreting long-term distributions as individual probabilities.

Just like the collective result of coin tosses can be described quite accurately by the binomial distribution, collective distributions of the wave functions can be described quite accurately by the wave equations, although individual quantum events may violate all of the laws of classical physics. This explains why the time-independent equations have been quite successful in solving quantum problems.

However, just like the failure in predicting event probability with long-term distributions of multiple coin tosses, we can say with certainty that the prediction given by a wave equation for a single point (in space and time) is as meaningless and unverifiable as the probability prediction that a coin has a 50% chance to turn up heads. Thus, the wave equations are expected to yield meaningless result for individual events; and experimental results show that they do.

With probabilities out of the picture, the solutions to the wave equations possess all of the properties associated with distributions. The most important property of long-term distributions is that they are deterministic within certain tolerance. Thus, it finally turns out that Schrodinger was correct. His (and Diracs) wave equations are all deterministic!!!

This chapter was written in the year 2001, exactly three quarter century after Max Born made his probability interpretation of Schrodinger equations in 1926, despite the protest from Schrodinger. It took a long time, but finally Schrodinger was vindicated.