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Saturday, November 20, 2004

Fool's Gold



Ludwig Boltzmann
(1844-1906)

In 1877 Boltzmann used statistical ideas to gain valuable insight into the meaning of entropy. He realized that entropy could be thought of as a measure of disorder, and that the second law of thermodynamics expressed the fact that disorder tends to increase. You have probably noticed this tendency in everyday life! However, you might also think that you have the power to step in, rearrange things a bit, and restore order. For example, you might decide to tidy up your wardrobe. Would this lead to a decrease in disorder, and hence a decrease in entropy? Actually, it would not. This is because there are inevitable side-effects: whilst sorting out your clothes, you will be breathing, metabolizing and warming your surroundings. When everything has been taken into account, the total disorder (as measured by the entropy) will have increased, in spite of the admirable state of order in your wardrobe. The second law of thermodynamics is relentless. The total entropy and the total disorder are overwhelmingly unlikely to decrease



However, don't be fooled! The charm of the golden number tends to attract kooks and the gullible - hence the term "fool's gold". You have to be careful about anything you read about this number. In particular, if you think ancient Greeks ran around in togas philosophizing about the "golden ratio" and calling it "Phi", you're wrong. This number was named Phi after Phidias only in 1914, in a book called _The Curves of Life_ by the artist Theodore Cook. And, it was Cook who first started calling 1.618...the golden ratio. Before him, 0.618... was called the golden ratio! Cook dubbed this number "phi", the lower-case baby brother of Phi.

How much wiser are we with the understanding that Curlies Gold told us much about what to look for in that One Thing?



The result is that the pinball follows a random path, deflecting off one pin in each of the four rows of pins, and ending up in one of the cups at the bottom. The various possible paths are shown by the gray lines and one particular path is shown by the red line. We will describe this path using the notation "LRLL" meaning "deflection to the left around the first pin, then deflection right around the pin in the second row, then deflection left around the third and fourth pins".


So, what is the value of PI, if a "point" on the brane holds previous information about the solid things we see in our universe now? Have we recognized the momentum states, represented by the KK Tower and the value of 1R as it arises from the planck epoch?

The statistical sense of Maxwell distribution can be demonstrated with the aid of Galton board which consists of the wood board with many nails as shown in animation. Above the board the funnel is situated in which the particles of the sand or corns can be poured. If we drop one particle into this funnel, then it will fall colliding many nails and will deviate from the center of the board by chaotic way. If we pour the particles continuously, then the most of them will agglomerate in the center of the board and some amount will appear apart the center. After some period of time the certain statistical distribution of the number of particles on the width of the board will appear. This distribution is called normal Gauss distribution (1777-1855) and described by the following expression:





1 comment:

  1. The link says:

    "Boltzmann's contribution was vital, but had a tragic outcome. Towards the end of the nineteenth century several puzzling facts (which eventually led to quantum theory), triggered a reaction against 'materialist' science, and some people even questioned whether atoms exist. Boltzmann, whose work was based on the concept of atoms, found himself cast as their chief defender and the debates became increasingly bitter. Always prone to bouts of depression, Boltzmann came to believe that his life's work had been rejected by the scientific community, although this was far from being true. In 1906, he committed suicide. If despair over rejection, or frustration over being unable to prove his point, were contributing factors the irony would be great indeed. Soon after Boltzmann's death, clinching evidence was found for atoms, and few would ever doubt their existence again."

    It is nice that the scientific community is never wrong, and that so many people are not all wrong. It is nice that they don't call people egotists or ignore work based on Mach's or Bohr's philosophy.

    Notice also that revisionist history avoids the statement that Jesus was crucified by the mass and only had 12 real followers, one of whom was a doubter and another of whom betrayed Jesus.

    Instead, revisionist history says Jesus was crucified deliberately to accord to supernatural scripture, and that Jesus was really a very popular figure!

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