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bob012345
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Sir Roger Penrose in his book Cycles of Time on page 19 states the result of a calculation of probability of mixing red and blue balls as an illustration of entropy as state counting and the Second Law. He assumes an equal number of each. There is a cube of 10^8 balls on an edge subdivided into smaller cubes of 10^5 on an edge. He states each smaller cube looks uniformly purple if the ratio of red/blue balls is between 0.999 and 1.001. Then he states there are around 10^23,570,000,000,000,000,000,000,000 different arrangements of all the balls that give the appearance of uniform purple and some 10^46,500,000,000,000 different arrangements of the "original configuration in which the blue is entirely on top and the red entirely on the bottom".
If anyone has read the book, I am seeking help understanding how he gets to those numbers. Not necessarily a complete solution but a hint on where to start. Thanks and Happy New Year!
If anyone has read the book, I am seeking help understanding how he gets to those numbers. Not necessarily a complete solution but a hint on where to start. Thanks and Happy New Year!