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Sidney chooses pies on the basis of popularity. Apple pie is more popular than blueberry pie. Apple pie is so popular that pie eaters have grown sick of it. They quickly gorge on the new cherry pie. When the fad dies down, they are still sick of apple pie and begin a blueberry revival. Sidney correctly predicts that blueberry will be more popular.
I have one exception to the description of timeless physics: Each node in the tree represents a different state than its parent node. This is a time step. A time step that is not instantaneous--we still observe the universe unfolding. Have you looked into cellular automata? This is how I view the universe.
http://en.wikipedia.org/wiki/Cellular_automata
P.S. I'm reading Harry Potter and the Methods of Rationality and absolutely loving it! Have you read Crimes Against Logic?