Quotes About Rearrangements

He always had trouble opening his heart. Tonight it was stuck again. It was a wooden chest secured by locked iron bands. An army duffel, rusted zipper. Kitchen cupboards glued shut. Tabernacle. Desk. Closet. He had to wedge apart doors, lift covers. He was always disappointed to find a drab or menacing interior. To make a welcoming place of his heart was mentally slippery work. Sometimes cleaning was involved, rearrangements. He had to dust. He had to throw out old junk to make room.

The entropy of a system is related to the number of indistinguishable rearrangements of its constituents, but properly speaking is not equal to the number itself. The relationship is expressed by a mathematical operation called a logarithm; don't be put off if this brings back bad memories of high school math class. In our coin example, it simply means that you pick out the exponent in the number of rearrangements-that is, the entropy is defined as 1,000 rather than 2^1000.

Notice that the value of the entropy and the amount of hidden information are equal. That's no accident. The number of possible heads-tails rearrangements is the number of possible answers to the 1,000 questions-(yes,yes,no,no,yes,...) or (yes,no,yes,yes,no,...) or (no,yes,no,no,no,...), and so on-namely, 2^1000. With entropy defined as the logarithm of the number of such rearrangements-1,000 in this case-entropy is the number of yes-no questions any one such sequence answers.