Wednesday, August 26, 2020

"Self-Organizing" Nails & Googol Gears

Entropy is often described casually as a measure of disorder. While that's an easy way to visualize what entropy quantifies, it can lead to confusion. More rigorously, entropy counts the number of possible configurations of a system's components that are consistent with the macrostate, i.e., the broadly observable state of the system as a whole. So, in the case of the box of nails, the components are the nails (each of which has various possible positions and orientations), and the macrostate is what the body of nails looks like without identifying and recording the position/orientation of each individual nail. When the nails are aligned at the bottom of the box, that same macrostate can be reproduced only by rearranging the nails and flipping their position by 180 degrees — whereas their mixed-up macrostate can be reproduced by many more combinations of nail positions, including being higher up in the box, and with arbitrary angles over all three dimensions of space. Therefore, we say that the ordered box has low entropy, and the disordered box has high entropy. .....
https://youtu.be/Pn5Iaq3XV-E

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