Over time, the threads of our clothes unravel, and once unraveled they do not spontaneously weave back together again. This tendency for things to decay and disorder is universal. In the mid-nineteenth century, it was realized that this tendency places fundamental limits on the things we can build: there are no perpetual motion machines, and running a refrigerator takes power. Fifty years later, it was realized the tendency toward unraveling has its roots in the behavior of atoms and molecules. One hundred years later, disorder was reinterpreted as missing information, and the possibility of measuring information flow provided the foundations for our modern technological world. It is astonishing that there is one mathematical idea - entropy - that unifies all these different problems. Entropy determines how much heat we need to boil water, and whether we can watch movies on our phones. There are even connections to black holes. I will try to explain all this, and to convey some of our wonder at the power of mathematics to describe the world.
