Heffalumps! And coheffalumps!
Most people know the story of the three blind men and the elephant. There were three wise blind men (the story goes) who had never before encountered an elephant. One day, an elephant was brought before them, and they were asked to describe it. The first wise man felt the trunk, and said "Elephants are like snakes", the second felt a leg, and said "Elephants are like tree-trunks", and the third felt an ear and said "Elephants are like bats".
This story gave rise to the title of the mathematician Peter Johnstone's epic work Sketches of an Elephant: A Topos Theory Compendium. Topoi, you see, can be described from several different viewpoints, and it's not at all obvious that the different descriptions all describe the same object.
As is so often the case, the story of the blind men and the elephant has a dual version, which is less well-known but (IMHO) equally interesting. It concerns three wise, blind elephants, who had never before encountered a human being. One day, a human was brought before them, and they were asked to describe it. The first elephant stepped forward, and felt the human with its front hooves for a while.
"Humans," the elephant pronounced, "are flat".
And both the other elephants agreed.
I once told the dual story to Peter Johnstone. He didn't appear to enjoy it.
This story gave rise to the title of the mathematician Peter Johnstone's epic work Sketches of an Elephant: A Topos Theory Compendium. Topoi, you see, can be described from several different viewpoints, and it's not at all obvious that the different descriptions all describe the same object.
As is so often the case, the story of the blind men and the elephant has a dual version, which is less well-known but (IMHO) equally interesting. It concerns three wise, blind elephants, who had never before encountered a human being. One day, a human was brought before them, and they were asked to describe it. The first elephant stepped forward, and felt the human with its front hooves for a while.
"Humans," the elephant pronounced, "are flat".
And both the other elephants agreed.
I once told the dual story to Peter Johnstone. He didn't appear to enjoy it.