doughnut, coffee cup, scissors, pretzel, ...
On 26/08/11 7:36 AM, Peter Moylan wrote:
Jonathan de Boyne Pollard wrote:
That might explain it, I guess. So if I see something before me that I
am inclined to refer to as a "coffee cup", how am I to tell whether or
not it actually _is_ a coffee cup in some essential way?
In fact, it could be your doughnut.
(Old topology joke.)
My doughnuts are generally not continuously deformable to coffee cups.
I'd have to poke them with a stick to make that true, and that would
squirt jam everywhere.
Would topology have still been the field it is today if doughnuts had
But when I was a child in England, doughnuts were amorphous lumps and
were definitely not ring-shaped and had no visible hole. It took me a
while before I understood what Americans writers were talking about when
they said "donut-shaped". I don't think I saw a toroidal doughnut until
I was in my twenties.