Topology is more general than geometry, being simply the study of CONNECTIONS (while geometry is the study of CONNECTED systems with specific SHAPE and SIZE).We grapple with topology from the very beginning of our lives! But parents are family members and neighbors and teachers don't know enough to tell us about this. The French dramatist has a character in one of his plays who discovers that he's been talking "prose" all his life and didn't know it, since no one taught him the word and its meaning. Similarly, each of us has been solving topological problems every day of our lives, but may not know it because no one taught us the word and its meaning.
Elsewhere, I mention the American mathematician, Edward Kasner, as the grandfather of the five-year-old boy who names "The Googol". Kasner once said that he found it easier to teach topology to kids than to grownups, because "kids haven't been brain-washed by geometry"!
Here are some topological experiences of tots:
- In infancy and childhood, trying to kick off blankets or covers.
- Struggling to Climb out of a playpen or a bed.
- Trying to put arms into sleeves, or remove arms from sleeves; similarly with pant legs.
- Trying to button buttons, or unbutton them.
- Trying to tie or untie shoe laces. (A vast field of topology is knot theory, of great importance in molecular chemistry and particle physics.)
- Trying to open or shut drawers, or doors.
- Opening or closing jars, cans, boxes, envelopes, etc.
- Crossing boundaries or rooms, yards, streets, etc.
Challenge: Keep a TOPOLOGY-DIARY, listing each experience every day in coping with THE CONNECTIONS OF TOPOLOGY.