Mathematicians are known for their ability to neglect non-essential
Looking at a knot, the topologist is blind for its:
- position in space,
The only thing which matters for her :-)
is the knot type.
On the other hand, physicists are known to pay excessive attention to
Is the velocity of a body not too high? If it is approaching c,
its energy starts diverging.
Is the number of neutrons in the nucleus of uranium not too low? If
it is, the nucleus becomes unstable.
Even when looking at an ordinary knot, physicists are constantly worried
by non-essential details
- Is its position in space safe? (If not, it can fall down.)
- Is its orientation right? (If not, it can start rotating.)
- Is its size proper? (If not, it can start shrinking or swelling.)
- Is its conformation ideal? (If not, it can start changing.)
In the physical world, knots are free to look for comfort: for the minimum
(at least local) of their energy.
No doubt, because of this freedom the realm of physical knots is more
intriguing. It is full of life.
Non-essential details play there essential roles.
Knots are not equal - even when they are of the same knot type.
Well. Mathematicians are not oblivious to real life..
Quite a lot of them started to peek in the world of physical knots.
As a matter of fact, they were the first to peek in there. :-)
They were the first to organize a conference on what they have seen.
If you want to know what it was, have a look at the post-conference
Knots: Knotting, Linking, and Folding Geometric Objects in R^3. J. Calvo,
K.C. Millett, and E. Rawdon, editors.
Look and shiver...