From the point of view of people tying real knots (canonically, sailors) mathematical knot theory ignores much of what makes the problem of knot-tying interesting. Some matters that come up in the study of physical knots include:
- To tie two ropes together, a sheet bend is strongly preferable to a square knot, because the latter tends to capsize.
- The grass bend is extremely prone to slip when tied in cord or rope, but is much safer when tied in flat belts.
- The clove hitch is good for round posts, but unreliable when tied around a square post.
- The constrictor knot, although similar to the clove hitch, is much more difficult to untie.
- The bowline is easy to untie when wet, but the water bowline is even easier to untie when wet.
Is there any sort of mathematical analysis of knots that predicts properties like these?