#PhysicsFactlet Sometimes you need to forgo the intuitive way to define stuff for the sake of actually being able to do anything useful with those definitions

[j_bertolotti@mathstodon.xyz]

#PhysicsFactlet
Sometimes you need to forgo the intuitive way to define stuff for the sake of actually being able to do anything useful with those definitions.
An example of this I always found funny is in knot theory, where a simple loop is considered to be a knot, while anything where the two extremes are dangling are not, including the common overhand knot.
This looks weird the first time you see it, but there is a very good reason to go with such a definition: you want to study what you can and can't do by manipulating the knot, and if you have the two extremes dangling, you can always untie any knot, making them all equivalent to a piece of string. In order to be able to say anything interesting about them you need to remove this trivial option, and thus accept the simple loop as a knot.
#knots

[6d03@mathstodon.xyz]

@j_bertolotti

There is another definition of knot, where the ends of the string are fixed to points on the boundary of your space.

[robjlow@mathstodon.xyz]

@j_bertolotti Whenever a definition is 'obviously wrong' it's worth thinking quite hard about why everybody uses an 'obviously wrong' definition.

[j_bertolotti@mathstodon.xyz]

@RobJLow Sometimes the suspicion that Mathematicians do this just to troll the rest of us is strong 😉