Comment on How about the digestive system?
SpaceNoodle@lemmy.world 1 day agoYou could make infinite indentations in an object with zero holes. That’s a very poor definition for a hope topologically.
And yet each indentation could hold something, like cheese or a kitten, so each indentation in functionally different from a smooth surface.
Deforming a shape changes it, thus topology is a special case of specifically ignoring most aspects of a shape.
But more importantly, calling any indentation a “hole” is a case of specifically ignoring the special significance of actual holes. You can’t pass through an indentation.
Guess I can’t dig holes either
Sure you can, they just gotta come out the other side. Otherwise it’s just a fancy divot
That’s why we have the compound word “through-hole”.
90% of important parts on living things are pockets and manipulations of surface area, two things completely ignored by topology. Topology is interesting mathematically, and has meaning for traversal and knot problems, but it’s not really useful to describe reality.
but it’s not really useful to describe reality.
Skill issue
really
Topology is immensely useful to describe reality.
but it’s not really useful to describe reality.
This is just not true.
What topology does for people practically, is it allows them to do a rough kind of geometric reasoning in a wide variety of cases. Further, the geometric notions defined via topology subsume many of the more intuitive notions you might already know of from the number line or the plane.
For example, continuity of functions, convergence of sequences, interiors and boundaries of sets, connectedness and many other things are inherently topological notions that any person who has taken a typical calculus sequence should have some intuitive idea of.
One of the biggest difference between actual pure topology and analysis is that analysis is just done in the context of really nice types of topological spaces called metric spaces in which notions of distance are available.
Any time people are using results of calculus in the sciences, under the hood they are using details about topology on R^n.
That’s why we have a diverse set of words such as “divot,” “indentation,” “pit,” “well,” and so much more!
Topology is a component of the language called “mathematics” we use to understand, describe, and model reality in concrete terms.
If you were to tell an average English speaker that you were going to dig an indentation, chances are high that they would misinterpret your meaning.
On the other hand, if you told them that you were going to dig a “blind hole,” I imagine they would have a much better understanding of your meaning and you would still be technically correct.
That’s part of why I try not to talk to average English speakers
Openings and indentations aren’t the same thing though, are they?
Correct, a hole is a topilogical feature.
But it’s a good definition if you are, say, putting a thing into each indentation. That’s why the two definitions are different.
Right, those wouldn’t be holes.
You seem to not be getting that words can have multiple (even if related) meanings. When some science or other discipline takes a common word and defines it really precisely for their purposes, that doesn’t change the definition of the common word for all usages and mandate that all lay people use it only with that discipline’s more precise definition.
Better precision leads to better communication.
ImgurRefugee114@reddthat.com 1 day ago
I’ll give it a try and get back to you