38 karma · joined December 7, 2021
Also, probably I'm too engineer to understand the phrase "independent homotopy/homology classes of 1-dimensional loops in the complement of the object" so I don't know how this definition covers the case but an interesting extension to question is adding "holes" to the straw sideways. (exactly face to face or randomly located?, different sized if face to face?)
I've transleted it from Turkish which is my native language. If the purpose of the question is to get some insight, I can give my intuition about it but that will be the opposite of "a full definition" (: When I see the word hallow ("oyuk" in Turkish) I think there is a opening in the structure otherwise has a solid body.
For example, a tree can have a hallow(hollow?)like this: https://www.elitetreecare.com/wp-content/uploads/2019/11/tre...
But it seems there is no strict boundary between the words, so if you say it is a hole I won't oppose that.
Any time I asked this question it produces some joyful brainstorming. It doesn't matter if it is a room full of highly technical people(engineers, mathematicians) or a family dinner.
I've already heard most of the arguments from the topological definition of a hole to difference between a hole, a cavity and a hallow but it is still very fun for me to watch people getting excited over such a boring looking question. (:
edit: also would appricate to able to zoom in.
I've both BsC and MsC in control and heavily used video lectures of Brian, I am probably one of his first patrons. His lecturing skills are amazing. If you interested about the topic I also suggest to look at 'Steve Brunton' YouTube channel. He is also a legendary teacher.
If you want to talk anything about control theory, please feel free to contact me.