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dusko (Jul 10 2023 at 14:56):i asked @John Baez the following by email:
i have a basic physics question. (i ask like this to make it easier to ignore, but can ask in public if it is fun.)
why does a ball thrown out with a backward spin “roll back” to me?
the answers that i am finding is that the air resistance rolls it back. but then it should also work if spun around any axis. as far as i can tell, it seems to be rolling back on a (nonexistent) plane under it, and not if i spin it around the vertical axis. so in my ignorance i am imagining that it has to do with momentum and gravity. aren’t the rotations of celestial bodies superimposed on their revolutions?…
sorry, it is probably a stupid question. but it does have to do with categories.
adjunctions can be thought of as a mechanism of parentheses underlying the syntactic processes. (this is the idea behind lambek’s pregroup grammars. it goes back to husserl.) it is implemented in our mind as a “charge-discharge” mechanism. BUT we don’t seem to carry the charges as references, but rely upon the adjunction counits to “bring back the spinning balls”...
John provided some quick and useful comments and suggested that it would be fun to see what others think.
it is hard to subsume a question under a stream without constraining the answers. (subsuming Noether's Theorem under "physics" would abstract away the Kleininan program aspect.) but of course i may be wrong. i am at a meeting and may not login tomorrow but will return as soon as i get a chance :)
Steve Huntsman (Jul 10 2023 at 19:14):dusko said:
i asked John Baez the following by email:
i have a basic physics question. (i ask like this to make it easier to ignore, but can ask in public if it is fun.)
why does a ball thrown out with a backward spin “roll back” to me?
the answers that i am finding is that the air resistance rolls it back. but then it should also work if spun around any axis. as far as i can tell, it seems to be rolling back on a (nonexistent) plane under it, and not if i spin it around the vertical axis. so in my ignorance i am imagining that it has to do with momentum and gravity. aren’t the rotations of celestial bodies superimposed on their revolutions?…
sorry, it is probably a stupid question. but it does have to do with categories.
adjunctions can be thought of as a mechanism of parentheses underlying the syntactic processes. (this is the idea behind lambek’s pregroup grammars. it goes back to husserl.) it is implemented in our mind as a “charge-discharge” mechanism. BUT we don’t seem to carry the charges as references, but rely upon the adjunction counits to “bring back the spinning balls”...
John provided some quick and useful comments and suggested that it would be fun to see what others think.
it is hard to subsume a question under a stream without constraining the answers. (subsuming Noether's Theorem under "physics" would abstract away the Kleininan program aspect.) but of course i may be wrong. i am at a meeting and may not login tomorrow but will return as soon as i get a chance :)
TL;DR: Lift + friction = more backwards impulse when in the vertical direction because the ball stays aloft longer than if spun along a horizontal axis
dusko (Jul 11 2023 at 08:56):thank you. sorry about TL.
Steve Huntsman (Jul 11 2023 at 09:18):I meant the article is TL, not you
Simonas Tutlys (Jul 19 2023 at 11:49):Tooting my horn again but i think one physical adjunction is between something that can sense the world and the world itself,akin to the syntax-semantics one.the two categories are states of the world and lets say states of the 'being'.the forgetful functor is reducing our viewpoint from a global perspective to just the state of the being,the free functor is inferring the state of the world from the state of the being.when my 'sabbatical' (burn out) is over i'm gonna try and finish my definition of fuzzy categories to see if this adjunction can be optimized.