Re:Linguistics Using Category Theory (2018)
by igravious on Thursday August 22, 2019 @06:14PM
(#20772885)
> It turns out that the usual categorical semantics for linguistics shares a lot with the categorical semantics for quantum mechanics
so?
Re:Linguistics Using Category Theory (2018)
by notfashion on Thursday August 22, 2019 @06:42PM
(#20773047)
One other thing that has a lot in common with those two is algebraic data types. Products and sums crop up in all these areas. Maybe it's enough to say that with category theory, we feel like we are revealing the "elementary particles" (or rules) of all of these systems.
Re:Linguistics Using Category Theory (2018)
by igravious on Thursday August 22, 2019 @07:53PM
(#20773457)
Type theory has also been applied to both linguistics and quantum mechanics.
What does it mean that both category theory and type theory have been applied to both linguistics and quantum mechanics?
"categorical semantics for linguistics" gives 0 hits in Google btw.
"categorical semantics for quantum mechanics" gives 5 hits all of which reference the same paper by Bob Coecke titled “Strongly Compact Closed Semantics”, which uses the phrase only once.
Re:Linguistics Using Category Theory (2018)
by wisnesky on Thursday August 22, 2019 @08:11PM
(#20773557)
I'm showing 1M and 200K Google results for those phrases, respectively.
It has been discussed on Hacker News at least a couple of times previously -- fairly recently, even. You might be interested to look at these discussions:
https://news.ycombinator.com/item?id=20376325
https://news.ycombinator.com/item?id=19701767
Edit to add:
You might also be interested to learn that categorical approaches to linguistics typically take as their starting point monoidal categories, in which there are notions of 'parallel' as well as 'sequential' composition. It turns out that the usual categorical semantics for linguistics shares a lot with the categorical semantics for quantum mechanics: roughly, meanings are vectors, like quantum states. You can read more about doing (finite-dimensional) quantum mechanics entirely using string diagrams (the formal diagrammatic calculus of monoidal categories) in the work of Bob Coecke, who also played a large part in originating these approaches to linguistics.
For example, on the quantum side, an excellent book is 'Picturing Quantum Processes' [0]. And on the linguistics side, the paper linked in the article is a good start: https://arxiv.org/abs/1003.4394
[0] Not freely available, but some slides are at https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf
Edit, again:
There is also of course Bartosz Milewski's book / blog series 'Category Theory for Programmers', which introduces category theory from the perspective of Haskell and C++ programming: https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
But the best introduction to category theory I have read is Leinster's book, 'Basic Category Theory': https://arxiv.org/abs/1612.09375
And as you might have guessed, I do agree with your statement!