
Physics, Topology, Logic and Computation: A Rosetta Stone (2009) [pdf] - sndean
http://math.ucr.edu/home/baez/rosetta.pdf
======
mrcactu5
Homotopy Type Theory by Vladimir Voevodsky is another possibility. This is an
attempt to link Topology and Computer Science

[https://homotopytypetheory.org/book/](https://homotopytypetheory.org/book/)

Back in the day there was Feynman's Lectures on Computation. Hint: pdf can be
found by searching

[https://www.amazon.com/Feynman-Lectures-Computation-
Richard-...](https://www.amazon.com/Feynman-Lectures-Computation-
Richard-P/dp/0738202967)

See also nLab

[https://ncatlab.org/nlab/show/higher+category+theory](https://ncatlab.org/nlab/show/higher+category+theory)

one should never forget Jacob Lurie's "Higher Topos Theory" which is 1000
pages just like that

[http://www.math.harvard.edu/~lurie/papers/croppedtopoi.pdf](http://www.math.harvard.edu/~lurie/papers/croppedtopoi.pdf)

Actually I recommend against readin it as it only covers 2 of the 4 topics you
discuss (Topology and Logic). However it certainly has applications to the
other two.

~~~
fmap
The infinity groupoid models of type theory have already revolutionized our
understanding of equality in type theory. So far, the 21st century has been an
incredible time for logicians.

There are also older, and very different topological models for typed lambda
calculi (see e.g.
[http://www.cs.bham.ac.uk/~mhe/papers/entcs87.pdf](http://www.cs.bham.ac.uk/~mhe/papers/entcs87.pdf)).
These motivate things like Escardo's "seemingly impossible functional
programs" ([http://math.andrej.com/2007/09/28/seemingly-impossible-
funct...](http://math.andrej.com/2007/09/28/seemingly-impossible-functional-
programs/)) and, along different lines, Abstract Stone Duality
([http://www.paultaylor.eu/ASD/](http://www.paultaylor.eu/ASD/)).

------
baq
excerpt:

> At present, the deductive systems in mathematical logic look like
> hieroglyphs to most physicists. Similarly, quantum field theory is Greek to
> most computer scientists, and so on.
    
    
       Category Theory    Physics    Topology    Logic          Computation
       --------------------------------------------------------------------
       object             system     manifold    proposition    data type
       morphism           process    cobordism   proof          program
    

yup, as a computer scientist by education, sounds about right - Greek and
hieroglyphs (and those are just names!)

while we're at it, we need an update with statistics, data science and machine
learning.

~~~
torustic
> while we're at it, we need an update with statistics, data science and
> machine learning.

See this post and its comments[0] to get some foundations upon which to think
about these correspondences.

[0]
[https://golem.ph.utexas.edu/category/2014/10/where_do_probab...](https://golem.ph.utexas.edu/category/2014/10/where_do_probability_measures.html)

------
justinjlynn
If you like this Propositions As Types by Wadler is also an excellent read. In
fact, the author cites PTLC: Rosetta.

[http://m.cacm.acm.org/magazines/2015/12/194626-propositions-...](http://m.cacm.acm.org/magazines/2015/12/194626-propositions-
as-types/fulltext)

------
kol
> It was then realized that the loose analogy between flow charts and Feynman
> diagrams could be made more precise and powerful with the aid of category
> theory

This is fascinating!

------
erik998
Also checkout Steve Awodey's Category Theory book.

[https://global.oup.com/academic/product/category-
theory-9780...](https://global.oup.com/academic/product/category-
theory-9780199237180?cc=us&lang=en&)

On a personal note, I remember Awodey from my Senior Thesis seminar. He was
very amicable and affable. During my presentation, I remember having to
demonstrate Cantor's diagonalisation argument. Luckily for me it was one of
the things I spent a good amount of time studying. Had a great time there.

~~~
Koshkin
Also, a book by B.Pierce [ISBN 9780262660716] is a very good short
introduction to Category Theory for programmers.

