Physics, Topology, Logic and Computation: A Rosetta Stone

I like Inverse types! While it's not novel idea, this seems like a very concise implementation of it. Inverse types are also known as negative types (https://legacy.cs.indiana.edu/~sabry/papers/rational.pdf) or holes. This concept is what needed to make a concrete category for computation compact (highly recommend: http://arxiv.org/abs/0903.0340) and make the connection to how our physical universe actually works on a quantum level, with antiparticles performing backward computation. I'm pretty sure this model of computation of filling holes with inference would allow us to understand advantages of quantum computation much better. Do you have any thoughts on HVM's SupGen for program synthesis? I would love to understand how interaction nets makes the notion of inverse types and filling holes more natural and efficient.

Even before I started the video, I had a feeling it was going to lead to a kind of "introspective" mathematics that can reason about its own reasoning. I was not disappointed, thank you. Physics, Topology, Logic and Computation: A Rosetta Stone - https://arxiv.org/abs/0903.0340

Wow, what a combo! I'd be interested in anything from each of the lecturers, but all 3 at the same course, is amazing. Category Theory could be the rosetta stone of many things(this is relevant https://arxiv.org/pdf/0903.0340.pdf).

See https://arxiv.org/abs/0903.0340 for a basic introduction to the issues, and https://arxiv.org/abs/0908.3347 for a slightly more extensive treatment, also mentioning proof nets. This does not explicitly say that these diagrams can be understood as the equivalent to sequences in something FORTH-like, but this is in fact what the papers are pointing out in a general sense, so I see it as a rather trivial remark.

This line of thought is very interesting indeed. Understanding the similarity/contrast to the join operator is really at the heart of what quantum is about. It comes down to, what do you mean by "and" ? Check out the breezy writing in this paper: https://arxiv.org/abs/1602.07618 Also, the Rosetta stone paper (more advanced): https://arxiv.org/abs/0903.0340

Isn't that what category theory is about, on the meta level, and in the result in case of specific isomorphisms, too? edit: at that I still have John C. Baez, Mike Stay - "Physics, Topology, Logic and Computation: A Rosetta Stone" on my reading list https://arxiv.org/abs/0903.0340

An interesting published review of this relationship is "Physics, Topology, Logic and Computation: A Rosetta Stone", by John C. Baez, Mike Stay https://arxiv.org/abs/0903.0340. The first author alos has lots of interesting stuff related to (quantum) computation on his website.