Constructor Theory as Process Theory

Hello and welcome everyone. It is September 19th, 2023, and we are in ACTIMF Math Stream number 7.1 at the Active Inference Institute. We're here with Vincent Wang Mashinitsa and guests. It should be quite a discussion, certainly a unique one by what we can already see. So thank you all for joining. We'll be looking forward to this presentation and interleaving discussion. Thanks, Dan. So hi, my name is Vincent and with me today also is Hamza in the audience. We're both authors on this paper that we'll be talking today, Constructor Theory as Process Theory. So what should the format of this discussion be? So I'd like to tell you a bit about Constructor Theory and Process Theory and then sort of have a discussion about the sort of diagrammatics of Process Theory, how that might fit with Active Inference. And all this, you know, you can view it as an exercise and sort of seeing things in a diagrammatic way. So I'll get started and the structure will be roughly I'll talk about what Constructor Theory is first, just from a conceptual level, because I'm the only non physicist among the authors of this paper. Hamza is a physicist, so any questions about specific examples is there to be directed to Hamza. And then, you know, after that, I'm going to do just a sort of lightning fast introduction to what a process theory is. And then we'll put the two together and then we'll have a discussion. And throughout, I will be making pauses to sort of invite questions and make sure everyone is on the same page conceptually. But everything should be super, super easy, because I think all the ideas really are, you know, fundamentally, they're quite simple. Okay, so without further ado, what is Constructor Theory? Constructor. So you may have heard of this already, because there's quite a lot of hype. They have a very good PR machine, if nothing else. So among other things, it's been described as, and I think this is from a Quanta article, a master theory, a set of ideas so fundamental that all other theories would spring from it. In fact, if you go to Deutsch's original paper on Constructor Theory, he goes so far to say that all other theories of physics, you know, we'll call them, you know, it doesn't matter if it's thermodynamics or quantum or relativity, gravity, whatever. We'll just call them subsidiary theories, because that's how big and important Constructor Theory is. And, you know, there's this eponymous book by Chiara Moleto, the science of cannon cats. I want to say that, oh, well, you know, Constructor Theory is about counterfactuals and what is and isn't possible in the domain of physics. And all this is all this sounds really impressive. But, you know, the question is, what do you mean by what do you mean by this? So how this how this all started is some of Chiara's students, Anisette and Rhea Villarres, they came over to the Wolfson Quantum Foundations discussion. And they were nice enough to sit down and tell us about what Constructor Theory really is, because, you know, historically, it's been really difficult to sort of pin down, you know, to pin down like, what is the math? What do you really mean here by all these words? And, well, you know, they're happy to say, look, you know, it's a meta theory, you can sort of bring your own mathematics, you know, what we really there's a sort of methodological approach of Constructor Theory. That's more important than the specific mathematics that you want to use to instantiate all these words, like what is a Constructor, what is possible, what is impossible. But, okay, I'll tell you conceptually what Constructor Theory is. So first, I want you to, let's talk about a space of conceivable processes. Conceivable is the word here. Conceivable is the word conceivable. Conceivable will become clear soon, because we're going to cut this space shortly. And what are the sorts of conceivable processes that we might have? Well, let's look at a limited subset. Let's talk about ice cream. There's…