Physics of Creation - Can the Free Energy Principle ground the construction of physical statespaces?

Good luck. Hello, I'm ready. I'm ready. Yes, we are in. It is January 23rd, 2023. We're here in Active Inference Guest Stream number 34.1 with Avel, Gwinn, Carlou. We're going to have a one hour presentation, Physics of Creation, Can the Free Energy Principle Ground the Construction of Physical State Spaces, followed by about an hour discussion. So if you're watching live, please feel free to add questions in the live chat and we'll also have some guests. So thank you, Avel, for joining and off to you for the presentation. Hello. So this is a complete presentation. I will first introduce myself and the work. I am Avel Gwinn, Carlou. I have a problem in Physics. I'm working in cognitive science under version of Andy Clark. This work is, essentially speaking, the product of Kairos Research, which is a laboratory which myself, Alexei Rosansky, who is present here today, and other people are funded to investigate issues of events to political through political evolution and cognitive science. I will be on the physics of creation. So creation is an atypical term, let us say. It will be contextualized in presentation, but let us first define that it corresponds to the construction of physical possibilities, physical spaces to talk in a more technical language. And the original question that motivated this research is whether or not the Frederick Principle, a piece of math that emerges in the cognitive science, which we will get to very soon, is capable of representing this process of creation. So first, I have tried a first run of this without getting into the technicals. It did not work. So I will address the technicals first. We will see some concepts in physics, what they do, how they work, how they relate to what people typically do in physics. And first, I'd like to take a look at how physics explain. So physics explain with laws. They think that in nature, you have laws. And those laws are basically formal statements that constrain the possible states of a system. And typically, those are entailing laws from which you can derive logically what the system will do. An example of natural entailing law is Maxwell's equation of Lectromagnetics. It is a different Maxwell than the one that is here. So what you see is four bits of vectorial calculus that will tell you how two fields are collectively the electromagnetic fields evolve with regard to another. So this is a formal constraint on what E and B can do. So the equality express a constraint by definition. And those can be used to derive basically fully E and B given boundary conditions, which is how you do things in electromagnetism. So what is of relevance here is that any of those laws presupposes basically that I can define E as a vectorial field. So it presupposes what is called a state space, which is mathematical space that represents the set of possible states. Before I state delta E and delta B is equal to this and this, I have to state that E exists and E can take such and such states. In that case, it is a vectorial space in three dimensions. And this set space basically does by construction to capture any difference that make a difference about the system that is targeted. For any change in E to be basically computable by math theory, it has to be represented in the set space. So by construction, I want the set space to categorify every variable of interest in my system, given the scope and measurement capabilities of my theory. You have underlying notion that is basically implicitly underlying the notion of flows and set space, that is the notion of symmetry. I cannot get into the gory detail here, but I will try to be as complete as possible. We specifically understand physical theories outside, specifically relativity theory and some weird quantum stuff, to derive from symmetries. Symmetries are, I will say it out loud, algebraic group of transformation of other set space that do not affect a system's dynamics as presented as Laplacian. You do not have to…