Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

hello everyone it's July 4th 2023 and we're in our first discussion on chapter two so let us head over there and before we jump into anything specific um does anyone have any General Reflections or or thoughts on chapter two just any any pieces that stuck with them from their reading or just overall reflections from chapter two on the low road yes if I could go I'm not sure whether yeah please um I was curious in terms of the equations uh that relate to free energy so the manifestations of free energy in those three or four equations mathematically how are those derived because in the textbook they kind of just seem to be axiomatically um placed there but I was wondering what is the underlying mathematical root of those equations from which we work thanks Ollie thank you yeah the derivations are the four equations at least 2.5 and uh 2.6 is um I mean we've done basically uh complete steps for the derivations of each of those equations and I'll upload a file explaining each step after the meeting if you want but I'm not sure where to put the files uh Daniel could you please uh I mean where do you think would be most helpful to put those files file format is it uh it's a document so what one option is to just at the top of the notes you could always just drag in a document or I just drop it here another option is to um in the GitHub repo for the textbook to add it there in some format um but yeah certainly dropping a document or taking screenshots in here would be awesome but yeah this is this is a great question and one more thing about the derivations of those Central equations is uh they're not necessarily uh evidence from the textbook or the way they're expressed in the textbook how we can get from each line of the equations to the next line so I agree we need some intermediary steps and even we need to employ some mathematical um some mathematical theorisms theorems and rules such as Jane's inequality rule to get to some of those equations but I hope I mean the derivations we've worked out would be helpful if people want to follow the exact details of each derivation yeah that's awesome work with um Ali and Jonathan and Jacob also did some of these preliminary um connections for a few of the equations cool oh and we're gonna come to to these equations and we'll talk about them a lot more soon but any other just overall chapter two thoughts or or reflections um at the something that was interesting to me is there's kind of a however loose identification between an agent an active inference and their priors this is pulling from page 39. that we can say in active inference the identity of an agent is isomorphic with its priors or the relationship between I suppose the the agent and their their preferences yeah the priors are what the thing brings through the needle of the present to confront the incoming observation to then be updated into the posterior but then that just becomes the prior for the next moment so like if it's not coming with you through the priors it's not making it through the bottleneck of the presence it has been forgotten so everything has to come through the presence in order for the past to influence the future that's like the markovian property of like a Markov chain so that Markov blanket necessarily but actually that is a markup blanket through time past only influences the future through the present so everything has to flow through the present in order to have influence but that is a very interesting claim any other um thought thoughts or ideas on two just overall cool we'll we'll look at some questions but just the big picture for the next month I guess for all of July two weeks on chapter two that's the low road and then two weeks on chapter three that's gonna be the high road so first we're going to talk about how and this is going to get us from the basic tautologically true Bayesian theorem all the way on through heuristics that are used to fit Bayesian models of perception and action that's going to get us…