Talk:Integrated information theory

For author to change:

I think it would be good to cite a few papers by other people that address IIT. It would increase the interest of the reader to know that the theory is stirring up debate and that variants of the theory have been proposed. I would be honoured if you would consider mentioning my papers on IIT:

Barrett, A.B. (2014). An integration of integrated information theory with fundamental physics. Front. Psychol. 5(63).

Barrett, A.B., & Seth, A.K. (2011). Practical measures of integrated information for time-series data. PLoS Comput. Biol., 7(1): e1001052.

Postulates para 1: “(unidirectional arrow in Figure 1)”. I don’t see an arrow in Figure 1.

In Figure 2/3 captions. I think it would help the reader if you could be more explicit about what is shown in the diagrams, e.g. say p= past, c=current, f=future, y-axis shows probability, x-axis shows possible states, and ABCc/ABCp means P(ABCp|ABCc=xxx) etc.

Intro para 1: minor wording change to phrase “(say, some neurons within my brain firing and some not)”

Postulates / Information: Reference to figure 3 added. Some small grammatical changes.

Postulates / Exclusion: Reference to figure 3 added. Small grammatical change.

Extension 6: Small wording change “The freer a choice, the more it is conscious”.

A few further punctuation/typos.

Recommendations for notation

There's a few notation errors. Here are some of the ones that stuck out to me.

1. In many cases the author into $y_t$ as $y_{t,i}$, and other times as $y_{i,t}$. Pick one and use it.
2. In the product for $p_{cause}(z_{t-1}|y_t) \equiv$, the top of the product should be $|y_t|$, not $|Y_t|$ (little y_t).
3. I'm pretty sure there needs to be a normalization constant (1/K) in the definition of $p_{effect}( z_{t+1} | y_t ) \equiv$.
4. In the definition of $CES(x_t)$, there's a qualifier missing. He probably means a \forall, which would make the final expression: $CES(x_t) = \{ CER( y_t, Z_{t +- 1}): ∀ (y_t, Z_{t+-1}) \in M(X_t) \}$
5. All of the expressions with a $min$ and $emd$ need to be within a \operatorname{}.
6. It'd be nice to know if the past and future purview are the same subsets of elements, or if they can be different.
7. In the definition of "physical system", instead of, "can be represented as a discrete time random vector", this should be, "vector of $n$ random variables".
8. In the definition of element, it says, "inputs that can influence these states, and outputs that in turn are influenced by these states". I see no reason for this restriction. If a system doesn't satisfy this then it would simply have zero-phi. I see no reason to have such a restriction in the definition of an element.
9. As GT's use of causation does not fall within the Pearl framework, it's now unclear to me that the do() operator is appropriate. This should be checked with someone who knows the Pearl framework well.

(publishing on behalf of one of the reviewers)