Thanks for getting into the details here. I'm brand new to this field of mathematics and this conversation is helping me get a much better handle on what's going on.

[Disclaimer: I am relying very heavily on ChatGPT to work my way through this stuff. I'm mostly using it to learn the math, sort through research papers and check my writing for errors. (Ironically, the reason my writings here contain mistakes is because I'm mostly writing it myself rather than letting the AI take over.) I just want to be upfront about this; I get the impression that you're using LLM-assisted research much less—if at all.]

I don't disagree with your blockquote rewrite in any substantive way applicable to the special case of biological neural networks.

You didn't use thermodynamic entropy anywhere. Personally, I come from a physics background, so my understanding of signal processing—especially in the context of physical systems—uses a lot of thermodynamic metaphors. Consequently, I end up thinking in mixed metaphors, which is bad. To fix this problem, I'm going to stop using the term "entropy" in this thread. (Perhaps I should stop using the word "chaotic" too.)

(Is there actually a proper term for the thing that increases as you move from subcritical to supercritical? I keep finding that I need ugly circumlocutions for want of one.)

Universally? No. But if I were to rewrite this post I would use "gain", since it works fine

but isn't Lyapunov exponent much the same thing as you're calling "gain"?…

Yes.

While "gain" can indeed be handwaved into Lyapunov exponent, jhana isn't just about gain. It's also about noise, which is an orthogonal axis.

What I think is going on is that there's two important factors: noise and gain. Jhana increases gain but decreases noise. In this way a jhanic state is more "ordered" in the lower noise sense. Jhana is closer to critical, because it has higher gain. In this sense it is more sensitive in the dynamical systems sense that small perturbations can get amplified into large-scale patterns.

Consider a leftover warhead from WWII. There are two things that could make it explode. One is if the bomb is sensitive (higher gain). The other one is if the whole room is shaking (higher noise).

(2) things about Complex Systems…never seem to give actual explicit definitions of the things they are talking about. Probably I have just not found the right things to read.

The original paper that led me down this rabbit hole in the first place used "DFA and the $fE/I$ ratio".

• DFA (Detrended Fluctuation Analysis) quantifies long-range temporal correlations.
• $fE/I$ is a proxy used to measure the ratio between excitation and inhibition.

PS: This is the first time you've commented on my posts where I don't want to crawl into a cave and die. My writing is improving! 🎉 I still need to do a re-write of this article that credits you at the end, but at least I won't have to throw the entire thing away.

This is indeed confusing, because I was writing about dynamical order/disorder, which is different from thermodynamic order/disorder.

Sub/supercriticality isn't just about order vs entropy (in the thermodynamic sense). For example, thermodynamic noise (which is about entropy) in metal has high disorder but is also subcritical. Sup/supercriticality is about gain and coupling. Supercritical systems are often chaotic, but this is not a definitional characteristic—the chaotic behavior is downstream of the gain. A linear amplifier, for example, is supercritical but not chaotic.

It is possible for jhana to decrease entropy while going in the direction of criticality, because these are different axes.

I have not experienced nirodha-sampatti. Therefore my definition here is secondhand. It is my understanding that vedana is a valence tag and sanna is labeling something into conceptual categories.

So maybe a better definition would be "An altered state beyond the 8 jhanas at perception does not congeal into the perceptions of valence and concepts"?

Also, I think that terminology can lead to specific induced states as it primes your mind for certain things.

Yep. For this reason, my favorite teachers often don't talk about specific insights until a student encounters it him/herself.

I don't think that insight cycles aren't limited to a certain way of practicing. I read about them from a Daniel Ingram's Therevada book, but my Zen teacher talks about them too—he just uses different words and emphasizes different aspects.

I have heard that the hard parts of insight cycles like dark nights are much easier if you do lots of morality work before getting deep into insight. In this way, different traditions can make certain parts of the path easier and harder.

As for a path that has no ground, there is a ground: it's compassion. The challenge is that a lot of norative intermediary priors are fundamentally groundless. This is a difficulty of the territory, and not an error in the map.

It is true that dark nights are predicated on having some degree of chronic suffering. That's true in two ways: ① without an encapsulation layer to penetrate there is nothing to see through with which to get access into a dark night and ② encapsulating world models cause chronic suffering.

Good point. I have added "Can manifest as an appreciation for sorrow and a disenchantment with joy (relative to normativity)."

Also this is why the tip to meet your meditation freshly wherever it is appearing is important because it is a criticality tuning process…?

Yep.

Agreed. Thanks. I have changed the wording.

I live in a place culturally similar to the Bay Area.

We're basically just fish with a few recent adaptations that allow us to live on land.

Thanks! I've changed the value to 36 and reordered the table.