This post is a founding pillar of my current understanding of Buddhism, insight meditation and awakening. I blieve this post (and, by extension, the whole sequence) creates a material reductive framework that solves—at least in broad strokes—a problem so important that it has founded at least one major world religion, the mechanics of which have been a mystery for at least two millennia. This post has been instrumental in improving my understanding of my own experiences with insight cycles.

Will this post be relevant 12 months from now? If this post is correct and human beings are alive in 1,000 years, this post will still be relevant just due to the Lindy effect. This post has been relevant for at least 2,000 years. We can expect it to be relevant for at least another 2,000.

Was this post invalidated by further work or other criticisms that came up? Not yet, and perhaps not ever.

[Meta: This comment is messy because I think that spewing out a large number of words in an attempt to gesture at what I'm thinking right at this moment is probably easier for you to understand than if I write in my usual concise style.]

I don't have much to say on your mathematical analysis, but I have some meditative contextual data that I predict could help put your analysis into context.

jhana isn't just about gain. It's also about noise

I originally claimed that:

Deep jhana reduces chaoticity and moves dynamics toward criticality.

That was clumsy of me to write. It's ambiguous at best and wrong at worst, depending on how I define terms. (And I defined terms—including "jhana"—right at the start of this article, so that oversight is on me.) By the logic of my post, deep samatha jhana ought to move the dynamics away from criticality, toward deeper subcriticality. Whereas deep insight (jhanas?) are what move the dynamics toward criticality.

I will try to set the record straight here. If I'm understanding you correctly, you seem to be taking seriously the idea that jhana and open awareness are opposites where jhana decreases Lyapunov exponent and open awareness increases it. Maybe I said or implied this, but to consider them entirely separate is, from a meditation perspective (not considering the math at all), too lossy of a simplification. To switch into Buddhist lingo for a moment, meditation always has both a samatha component and an insight component. Deep samatha jhana usually contains an insight element, and getting to insight usually requires a samatha element. If you want to do Zen nondual open awareness meditation, you have to bootstrap yourself there through a phase of stabilized attention. This seems to imply that there's a common factor moving the mind toward both ends of this meditative spectrum simultaneously. Which means that what's going on can't be a single variable like Lypunov exponent. There has to be at least two important dimensions that we care about. One dial is the deepness of your meditation. The other dial is a spectrum from samatha to insight.

It is possible to do deep jhana without moving your brain toward criticality. This is considered a mistake, from an insight perspective, if that's all you do, but it can and does sometimes happen.

Here's my current theory as of writing this comment. There's two important dimensions: noise and gain (Lypunov exponent). Your brain can only handle a certain amount of combined noise + gain without running into problems. All meditation lowers noise. Some meditation (samatha) just leaves it at that, and may not bring you closer to criticality. Open awareness meditation uses this low noise to increase gain. (A very common, effective meditation technique is to start with samatha and then transition into open awareness.)

[I hope this doesn't come across as wishy-washy. Even without the math, explaining how to do insight meditation is notoriously prone to miscommunications.]

If we're thinking about the brain as a dynamical system, how is this noise being represented? Maybe as arising from inputs coming in from outside

Samatha jhana mostly ignores inputs from the outside. Open awareness states do allow sensory inputs to reach consciousness, but they don't result in destabilization of attention.

Much noise is internally-generated. If you're talking to yourself in your head, then that's noise, even if you do it while physically motionless.

…it's all kinda phenomenological, looking at the outputs of the system rather than at the system itself.

Which may very well be the best one can do with a brain, but it's all a bit frustrating when trying to understand exactly what's going on.

I believe you are correctly describing the current state of the science.

About tactfulness: When I see your name in the comments it means I messed something up. You're perfectly tactful. :)

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.