[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.)
state
noise
gain
normative human
high
nominal
samatha jhana
low
IDK
open awareness (jhana?)
low
high
[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.
state
effect of sensory inputs on consciousness
effect of sensory inputs on motor action
normative human
nominal
yes
samatha jhana
low
no
open awarenesss
high
no
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. :)
I hope I will return to this when I have time to read it properly and think about it properly, but for now I’ll just drop in two things at the meta-level: (1) I don’t know how comprehensible I’d have found something more in your usual concise style, but the above certainly seems nice and clear so it seems like you probably made a good choice. (2) I’m glad to hear that I’m perfectly tactful but now I’m worried about a different issue, namely that maybe I never say anything unless I have something mean^H^H^H^Hcritical to say, which I’m aware is the exact opposite of what generations of parents have been teaching their children to do :-). (I definitely do lean in that direction, and I’m somewhat prepared to defend it in that offering hopefully-informative criticism is arguably more useful than offering compliments, but it’s still probably suboptimal.)
[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.
I originally claimed that:
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.]
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.
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. :)
I hope I will return to this when I have time to read it properly and think about it properly, but for now I’ll just drop in two things at the meta-level: (1) I don’t know how comprehensible I’d have found something more in your usual concise style, but the above certainly seems nice and clear so it seems like you probably made a good choice. (2) I’m glad to hear that I’m perfectly tactful but now I’m worried about a different issue, namely that maybe I never say anything unless I have something mean^H^H^H^Hcritical to say, which I’m aware is the exact opposite of what generations of parents have been teaching their children to do :-). (I definitely do lean in that direction, and I’m somewhat prepared to defend it in that offering hopefully-informative criticism is arguably more useful than offering compliments, but it’s still probably suboptimal.)