This got me thinking about people. Compared to things of similar size and energy we get very poor predictions of an individual humans behaviour. So considering your matrix analogy we can say there’s some degree of non locality acting within the human? This definitely occurs over time: at any moment we can remember something from any point earlier in our life which can change our behaviour
It’s hard to say whether human action is outside the validity of what our EFTs could predict in principle, at present. We certainly is not close to doing it in practice yet. But if you are anyway not also modeling all of earth at the same time, environmental randomness would completely swamp any randomness caused by unknown laws of physics in an effort to predict a brain.
I would not say that non-locality is directly operating at such large scales as a human brain. But if there is non-locality at really really tiny scales, these can influence really long chains of computation that do happen at large scale. But most importantly, as mentioned above, human brains are open systems, so random environmental effects (like wind blowing into your ear) are many many many orders of magnitude larger, so this randomness would completely swamp the non-locality randomness. That said, thanks to the butterfly effect there might be some way to say that it has a real effect, although quantifying this is hard.
Great read even if I did not get all the math. This reminded me of Bernardo Kastrup saying that the universe cannot compute its next outputs even though they are deterministic and thus experiencing is the best way to know what happens next (I’m paraphrasing from memory so I apologize if I am not being precise). I would love to know your perspective on free will based on your background.
I enjoyed this article even with all the numbers and equations in it.
I recently finished reading through the collected correspondence between Wolfgang Pauli and Carl Jung. Among other things they discussed in detail came the idea that the complementarity of opposites in physics, between energy-momentum and time-space position, has a real parallel with the opposition between conscious mind and the unconscious.
This strikes me as a different angle on, or at least quite close to your point about the great abyss of the unknown that lies outside our best (real or possible) physical theories.
I'm confused as to how it could both be the case that, 1) as we zoom in on nature, more details reveal themselves and this could potentially go on forever, AND ALSO 2) there is finite information in finite space.
Is more detail at smaller and smaller scales not more information?
yeah, this is an excellent question. I should make an edit clarify this!
I talked about more and more laws revealing itself before I came to the universe being finite. It is definitely true that once it is finite, there cannot be an infinite set of laws. However, instead it will be a "cut off" infinity. You will keep sifting through all degrees of freedom and find either laws or "spirits" (incompressible phenomena) until you have looked at it all. Thanks for the excellent question
I’ve been thinking about related ideas from a very different angle—more in terms of cognition and non-Markovian models of memory and time. I’m not a physicist, but I’ve been exploring the idea that systems (including human cognition) are fundamentally autoregressive: each state is generated from the lingering, decaying influence of prior states.
In this view, the past isn’t “deleted” and forgotten, ever; it’s folded into the present. Its signal may decay, but it remains measurable and keeps steering what comes next.
The way you describe renormalization—where degrees of freedom are integrated out but still exert influence—feels deeply analogous. That “ghost pressure” of the past, even when compressed, seems like a universal structural feature of generative systems
Brilliant. And there is yet another limit to scientific laws, namely that our laws govern two-body systems or well-behaved aggregates of two-body systems. As soon as one goes to the next step (of indefinitely many such steps) of complexity, equations of motion cannot be integrated over time. We call this “chaos” but it is really the onset of neo-Aristotelian teleological order. The cosmos is much more like a garden than a machine. BTW, I am a former particle physicist who is now a Catholic priest.
As for teleological order I'll have to admit my ignorance on the exact meaning of this. Def curious what you mean about many body physics in particular though. Many body systems are rarely integrable, but quantum field theory does allow many-body interactions straight forwardly. Is the point that in four dimensions all higher order many body interactions that do not imply 1->2 (decay) or 2->2 (scattering) is non-renormalizable? Like phi^6 theory.
You’re a great writer and a formidable thinker and this was a great read, but:
(1) The word “spirits” anthropomorphizes the phenomena about which you’re speaking, whether you want it to or not. And that *really* doesn’t sit right with me.
(2) >>”I can think of no phenomena more worthy of the name Spirits.” Honestly, it just sounds to me like you’re talking about something like “outliers.” If all theories are compressions (and I very much agree with that) then all theories lose some data, some richness, some possible-but-extremely-uncommon-and-therefore-impossible-to-account-for data, and so all theories, even the most exact, will fail to account for certain outliers that are only outliers because they have some causal force but are nevertheless very uncommon and diverge strongly from the general pattern or tendency … If you don’t like the term “outliers” (and I could see why you might not), then might I suggest “clinamina” (the plural of clinamen; with reference to Lucretius and Deleuze’s work on him)? … Honestly, just anything but “Spirits.”
I would not say outliers is an apt term here. I am referring here to a phenomenon that fundamentally is un-modellable given the constraints of our universe. Outliers as a word not even close to capturing this aspect, although
I also want to point out that lossless compression is a really thing. It is still a possibility that there exist a fundamental theory of natural that genuinely achieves lossless compression - I cannot rule that out, although it is not my intuition.
A spirit is usually taken as a non-natural or supernatural phenomenon interacting with the universe. I don't acknowledge the naturalist/supernaturalist dichotomy as meaningful for reasons described in my previous post ("God is NaN"), yet I find the term apt. This phenomenon of possible pattern in nature being fundamentally impossible to model, is as close a programatic definition of "supernatural" as I can think of.
Yeah, I understand what you’re referring to here, and in fact—since my baseline assumption is that lossless compression probably isn’t possible at all or, rather, may only be possible within very particular, extremely well-controlled parameters, which, for any non-trivial outcome, amounts to the same thing—I definitely think that there exist fundamentally unmodellable phenomena that exert some causal influence over at least some (and probably many, even most) non-trivial outcomes.
But if we make the following assumptions—(1) that lossless compression isn’t possible outside of very particular, very well-controlled parameters, and (2) that anything that exerts a causal force can be measured indirectly (despite being un-accountable or unmodellable)—then I think that you’re basically just talking about outliers or, at the very least, something a lot less sexy and (yes, I’ll maintain) anthropomorphic than “Spirits.” (I’ll return to this word in a second.)
I’ll admit that I don’t think that term “outliers” is perfect because in common usage, an “outlier” tends to refer to an observed outcome, not a cause, and is also probably model-neutral, in the sense that some outlier phenomena can be causally explained while some can’t (due, again, to the limits of compression). But take a weather system (or any other system subject to complex, chaotic dynamics). For that kind of system, (1) lossless compression is impossible to achieve, and (2) unmodellable causal forces can be indirectly observed by observing the evolution of the system over time. (That’s chaos theory in a nutshell, right?) In these kinds of systems that are so extremely sensitive to initial conditions and to the complex dynamics involved in their evolution over time, unmodellable *outlying* or “outlier” factors exert a causal force which can be indirectly observed. To me, it sounds very strange to say that the outcomes of these systems are caused by Spirits, but to say that these systems are caused by “outlier factors” or even just “unmodellable factors” or even just “noise” or “stochastic factors” or whatever … that sounds a lot more reasonable and (frankly) accurate.
Which leads me back to the word “Spirits.” The etymology of that word ties it to breath, souls, and an animating, vital force present primarily (but not exclusively) in humans and animals. So while it may not be strictly true to say that it anthropomorphizes outlying or stochastic factors (or whatever we want to call them), I would at least say that it bio-morphizes them. Likewise, I am definitely not a fan of the “supernatural” connotations, since I don’t think that there’s anything supernatural nor non-deterministic about unmodellable factors.
… But, on the other hand, maybe that’s not the worst thing in the world? I mean, the evolution of biological life follow complex dynamics that are somewhat analogous and generalizable to those that govern weather systems and other systems with fundamental modeling limits. (That’s complex systems theory, right?) Likewise, I’m open to the idea that some types of spirituality/ religiosity were developed to account for and explain the unaccountable, so maybe it’s not the worst thing in the world to draw upon this lexicon in order to name the unnamable.
But, on the other hand, given the overwhelming presence of religiosity and spirituality in our society today (with only something like 3% of people identifying as atheists and with the overwhelming majority of religiously unaffiliated people identifying as “spiritual, not religious”), I don’t think that anyone will hear the word “spirit” and think “Oh, he means unmodellable causal factors.”
Ultimately, it doesn’t matter very much, I guess. But I have a (very-epistemically-uncertain) hunch that knowledge and understanding of the world are fundamentally (or, at the very least, in the long-term) limited by cognitive tendencies like observer’s bias, anthropocentric and even bio-centric bias, the mind-projection fallacy, etc. (We understand the solar system and the universe much better, for example, for realizing that we are not the center of the former and hold no privileged position in the latter.) And so I worry (or am maybe disappointed?) when people use anthro- or bio-centric terms—especially those culled from spirituality/ religion—to explain ideas that should, to my mind, if properly understood, really push us away from our human-experience-centric epistemic baseline/ tendency or, to put it more metaphorically, our tendency to think of ourselves as the “center of the universe” and to think of our experience as being far more epistemically valuable than it is.
Again, I feel *a lot* of uncertainty about the chain of reasoning in that last paragraph and can imagine at least some reasons why it may be wrong … On some level, it might just ultimately be motivated by the fact that I am a devout atheist/ (weak) physicalist and just wanna see more people out there who reflect those epistemic baselines and the value systems that (to my mind and in my experience) tend to follow from them.
On the other hand (and, I’ll admit, that this kind of reasoning is probably engaged in by spiritual/ religious people also, which is only one reason to be suspicious of it), I have found a lot of personal, psychological, axiological, moral, epistemic, and practical value in my atheism and weak physicalism, and so I think that part of my motivation is at least somewhat altruistic. … I just think the world would be a better place if everyone realized that (objectively speaking) nothing matters, that our lives are little more than the consequence of highly complex, chaotic causes (some of which are modellable and some of which are not, lol), that we’re all going to die, that this life and experience is all we have, that any impact we have upon the world will eventually fade, and that none of us, in the grand arc of time, are more special or important than anyone else.
Isn’t that all just obvious?!?! Can’t we all just get along?!?! hahah
Anyway, sorry for this overly-long, overly-self-reflective, overly-soapbox-y response. (I’m giggling at my own ridiculousness right now.) This discussion just touches on stuff that I, obviously, have a lot of thoughts about and like talking about, so it can be a little hard to stop or limit myself, haha.
I hope this does not come across as self promotion, but what you are writing here resonates strongly with this post I wrote a while ago: https://mariopasquato.substack.com/p/regression-discontinuity-and-chaotic Quite a different angle given that I am focusing on causality, but still I suspect we are getting at the same thing
This got me thinking about people. Compared to things of similar size and energy we get very poor predictions of an individual humans behaviour. So considering your matrix analogy we can say there’s some degree of non locality acting within the human? This definitely occurs over time: at any moment we can remember something from any point earlier in our life which can change our behaviour
It’s hard to say whether human action is outside the validity of what our EFTs could predict in principle, at present. We certainly is not close to doing it in practice yet. But if you are anyway not also modeling all of earth at the same time, environmental randomness would completely swamp any randomness caused by unknown laws of physics in an effort to predict a brain.
I would not say that non-locality is directly operating at such large scales as a human brain. But if there is non-locality at really really tiny scales, these can influence really long chains of computation that do happen at large scale. But most importantly, as mentioned above, human brains are open systems, so random environmental effects (like wind blowing into your ear) are many many many orders of magnitude larger, so this randomness would completely swamp the non-locality randomness. That said, thanks to the butterfly effect there might be some way to say that it has a real effect, although quantifying this is hard.
Great read even if I did not get all the math. This reminded me of Bernardo Kastrup saying that the universe cannot compute its next outputs even though they are deterministic and thus experiencing is the best way to know what happens next (I’m paraphrasing from memory so I apologize if I am not being precise). I would love to know your perspective on free will based on your background.
I enjoyed this article even with all the numbers and equations in it.
I recently finished reading through the collected correspondence between Wolfgang Pauli and Carl Jung. Among other things they discussed in detail came the idea that the complementarity of opposites in physics, between energy-momentum and time-space position, has a real parallel with the opposition between conscious mind and the unconscious.
This strikes me as a different angle on, or at least quite close to your point about the great abyss of the unknown that lies outside our best (real or possible) physical theories.
Fascinating stuff.
I'm confused as to how it could both be the case that, 1) as we zoom in on nature, more details reveal themselves and this could potentially go on forever, AND ALSO 2) there is finite information in finite space.
Is more detail at smaller and smaller scales not more information?
yeah, this is an excellent question. I should make an edit clarify this!
I talked about more and more laws revealing itself before I came to the universe being finite. It is definitely true that once it is finite, there cannot be an infinite set of laws. However, instead it will be a "cut off" infinity. You will keep sifting through all degrees of freedom and find either laws or "spirits" (incompressible phenomena) until you have looked at it all. Thanks for the excellent question
Thanks for your response. That's a bit clearer, but I'm still a bit confused. That's okay though, I don't understand a lot about how infinity works.
I’ve been thinking about related ideas from a very different angle—more in terms of cognition and non-Markovian models of memory and time. I’m not a physicist, but I’ve been exploring the idea that systems (including human cognition) are fundamentally autoregressive: each state is generated from the lingering, decaying influence of prior states.
In this view, the past isn’t “deleted” and forgotten, ever; it’s folded into the present. Its signal may decay, but it remains measurable and keeps steering what comes next.
The way you describe renormalization—where degrees of freedom are integrated out but still exert influence—feels deeply analogous. That “ghost pressure” of the past, even when compressed, seems like a universal structural feature of generative systems
Brilliant. And there is yet another limit to scientific laws, namely that our laws govern two-body systems or well-behaved aggregates of two-body systems. As soon as one goes to the next step (of indefinitely many such steps) of complexity, equations of motion cannot be integrated over time. We call this “chaos” but it is really the onset of neo-Aristotelian teleological order. The cosmos is much more like a garden than a machine. BTW, I am a former particle physicist who is now a Catholic priest.
Thank you Andrew!
As for teleological order I'll have to admit my ignorance on the exact meaning of this. Def curious what you mean about many body physics in particular though. Many body systems are rarely integrable, but quantum field theory does allow many-body interactions straight forwardly. Is the point that in four dimensions all higher order many body interactions that do not imply 1->2 (decay) or 2->2 (scattering) is non-renormalizable? Like phi^6 theory.
You’re a great writer and a formidable thinker and this was a great read, but:
(1) The word “spirits” anthropomorphizes the phenomena about which you’re speaking, whether you want it to or not. And that *really* doesn’t sit right with me.
(2) >>”I can think of no phenomena more worthy of the name Spirits.” Honestly, it just sounds to me like you’re talking about something like “outliers.” If all theories are compressions (and I very much agree with that) then all theories lose some data, some richness, some possible-but-extremely-uncommon-and-therefore-impossible-to-account-for data, and so all theories, even the most exact, will fail to account for certain outliers that are only outliers because they have some causal force but are nevertheless very uncommon and diverge strongly from the general pattern or tendency … If you don’t like the term “outliers” (and I could see why you might not), then might I suggest “clinamina” (the plural of clinamen; with reference to Lucretius and Deleuze’s work on him)? … Honestly, just anything but “Spirits.”
Thanks for your comment Connor!
I would not say outliers is an apt term here. I am referring here to a phenomenon that fundamentally is un-modellable given the constraints of our universe. Outliers as a word not even close to capturing this aspect, although
I also want to point out that lossless compression is a really thing. It is still a possibility that there exist a fundamental theory of natural that genuinely achieves lossless compression - I cannot rule that out, although it is not my intuition.
A spirit is usually taken as a non-natural or supernatural phenomenon interacting with the universe. I don't acknowledge the naturalist/supernaturalist dichotomy as meaningful for reasons described in my previous post ("God is NaN"), yet I find the term apt. This phenomenon of possible pattern in nature being fundamentally impossible to model, is as close a programatic definition of "supernatural" as I can think of.
Yeah, I understand what you’re referring to here, and in fact—since my baseline assumption is that lossless compression probably isn’t possible at all or, rather, may only be possible within very particular, extremely well-controlled parameters, which, for any non-trivial outcome, amounts to the same thing—I definitely think that there exist fundamentally unmodellable phenomena that exert some causal influence over at least some (and probably many, even most) non-trivial outcomes.
But if we make the following assumptions—(1) that lossless compression isn’t possible outside of very particular, very well-controlled parameters, and (2) that anything that exerts a causal force can be measured indirectly (despite being un-accountable or unmodellable)—then I think that you’re basically just talking about outliers or, at the very least, something a lot less sexy and (yes, I’ll maintain) anthropomorphic than “Spirits.” (I’ll return to this word in a second.)
I’ll admit that I don’t think that term “outliers” is perfect because in common usage, an “outlier” tends to refer to an observed outcome, not a cause, and is also probably model-neutral, in the sense that some outlier phenomena can be causally explained while some can’t (due, again, to the limits of compression). But take a weather system (or any other system subject to complex, chaotic dynamics). For that kind of system, (1) lossless compression is impossible to achieve, and (2) unmodellable causal forces can be indirectly observed by observing the evolution of the system over time. (That’s chaos theory in a nutshell, right?) In these kinds of systems that are so extremely sensitive to initial conditions and to the complex dynamics involved in their evolution over time, unmodellable *outlying* or “outlier” factors exert a causal force which can be indirectly observed. To me, it sounds very strange to say that the outcomes of these systems are caused by Spirits, but to say that these systems are caused by “outlier factors” or even just “unmodellable factors” or even just “noise” or “stochastic factors” or whatever … that sounds a lot more reasonable and (frankly) accurate.
Which leads me back to the word “Spirits.” The etymology of that word ties it to breath, souls, and an animating, vital force present primarily (but not exclusively) in humans and animals. So while it may not be strictly true to say that it anthropomorphizes outlying or stochastic factors (or whatever we want to call them), I would at least say that it bio-morphizes them. Likewise, I am definitely not a fan of the “supernatural” connotations, since I don’t think that there’s anything supernatural nor non-deterministic about unmodellable factors.
… But, on the other hand, maybe that’s not the worst thing in the world? I mean, the evolution of biological life follow complex dynamics that are somewhat analogous and generalizable to those that govern weather systems and other systems with fundamental modeling limits. (That’s complex systems theory, right?) Likewise, I’m open to the idea that some types of spirituality/ religiosity were developed to account for and explain the unaccountable, so maybe it’s not the worst thing in the world to draw upon this lexicon in order to name the unnamable.
But, on the other hand, given the overwhelming presence of religiosity and spirituality in our society today (with only something like 3% of people identifying as atheists and with the overwhelming majority of religiously unaffiliated people identifying as “spiritual, not religious”), I don’t think that anyone will hear the word “spirit” and think “Oh, he means unmodellable causal factors.”
Ultimately, it doesn’t matter very much, I guess. But I have a (very-epistemically-uncertain) hunch that knowledge and understanding of the world are fundamentally (or, at the very least, in the long-term) limited by cognitive tendencies like observer’s bias, anthropocentric and even bio-centric bias, the mind-projection fallacy, etc. (We understand the solar system and the universe much better, for example, for realizing that we are not the center of the former and hold no privileged position in the latter.) And so I worry (or am maybe disappointed?) when people use anthro- or bio-centric terms—especially those culled from spirituality/ religion—to explain ideas that should, to my mind, if properly understood, really push us away from our human-experience-centric epistemic baseline/ tendency or, to put it more metaphorically, our tendency to think of ourselves as the “center of the universe” and to think of our experience as being far more epistemically valuable than it is.
Again, I feel *a lot* of uncertainty about the chain of reasoning in that last paragraph and can imagine at least some reasons why it may be wrong … On some level, it might just ultimately be motivated by the fact that I am a devout atheist/ (weak) physicalist and just wanna see more people out there who reflect those epistemic baselines and the value systems that (to my mind and in my experience) tend to follow from them.
On the other hand (and, I’ll admit, that this kind of reasoning is probably engaged in by spiritual/ religious people also, which is only one reason to be suspicious of it), I have found a lot of personal, psychological, axiological, moral, epistemic, and practical value in my atheism and weak physicalism, and so I think that part of my motivation is at least somewhat altruistic. … I just think the world would be a better place if everyone realized that (objectively speaking) nothing matters, that our lives are little more than the consequence of highly complex, chaotic causes (some of which are modellable and some of which are not, lol), that we’re all going to die, that this life and experience is all we have, that any impact we have upon the world will eventually fade, and that none of us, in the grand arc of time, are more special or important than anyone else.
Isn’t that all just obvious?!?! Can’t we all just get along?!?! hahah
Anyway, sorry for this overly-long, overly-self-reflective, overly-soapbox-y response. (I’m giggling at my own ridiculousness right now.) This discussion just touches on stuff that I, obviously, have a lot of thoughts about and like talking about, so it can be a little hard to stop or limit myself, haha.
I hope this does not come across as self promotion, but what you are writing here resonates strongly with this post I wrote a while ago: https://mariopasquato.substack.com/p/regression-discontinuity-and-chaotic Quite a different angle given that I am focusing on causality, but still I suspect we are getting at the same thing
Thanks I’ll have a look!
Great writing about complicated but important ideas.
I think you should read my Substack.