Speaking educationally, I'll argue that the ladder (heck, "The Ladder") is actually pretty dang close to being what science IS, and that the fact that we don't make this obvious to kids through how we structure science is near the heart of why science education fails (e.g. 32% of Americans think an electron is bigger than an atom).
FWIW, I'm actually working to fix this with a "spiral" approach (we put a topic from physics, chemistry, microbiology, anatomy, zoology, and planetary science in each year's lessons — see scienceisweird.com/everything for a picture), and I can say (anecdotally, natch) that it opens up the kids to be pondering some of the big questions of philosophy to a degree I never experienced in my "a-discipline-a-year" science classes.
Yup! At the moment most of our families are homeschoolers, but we're branching out to schools as well. (There'll be a pilot of it in an few Italian schools this year.)
Really looking forward to reading this! The idea of Causal Emergence is one of my favorite parts of The World Behind the World and one of the most thought-provoking ideas I've seen in a while.
Also, before I read, wanted to note this thought while the association is fresh, and because you talk about Markov chains in the abstract: are you aware of this work that the physicist/philosopher Jacob Barandes is doing on reformulating quantum mechanics at Harvard? His formulation is based on very abstract non-Markovian random rules called Indivisible Stochastic Processes. They're basically, if I understand it correctly, processes where you can't iterate from any single step to any other single step, but only forwards from (and I think back towards) points called Decision Events. The upshot is this can recover the predictions of standard quantum mechanics using classical particles and no wave functions, and it models "measurements" as those Decision Events where the system under observation interacts with another system. I mention this because the way that seemed to me to work is that by interacting with a larger system (which itself is made up of smaller systems) has an effect that changes that can change the behavior of the smaller system in a way that can't solely be derived the previous behavior of the smaller system, and that reminded me of your idea of Causal Emergence. I wonder if you and Barandes are working along parallel tracks in two different disciplines/directions?
Caveat: Just a poet who is very enthusiastic and interested in all this stuff, so I may be way off base!
Science as a ladder of dimension reductions resonated with me through Jorge Wagensberg's paragraph:
"Physics comprises less complex objects than biology, biology less than psychology and psychology less than politics, so that politics contains more ideology than psychology, psychology more than biology and biology more than physics; however, they are all equally scientific if they maximise their objectivity, their intelligibility and their dialectics."
Erik, a renweal appointment with Tufts? Interesting. No where near the quantitative level to grasp your emergence theory perspective, I thank you for your example of Free Will. Yes, it is an argumentative inciter, a linguistic disruptor. Nonetheless fsascinating. Please unpack the two key words, "free" and "will." The former is way down the field, as you put it, continuously re-conceptulalized. If you have not read Timothy Snyder's "On Freedom", I hope you do. Using Ukraine as a historical case, Snyder distinguishes between "Negative Freedom" and the Positive kind (affirmative). In other words, freedom for and freedom against. To me, Snyder's run right into the End Zone.
Have you done any simulations on whether running the Infomap community detection algorithm on the state-transition graph is an efficient heuristic for finding coarse-grainings? It certainly has the right "flavor" (finding compressible representations of micro-scale transitions?)
Generally it seems plausible to me that compressing a particular "lifetime" (time series generated by running the system forward) should provide an efficient compression of the underlying state-transition structure.
Great thoughts. My guess is that the infomap community detection would be very good as a heuristic here. Admittedly (as I say in the paper), the main limitation right now is exactly that issue of applicability. I think there is an ideal formulation that basically solves all the issues of applicability while also being more elegant than a single micro -> macro path (which makes a great deal of sense conceptually, and sometimes are desired, but the issue is that it leads to a combinatorial explosion and there can be non-commensurate paths). But, from a conceptual and rigor perspective, I think this is most of the way there, and there are clear paths to how to make the theory operate more like "I click a button and get the causal distributions of large systems in an elegant way."
I have not read your paper yet, but over the last year I had your viewpoint of semantic non-reducibility think in: I guess emergence is equivalent to a phase transition were a new order parameter is coming into existence describing the new property on higher scales. An example would be wetness and viscosity of fluid water as compared to H20 molecules. Some of these transitions however add something really new like chemical reactions, biological function, and cognitive meaning. Causality can be defined by linking to the possibility of changing the state of a system which describes meaning of an action or intention.
It is entirely possible that novel properties come in, just as you say! But this can be a bit tricky, as it must be in a way that violates a form of reductionism that most assume, which is that some sort of "bridge laws" necessarily exist such that, e.g., the wetness and viscosity of fluid water could not be deduced in principle from H20 molecules. Basically, causal emergence works orthogonally to that. If they did, that'd be great, and you could adapt the causal emergence framework to then ask what the "new and irreducible" macroscales add. But it doesn't require it. Even in a world where everything is totally reducible, you can still have causal emergence.
That’s what I was going to ask. If I understood correctly, your theory would apply even if there was no quantum uncertainty or new laws at higher scales, right?
In a universe where the microscale is fully deterministic (“billiard balls physics”) and where biology and chemistry can still be deduced from physics (in principle), would you still expect causal emergence to take place and extra-information to be generated?
If so, this is really a very unique approach (sounds impossible but that’s what makes it interesting!).
Even if its fully deterministic, there can still be common causes, which in the theory provides uncertainty for macroscales to minimize.
But, there is a case (which I'm open about, I discuss it in Section 5.4 on conceptual implications) where the universe is (a) at the ultimate microphysical, fully deterministic and non-degenerate (no common causes) and (b) you take the entire universe as a closed causal model (otherwise there can be outside noise to an individual model of a system, which are necessarily open). In that case, you wouldn't see any causal emergence, provably. But I think that (i) physics isn't over, so calling this is a pretty strong stance, and (ii) as Judea Pearl has pointed out, the (b) case also necessitates a lack of causation in general, because in a closed model with those properties that spans the whole universe there's nothing "outside" to consider interventions or counterfactuals, so causation disappears. Therefore, it's sort of unsurprising that something called "causal emergence" wouldn't apply in the same (veeerrrry stringent) conditions that causation itself doesn't apply.
Wow! Have you read The Infinite Staircase: What the Universe Tells Us About Life, Ethics, and Mortality by Geoffrey Moore? He has a similar theory, but his system is more self-help and less formal. Here is an excerpt from the book:
In the chapters that follow, we are going to take a linear path up through Earth's systems hierarchy from bottom to top, leveraging the principles of emergence and self-organization as best we can perceive them. At each step in our staircase, a higher level of complexity will emerge and take its place as the next defining level of organization in the hierarchy. Each of these levels is made possible by those below it, and, in turn, each makes possible those above. I am not claiming that this framework addresses every possible level, only that the ones it does address are essential, and that they are presented in their proper order. There is, in other words, one and only one sequence for the staircase, and it is as follows:
The Infinite Staircase
(as far as we can see)
11. Theory
10. Analytics
9. Narrative
8. Language
7. Culture
6. Values
5. Consciousness
4. Desire
3. Biology
2. Chemistry
1. Physics
The fundamental claim here is that each lower level in the staircase is prerequisite for the emergence of the stair above it. That means each higher level entails all the levels below it—they are necessarily included in its reality. In half the cases, this claim is pretty easy to grant:
Conversely if the basic levels of the hierarchy are not deterministic, it frees up the higher levels to be in deterministic. And quantum mechanics says the lower levels are indeterministic, which shows that free will is possible. I know some say that the end determines of quantum mechanics cancel from ourselves out when you get to the higher levels, but that is an inductive generalization which is probably impossible to prove.
Quantum decoherence is a well-established scientific fact, so the burden of proof is on the scientific anti-determinists to show how quantum indeterminacy could lead to free will. This is only one of the problems that a quantum free will theory would have to solve, and there is no plausible model.
Good ideas. You may want to check Michael Levine of Xenobots fame who has many similar ideas on bottom up differentiated 'problem solving" and horizon of influence of macroscale to microscale
The other philosophy is in Vedic ( Hindu) the notion of Dharma where a being emerges and evolves as per intrinsic nature . This has branches assigning agency to what we may label inanimate matter
"A viable scientific definition of free will would then have a necessary condition: that you have a relatively “top-heavy” distribution of causal contributions, where your psychological macrostates dominate the spatiotemporal hierarchy formed by your body and brain. In which case, you would be primarily “driven,” in causal terms, by those higher-level macroscales, in that they are the largest causal contributors to your behavior."
Well, actually specifying how to get the causal contributions is unique, I think, right now to CE 2.0, since there's no other way I know of to make the "top-heavy" judgement I'm talking about - that analysis is new to this paper and its framework.
But you're right more generally on the approach. I'm in partial agreement with both those authors. Kevin's work is great, and I've talked with him about causal emergence and the overlap with his ideas before (see this podcast here: https://www.youtube.com/watch?v=vEA6TvgaOtI).
List, funnily enough, goes the exact other way and says that macroscales should be more indeterministic than their microscales (something to do with the indeterminacy being important for his notion of free will, if I'm remembering correctly).
I went through the paper only superficially but, as far as I can see, it isn't relevant to free will questions. It certainly points out important aspects on how the description of complex systems and its top-down causation needs to be extended. I'm also fine with the idea that higher-level macroscales are the largest causal contributors to our behaviors. But this, in and of itself, isn't an argument for free will. It still remains inside a deterministic paradigm that leaves no space to "chose otherwise." The same problem I see with Mitchell's approach. A "top heavy" theory may be true but, IMO, should be kept separate from free will speculations. There is no connection between the two.
I would be interested to see discussion of how this formulation of causal emergence fits into the framework for emergence introduced by Sean Carroll and Achyuth Parola: https://arxiv.org/abs/2410.15468
Looking forward to this, Erik! Have you read Peter Tse's "Neural Basis of Free Will"? He describes a mechanism called "criterial causation" in that book that he argues accounts for mental causation—essentially by using current local interactions (of neurons, etc.) to set up the possibility of different interactions in the future. Could be interesting to you as you think through the free will implications of the causal emergence theory.
Fascinating! I think you're on to something deep here, Eric. It seems to me that your emergentist / multi-scale picture creates plenty of "elbow room" for the kinds of free will worth wanting. Put differently, your work here could end up vindicating compatibilism (the idea that level 1 physical determinism is compatible with level X psychological freedom). As Daniel Dennett put it, freedom evolves.
I saw the image used and got interested, because I, too, grapple with emergence. My interests sit outside my training, and thus the uphill task has been to dive into the literature, unguided, on how this could have come about.
Evolution forms my interests. Complexity is the other, but I'm basically a novice. My training was biology-heavy with barely any math involved. Most of math we do is converted doses when administering infusions in ICU patients.
Nevertheless, I was driven to your work because I believed I had developed a way of viewing emergence using the simple tool of probability. This, yet again, is the very basic calculus of probability, but one which I think holds potential grounds for explaining just as much as you have described, albeit briefly, in this article.
I like to think of entities as probabilities, and when they merge, they develop into a form of entity, an emergent entity which can also be explained through probability. I try severally to explain these ideas through some of my posts, but feel my mathematical skills are too rudimentary. I take courage, however from scientists like Faraday and Fermat, who considered themselves amateurs.
Also, I completely resonate with your final thoughts on people initially agreeing with your idea and running with it, a different scene from how you had played it in your mind.
I’m fascinated by this paper…and fear I need a GEB(Lewis Carroll)-style Achilles-Tortoise dialogue to properly understand it!
Well, now I *have* to do it, because that's such a good idea.
Speaking educationally, I'll argue that the ladder (heck, "The Ladder") is actually pretty dang close to being what science IS, and that the fact that we don't make this obvious to kids through how we structure science is near the heart of why science education fails (e.g. 32% of Americans think an electron is bigger than an atom).
FWIW, I'm actually working to fix this with a "spiral" approach (we put a topic from physics, chemistry, microbiology, anatomy, zoology, and planetary science in each year's lessons — see scienceisweird.com/everything for a picture), and I can say (anecdotally, natch) that it opens up the kids to be pondering some of the big questions of philosophy to a degree I never experienced in my "a-discipline-a-year" science classes.
I just skimmed through this website and it looks amazing. Am I correct in thinking this is intended as a foundational curriculum for children?
Yup! At the moment most of our families are homeschoolers, but we're branching out to schools as well. (There'll be a pilot of it in an few Italian schools this year.)
Really looking forward to reading this! The idea of Causal Emergence is one of my favorite parts of The World Behind the World and one of the most thought-provoking ideas I've seen in a while.
Also, before I read, wanted to note this thought while the association is fresh, and because you talk about Markov chains in the abstract: are you aware of this work that the physicist/philosopher Jacob Barandes is doing on reformulating quantum mechanics at Harvard? His formulation is based on very abstract non-Markovian random rules called Indivisible Stochastic Processes. They're basically, if I understand it correctly, processes where you can't iterate from any single step to any other single step, but only forwards from (and I think back towards) points called Decision Events. The upshot is this can recover the predictions of standard quantum mechanics using classical particles and no wave functions, and it models "measurements" as those Decision Events where the system under observation interacts with another system. I mention this because the way that seemed to me to work is that by interacting with a larger system (which itself is made up of smaller systems) has an effect that changes that can change the behavior of the smaller system in a way that can't solely be derived the previous behavior of the smaller system, and that reminded me of your idea of Causal Emergence. I wonder if you and Barandes are working along parallel tracks in two different disciplines/directions?
Caveat: Just a poet who is very enthusiastic and interested in all this stuff, so I may be way off base!
Looking forward to reading the paper later today!
Ty Billy! That's a good tip, I hadn't heard of Jacob Barandes - I will check out his work for connections.
Science as a ladder of dimension reductions resonated with me through Jorge Wagensberg's paragraph:
"Physics comprises less complex objects than biology, biology less than psychology and psychology less than politics, so that politics contains more ideology than psychology, psychology more than biology and biology more than physics; however, they are all equally scientific if they maximise their objectivity, their intelligibility and their dialectics."
Erik, a renweal appointment with Tufts? Interesting. No where near the quantitative level to grasp your emergence theory perspective, I thank you for your example of Free Will. Yes, it is an argumentative inciter, a linguistic disruptor. Nonetheless fsascinating. Please unpack the two key words, "free" and "will." The former is way down the field, as you put it, continuously re-conceptulalized. If you have not read Timothy Snyder's "On Freedom", I hope you do. Using Ukraine as a historical case, Snyder distinguishes between "Negative Freedom" and the Positive kind (affirmative). In other words, freedom for and freedom against. To me, Snyder's run right into the End Zone.
Have you done any simulations on whether running the Infomap community detection algorithm on the state-transition graph is an efficient heuristic for finding coarse-grainings? It certainly has the right "flavor" (finding compressible representations of micro-scale transitions?)
I've never really put the idea through its paces, although I've noodled around with it, see Fig. 4 here: https://www.mdpi.com/1099-4300/25/1/54).
Generally it seems plausible to me that compressing a particular "lifetime" (time series generated by running the system forward) should provide an efficient compression of the underlying state-transition structure.
Great thoughts. My guess is that the infomap community detection would be very good as a heuristic here. Admittedly (as I say in the paper), the main limitation right now is exactly that issue of applicability. I think there is an ideal formulation that basically solves all the issues of applicability while also being more elegant than a single micro -> macro path (which makes a great deal of sense conceptually, and sometimes are desired, but the issue is that it leads to a combinatorial explosion and there can be non-commensurate paths). But, from a conceptual and rigor perspective, I think this is most of the way there, and there are clear paths to how to make the theory operate more like "I click a button and get the causal distributions of large systems in an elegant way."
That looks interesting Thomas, would be curious to see it applied to lineages of differentiating cells in developmental biology…
So wait, come on, you can't leave us hanging like that! Free will, which is it, macro or micro? (I have my personal bet but I'd love to know!)
I have not read your paper yet, but over the last year I had your viewpoint of semantic non-reducibility think in: I guess emergence is equivalent to a phase transition were a new order parameter is coming into existence describing the new property on higher scales. An example would be wetness and viscosity of fluid water as compared to H20 molecules. Some of these transitions however add something really new like chemical reactions, biological function, and cognitive meaning. Causality can be defined by linking to the possibility of changing the state of a system which describes meaning of an action or intention.
It is entirely possible that novel properties come in, just as you say! But this can be a bit tricky, as it must be in a way that violates a form of reductionism that most assume, which is that some sort of "bridge laws" necessarily exist such that, e.g., the wetness and viscosity of fluid water could not be deduced in principle from H20 molecules. Basically, causal emergence works orthogonally to that. If they did, that'd be great, and you could adapt the causal emergence framework to then ask what the "new and irreducible" macroscales add. But it doesn't require it. Even in a world where everything is totally reducible, you can still have causal emergence.
That’s what I was going to ask. If I understood correctly, your theory would apply even if there was no quantum uncertainty or new laws at higher scales, right?
In a universe where the microscale is fully deterministic (“billiard balls physics”) and where biology and chemistry can still be deduced from physics (in principle), would you still expect causal emergence to take place and extra-information to be generated?
If so, this is really a very unique approach (sounds impossible but that’s what makes it interesting!).
Even if its fully deterministic, there can still be common causes, which in the theory provides uncertainty for macroscales to minimize.
But, there is a case (which I'm open about, I discuss it in Section 5.4 on conceptual implications) where the universe is (a) at the ultimate microphysical, fully deterministic and non-degenerate (no common causes) and (b) you take the entire universe as a closed causal model (otherwise there can be outside noise to an individual model of a system, which are necessarily open). In that case, you wouldn't see any causal emergence, provably. But I think that (i) physics isn't over, so calling this is a pretty strong stance, and (ii) as Judea Pearl has pointed out, the (b) case also necessitates a lack of causation in general, because in a closed model with those properties that spans the whole universe there's nothing "outside" to consider interventions or counterfactuals, so causation disappears. Therefore, it's sort of unsurprising that something called "causal emergence" wouldn't apply in the same (veeerrrry stringent) conditions that causation itself doesn't apply.
Wow! Have you read The Infinite Staircase: What the Universe Tells Us About Life, Ethics, and Mortality by Geoffrey Moore? He has a similar theory, but his system is more self-help and less formal. Here is an excerpt from the book:
In the chapters that follow, we are going to take a linear path up through Earth's systems hierarchy from bottom to top, leveraging the principles of emergence and self-organization as best we can perceive them. At each step in our staircase, a higher level of complexity will emerge and take its place as the next defining level of organization in the hierarchy. Each of these levels is made possible by those below it, and, in turn, each makes possible those above. I am not claiming that this framework addresses every possible level, only that the ones it does address are essential, and that they are presented in their proper order. There is, in other words, one and only one sequence for the staircase, and it is as follows:
The Infinite Staircase
(as far as we can see)
11. Theory
10. Analytics
9. Narrative
8. Language
7. Culture
6. Values
5. Consciousness
4. Desire
3. Biology
2. Chemistry
1. Physics
The fundamental claim here is that each lower level in the staircase is prerequisite for the emergence of the stair above it. That means each higher level entails all the levels below it—they are necessarily included in its reality. In half the cases, this claim is pretty easy to grant:
Chemistry necessarily entails physics.
Biology necessarily entails chemistry.
Desire necessarily entails biology.
In this essay, I argue, following Robert Sapolsky, that emergence free will theories fail because, if basic levels operate deterministically, then higher, emergent levels must necessarily also. How would you respond to this criticism? https://open.substack.com/pub/eclecticinquiries/p/the-pseudoscience-of-free-will?r=4952v2&utm_campaign=post&utm_medium=web&showWelcomeOnShare=false
Conversely if the basic levels of the hierarchy are not deterministic, it frees up the higher levels to be in deterministic. And quantum mechanics says the lower levels are indeterministic, which shows that free will is possible. I know some say that the end determines of quantum mechanics cancel from ourselves out when you get to the higher levels, but that is an inductive generalization which is probably impossible to prove.
Quantum decoherence is a well-established scientific fact, so the burden of proof is on the scientific anti-determinists to show how quantum indeterminacy could lead to free will. This is only one of the problems that a quantum free will theory would have to solve, and there is no plausible model.
Good ideas. You may want to check Michael Levine of Xenobots fame who has many similar ideas on bottom up differentiated 'problem solving" and horizon of influence of macroscale to microscale
FYI https://www.youtube.com/watch?v=c8iFtaltX-s&t=7437s&pp=ygUSVGVkIE1pY2hhZWwgTGV2aW5l
The other philosophy is in Vedic ( Hindu) the notion of Dharma where a being emerges and evolves as per intrinsic nature . This has branches assigning agency to what we may label inanimate matter
"A viable scientific definition of free will would then have a necessary condition: that you have a relatively “top-heavy” distribution of causal contributions, where your psychological macrostates dominate the spatiotemporal hierarchy formed by your body and brain. In which case, you would be primarily “driven,” in causal terms, by those higher-level macroscales, in that they are the largest causal contributors to your behavior."
In what sense does this differ from Kevin Mitchell's notion of free will (https://philpapers.org/rec/MITUFW) and/or Christian Lists's 'levels of description' (https://philpapers.org/rec/LISLOD + https://philpapers.org/rec/LISWFW)?
Well, actually specifying how to get the causal contributions is unique, I think, right now to CE 2.0, since there's no other way I know of to make the "top-heavy" judgement I'm talking about - that analysis is new to this paper and its framework.
But you're right more generally on the approach. I'm in partial agreement with both those authors. Kevin's work is great, and I've talked with him about causal emergence and the overlap with his ideas before (see this podcast here: https://www.youtube.com/watch?v=vEA6TvgaOtI).
List, funnily enough, goes the exact other way and says that macroscales should be more indeterministic than their microscales (something to do with the indeterminacy being important for his notion of free will, if I'm remembering correctly).
I went through the paper only superficially but, as far as I can see, it isn't relevant to free will questions. It certainly points out important aspects on how the description of complex systems and its top-down causation needs to be extended. I'm also fine with the idea that higher-level macroscales are the largest causal contributors to our behaviors. But this, in and of itself, isn't an argument for free will. It still remains inside a deterministic paradigm that leaves no space to "chose otherwise." The same problem I see with Mitchell's approach. A "top heavy" theory may be true but, IMO, should be kept separate from free will speculations. There is no connection between the two.
I would be interested to see discussion of how this formulation of causal emergence fits into the framework for emergence introduced by Sean Carroll and Achyuth Parola: https://arxiv.org/abs/2410.15468
Looking forward to this, Erik! Have you read Peter Tse's "Neural Basis of Free Will"? He describes a mechanism called "criterial causation" in that book that he argues accounts for mental causation—essentially by using current local interactions (of neurons, etc.) to set up the possibility of different interactions in the future. Could be interesting to you as you think through the free will implications of the causal emergence theory.
Fascinating! I think you're on to something deep here, Eric. It seems to me that your emergentist / multi-scale picture creates plenty of "elbow room" for the kinds of free will worth wanting. Put differently, your work here could end up vindicating compatibilism (the idea that level 1 physical determinism is compatible with level X psychological freedom). As Daniel Dennett put it, freedom evolves.
I saw the image used and got interested, because I, too, grapple with emergence. My interests sit outside my training, and thus the uphill task has been to dive into the literature, unguided, on how this could have come about.
Evolution forms my interests. Complexity is the other, but I'm basically a novice. My training was biology-heavy with barely any math involved. Most of math we do is converted doses when administering infusions in ICU patients.
Nevertheless, I was driven to your work because I believed I had developed a way of viewing emergence using the simple tool of probability. This, yet again, is the very basic calculus of probability, but one which I think holds potential grounds for explaining just as much as you have described, albeit briefly, in this article.
I like to think of entities as probabilities, and when they merge, they develop into a form of entity, an emergent entity which can also be explained through probability. I try severally to explain these ideas through some of my posts, but feel my mathematical skills are too rudimentary. I take courage, however from scientists like Faraday and Fermat, who considered themselves amateurs.
Also, I completely resonate with your final thoughts on people initially agreeing with your idea and running with it, a different scene from how you had played it in your mind.