Bio from Bit by Sara Imari Walker

Sara Walker

Essay Abstract

Understanding the origin(s) and nature of life poses a perplexing problem for physics. On the one hand our approaches to physics are incredibly adept at describing the material world. On the other hand abstractions such as what we commonly describe as information are important in biology, but their role in the physical world is not yet fully understood. In this essay I discuss how information (as we understand it in biology) is a window into causal structures that bridge counterfactual histories (and futures) and allow the possible for transitions between histories. It is this multiple realizability that is one of the most distinctive properties of living systems. It also leads to some of their most interesting - and difficult to explain - features, such as their apparent goal directedness.

Author Bio

Sara Walker is an Assistant Professor in the School of Earth and Space Exploration at Arizona State University. Her research focuses on the origins and nature of life.

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Donald Palmer

Hello Sara,

A very well written and supported essay!

You pull from a number of different (several non-physics) areas and tie them together in a powerful way. I think you have done a great job in defining how goal-directedness (including aims and intentions) can occur without identifying specific particles or low-level entities that cause them. This is up there with the best essays I have read for this contest.

At first I thought you were going to just be constrained to 'microstates' and 'macrostates' as limited to two levels. However, you then state parenthetically that: "this should always be assumed to include a hierarchy of nested levels across scales". Even more you go on to state that there is "no a priori reason to assume that we should not treat all levels equally".

I concur wholeheartedly with this statement, as I believe that all levels of scale are part of the same unified reality we experience and can interact between them. We are already entering an era where us larger beings (as macrostates) are starting to alter our own molecular structures (as microstates) as well as altering particle level structures (I am not suggesting we really know what we are doing here, just that we are doing it). I have yet to hear a physicist explain how an entirely reductionist perspective (everything builds from the smallest level only) can account for what physicists do today by building particle accelerators (which is sort-of this essay contest topic).

I did have to look up a few terms you use to understand what you mean (eg. counterfactual) and your range of terms from different areas involved, for me, additional research. Your last example proved difficult to fully comprehend, although I think I understood the gist of it.

I think your broad range solution is quite enticing, although you seem to become entrenched into a heavily modeled final example and conclusion explained via models rather than more understandable examples (trying to finish in under 9 pages?).

Please be aware of the limitations of the modeling tools you are using:

1) Statistics (and probability) are one-way tools, since they can only derive higher level structures from lower level ones. These tools do not allow the possibility of higher level actions to impinge on lower level ones and therefore any models built on them will involve the same limitations (eg. statistical mechanics). This would suggest that statistics is not an appropriate tool to model higher level actions impinging upon lower level entities (such as physicists building particle accelerators). It may indicate we need new mathematical tools for this purpose.

2) Attractors may provide good models; however, they presume an already defined goal that 'attracts' individual entities via actions toward it (seeming to be guided by an external source). The reality could be that individual entities act purposefully toward internally defined goals that are not externally located or defined (no external attractor). I think you are aware of this based upon your statements regarding the 'backbone motif' and integrated fission yeast cell cycle network.

It will be difficult to overcome the momentum of physics that 'everything starts from the smallest' particle, although there does appear to be progress being made (such as your essay).

As a final consideration: Consider that actions on all different scales may operate at the same time and that touching with our finger involves 'touch' at our level, at the cellular level, at the protein and macro-molecular level, at the molecule and atomic level, and at the particle level - all at the same time. This means our body exists at all these levels, each of which we model via a 3-dimensional space. Stacking 3-d spaces 'on top' of each other produces a 4-d space. If we model our bodies (and reality) as 4-d entities, then we would be able to model actions across these different levels (in the 4-d direction), including feed-back loops like constructing a nuclear reactor producing electric power for our TVs.

Take care,

Don

Sara Walker

Hi Don,

I agree with your points 1 and 2. I tried to stick with explicit examples that illustrate important concepts but recognize they are limited and that none of them captures everything about what is really going on (I like your point that we may not have the right mathematical tools, I very much agree and feel dissatisfied with statical approaches but find them useful in lieu of something better in the interim).

I am not sure on your last example, could you explain a bit more what you mean? Since 'levels' are different descriptions of the same thing I am not sure it requires embedding them in a higher dimensional space to understand their structure. I may agree with you but I've not thought about it this way so it would be good to see if we are indeed thinking along similar lines.

Thanks for the thoughtful comments on my essay!

All the best,

Sara

James Arnold

Sara,

A masterful essay!

From my anti-deterministic bias, it seems to me that a biological attractor can best be understood as the goal that organizes the micro-dynamics, not as the product of "mindless mathematical laws." Can deterministic physical systems be plausibly expected to produce anything but "strange" attractors?

Sara Walker

This is an interesting thought. I go back and forth about whether I think everything is deterministic or if randomness is essential. Since the descriptions in the biological model I discussed are all at the macro level, the micro-dynamics do not need to be deterministic, so I am not sure these things are antagonistic. But why do you think deterministic systems would only produce "strange" attractors?

All the best,

Sara

Conrad Johnson

Hi Sara -

I was hoping to find an essay from you here, and at the last minute one appears. I like very much the point you make at the beginning, that knowledge has power because it lets us do things... and that this applies not only to us human theorizers, but also to biological systems. What I take from this is that gaining information about the world is not only a matter of modeling, and not only of predictive modeling (per this essay by Sofia Magnúsdóttir), but also of making things happen in the world and getting feedback about what works.

What I find puzzling - as you note at the end - is that there still seems to be a widespread notion that emergence is somehow incompatible with deterministic physics. There are quite a few essays here - those by Ellis and Lisi for example - that deal sensibly with emergence, but there are also quite a few otherwise intelligent essays that assume the entire world has to operate according to a single set of rules.

I suppose that notion is implicit in the contest question, but I still find it strange. Empirically, it seems so obvious that the rules of quantum physics are very significantly different from those of classical physics, that the rules of chemistry are different too, and so forth. Apart from the quantum-classical transition, there's no mystery about how atomic physics supports chemistry, or about how molecular physics supports self-replicating life-forms, or why organisms evolve goal-directed behavior.

Surely there are still important mysteries to investigate - as your paper on "the hard problem of life" aimed to show. But my sense is that confusion arises from trying to grasp too much in a single theoretical view. If we imagine the entire history of the universe as a single process, then understanding that process presents quite a challenge - but not necessarily a useful one, in terms of generating knowledge that helps us do things. In my own essay I try to describe this vast history as the work of three quite different basic recursive processes, in physics, biology and human communication, emphasizing the different conditions in which each of them operates. That seems quite "reductive" enough!

As to the question you come to focus on here, about whether higher-level systems have causal efficacy... I certainly agree with your conclusion that they do. I would only question why this is not obvious. The fact that living organisms operate based on the laws of atomic physics is clear, and it's also clear that self-reproducing systems are subject to radically different forms of selection (p.3 of my essay). As a result, physical interactions happen in living cells that can't happen anywhere else (except in our labs) - just as gold can only be created by stars. The higher-level structure evidently makes things possible that wouldn't happen otherwise... so perhaps the issue you're dealing with here is whether or not this counts as a form of "causality"?

In any case, I'm glad you got this essay in under the wire - thanks!

Conrad

Sara Walker

Hi Conrad,

Thanks for the comments - and for pointing me to a few additional essays to read here! I obviously agree it is obvious that higher-level entities can have causal power. The point is that we still need to understand how this works, why it happens, and why some physical systems (i.e. living entities including us) seem to have more "causal power" than others. As an example, it was obvious that the the planets moved across our night sky to the ancients but it took understanding gravity to allow us to do things with that knowledge. Likewise, if we understand how macro-causation works we should be able to do interesting things with that knowledge (so clearly here as in my essay my interest is not in the predictive power of our theories but in what they allow us to do). Also, there remains the fact that not everyone agrees that higher level systems can have causal efficacy, and if it exists it should be something we can quantify (and in turn hopefully use to quantify 'life').

The most interesting part is why some systems have more "causal power" than others and what "problem" that solves. My feeling is that those systems that have higher levels causes are dynamically richer - they make things possible that wouldn't happen otherwise. I am not specifically interested in whether this counts as a form of "causality" (you can call it what you will, I do happen to think it is causality but that is an interesting discussion in its own right). I am more interested in whether this idea that higher level causes allow things that would be not be possible otherwise underlies the physics of living systems, such that life is a process that increases the number of transformations that could be caused to occur (leading to an "arrow" of complexity for living and technological processes). So the combination of the (causal) hierarchy and how it defines/redefines dynamical possibilities is my primary interest and motivates most of my approach to these problems these days.

Hope this clarifies and thanks again for the comments!

All the best,

Sara

Simon DeDeo

Dear Sara,

Reading this was an excellent way to wake up this morning.

We often use the non-determinism that arises from coarse-graining to argue for the *destruction* of patterns--e.g., the second law of thermodynamics. In those cases, we think of coarse-graining in a state-space like position/momentum (using a grid as in your Figure One). In those cases, when we lose the fine-grained details, the trajectories tend to mush out in the usual ergodic fashion.

But in the cases you discuss, the coarse-graining has the opposite effect. It leads to robustness in goal directed behavior (the yeast case). Or, more generally, to non-trivial behavior as in your Rule 150 example.

Your essay make it clear that an obvious question has been hiding out all along. Which coarse-grainings work? (More formally, when coarse-grainings lead to goal-directed behavior, what do they tend to have in common.) Or, conversely, which systems tend to coarse-grain this way?

As an example of triviality: I'm finishing up some lectures for the SFI MOOC on renormalization, and one of my examples is renormalizing a Markov chain by coarse-graining in time. This invariably leads to hyper-simple, 2nd-law behavior where if you wait long enough everything equilibrates. In that case, the simplicity I think is due to the finite nature of the underlying system. With a CA, the light-cone can project backwards arbitrarily wide, and this makes them capable of all sorts of cool things if you wait long enough.

You take a few more steps there, even, to suggest that hierarchies and boundaries in the coarse-graining prescription are part of the story. It would be interesting to quantify the focusing effect (as in your Yeast case) as it competes with the second-law like equilibration effect in your CA models. You might find all sorts of interesting patterns, or at least covariances in the different properties.

For example, what's the average path length between a focusing event (a node with many incoming arrows) and an equilibration event (a node with many outgoing arrows)? How does the coarse-graining choice affect it? You might be the first person to actually have a good example of Maximum Entropy Production in action.

My interpretation here of the MEP in your framework, is that MEP would be where you have lots of focusing in to a node that then blasts everything out again--the system moves rapidly to subspace of its state-space that dissipates free energy super-efficiently, a kind of Grand Central Station node that equilibrates the system like a highly-organized hurricane.

Thanks again for what I hope my notes here suggest was a terrific read,

Simon

Sara Walker

Hi Simon,

Thanks! This is great fun - i really like your Grand Central Station example. I think there are some things I can do with your suggestions ... will be interesting to play around with.

All the best,

Sara

Erik Hoel

Sara - great essay! I thoroughly enjoyed it, and it's an excellent overview of the latest in the field. Of course, I may be a little biased in that I'm always happy to see causal emergence make an appearance!

You can check out my own essay on causal emergence and how it relates to agents: http://fqxi.org/community/forum/topic/2873

I did have a question though. At the end of your essay you give a new analysis, which is important because you say "The point of this essay is to suggest that life is like the right of Fig. 5 rather than the left (and is not merely a coarse-grained macrostate of the left)."

The new analysis concerns ECA rule 150. You say that "Shown on the right, is the state transition diagram where a property like 'top-down' causation is explicitly introduced, and the dynamics are run again with Rule 150. Here macro causal interactions are are introduced by blackboxing the width w = 6 CA into two subsystems."

I'm wondering if you could go into further detail about exactly what it means that "a property like 'top-down' causation is explicitly introduced?"

How exactly did you implement these macro causal interactions? Did you add some extra update rules to represent some outside unknown kind of top-down causation? I ask because, if you did merely black box, there should be less states (as some are black boxed) but there are an identical number of states in each picture of the state-transitions. Black boxing would be leaving some states out of your model of the system, so there should be less on the right image.

Additionally, on the left, there are some states that lead only to themselves. But then on the right this isn't true anymore. I'm amazed black boxing could somehow, by itself, change that, as by definition, black boxing is just leaving states out of the model is just choosing to represent a subset of the state-space.

If you did add in some kind of extra macro-only update rules to represent top-down causation, I'm wondering exactly what that shows? We can obviously take any system, add in some outside source of causation or add in new rules, and that system may operate very differently. But the system operating differently will have some microscale description that has those rules in it... so I'm not sure what is being gained. I was just looking for more detail on that analysis.

Anyways, I greatly enjoyed the essay and how nimbly you present the field - thanks so much for the read!

Erik P Hoel

Sara Walker

Hi Erik,

Thanks for the enthusiasm! I've really enjoyed your work on causal emergence.

I am still playing around with these examples and finding the best way to describe and motivate them, so your questions are really great. My main motivation is that I am interested in how you can get different dynamics from the same initial state and fixed dynamical law by partitioning systems in different ways. This is what I think is more "life-like".

I do introduce a new "macro rule" to do this. To do this I partitioned the system in two subsystems A and B. Each updates according to rule 150. The "macro rule" is the interaction. I will focus on what happens for A (but the interaction in the essay is symmetric). B is a boundary for A. In usual CA we would assign one cell in B to be the input to A. I instead assumed that the states of B are partitioned into two disjoint sets, each 'causes' a different transformation in A. If you want a fully micro narrative, this amounts to a CA with a state-dependent topology. State-dependent topology is more general than what I did, but I wanted to explicitly look at cases where you could describe A as getting 'information' only about a coarse-grained state of B. The interaction with A is not really coarse-graining B because it is not an average property of B that matters but a set of states, so I call it 'black boxing' (probably too loose a use of the term and hence the confusion). The information is lost for A (it has no capacity to distinguish the microstate of B). B has the same kind of interaction with A. So the 'black boxes' in this case are not an external description of the system but define the interactions between the two systems by defining what subspace is relevant for their interaction. I then look at the state transitions that are possible for both subsystems jointly and that is what is in the right panel. The full state space is not reduced in how we can externally describe it.

For your "what is gained" question (its a good one, and I am still grappling with this myself!) the motivation is that we could of course just look for some outside source of causation. Typically if we did that it would be a state, rather than a set of states (macrostate). If it is a state then the entire system (system outside causes) should follow a single trajectory defined by its initial state (at least for the CA example, we can debate if this is true of reality). To describe life, I'd like solutions where there are many paths that can be traversed defined by the interactions, coupling the systems in this way gives that kind of flexibility. To be more fair, I should perhaps compare my 3-bit subsystems to the dynamics that a 3 bits of an ECA could do, embedded within a 6-bit CA. Based on other experiments I've run, I am pretty sure it would still be the case that the construction in the paper would allow more dynamical possibilities then assuming a 3-bit CA is open to an environment, but I will do that.

You could always do a cheat where you have open boundaries with some sort of fixed or time-dependent input. But I am interested in cases where the boundary obeys the same laws at the micro level as the system you are studying. In that case you are not free to arbitrarily set the outside source of causation to anything you want to drive the dynamics you want to see. If only the microstate matters than you are really limited in the dynamics the coupled system can achieve. By allowing interactions through macrostates much more interesting stuff can happen. As a side note, if you wanted to choose any sort of fixed or time-dependent boundary condition then for that to obey the same 'laws' at the micro level as the system of interest you are already assuming 'macrocausation' by top-down causation. Basically I think we do this all the time by modeling open systems (or any system where the rules are not the same everywhere), but I am trying to make explicit cases where that openness must be made compatible with uniform deterministic dynamical laws that are the same everywhere at the microlevel. And, to do this with still allowing the possibility to explore many paths through state space (which is what I am assuming life does).

This is a bit of a difficult format to explain these things (much easier with a whiteboard) so I hope this helps to clarify.

All the best,

Sara

Erik Hoel

Thanks so much for the detailed response Sara! Really appreciate it, and you did a good job clarifying it.

"To describe life, I'd like solutions where there are many paths that can be traversed defined by the interactions, coupling the systems in this way gives that kind of flexibility."

I completely agree - I think looking particularly at openness is a really good idea, as you say. This leads to the question of: what's the difference between open and closed systems in terms of the causal structure, and does an open causal structure make a system more "life like"? I have an example in my own essay where being open enriches the causal structure of a system and makes all sorts of intrinsic causal paths available that the same system, in a closed environment, doesn't have.

"But I am interested in cases where the boundary obeys the same laws at the micro level as the system you are studying."

I think you're right that this is key, especially because it seems to me the only way to make a fair comparison. Not everyone always makes fair comparisons, which is why it's so applaudable that you're well-defining the open systems within the context of dynamic deterministic laws.

Anyways, thanks again for the detailed response, and looking forward to talking to you more in the future, especially if we can get our hands on a whiteboard :)

EPH

Dizhechko Semyonovich

Dear, Сара Имари Уокер.

I inform all the participants that use the electronic translator, therefore, my essay is written badly. I participate in the contest to familiarize English-speaking scientists with New Cartesian Physic, the basis of which the principle of identity of space and matter. Combining space and matter into a single essence, the New Cartesian Physic is able to integrate modern physics into a single theory. Let FQXi will be the starting point of this Association.

Don't let the New Cartesian Physic disappear! Do not ask for himself, but for Descartes.

New Cartesian Physic has great potential in understanding the world. To show potential in this essay I risked give "The way of The materialist explanation of the paranormal and the supernatural" - Is the name of my essay.

Visit my essay and you will find something in it about New Cartesian Physic. After you give a post in my topic, I shall do the same.

Sincerely,

Dizhechko Boris

William Stubbs

Professor Walker,

Congratulations on a very interesting and well-written essay that discusses aspects of the theme of the contest.

It seems you believe only living systems exhibit goal-directed behavior and I share that belief with you. From that, I had hoped you would develop an argument for how the capacity for living systems to exhibit the behavior is born out of the conglomeration of mindless mathematical laws. However, you chose to "recast" the theme question, 'how mindless mathematical laws can give rise to goal-directed behavior,' into 'how it is that macroscopic systems can appear to cause transformations under the constraints of deterministic laws.' These are two fundamentally different issues and, in my opinion, you "transformed" the rules by altering the question (which is likely acceptable).

Rather than proposing how physical systems evolved into ones that exhibit the features of life, including goal-directed behavior, you discuss how living entities (which we know are the result of the mindless laws) configured themselves to exploit their capacity to seek goals. You mention that 'a whole can be more than the sum of its parts,' and that 'a system is integrated when, cut into parts, it loses cause-effect power,' but, as far as I can see, you do not discuss what causes the synergy. What is it about the configuration of the living system that causes it make the jump from inert matter to a living entity? You describe how the integration works, but not why it works. What is it about a living entity that sparks the integration? (You may have done this and I just missed it. Some of your essay is beyond my current knowledge of the subjects you discuss.)

This is not to suggest that I believe you have not done good, useful work - I think you have. Compared to the bulk of the essays submitted (including mine), you deserve a relatively high score and I am glad that you currently have one. It is just that, given your apparent knowledge of the subject; your insights into what makes systems transition from deterministic entities, their fates driven by their environments, into living entities whose fates are determined by their wills, are likely invaluable.

Bill Stubbs

Jack James

Dear Sara

What an excellent essay. One of the few to approach it from biology, or highlight the importance of what can be learnt from it to answer the question. I think Ellis and mine and a couple more the only others, though mine is epistemologically focused. Will happily rate this essay in top percentage, perhaps u can read and rate mine but understand your busy. I wonder this simultaneous electric in and through neurons, how is it consciousness? Still the illusive internal external hard problem remains - but your solving the wiring issue!

Best

Jack Hamiltion James

Philosopher.io

Alfredo Oliveira

Dear Sara Walker

I read your essay with great interest. One of the two essays that so far have interested me more. I think that there is a great similarity between your line of reasoning in the biological side and mine in the physical side. I would say that you wonder on bit-to-bio while I wonder on abio-to-bit.

In my essay I dare to enter also in the biological field, introducing something that may help to understand why life evolved as it did. Life seems to be prone to evolve in all possible directions; yet, it evolved towards human society as if this was a goal. You show that life has the power to evolve - you present the basic process of intelligence of life, and we can say that life has "intelligence" (according to my non-anthropomorphic definition of intelligence)- but "intelligence" either needs a goal or an external pressure to determine the way to follow. Intelligence is always the result of two processes, to which I call Hypothesis generation and Selection. And this happens at all levels within life, as you show, which is very important. I present a new Selection factor at the upper level that may have conditioned Selection processes all the way down to the bit, therefore may be important for your analysis. Once we understand the "generation of hypotheses", it is in the understanding of the Selection processes that we may find whether there is a goal or not. I think that our essays gave complementary contributions to this issue, are tow pieces of this magnum puzzle.

All the best,

Alfredo Gouveia Oliveira

Satyavarapu Gupta

Nice essay Sara Walker,

Wonderful opening sentences!..... "the extreme such as what happens under gravitational collapse or how the nucleus is bound together. However, so far our best theories of physics have not yet been able to explain why physical systems exist that can and do create theories to describe the world (Krakauer, 2014). Arguably this is the most interesting feature of having laws at all"

Here this Dynamic Universe Model answers many physics questions starting from Micro level, Solar system level, Galaxy level and to the Universe level............

..................... Hence at this point, I want you to ask you to please have a look at my essay ALSO, where ...............reproduction of Galaxies in the Universe is described. Dynamic Universe Model is another mathematical model for Universe. Its mathematics show that the movement of masses will be having a purpose or goal, Different Galaxies will be born and die (quench) etc...just have a look at the essay... "Distances, Locations, Ages and Reproduction of Galaxies in our Dynamic Universe" where UGF (Universal Gravitational force) acting on each and every mass, will create a direction and purpose of movement.....

I think intension is inherited from Universe itself to all Biological systems

For your information Dynamic Universe model is totally based on experimental results. Here in Dynamic Universe Model Space is Space and time is time in cosmology level or in any level. In the classical general relativity, space and time are convertible in to each other.

Many papers and books on Dynamic Universe Model were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

Many predictions of Dynamic Universe Model came true, like Blue shifted Galaxies and no dark matter. Dynamic Universe Model gave many results otherwise difficult to explain

Have a look at my essay on Dynamic Universe Model and its blog also where all my books and papers are available for free downloading...

http://vaksdynamicuniversemodel.blogspot.in/

Best wishes to your essay.

For your blessings please................

=snp. gupta

Jesse Liu

Dear Sara,

Thank you for such a finely crafted and interesting essay, with thought-provoking ideas exploring the role of information in scientific theories. As a particle physicist, one thing I definitely agree with you is the underappreciation that emergence and reductionism are not at odds with each other.

While researching for our essay, my coauthor and I were influenced by your earlier work from the wider literature, in particular 'The algorithmic origins of life' regarding the transitional roles of information giving rise to biology and other goal-directed structures. I'd just like to personally extend our compliments to you here as it is always a pleasure reading your insightful arguments.

Best,

Jesse

Lawrence Crowell

Dear Sara Walker.

I found your essay to be quite superb, and I boosted your rating here. It is one of the dozen or so that I have downloaded as a keeper. The branching pattern for emergence is an aspect of something called MERA. This in the biological setting is seen with the branching pattern, such as with figure 2. These set up competing "tracks" of causal development, and a large domain of complexity as seen with the Bell number.

If you look at my essay I discuss causal domains and the open world. I have a review of the MERA tensor network quantum field method in anti de Sitter spacetime. This leads to causal domains as a fundamental aspect of the universe. I think there is a sort of duality between bottom up and top down perspective on the emergence of complexity in the universe.

Cheers LC

Joe Fisher

Dear Professor Sara Imari Walker [,

Please excuse me for I have no intention of disparaging in any way any part of your essay.

I merely wish to point out that "Everything should be made as simple as possible, but not simpler." Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

Only nature could produce a reality so simple, a single cell amoeba could deal with it.

The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

Joe Fisher, Realist

Stefan Keppeler

Dear Sara,

this is a nice contribution. I particularly like how you describe goal-directedness in terms of a primary attractor. I strongly support that "there is no a priori reason to assume that we should not treat all levels equally" and that "emergence and reductionism are not at odds" -- points I also make in my essay. Reductionism and emergence are two sides of the same coin.

Cheers, Stefan

PS (one minor remark): The formula you give for the Bell numbers,[math]\sum_{k=0}^n \left( \begin{matrix} n \\ k \end{matrix} \right) ,[/math] yields just [math]2^n .[/math] The Bell numbers satisfy the recursion relation [math]B_{n+1}=\sum_{k=0}^n \left( \begin{matrix} n \\ k \end{matrix} \right) B_k .[/math] Of course, this doesn't affect any of your arguments.