Thanks so much George! Actually, Larry was on my PhD thesis committee at UW-Madison. He does excellent work.

There's a handful of analytic philosophers who have thought about these issues, starting with Yablo. There's also List and Menzies, as well as Shapiro and Sober. All these people do incredible work and have all touched on issues related to causal emergence at some point or another, although most are focused more on problems of mental causation. None have, as far as I know, argued explicitly for the theory laid out here and elsewhere.

One constant problem that I have with this research is the consequence of framing it in terms of the exclusion problem. It's a good way to frame it because it hammers the problem home, but it's a bad way because the exclusion argument is a well-known philosophical issue and people then immediately assume this is a philosophical solution to a philosophical problem. But as I indicate in the essay, I'm using the exclusion argument as a stand-in for a more general issue concerning causal structure, information, and model choice.

Ultimately, I think this requires a scientific (or mathematical) theory, composed of: A) formalizing supervenience as changes in scale or as highlighting only subsets of the system's state-space; B) some sensitive measure of causation and/or information (I've used information theory and Pearl's causal calculus) that can handle things like noise, is proven to be related to various important causal properties, doesn't give nonsensical answers for simple scenarios, etc; C) actually checking and proving that B can be higher across various scales made with A; D) explaining why it's theoretically even possible that the macro can beat the micro; E) hopefully some applications.

Originally we argued in 2013 for the D that macroscales reduce the noise in the system (over both the past and the future), and that's how causal emergence occurs. I think there's another interesting way of framing it, which is that macroscales can be thought of as codes (as I argue here and elsewhere), and the macro can beat the micro because of Shannon's noisy-channel coding theorem. Hopefully both these explanations help with E: actual applications.

Dear Dr. Erik P Hoel,

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

Hi Ted - thanks so much for stopping by. I strongly agree that we all make assumptions.

I checked out your essay and was very glad to see you mention Rafael Yuste - he's my principal investigator here at Columbia University. I did want to say that, while I disagree with some of your examples seriously challenging contemporary neuroscience, I absolutely agree with you that little attention has been paid in neuroscience to the consequences of hydrocephalus. IF it's true that people are operating normally but have drastically reduced gray matter (such as 10 to 20%) we're going to need to drastically rethink some things. However, if I remember correctly recent research has questioned these numbers.

http://blogs.discovermagazine.com/neuroskeptic/2015/07/26/is-your-brain-really-necessary-revisited/#.WMVsVRLyuRs

Thanks so much for reading!

Erik P Hoel

Hi Erik

Your essay is awesome, you basically crushed it. The point about the kinetics of the system and the signal propagation time setting scales for "identity" was the first point that I found truly insightful, it reminded me of the idea that if we wanted to imagine something crazy like the universe being one big mind then it would never be able to actually finish a thought because it is expanding faster than it is possible to send signals back and forth across its entirety, and probably can't cross the percolation threshold for correlations as a result. The other point I loved was about needing to include the environment in Romeo's causal structure. In the phenomenological tradition, it was clear since Husserl that "consciousness" can only ever be "consciousness of phenomena", it's only really since philosophy of mind took this very ahistorical turn against "reductionism", I feel, that we lost sight of this fact. All of your other claims are correct, lucid, and I think should be uncontroversial for anyone familiar with modern neuroscience, information theory or stochastic dynamics. But it's exceptionally well-argued and clear. If you have a moment to look at my own entry at any point, I think we make many of the same arguments though I wrote in a somewhat different style. In any case I'd appreciate any feedback you could offer.

Again, total slayer of an essay.

Joe

Thanks so much Joe - highly appreciate it. Although I wouldn't say any of this is "uncontroversial"! Try getting funding for it hahaha.

I just finished your essay, which I enjoyed, particularly your writing. There's lots of stuff going on in there but just wanted to mention the relationship to my own essay here, which is your segment on higher-level explanations. You say: "In this way, we compress our explanations of phenomena, with the useful result that they can be communicated and shared with fewer bits, thus requiring less work to understand."

I completely agree - this is totally necessary for human communication, or something like science where we communicate facts or data to one another. What I argue in my essay is that there's another possibility for an information theory metaphor beyond just compression for these types of cases: coding. So higher-level explanations aren't always *merely* compressions, sometimes they are also codes; in addition to being compressed, they also error-correct, meaning they can have in theory more information than whatever underlies them.

Thanks for commenting, and I enjoyed your essay,

Erik P Hoel

    Dear Erik,

    I also find your essay excellent and very stimulating. A few questions.

    The emergence of (apparently) purposeful behavior, intentions, goals, agency, is clearly a complexity booster, and it would be great if we could see it at work even in discrete, finite, *deterministic* formal systems, below the level of biology.

    In my mind, one of the best examples of emergence is represented by the 'digital particles' of cellular automata (Conway's GoL gliders, Wolfram's ECA 110 trajectories), and you do mention them in your essay. However, those are completely deterministic systems, while the causal emergence that you formalise in terms of input state and output state distributions, their correlations, mutual information etc., seems to fundamentally require a stochastic basis. Is there a way out to this difficulty? Can the theory be extended to formal, algorithmic, deterministic models? That would be very useful since in that context, as far as I know, emergent phenomena cannot yield more two-levels -- a limitation pointed out also by G. Ellis (I can't remember where, but earlier than in his current essay).

    The idea of substrate independence, or multiple realisability, is exciting, and provides a new (at least to me) perspective for looking at the whole business of emergence. However, while I find the example of waves quite appropriate -- with laws that are independent from the nature of the molecules in the medium -- I am not convinced that cellular automata are a good example. In the Game of Life, localised structures emerge only from a very specific underlying rule: should you change a single bit of that rule, those structures would vanish. What is true is that the digital particle, say a glider, is 'implemented' by an ever changing subset of underlying cells, but I don't think this counts as 'substrate independence..., or does it?

    To me, the idea that the fully-fledged causal structure of an open system may require the participation of the environment has appeared intriguing at a first reading but ... obscure at a second one :-] How should one interpret the red transition arrows in Figure 3? What is the formal meaning of 'outsourcing causal structure' to the environment, in terms of state transition systems? Should I imagine that some of the states of Romeo's brain are out in the environment. In which sense?

    Finally, I'd be curious to check the possible applicability of causal emergence to the very fundamental model of causal sets (Sorkin, Bombelli, Rideout, Dawker, etc.), which is essentially based just on causal relations between unstructured events. Any idea?

    Thank you and all the best!

    Tommaso

    http://fqxi.org/community/forum/topic/2824

      Thanks so much for the close read Tommaso! You ask some really great questions - so forgive the lack of brevity in my replies!

      "one of the best examples of emergence is represented by the 'digital particles' of cellular automata (Conway's GoL gliders, Wolfram's ECA 110 trajectories), and you do mention them in your essay. However, those are completely deterministic systems, while the causal emergence that you formalise in terms of input state and output state distributions, their correlations, mutual information etc., seems to fundamentally require a stochastic basis. Is there a way out to this difficulty? Can the theory be extended to formal, algorithmic, deterministic models?"

      Actually, causal emergence can work in completely deterministic systems (see Hoel et al. 2013 "Quantifying causal emergence" in PNAS for some examples). I mention this in the essay but only very briefly in the technical endnotes (section D). What is necessary is that these deterministic systems are degenerate - that is, multiple states can deterministically lead to the same state. As far as I know, a lot of CAs (in fact, most) fit this bill, so this could be comfortably applied to CAs. However, for totally time-reversible systems, if you take that system as a whole (the entire CA board, as it were) causal emergence cannot work. I also address this objection in the endnotes (section D).

      "That would be very useful since in that context, as far as I know, emergent phenomena cannot yield more two-levels -- a limitation pointed out also by G. Ellis (I can't remember where, but earlier than in his current essay)."

      Interesting. I address this a bit in the conclusion and also in the endnotes (E) where I ask what this all means metaphysically. The two options I find attractive are supersedence (like the total causal work of a system is x and the winning level gets all of x) and layering (x is distributed in some way based). In the former case there is only ever one level, and in the latter case, there could be far more than two levels.

      "To me, the idea that the fully-fledged causal structure of an open system may require the participation of the environment has appeared intriguing at a first reading but ... obscure at a second one :-] How should one interpret the red transition arrows in Figure 3? What is the formal meaning of 'outsourcing causal structure' to the environment, in terms of state transition systems? Should I imagine that some of the states of Romeo's brain are out in the environment. In which sense?"

      Great questions. Wish I had had the space to elaborate more and give a more formalized definition of teleological (apparent or otherwise, I'm neutral) causal relationships. I tried to get it across in a thought experiment of Romeo's brain: if you take a system in isolation, you can still derive a causal structure from it. There's a certain set of causal paths within that system, from state to state. Let's say that for this system that causal structure is pretty sparse (not very complex). Now you expose the system to the environment. You can imagine several different responses. Maybe the causal structure stays sparse. Maybe it becomes extremely noisy and the causal structure loses a lot of its complexity (like every state leads to every other state over time, or something). Or maybe you expose all these "hidden" structured causal paths (one example is shown by the red arrow of a single relationship that is exposed by interacting with the environment). The internal causal structure is no longer sparse - it has gained in complexity.

      Just to make it even more concrete and simple, imagine a simple generally feedforward neural network with input nodes and output nodes, but considered in isolation. Sparse internal causal structure. Then imagine hooking up the output nodes to the input nodes in some complex or interesting way. You could change the internal causal structure pretty significantly, just by "crossing the streams" (sorry) and allowing higher-up events to influence lower-down events in the network now. The formal definition that would go along with the thought experiment would be the degree of that change. The thing that makes this "teleological" in the case of Romeo's brain is that those output-to-input connections that complexify the internal causal structure exist solely through Romeo's interaction with his environment, not through explicitly added physical connections (but mathematically it might be the same). So it's not that the states themselves change, it's the connections between the states may be enriched. In analytic philosophy language, the formal way of phrasing this (mentioned only briefly in the essay) is that the full causal structure of Romeo's brain is not locally supervenient on the physical structure itself.

      "Finally, I'd be curious to check the possible applicability of causal emergence to the very fundamental model of causal sets (Sorkin, Bombelli, Rideout, Dawker, etc.), which is essentially based just on causal relations between unstructured events. Any idea?"

      It's a great possible connection! But I don't want my speculative reach to exceed its grasp by any more than it already has!

      Thanks so much for your wonderful questions and detailed reading,

      Erik P Hoel

      Dear Dr. Hoel,

      I am quite interested in your essay, with its emphasis on the emergence of agency from lower-level structures.

      I also address the issue of agency in my own essay, "No Ghost in the Machine". However, rather than a vague spontaneous emergence at some level of complexity, I argue that recognition of self, other agents, and a causal narrative are built into specific evolved brain structures that create the sense of consciousness as part of a dynamic model of the environment. The reason that this is such a difficult problem is that we are being misled by the subjective perceptions of our own minds.

      Alan Kadin

        Nice essay Dr Hoel,

        Your ideas and thinking are excellent, 'Kublai Khan remains silent, reflecting. Then he adds: 'Why do you speak to me of the stones? It is only the arch that matters to me.' Polo answers: 'Without stones there is no arch

        Agents are generally somewhere above biological mechanisms but below economics on the ladder. They are a major part of the slim section that corresponds to the scale of our everyday experiences etc...'

        I fully agree with you Here I am proposing still higher level agent, at the universe level ............

        .....................please have a look at my essay, 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 my 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

        Dear Erik,

        congratulations to your beautiful essay. It is both brilliantly composed and very interesting. I'm also always keen to learn about new aspects of IIT.

        I have two comments:

        -First, a minor criticism: Of course "quark clouds" do not constitute atomic physics. Quarks constitute the atomic nucleus while chemistry depends on processes involving electrons in the atomic shells.

        -Second, is "causal emergence" really so surprising? To me "causal emergence" seems to appear whenever an experimentalist is performing a series of measurements and statistical uncertainties average out (essentially the "law of large numbers" in stochastics). Probably even more prominently in quantum mechanics the fundamental level appears to be less deetermined than macroscopic classical physics. Can you elaborate a little more about whether the causal emergence you are talking about is different? Do I misunderstand the concept?

        Also I'm a little confused about the exact relationship of under- and overfitting (overfitting seems clear to me but can somethink like underfitting be possible without causal breaks?)

        When you talk about the emergence of teleology in agents I was also wondering how strongly this phenomenon is related to what you call substrate independence and to the relationship between matter and information. One may argue that pure information-based conecpts such as the "bill of rights" or the "contents of the bible" are totally substrate independent, and that agents exist somehow in between such imaterial objects and material physics. Would you agree with this interpretation? Finally, especially exciting to me are the role of the environment and of the perspective, also since that may provide a link to the foundations of quantum mechanics and to our own essay.

        Best regards, Heinrich

          Thanks so much Alan for reading. I don't think of this as a form of vague or spontaneous emergence - it's quite structured and non-arbitrary. It's nothing like the example you give in your own essay of the idea that past a certain (arbitrary) level of complexity, consciousness spontaneously arises. I have some thoughts on your own essay that I will comment on there - thanks so much!

          Erik P Hoel

          Thanks so much for your thoughtful comments. Causal emergence was first shown as a separate phenomenon in (Hoel et al. 2013), but you're right that we then later showed that it is at work in IIT: systems can have higher integrated information at larger scales (Hoel et al. 2016 in references).

          As to your comments:

          "..."quark clouds" do not constitute atomic physics. Quarks constitute the atomic nucleus while chemistry depends on processes involving electrons in the atomic shells."

          Took me a second to find what you're talking about (which is the arrow on the second to bottom step in the ladder in Figure 1). Yes, the picture is infinitely more complicated than shown! I certainly can't draw out all the supervenient arrows also because scientists don't spend a lot of time looking for what Ernest Nagel called "bridge laws." In retrospect I could have just put "elementary particles in the standard model" which covers more bases.

          "Second, is "causal emergence" really so surprising? To me "causal emergence" seems to appear whenever an experimentalist is performing a series of measurements and statistical uncertainties average out (essentially the "law of large numbers" in stochastics). Probably even more prominently in quantum mechanics the fundamental level appears to be less deetermined than macroscopic classical physics. Can you elaborate a little more about whether the causal emergence you are talking about is different? Do I misunderstand the concept?"

          Well, let's differentiate between whether causal emergence is surprising vs whether it's rare. I think it is very surprising given that conceptually it is not at all obvious how higher scales can do extra causal work and generate more information. So it's conceptually surprising. But I don't think that it's rare, in fact, I think that it's pretty much everywhere to greater and lesser degrees. But it's not so common that it's just whenever there's an average in an experiment (and not all higher scales are averages). You can have plenty of averages, or let the law of large numbers work, without causal emergence. For example, rolling a die over and over won't give you any causal emergence. However, regularly in science experimenters treat higher scales as causally-manipulatable variables. This can be reflective of causal emergence. For instance, assessing the causal relationship between two neurons (not their underling elementary particles). Causal emergence explains why that's not just about using a simpler representation. You're possibly gaining something in this scenario: extra information about the causal structure that's not available at the microscale, because at the scale of neurons there is error-correction, whereas at the scale of elementary particle physics there is no error-correction. If you believe the hypothesis I lay out of the ladder of science being reflective of each step causally emerging from the one below it, causal emergence should be incredibly common, especially in the special sciences (like biology).

          As for quantum physics being less determined than classic physics - well, that's a good scale to look for causal emergence at.

          "Also I'm a little confused about the exact relationship of under- and overfitting (overfitting seems clear to me but can somethink like underfitting be possible without causal breaks?)"

          Glad it came across. I don't think underfitting is possible without causal breaks - that's why I describe teleology as "breaks in the causal chain" and say that it leads to underfitting by a causal model. So I think it's an extended aspect of causal emergence that's unique to agents (or things with equivalent apparent teleology).

          "One may argue that pure information-based conecpts such as the "bill of rights" or the "contents of the bible" are totally substrate independent, and that agents exist somehow in between such imaterial objects and material physics. Would you agree with this interpretation?"

          It's a nice idea but I wouldn't agree. First, I don't think anything is actually fully substrate-independent, more like things are substrate-constrained to greater or less extents. Second, I don't think there's some immaterial world that anything is closer to.

          Thanks so much for your great questions and your interesting thoughts. I will definitely check out your essay!

          Erik P Hoel

          Hi again Eric P. Hoel,

          I am getting back having seen your Discovery article followup to Lorber et al's claims on small-brained performance. Two points,

          1. That article really doesn't do much to deflate the implications of Lorber's findings.

          2. That was simply a warmup example in my essay (which itself is a warmup example) as it nicely followed Sean Carrol's quote. I re-suggest that there are basic challenges - and lessons to be learned - by looking beyond the textbooks.

          Good luck with your work,

          Ted Christopher

          Erik--

          Point taken about the funding! I'm going to be looking for a new job in the coming months and perhaps I'm just trying to be overly optimistic about how popular the worldview expressed in your essay really is! Also I managed not to notice that you are at Columbia the first time I looked this over, we collaborate with the Banta group and the Venkataraman group on different projects, and I'm literally a subway stop north of you. Feel free to come see our lab at City anytime. We design proteins and characterize them with spectroscopy; we have lots of cool lasers.

          And we should discuss coding in biology while you're there too. I didn't focus on it in my essay because it didn't fit neatly into my narrative, but I completely agree that coding or perhaps more generally "translation" of information is an ubiquitous phenomenon that is not merely compression from coarse-graining but involves emergent dynamics from interactions that do not appear in the local microscopic dynamics. I think the genetic code is actually the perfect example of that. I taught a course at city college on principles of statistical physics in biology and we spent a week or so discussing what makes translation of nucleic acids into proteins a much more interesting and physically difficult to explain phenomenon than transcription of DNA to RNA. The translation step is what makes it a code rather than just chemistry, because there is no direct structural connection between a codon and an amino acid, and the code only appears when you look at the correlations in the network structure. I actually have a ton of thoughts on this issue and I'd love to pick your brain too and since you're just up the street I think we should probably make it happpen!

          Joe

          • [deleted]

          • Post #53

          Hi Erik,

          You're probably not going to like what I say. I am going to bring up two points concerning your article and none of them are addressed in your article.

          The first point is simple. You plopped yourself in the middle of religion without even realizing it. It concerns the Romeo and Juliet argument you bring up. You seemed to miss that there was a wall at the end of the story that neither Romeo or Juliet could circumvent that was Death. Since you discuss the internal architecture of Romeo's brain we will go with that. Romeo has received new information from the environment. Juliet is dead. S_d to S_k no longer exist. Or do they? A new S_k could be, Romeo will meet Juliet in the afterlife. That is religion. I'm not going to get into beliefs and the ends people use to extend them.

          At the end of the 19th century, a certain scientist named Planck formulated his "Black body radiation" law. This law used the smallest thing currently known to man to describe the radiation of a black body. But it is not limited to black bodies, it includes the human body, our sun, our galaxy, and the CMB. How is any large scale effecting the smallest scale. To believe your model you would think the Planck's constant doesn't exist above atoms.

          I See all the superlatives other people have given your article. I can't join them. I was drawn to your article by a tweet from Natalie Wolchover and calls your article "the %#*&". Good luck in the contest.

          Jim Akerlund

          FQXi logged me out so I am not really "Anonymous".

          Jim Akerlund

          Interesting article that tries to understand the influence of the dimensional scales in human psychology and consciousness.

          But taking into account that the composition of all living beings (known) is formed of very similar cells and molecules, we should deduce that the greatest differences occur in the higher levels and not in the lower levels as I understand you propose.

          Please read my article (http://fqxi.org/community/forum/topic/2925) that also deals with the SPACE SCALES applied to Cosmology.

          Congratulations on your proposal!

            Dear Erik,

            You have already received so many comments that I am not sure, if this will add much to that. Yet ...

            In many statements in the essay, there is one point reverberates as a non-violative presumption that the nature is deterministic in the absolute sense at the most fundamental scale (level). For example,"In this reductionist view, a biologist studying a cell is really referring to some astronomically complex constellation of quarks." The function at the cellular level may not be entirely determined by the quarks, if there is a certain degree of indeterminism in the processes at any scale.

            In statements like, "Recent research has argued exactly this [14, 15] by demonstrating the possibility of causal emergence: when a macroscale contains more information and does more causal work than its underlying microscale.", it is not clear what is referred to as more vs less information. I suppose, you just showed all along that complete description of microstates carry more information than any abstraction of the same at a macrostate. As you also mentioned Shannon's quantification principle, the detail in microstate can distinguish a state among much larger set of states, therefore contains more information. But the quoted statement seems to violate that.

            Though, as I have shown that ignoring certain detail gives rise to emergence of abstraction that is not present in any one the components. This is a process of generalization that applies to all objects, say states, relations, functions, and processes. But in Shannon's view, it corresponds to loss of information.

            With respect to transition matrix, Smicro and Smacro, I am not claiming that I understand it completely, but this is what appears to me. Imagine the micro states are designated as (a,b,c,q), and after ignoring the distinction between a, b and c, we call the resultant macrostate as p. So, if the elements of the transition matrix are probabilities of transitions, then the following points can be noted, 1) 'a' may transition into a, or b, or c, with equal probability of 1/3. The same is true for b and c. Whereas, with Smacro, p remains p, and q remains q for all times. So, I conclude that Smicro certainly has more information distinguishing among finer transitions than Smacro. Keeping the same logic as proposed by you, if we ignore all internal state details and transitions of elements in universe U, then U remains U in perpetuity, a very definitive statement, no degeneracy, absolutely deterministic, but that hardly tells anything worth distinguishing. 2) If the elements of transition matrix are probabilities, that means it is not a fully described system, as per the presumption of determinism, or the determinism does not hold, or determinism is limited. That is, Smicro is also already an abstraction of even more fundamental description. Talking the language of quantification of information, I can represent the Smacro with mere 4 bits, but Smicro would take many more. But in my view Smacro is an abstraction of Smicro, where certain details are of no importance.

            Given your definition of teleology, are we to understand that bacterium also possesses a sense of goal and purpose, acts accordingly to discover resource?

            Rajiv

              Thanks so much for reading David. I appreciate it.

              I just checked out your article - I think figure 2 is a really wonderful representation of the truly diverse range of scales.

              Thanks again,

              Erik P Hoel

              Thanks so much for reading Rajiv, I appreciate it.

              I'll try to address some of these objections, which are rooted in misunderstandings or misconceptions.

              "The function at the cellular level may not be entirely determined by the quarks, if there is a certain degree of indeterminism in the processes at any scale."

              This is a misunderstanding between determinism and supervenience (where the lower levels determine, or fix, the higher levels). A non-deterministic system will still have strictly fixed supervening levels. The state of the cell supervenes (is determined by) the constellation of elementary particles below it.

              "In statements like, "Recent research has argued exactly this [14, 15] by demonstrating the possibility of causal emergence: when a macroscale contains more information and does more causal work than its underlying microscale.", it is not clear what is referred to as more vs less information. I suppose, you just showed all along that complete description of microstates carry more information than any abstraction of the same at a macrostate"

              This is the opposite of what is shown in my essay (and the associated papers). The definition of more or less information is pretty clear in the essay itself (given in the equation for effective information), and in the associated papers there are numerous examples demonstrating how to calculate this information and showing it done on model systems.

              "If the elements of transition matrix are probabilities, that means it is not a fully described system, as per the presumption of determinism, or the determinism does not hold, or determinism is limited."

              It's a metaphysical assumption on your part that all systems are deterministic. And it's simple not true - any open system will experience noise (for instance, a cell being bombarded by cosmic rays). Even in the deterministic universe the only way to get rid of any notion of noise is to avoid partitioning the universe into notionally separate systems (like a cell, by itself). If you can't do this, it leads to very serious problems (discussed in Appendix D). And besides, as said in the essay, the point is moot anyways, because causal emergence can occur even in deterministic systems.

              "Given your definition of teleology, are we to understand that bacterium also possesses a sense of goal and purpose, acts accordingly to discover resource?"

              Great question. It may be possible to design even simple systems with the kind of teleology I propose. I would view it as a matter of degree, not a binary answer, where humans might have orders of magnitude more "teleology" than a bacterium.

              Thanks again,

              Erik P Hoel