Thanks for commenting again Conrad - and I'm very glad to hear it had an impact.

As to your point, I actually generally agree with you on this. It may *not* be the case that all of science can be described in terms of a non-broken hierarchy of supervenience. Perhaps very strange stuff is going on at the microscale and causal structure of any kind can only exist at some level above the ultimate microscale anyways. However, causal emergence is relative to levels; so for instance, if biology does supervene on chemistry, biology could causally emerge from chemistry (regardless of whatever is going on beneath chemistry). It's also very probably that causal emergence can apply to non-strictly supervening scales - because again it's just comparing the macro to the micro causal structures. So these are really great questions - I'm not going to a priori ruling anything out. This is just the clearest way to present the idea without getting into all sorts of caveats about whether and where supervenience holds and how strict it is; which is, in a sense, a different (although just as interesting) problem. Certainly in the systems I'm working with supervenience always holds, which I view as the most difficult scenario in which to make a strong case for emergence, so that's why I always enforce that.

EPH

Hello Erik Hoel,

I enjoyed your paper and I think that the ideas in your paper are a step in the right direction. But I do not think that your argument is sound. You assume in your first paragraph that agents have 'goals, intentions, and purpose', which, I believe, is the end point of the question as asked. I do not see how you link mindless mathematical laws to aims and intension.

I do not think that supervenience is the right concept. There are at least two hierarchies: the physical hierarchy and the conceptual hierarchy. The physical hierarchy starts at the Plank distance and extends at least 70 orders of magnitude to the size of the observable universe. The physical hierarchy is the realm of physical process behavior as summarized by mindless physical-mathematical laws . The conceptual hierarchy of the sciences is a human semantic overlay on the physical hierarchy. In either case, the guiding mathematical laws or science of the higher levels to not necessarily reduce to those at the lower levels - the rules of organic chemistry does not really reduce to sub-atomic physics; and the rules of baseball do not reduce to biology. What can be said is: the lower levels implement the higher levels, and things that appear at the higher levels are not predictable by the laws of the lower levels.

I think that implementation completes the emergence story. Emergence brings into being the parts that implement the next level up, but I think that implementation does a more natural job of 'carving nature at its joints'. Implementations are assemblies of parts selected from collections of what emerges from below.

Thanks for the good read.

Cheers,

Bruce Amberden.

    Dear Sirs!

    Physics of Descartes, which existed prior to the physics of Newton returned as the New Cartesian Physic and promises to be a theory of everything. To tell you this good news I use «spam».

    New Cartesian Physic based on the identity of space and matter. It showed that the formula of mass-energy equivalence comes from the pressure of the Universe, the flow of force which on the corpuscle is equal to the product of Planck's constant to the speed of light.

    New Cartesian Physic has great potential for understanding the world. To show it, I ventured to give "materialistic explanations of the paranormal and supernatural" is the title of my essay.

    Visit my essay, you will find there the New Cartesian Physic and make a short entry: "I believe that space is a matter" I will answer you in return. Can put me 1.

    Sincerely,

    Dizhechko Boris

    Hmmm, let me try to clear some of this up.

    "I do not think that your argument is sound. You assume in your first paragraph that agents have 'goals, intentions, and purpose' which, I believe, is the end point of the question as asked."

    As I outline in the essay, the question is not whether agents can be described as having goals, intentions, and purpose. You do that every day, I do that every day, every human describes agents this way throughout their lives. Many scientific and quantitative fields also describes agents in this way, and even have associated mathematics and formalisms, as I point out. The real question is not whether some physical systems (agents) can be described as having goals, intentions, and purposes, because clearly they can, but whether those things are actually causally efficacious. That is, are they epiphenomenal, or can they be reduced to the mindless mathematical laws and relations of the microscale?

    "I do not think that supervenience is the right concept."

    Supervenience means that if you fix the properties x at a lower scale you then fix y at a higher scale. Your example of baseball not being reducible to biology isn't capturing that. Obviously, given the set of fundamental physical properties that underlying a baseball game being played, whether or not someone is on first is fixed by those fundamental properties. Imagine fixing the fundamental makeup of a computer; that fixes the higher scale of the logic gates in the computer. That's supervenience. It sounds to me like you are talking about reduction between laws rather than supervenience between scales: do the laws of organic chemistry reduce to the laws of sub-atomic physics? This is actually a different question than: if you fix the set of fundamental physical properties in a system, do the higher level properties of that system follow? In fact, your very definition, that "lower levels implement the higher levels" implies supervenience (why else would implementing higher-level property y via lower-level properties x bring about y unless fixing x meant fixing y?). When talking about these issues it pays to be precise, and unfortunately special jargon is needed, and thus careful attention must be paid while reading to understand the definitions.

    All the best,

    EPH

    Hi dear Erik

    I have read your amazing work today only (and a little bit in hurry - sorry)

    I can evaluate it as high because it are well written and attractive-interesting, especially your underlining on the causal principle of arising of intentionality, coming from components-agents, which seems to me important. I have understand also that you had look somewhat pessimistically on the possibility to solve offered problem in whole, - for today. It seems to me important because I'm are inclined to approach to this discussion theme some critically. Hope you can look my essay in this short time and say some words (please in my page) that will be valuable for my.

    I wish you success in this contest!

    George Kirakosyan

      Thanks so much for commenting even though you were in a hurry George! I appreciate it all the more.

      And you're absolutely right - I'm trying in this essay to solve what I view as the underlying, fundamental, or ultimate problem which all approaches to the question will have: regardless of exactly how the goals/intentions/aims arise, there will be an ultimate problem for these descriptions, and that is whether they can possibly be causally efficacious.

      All the best - good luck in the contest,

      EPH

      Jonathan - I posted a link to my own twitter followers to read my essay. I don't think it's at all self-promotional or strange for someone to assume that their own followers might want to read their essay first. In fact, as far as I can tell, most everyone who is on twitter and in this contest has posted a link directly to their own essay at some point or another to their followers. Since I'm assuming you don't follow me on twitter, you obviously saw that my tweet got retweeted by @FQXi today - but who retweets my tweets isn't up to me! I don't have any control over @FQXi, and I think it's a serious moral category error on your part to assume that and to have read as much into it as you have.

      EPH

      Perhaps I misunderstand Twitter..

      Because I reject the Twitter mentality, and studiously avoid sites that would require me to authenticate myself via social media, I choose to isolate myself from that crowd. Ironically; this leaves me unable to edit my own page on MTV dot com. I find it suitable for folks in the Music profession to hype themselves to the max, in order to boost their standing. So I excuse my colleagues in Music for doing so. I find this far less palatable in academic professions, despite its recent popularity. It's not just you Erik; it sours my stomach to see any scholar behave that way.

      I might have erred to assume that you were posting directly to #FQXi when you posted to your own Twitter link and it was re-tweeted. But the content was yours to start with, and you should know that once something is on the Internet, you can't control who re-purposes it. So it is incumbent on you as a scholar to retain or portray a certain sense of dignity. I don't resent so much that you were preaching to the choir (your own 'followers') but seeing it on top of the FQXi feed still soured my stomach. So I own my emotional reaction, but I won't excuse it. I reserve the right to feel as I feel, and I'm sorry if my expressing that offends you.

      Regards,

      Jonathan

      Oh that should be..

      Pete Seeger's cabin... Pete was rather down to Earth and kept a low profile for someone of his stature. I guess I try to emulate his 'walk the talk' attitude, which kind of rubbed off after years of working with him. I could go on and on about contact with celebrities, conversations with various scientists, and so on. But that has lost its luster and I'd rather do some serious work instead. I am sorry to bristle at you, rather than understanding the context.

      Warm Regards,

      Jonathan

      Dear Erik P Hoel,

      I was impressed with your comments early in the contest. You commented upon my essay before you posted your own essay, and, having exchanged thoughts with you, I forgot that I had not read your essay.

      Having read it now, I enjoyed it very much, beginning with your toy system where you demonstrate that macroscale transitions are more deterministic and less degenerate, so interventions at the macroscale are essentially more effective. This may explain some of the power of the 'qubit' in statistical spin systems. The 0.81 -> 1.0 bit of information was extremely interesting.

      And I agree with your conclusion: "attempting to describe an agent down at the level of atoms will always be a failure of causal model fitting."

      Thanks for your excellent analysis and good luck!

      Best wishes,

      Edwin Eugene Klingman

        Glad to hear it Edwin - I definitely remember your own essay as being one of the ones that really interested me early on.

        Thanks for commenting and I'm glad you found the analysis of macro vs micro interesting/useful - the connection you see to qubits is intriguing.

        All the best!

        EPH

        So sorry that science has stooped so low. While multi-cellular life has clearly "emerged" from particles, atoms, molecules and cells, emergence models are largely an edifice of spin. The emperor has no clothes.

          Sorry you didn't like the essay Lorraine! I think it's true that theoretical work on emergence does sometimes have some spin; however, there's also a lot of serious content from people really trying to do something rigorous and interesting. Let's not throw the baby out with the bathwater.

          EPH

          Hi Erik, very well written essay. You do not mention feedback from higher to lower level at all, and so just have the ascending ladder of micro to macro giving causality. However, for example, social relations and/or a complex environment can cause stress to an organism that then affects the concentrations of biochemicals such as hormones and neurotransmitters in the individual that can subsequently affect it's (the organism's) behaviour. So tracing the behaviour only to the biochemical concentrations misses out on the why the levels are what they are; and misses an important feedback in the causal chain. Kind regards Georgina

            Thanks for reading Georgina.

            The reason I focus on an ascending ladder is because it's easy to slide between definitions when talking about this stuff, and working with discrete finite models with discrete finite sets of supervening scales forces rigor. For example, sometimes people talk about "top-down causation" when they are really talking about something that's probably more clearly described as "whole/part" causation. Your example of an organism that's stressed from the surrounding social relations is more like how part might influence a greater whole (the social structure). Talking about feedback makes a lot of sense in that regard. However, wholes don't share an identity with individual parts. A higher scale, however, does seem to have something like an identity relationship with its lower scales (there may be some caveats to this, but in general for discrete finite systems this seems solid). So what would it mean for there to be feedback between a thing itself across scales? My point is not that it can't possibly happen, but rather that it's a) different than the more obvious whole/part feedback and b) there are simpler (i.e., more rigorous) ways of investigating the phenomenon first. I think you are completely correct that this isn't the final story, and you're right to ask the question: about the intermediary scales? What you refer to as the "causal chain" is something I mention in terms of future directions in some of the supplementary material (E).

            2 months later

            If you're listening, there may be more comments here because of the Quanta post https://www.quantamagazine.org/a-theory-of-reality-as-more-than-the-sum-of-its-parts-20170601/. At this point the contest looks to be going well for you, so an early congratulations for that at least, as well as for the mention at Quanta.

            I have a query about your 4x4 matrix on page 4, and its reduction to 2x2. Surely the choice to make the reduction by projection to 3+1 dimensional subspaces instead of to 1+3 or to 2+2 introduces significant information? Indeed, a projection to arbitrary subspaces could be introduced, resulting in almost any 2x2 matrix. Your text offers that "a macroscale is constructed of a grouping (coarse-­‐grain) of the first three microstates (it is multiply realizable)", which uses information contained in the matrix to choose the particular 3+1 projection. The choice of "multiple realization" would seem to identify a particular algorithm for identifying subspaces, with the implication of some degree of algorithmic complexity. I'm sadly no expert on information theory, however.

            If you answer this, I may formulate further questions or comments.

              Hey Peter - yup, still receiving the emails if someone posts here. Thanks for the congrats about Quanta, I was pretty happy at the level of complexity in which the author wrote about the research and hopefully it attracts more researchers into the area.

              To answer your query about the 4x4 matrix: if I understand you correctly, your intuition is correct that there are many possible projections, many of which may lead to different values. You're right. The conceptually simplest way to deal with it is to brute force it. Just try all possible projections, and one will have the most information. However, I'm not sure what you mean by saying that the choice of multiple realization would identify a particular algorithm for identifying subspaces. There's a certain mapping associated with it, but I wouldn't call it an algorithm. You are definitely correct that all this has some connection to the algorithmic complexity - in general, program length should decrease for any macroscales.

              I think it is, but I won't go to the wall over whether the choice of mapping as a nonlinear function of the matrix elements is an algorithm; in any case this is mostly an illustrative toy model for you.

              I left a comment at Quanta. The first paragraph is specific to the Quanta article, and I'll paraphrase the second paragraph as saying that I think you are too dependent on conventional thinking about real-space renormalization (which is by its nature rather ad-hoc, but there's largely no alternative), but I'll repeat the third paragraph here:

              ««The idea that macroscopic observables might be more than is given by microscopic observables can be presented much more abstractly in the context of the Haag-Kastler axioms as a failure of Additivity (which is that the algebra of observables associated with a union of two or more regions is the same as the algebra that is freely generated by the algebras of observables associated with each region separately). A weakening of the Wightman axioms is also possible (which is inevitably much more concrete, but it would need a dozen pages to describe). Hoel will eventually need something like such constructions in order to make contact with the causal structure of quantum (field) theory. I think Hoel's constructions here and in the FQXi essay are very helpful, nonetheless they seem to me ad-hoc enough relative to the underlying cellular, biochemical, and atomic structure as we understand them to make it difficult to make precise claims about causality.»»

              All except the last sentence of that is so specific to my perspective on QFT and (correct me, but I suppose) out of your range of expertise that I don't expect an answer. The last sentence is mostly for future reference; IMO, claims about causality have to be very carefully formulated.

              Natalie Wolchover is one of the very best Science Writers. You were very lucky to get her. I presume that she represented Scott Aaronson's response more-or-less accurately; I take his (somewhat but not totally dismissive) response partly to reflect my feeling that you don't yet have a formal enough presentation to make the suggestiveness of your approach really stick.

              I hope that's helpful, but I am a crazy old bat. I'm fairly close to you, in New Haven, so if it seems curious enough I would be interested to meet you.

              Over on Shtetl-Optimized, you mention "I'm not answering all things people toss out as I don't want to spam the thread." I expect you're not even referring to me, but FWIW I'll repeat my comment there (which reels in a little my comment above that I wouldn't go to the wall over the choice of mapping),

              «Hoel works with Markov processes, but specializes to systems that have an exact macro-state separation: that is, having a diagonal block-matrix presentation. Physical systems, however, are only separable in this way for limited lengths of time. There are small probabilities, for example, of interactions between my fingers, subsystems of my body, and my toes; infrequently, I have to cut my toenails. In general, every entry in a Markov matrix is likely to be non-zero and different from other entries.

              To identify how to coarse-grain in the general case, we have to consider either the matrix entries or we have to consider whatever information is not encoded in the Markov matrix (physical adjacency, for example). If the former, an algorithm might, for example, compute an eigenvector basis (over the complex numbers) and compute which to discard (but there's likely a better algorithm!); the algorithm is clearly a source of extra information. If the latter, there's an even clearer source of extra information. In both cases, the Markov process is embedded in a larger system of other degrees of freedom, but we can't just move Hoel's argument to that larger system, because the same problem applies to it (perhaps more so, because now either the matrix or the external information is more complex).»

              Perhaps even this doesn't engage with or misunderstands your approach too much for it to be fruitful to engage with it? I always thought my reach into Axiomatic QFT (or more generally, any algebra of observables approach) would likely be too much in my own way of thinking for you, but I'm curious whether you think this later thought illuminates your formalism.

              Hey Peter - I definitely wasn't referring to anyone in particular. I didn't want to spam Scott's thread with replies to questions, so I was honest that I wouldn't be answering everyone. I'm happy to answer anything posted here, however.

              To your question about whether physical systems are separable enough for coarse-graining (if I understood you correctly): there's no requirement that groupings don't interact, or that they stay steady across time. But you're right in that for the examples everything is pretty stationary. It's interesting to think about what could happen. Groupings could change moment to moment, but this gets more complicated because there are also spatiotemporal groupings. I'm not sure off the top of mind if it applies, but there's an interesting thing called a Markov blanket that might be relevant here.

              As you suggest, it is possible to use something like physical proximity in the calculations. But I'd view it as a heuristic aspect to the calculation, not something to directly weight the result by. However, the theory is physics-neutral so perhaps something about our physics would need to make that true (just throwing stuff out there).

              All the best! Thanks for reaching out - Erik