Correction: I should know by now not to trust my memory. Einstein's "stubbornly persistent illusion" remark was on the death of his friend Michele Besso, not Godel.
Tom
Recognising Top-Down Causation by George F. R. Ellis
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Is the quantum gravity problem or pseudoproblem?
Dear George,
After initially struggling with the idea, I've been thinking a bit about how your top-down causation idea might look from the perspective of nonmanifold models of fundamental spacetime structure that emphasize the role of causality. It seems that top-down causation might provide an interesting new perspective on such models. For definiteness and simplicity, I use Rafael Sorkin's causal sets approach as an example.
Causal sets, as currently conceived, are by definition purely bottom-up at the classical level. Causality is modeled as an irreflexive, acyclic, interval-finite binary relation on a set, whose elements are explicitly identified as "events." Since causal structure alone is not sufficient to recover a metric, each element is assigned one fundamental volume unit. Sorkin abbreviates this with the phrase, "order plus number equals geometry." This is a special case of what I call the causal metric hypothesis.
In the context of classical spacetime, top-down causation might be summarized by the statement, "causal relationships among subsets of spacetime are not completely reducible to causal relations among their constituent events." In this context, the abstract causal structure exists not at the level of spacetime itself, but at the level of the power set of classical spacetime, i.e., the set whose elements are subsets of spacetime. Discrete models very similar to causal sets may still be employed, with the exception that the elements would correspond not to events, but to families of events. Two-way relationships would also come into play.
Initially this idea bothered me because of locality issues, but such a model need not violate conventional classical locality, provided that appropriate constraints involving high-level and low-level relations are satisfied.
This idea is interesting to me for the following reasons:
1. The arguments for top-down causation presented by you and others are rather convincing, and one would like to incorporate such considerations into approaches to "fundamental theories," particularly those emphasizing causality.
2. One of the principal difficulties for "pure causal theories" is their parsimony; it is not clear that they contain enough structure to recover established physics. Top-down causation employed as I described (i.e. power-set relations) provides "extra structure" without "extra hypotheses" in the sense that one is still working with the same (or similar) abstract mathematical objects. It is the interpretation of the "elements" and "relations" that becomes more general. In particular, the causal metric hypothesis still applies, although not in the form "order plus number equals geometry."
3. There is considerable precedent, at least in mathematics, for this type of generalization. For example, Grothendieck's approach to algebraic geometry involves "higher-dimensional points" corresponding to subvarieties of algebraic varieties, and the explicit consideration of these points gives the scheme structure, which has considerable advantages. In particular, the scheme structure is consistent with the variety structure but brings to light "hidden information." This is analogous to the manner in which higher-level causal structure is consistent with lower-level structure (e.g. it does not violate locality), but contains important information that might be essential in recovering established physics.
4. As far as I know, this approach has not yet been explicitly developed.
I'd appreciate any thoughts you might have on this. Take care,
Ben
Over on the Rationally Speaking blog, Massimo Pigliucci has an interesting posting: Essays on emergence, part I , including a link to a a very interesting paper by Robert Batterman.
An ensuing interaction with Sean Carroll includes the following post by Carroll:
"Sean CarrollOctober 11, 2012 4:46 PM
I don't know what it would mean to "derived physical reductionism," nor do I think that qualitatively new emergent behavior is absent from Newton's laws (depending on definitions). The point is simply that Newton's laws, applied to a set of particles, gives you a closed set of equations. With appropriate initial conditions, the solutions are unique. There is no room for additional causal influence. The equations give unique answers; you can't get a different answer without violating the equations.
There is an important and interesting discussion to be had about emergence, and it has nothing to do with being unable to predict behavior from component parts, nor with new "causal powers." "
Pigliuicci's response (October 12, 2012 8:25 AM) includes, "I find that argument wholly unconvincing. First, Newtonian laws are known to be approximations, so clearly there *is* room, in a sense. Second, those laws tell you precisely nothing about all sorts of complex systems, like the temperature of phase transitions of water, or the functioning of ecosystems, so to claim (global) causal closure seems strange."
He does not however make the points I make in Part 6 of my essay, including particularly the point I make in my posting here on Sep. 17, 2012 @ 18:15 GMT:
" The mechanism of superconductivity cannot be derived in a purely bottom up way, as emphasized by Nobel Prize winner Bob Laughlin; see the Appendix to my essay for Laughlin's statement in this regard. The reason is that existence of the Cooper pairs necessary for superconductivity is contingent on the nature of the ion lattice, which is at a higher level of description than that of the pairs; they would not exist without this emergent structure."
These arguments, it seems to me, completely undermine Sean's billiard ball point of view, based in Newtonian physics. They provide good reasons that top down causation can take place in computers and the brain without contradicting the underlying physics. And that is why the existence of computers such as the one you are using at this moment is possible, without invoking magic. It is the result of top down causation from the human mind into the physical world.
George
Tom,
thanks for all that. I'll have to take time to digest it - I'm travelling at the moment (will be in Boston Sunday evening to Tuesday afternoon before flying home via New York) and have to do other stuff.
But yes Bar Yam seems really interesting: much deeper than Per Bak, who tries to construct stuff in a purely bottom up way. There's a strict ceiling to what that can achieve. Sand piles, bird flocks, reaction-diffusion patterns, etc. are a step on the way but they are not the real thing.
George
Hi Ben
I think that is an exciting possibility to pursue. Please note that it might relate also to my posting of Oct. 2, 2012 @ 07:24 GMT. I am a fan of Causal Set Theory, and trying to develop it the way you suggest would be a great project.
Maybe there is a Wheeler-like dictum here: "Part from whole!"
George
Thanks, George. Perhaps you will find time to say hello to Bar-Yam yourself, while in Boston. And it's a particularly great time to be in New England -- the Fall leaves should be peaking in color about now.
Have a pleasant flight.
Tom
Dear George Ellis,
As the thermo-dynamics of universe prevents the universe from gravitational collapse, gravity is the causation that is descriptive in top-to-bottom approach, in that the thermo-dynamics of the matters of universe and the gravity of universe are in balance. This implies Homeomorphic segmental-fluctuations of universe in causality cycles and thus Holarchial clustering of matters is ascribed in Coherently-cyclic cluster-matter paradigm of universe. In this paradigm the flow of time that correlates the dynamics of matters of universe, is in references with the discrete-times that emerge from Eigen-rotational quanta of strings in the Holarchy of universe, in that the nature of reference-time is expressional as cyclic.
With best wishes
Jayakar
I've contributed the following further comment over there:
Sure the lattice emerges according to well defined bottom up principles. Once this has happened, it then exists as an entity at a higher level of scale than the particles out of which it is composed (you have to use quite different variables to describe this lattice structure than you do to describe the particles: these variables are not reducible to lower level variables). The key point is that until it has so emerged, no Cooper pairs are possible. Once it has emerged, they can come into existence. Thus it is the very existence of the higher level structure (the lattice) that enables the lower level constituent entities (the Cooper pairs) to come into being.
Sure you can work out in a bottom up way what effects the Cooper pairs mediate. But they can't act in a bottom-up way to create any physical effects at all until they exist - and their existence is contingent on the detailed nature of the higher level structure. That's a clear case of the causal effects of context on lower levels - that is, by any reasonable definition, causation flowing downwards in the hierarchy of structure. But if you dislike the word "causation", just call it a contextual effect,
It is because superconductivity depends on this mechanism that you can't derive it in a purely bottom up way. This is stated strongly by Laughlin in his Nobel Prize lecture as follows:
"One of my favourite times in the academic year occurs in early spring when I give my class of extremely bright graduate students, who have mastered quantum mechanics but are otherwise unsuspecting and innocent, a take-home exam in which they are asked to deduce superfluidity from first principles. There is no doubt a very special place in hell being reserved for me at this very moment for this mean trick, for the task is impossible. Superfluidity, like the fractional Hall effect, is an emergent phenomenon - a low-energy collective effect of huge numbers of particles that cannot be deduced from the microscopic equations of motion in a rigorous way, and that disappears completely when the system is taken apart ... The students feel betrayed and hurt by this experience because they have been trained to think in reductionist terms and thus to believe that everything that is not amenable to such thinking is unimportant. But nature is much more heartless than I am, and those students who stay in physics long enough to seriously confront the experimental record eventually come to understand that the reductionist idea is wrong a great deal of the time, and perhaps always... The world is full of things for which one's understanding, i.e. one's ability to predict what will happen in an experiment, is degraded by taking the system apart, including most delightfully the standard model of elementary particles itself."
[R B Laughlin (1999): `Fractional Quantisation'. Reviews of Modern Physics 71: 863-874]
The same basic effect - lower level entities only exist by courtesy of the detailed nature of the higher level structure - occurs all over the place in biology, for example in symbiosis, in ecosystems, and in the case of say blood cells in the human body.
George
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Prof. Ellis, are physics and causation fundamentally limited to vision or visual experience?
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Hi,
Your local/global variable example is a really good illustration of a really good idea. Forgive me if I'm preaching to the choir: Your illustration reminds me specifically of plain old thread synchronization, where a child thread's code executes (or not) based on the state of some parent-owned (non-local) lock variable with atomic read/write operations. Adding in dozens or hundreds of child threads all sharing the same lock, and it reminds me of one giant, complicated dance between the parent thread and the child threads, where both top-down and bottom-up causation play a critically important role (the children not only read the lock, they write to it). It is unusual for me to catch someone reveling so much in such a thing, and so I thought I'd try to share -- this computer stuff is fun and wonderful when you look at it the right way.
- Shawn
If you want to understand what physics is about, you should read a basic textbook on the subject. I suggest Conceptual Physics by Paul Hewitt. The chapter headings will give you an idea what basic physics covers:
1. Mechanics; 2. Properties of matter; 3. Heat; 4. Sound; 5: Electricity and magnetism; 6. Light; 7. Atomic and nuclear physics; 8. Relativity.
A more advanced text would include chapters on statistical physics and quantum physics, as well as topics such as plasma physics. Specialised texts will deal with biophysics, which is relevant to vision, but it is a very small part of physics.
In response to a post by Peter Bokulich over on Massimo's blog (see my post here of Oct. 13, 2012 @ 08:53 GMT), I've now posted the following response:
Hi Peter,
I appreciate your approach. The key issue for me is that you agree that there are real high-level causes. Good. I agree that given the lower level dispositions of states resulting from those higher causes, the lower level physics gives a complete causal account; but overall, the causal account is incomplete without taking into account the way higher level causes lead to those specific lower level dispositions. A good example is a digital computer, where an engineering computation is taking place because a) C++ has been loaded as the current high level software, b) simulation software incorporating the relevant finite element algorithms has also been loaded, and c) specific initial data to run the relevant algorithms has been entered via the keyboard. The outcome that occurs is then a unique result of the lower level electronic states resulting from a), b) and c). However there is no way that the numerical algorithms embodied in the patterns of lower level excited states can be derived in a purely bottom up way from the underlying physics. It's a category error to assume that purely physical processes can lead to existence of any such algorithms.
Whether we agree on causation or not depends on the weight you put on the words "nothing but" in the phrase "are nothing but constrained, structured, microphysical causal features". I think the explanation above says it's a mistake to use the phrase "nothing but", because significant other causal effects are at work. Part of the problem for a true reductionist is that the electronic gate states are "nothing but" specific states of quarks and electrons; and these again are "nothing but" excitations of superstrings - if they exist, which may or may not be the case. Which level are you claiming is the true microphysical level? The embarrassment for a true reductionist is that we don't know what the lowest level structure is - we don't have any viable theory for the bottom-most physical states. Thus if we take your phrase at face value, all physics is "nothing but" we know not what. Why not leave those words out?
As to quantum indeterminism: it plays two significant roles. Firstly, it ensures that outcomes on Earth today cannot have been uniquely determined by initial conditions in the early universe, inter alia because cosmic rays have altered our genetic history significantly, and emission of a cosmic ray photon is (assuming we believe standard quantum physics) an inherently indeterminate process. The complex structures that exist have come into existence through emergent processes with their own logic that is independent of the underlying physics. Secondly, the most important such process is adaptive selection, which is guided by selection effects operating in a specific ecological context; and that is an inherently top-down process (see "Natural Selection and Multi-Level Causation" by MartÃnez and Moya in Volume 3 (2011) of Philosophy and Theory in Biology, available from Massimo's website). In the example just given, quantum uncertainty plays a key role in providing the repertoire of variant states on which adaptive selection can operate (without the cosmic rays, there would have been fewer such states to choose from). The conjecture is that perhaps something similar might be true in the way the brain works. But that's very hypothetical.
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Hi George,
i always enjoy your insightfull comments here. Your example with the digital computer is, as always, very interesting. Some years ago i answered to Florin Moldoveanu here at fqxi in the same way. The question was if nature is as deterministic as maths, should mean, if nature is strictly deterministic or not and if there is something like a proof for this strict determinism. I argued that a strict determinism is a closed system as for example the Godel's incompleteness theorem and therefore - if strict determinism is true - this system cannot be consistent in every detail. What follows from this is, that it is inconsistent to try to achieve a proof of strict determinism via strictly deterministic procedures (for example via maths).
Florin replied that a computer - and therefore the underlying maths/logics has to be strictly deterministic. I replied that it isn't guaranteed at all that for the same input and output data of a computer the QM microdynamics that lead to the same macroscopic results must necessarily be the same.
A programming language like C++ surely is a man-made construct. It is based on logic, implemented into the hardware of the PC, but without the possibility of humans to exist, there would be no computers and hence no example of top-down causation to consider here. If one argues this way, we arrive at the well known anthropocentric questions about wether there is some special, "unphysical", determinism-contradicting entity in nature that enables consciousness, free will and so on or not. the main point for me here seems to be that, again there is no way to prove in a strict and deterministic way that the fact that there are observers possible in nature is a result of a strict determinism in nature.
What i assume to be fundamental, - as i outlined in my essay here - is, that those regularily re-appearing undecidabilities (determinism/indeterminism, free will/subjective lack of knowledge, completeness/consistence, which-way information/interference, non-locality/non-reality etc.) stem from a CLOSED SYSTEM itself. This system i have labeled with "logic of opposites" - it doesn't allow -due to its inherent rules- the possibility of another logic that isn't grounded on mutually exclusive possibilities. This logic of opposites (Boolean logic) doesn't allow to contrast it with something that hasn't mutually exclusive features. Because this would contradict that there are only mutually exclusive features possible at all. The "something" i spoke of is surely close to QM and its features like superposition. Mathematically spoken, it is simply the abandoning of completeness in favour of having consistence and truth as the fundamental features of reality. If one considers the problem of mutually exclusive possibilities concerning the scientific/philosphical questions raised above, then it is possible to gain an insight that nature has some top-down, acausal features. Because by giving up the completeness criterion, we at the same time give up the "strictly deterministic" criterion. This is possible not due to arbitrary wishes but due to the consideration of systems in maths, cognition, complexity theory and so on. It is always the same pattern there: By giving up the assumption of closed systems, we gain - as Godel has proven on a deterministic basis BUT with some considerations to the necessity and stronger meaning of consistence over completeness - consistence and truth must be more fundamental than completeness. Otherwise sience would state itself as an inconsistent system and all our lines of reasoning would be highly questionable right from the beginning. That the latter could be indeed true in nature, is at least in my opinion, very unlikely, because of the huge success in science, physics and the human mind to decipher nature.
The counter-argument of a strict determinism then can only be one that assumes a huge "coincidence" out of a somewhat wild "chaos". I assume the former to be true - on the grounds of my essay's considerations, and the latter to be absurd, inconsistent and illogical from the very start.
"Coincidences" for me are then just another term to explain that QM-dynamics is fundamentally about generating consistence in nature - a result that i consider as somewhat very fundamental and meaningfull.
Best wishes,
Stefan
Hi Stefan
Thanks for that. Well the deep issue you raise is, "Is the universe causally closed?" My answer is, if you mean only the physical universe, the answer is no! Ok hackles are rising and squeals of protest fill the air, but please hear me out.
This depends on issues of ontology: What kinds of thing exist? I addressed this in my paper True Complexity and its Associated Ontology. As in my essay, I define something as existing if it either (i) is a material entity, or (ii) has an undeniable causal effect on material entities. You'll find various non-physical examples there, but the key one for present purposes is:
Mathematics and logic: A Platonic world of (abstract) realities that are discovered by human investigation but are independent of human existence. They are not embodied in physical form, but can have causal effects in the physical world.
Roger Penrose [The Large, The Small, and the Human Mind], Alain Connes, and many others have argued for such a Platonic world of mathematics, which is not invented but humans - its nature is discovered by them (e.g. we did not wish to discover that the square root of 2 is irrational: we were forced to acknowledge that this is a mathematical fact through a process of logical investigation). How does it have a causal influence in the physical world? Through the human mind, which uses calculus and facts such as the value of pi as the basis for engineering calculations.
The relevance to my previous post is that there is also space of all possible logical algorithms out there, waiting to be discovered. This is the ultimate source of computer algorithms. They become causally effective once discovered and implemented, but their existence is independent of such discovery. They are independent of time and place and culture, and (like mathematical truths) can be discovered by any intelligent beings anywhere in the universe. Thus for example there is a finite number of ways to sort a column of letters or numbers into ascending order. Any algorithm you may employ for this purpose will necessarily be one of this finite set of algorithms (e.g. Quicksort). They have causal power in terms of events in the physical world, because they lead to printouts of sorted numbers (which cannot exist if one does not employ one of these algorithms).
So the world of material entities is not causally closed: it can be causally affected by abstract entities, such as algorithms, which underlie all computer operation. This is an existence proof for causally effective non-physical entities. There are other kinds of such entities , e.g. human plans for building a Jumbo jet airliner. My paper cited above discusses them.
George
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George,
You have managed to engage and referee a very spirited and tenacious debate about top down causality, but doesn't it eventually have to lead to larger issues in how the discipline of physics is currently structured? Since bottom up causality is primarily based on reductionism, wouldn't the opposite be wholism? By this, I mean "oneness," as opposed to the "one" it is usually reduced to. As Stefan explained above, consistence rather than completeness. I would describe it as the network being foundational to the node, not the other way around. As I argue on occasion, when we add, we are adding the sets and coming up with a larger set, rather than adding the contents of the sets. Say 2 sets of 5 apples = 1 set of ten apples. If we actually added the apples together, it would be applesauce. More directly, all the parts of our bodies and our lives add up to a particular person. I think in this way, top down causality seems quite obvious. We can have infinite complexity, but sometimes the complex becomes simple again, much like the cycle of the chicken and the egg. Physics is currently dissecting the details of the details of the details, but I find that when I offer up ways different features may be different descriptions of the same thing, it seems like I'm stepping on toes to make such connections. For example, in a recent conversation I compared time and temperature to frequency and amplitude and the rejection was automatic.
I guess my point is as I stated to begin with, doesn't a full discussion of top down causality lead to re-examining the structure of physics to date?
A related point would be; Wouldn't true emergence mean the principles of math are as emergent as the structure they inform. Simply because they are repetitious only means the same processes are being followed. As Stephan Wolfram said; It would take a computer the size of the universe to compute the universe. I think Robert H McEachern made some interesting observations regarding this in his entry.
That would be infinite complexity, so to take it the other direction, towards the absolute, if we had nothing, consequently there would be no computability. So to the extent we have bottom up emergence, we have top down structural/mathematical integrity, ie, Stefan's consistence.
Keep up the good work.
Hi John
yes I agree with you about physics - and will be pursuing this. I'm just reading Robert Rosen's very deep book "Life Itself" which argues that causation is much wider than usually considered in physics - indeed that reductionist physics is a special case of the much wider kind of causation that operates in the real universe.
He also looks at the case of mathematics and how it fits in. You might enjoy this book.
Just one point: I avoid the word "infinite" in this context. This is needed as a mathematical concept, but does not occur in physical reality (Hilbert). No real causal system is infinite.
George
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George,
Yes, emergence is like stepping out of a closed and ordered space, into one that is open and unconfined.
Instead of infinite, how about "continuous?"
Georgina and I have been discussing the dichotomy of information as static and energy/reality as dynamic, in which I made the following point;
"We live in a very dynamic reality and it's that reality we perceive. When we try to understand it, we create these conceptually static models, such as Julian's triangles. Or saying 1+1=2. Then because our most distilled and concentrated knowledge is impervious to change, or we wouldn't consider it fundamental if it was subject to change, then we assume reality must be also fundamentally static. It is a form of circular logic."
I thought that might also apply to defining what is known and what is understood.
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Dear Dr. Ellis,
My opinion:
Top down or bottom up causations in the universe are not separate choices although they are presently ingrained as such in theoretical physics. I say this because theoretical physicists invented bottom up causes in support of their belief in reductionism. It is indequate by virtue of its lack of purpose which amounts to, as the same thing, lack of explanation of cause. No one knew then, during the guesswork of early theory, what is cause. It was recognized that the existence of effects required the existence of cause as part of theoretical physics, although, cause was not itself observable. Still today no one knows what is cause.
The universe evolved by means of bottom up processes because it contained, right from the beginning in potential form, the top down causation properties necessary to allow for the evolution of the universe to follow an effectual, prescribed for, bottom up process. Neither the fog of complexity nor observed feedback loops changes or obscures this requirement. Progress is possible if theoretical physicists remove the invented seperate mechanical causes of theoretical physics.
Theory can be developed with just one cause if the theorist will put forward a model of cause, to be used in their modeling equations, that is directly referenced to empirical evidence. In my essay, it is shown that the first step in this process is to defined mass in the same terms as is its evidence expressed. Its evidence is changes in patterns of changes of velocity of objects. Changes of velocity are expressed in units of seconds and meters.
Theoretical physicists should recognize and seek the cause, at least in name, for the existence of interpretation of information. This effort cannot be satisfied by efficiently cataloguing information. The cataloguing of effects as information, especially that which results from empirical evidence in the form of differences in patterns in changes of velocity, should not be put forward as explaining cause. Cause is its opposite. Cause is the meaningful, purpose filled interpretation, at all levels of operation of the universe, of information.
What should be avoided at all times during the development of theory is the tendency to accept givens, beyond the inescapable First one, whether proclaimed to be fundamental forces or its belated appearance called emergent properties. Properties appear because they are provided for. Lack of explanation is no justification for abruptly introducing the births of new properties after the beginning of the universe.
James
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James,
thanks for that, you are looking at deep issues here.
"Properties appear because they are provided for." - Indeed. This is through what I call Possibility Spaces, see the link I give in my posting of Oct. 22, 2012 @ 12:29 GMT. The deep issue is why these possibility spaces are what they are; the complication is that they are interrelated, for example the possibility space of physics underlies the possibility space of biology.
As to cause, as I mentioned in my last post, Robert Rosen has a deep analysis of this concept in his book Life Itself.
George