Examples of downward causation?


[Note: updated 04/08/07 with examples from Carl Craver's paper.]

I just culled together a bunch of putative examples of downward causation, some from advocates, some from detractors. Particularly interesting and promising is the article by Robert Bishop, Downward causation in fluid convection, and Bechtel/Craver’s article  Top-down causation without top-down causes, for which brief quotes will not do justice. (Note Craver contributes on this forum: nice paper Carl!)  I thought it would be helpful to have these examples here to gnaw on. Most people think top-down causation is just poppycock, but perhaps some of these examples (and especially Bishop’s paper) will help reveal that there is an extension to the term ‘downward causation’, even if the term is ill-chosen. Frankly, I am not sure what I think.

From http://pespmc1.vub.ac.be/DOWNCAUS.html:


Let me illustrate this with an example. It is well-known that snow
crystals have a strict 6-fold symmetry, but at the same time that each
crystal has a unique symmetric shape. The symmetry of the crystal
(whole) is clearly determined by the physico-chemical properties of the
water molecules which constitute it. But on the other hand, the shape
of the complete crystal is not determined by the molecules. Once a
shape has been formed, though, the molecules in the crystal are
constrained: they can only be present at particular places allowed in
the symmetric crystalline shape. The whole (crystal) constrains or
“causes” the positions of the parts (molecules).

From http://www.lehigh.edu/~mhb0/physicalemergence.pdf:

Certainly, there seems to be no shortage of examples of downward causation. Certain psychological states (e.g., prolonged anxiety, embarrassment) can cause physiological effects (heightened blood pressure, eczema, blushing) in a human body. McClelland’s experimental studies of human motivation showed that affiliative motives (the capacity to love and be loved) promote better health. For example, the salivary immunoglobulin A levels of subjects were significantly increased when they view a film of Mother Teresa designed to arouse affiliative motives.30 Again, the functional molecules (DNA, proteins, fatty acids, etc.) within a cell are fabricated within internal processes of the cell itself; they are generated through the web of interactions of the whole system. That downward causation occurs is a fact; how to understand the phenomenon is the contentious issue.

From Roger Sperry at http://www.noetic.org/publications/review/issue04/r04_Sperry.html:

As such an illustration, consider a molecule in an airplane leaving Los
Angeles for New York. Our molecule, say in the water tank or anywhere
in the structure, may be jostled or held by its neighbors—but, these
lower level actions are relatively trivial compared to the movement
across the country. If one is plotting the space-time trajectory of the
given molecule, those features governed from above by the higher
properties of the plane as a whole make those governed at the lower
molecular level insignificant by comparison.


The same principle applies throughout nature at all levels. The atoms
and molecules of our biosphere, for example, are moved around, not so
much by atomic and molecular forces as by the higher forces of the
varied organisms and other entities in which they are embedded. The
atomic, molecular and other micro forces are continuously active but at
the same time they are enveloped, submerged, superseded, “hauled and
pushed around” by, or ‘supervened” by an infinite variety of other
higher molar properties of the systems and entities in which the micro
elements are embedded—without interfering with the physico-chemical
activity of lower levels.

Someone else discussing a different Sperry example, one from the 1960s (found at http://www.nbi.dk/~emmeche/coPubl/2000d.le3DC.v4b.html):


One of the central examples given by Sperry (1969) is quite simple: a
wheel running downhill. None of the single molecules constituting the
wheel or gravity’s pull on them are sufficient to explain the rolling
movement. To explain this one must recur to the higher level at which
the form of the wheel becomes conceivable.


Just one little snippet from the Bishop paper, where he uses the example of fluid convection patterns as a nice case study. This is one example where I’m not sure the Bechtel/Craver framework will work (I’m not sure it won’t either). Again, this paper is at
http://philsci-archive.pitt.edu/archive/00002933/01/Downward.pdf :


Worries about [causal closure] normally arise in the context of philosophy of mind, but in the context
of Rayleigh-Bénard convection, higher-level physical structures (Bénard cells) constrain and modify the behaviors of the lower-level system constituents (fluid elements).

And two nice examples from the Craver/Bechtel paper (I left these out by accident in my original post), which can be found at http://philosophyfaculty.ucsd.edu/faculty/pschurchland/classes/cs200/topdown.pdf:

Ignatius, with much labor and strain to his valve, coaxed his hotdog cart to the corner. The cart was full of hotdogs. What caused the hotdogs (and the molecules in the hotdogs, and the atoms comprising the molecules, and so on) to arrive at the corner? Ignatius. The hotdogs (and the molecules, etc.) were part of the cart that he labored to bring to the corner, and when the cart arrived, so did the hotdogs (and their molecular constituents[)].

and:

Hal steps onto the court, serves, and so begins the tennis match. Very quickly, blood borne glucose is taken up through the cell membrane. Once inside, it is phosphorylated and bound into molecules of hexosediphosphate. This is not a case of simply being carried along for the ride. Hal’s muscle cells are, it is true, carried along when he swings his racket. But Hal’s tennis-playing also alters the behavior of innumerable biochemical pathways and cellular mechanisms that are involved in his tennis playing, both in the short-term and in the long-term. Why did Hal’s cells start using more glucose (i.e., binding glucose into molecules of hexosediphosphate)? Because Hal started to play tennis. Similar stories could be told about Hal’s respiratory mechanisms, visual system, and many others besides. Changing the behavior of the mechanism as a whole changed the activities of its components. It may be appropriate to say that the components are along for the ride, but if so, this is a different, more active, kind of ride than Ignatius’s hotdogs received. Hal’s glucoregulatory mechanisms are enlisted in the ride.

05. April 2007 by Eric Thomson
Categories: Metaphysics, Philosophy of Science | 37 comments

Comments (37)

  1. Thanks for this nice list of examples. It seems to me that they can all be treated within Bechtel and Craver’s mechanistic framework (in the paper you cite), without involving anything spooky. I agree with you that their paper is very nice.

  2. Gualtiero: I just went through the Bishop paper more closely, and on further inspection it kind of falls apart, with half of the points including hand-waving obfuscation, and half vanilla “along for the ride” Sperry-wheel type example. I expect someone from the Kim camp will be able to easily dismantle the paper. Also, to the extent that Carl’s framework can gracefully handle Sperry wheeel type examples, it should easily be able to subsume Bishop’s tendentious paper.

    While his metaphysical conclusions are bologny, I think Bishop has provided a service at the least by providing an example (convection cells) that is well worked out quantitatively, a kind of philosophical model system for Sperry-style top-down causation.

  3. Hi all, I just want to say that I think the Bishop paper, and other work by him, is indeed very interesting.

    And I actually do not think that such a position collapses quite as easily as is commonly thought when pressed on the metaphysics. But that is a position I have pressed over a number of years in various papers, the most recent being a paper on Samuel Alexander that just came out in Synthese. I think that the kind of metaphysical position outlined in my papers might be a theoretical framework that can be used underwrite Bishop’s claims, and I think his kind of work on the case may provide an example to bolster the metaphysical variant of physicalism I outline in theory. (Though I should note that I am not endorsing any of his claims about particular cases, mainly because Bishop deals with real examples in all their richness and it takes a while to evaluate what to say about such examples).

    There is more that might be said, particularly about the need to understand the richer kinds of reductionism that Bishop is actually trying to engage. But I have to get back to writing.

    Mainly, I just wanted to say I found Bishop’s stuff quite stimulating and refreshing. Sorry for the lack of more argument for that, very best, Carl

  4. Carl: your paper looks very good: I’ve read the first half, and it is an interesting and fun exegesis of Alexander. I’ve already learned quite a bit.

    Bishop’s paper, OTOH, has so much hype and jargon, with such a tendentious reading of the physics, that it is hard to take seriously. The convection cells, which while interesting and a good model system, just don’t provide any plausibility for the type of top-down causation he wants.

    If I were to write a critique, it would be hard to know where to start. Perhaps page 2 with his odd claim that nonlinearity implies you need a ‘nonlocal’ or ‘global’ description of the system. That’s on page 2. This is misleading, confused, and if shored up to be coherent, probably false. But it is embedded in enough techy-sounding mathematical jargon that the average philosopher won’t know what to make of it, and will likely just believe him, be bowled over by his technical jargon. The rest of the paper is full of similarly glib and misleading readings of the technical material.

    Unfortunately, the amount of time it would take to fully respond to that paper doesn’t justify the endeavor. Perhaps a philosopher with some physics background will do it. But suffice to say it is just like the Sperry wheel case: the water molecules are ‘along for the ride’, and Craver/Bechtel do an interesting job with such cases.

    I’m a little embarassed that I initially recommended the paper. It doesn’t deserve the press I gave it.

  5. Carl: your paper looks very good: I’ve read the first half, and it is an interesting and fun exegesis of Alexander. I’ve already learned quite a bit.

    Bishop’s paper, OTOH, has so much hype and jargon, with such a tendentious reading of the physics, that it is hard to take seriously. The convection cells, which while interesting and a good model system, provide zero plausibility for the type of top-down causation he wants.

    If I were to write a critique, it would be hard to know where to start. Perhaps page 2 with his odd claim that nonlinearity implies you need a ‘nonlocal’ or ‘global’ description of the system. This is misleading, confused, and if shored up to be coherent, probably false. But it is embedded in enough techy-sounding mathematical jargon that the average philosopher won’t know what to make of it, and will likely just believe him, be bowled over by his technical jargon. The rest of the paper is full of similarly glib and misleading readings of the technical material.

    Unfortunately, the amount of time it would take to fully respond to that paper, to show exactly why he is being glib and misleading, doesn’t justify the endeavor. Perhaps a philosopher with some physics background will do it. But suffice to say it is just like the Sperry wheel case: the water molecules are ‘along for the ride’, and Craver/Bechtel do an interesting job with such cases.

    I’m a little embarassed that I initially recommended the paper. It doesn’t deserve the press I gave it.

  6. I read the Bishop (B) and the Craver/Bechtel (CB) papers.

    I found the CB to be clear and compelling. I appreciate their defining their specific notion of “level” before discussing whether levels can interact causally. I think I can say that I agree with every claim in the paper. I just have two quibbles for your consideration.

    (1) The title is misleading, because the paper argues that higher levels do not act causally on lower levels. (For this reason it may also be misleading to quote their example as an example of top-down causation advanced in the literature, since they argue that is is NOT.)

    (2) My other concern with CB is that they limit their discussion to cases involving no “strong emergence.” Maybe it’s not really fair of me to complain that I wished they had written a different article, and they were justified in that they focused on the tractable part of the problem…but, when people like Bishop talk about top-down causation, they are explicitly thinking in terms of strong emergence, where there is a “global-to-local (‘downward’) determinative influence on the dynamics of the components….”

    I don’t understand the motivation for retaining the phrase “top-down causation” in a scenario where by assumption it can never exist.

    Still, I think the BC recipe clearly shows why Bishop is wrong to claim that convection cells as described by the given dynamical equations exhibit strong emergence or top-down causation. The higher-level cells and their dynamics are entirely constituted by the lower-level parts, rather than somehow “acting back on the parts.”

    B’s appeals to (putative) empirical evidence about top-down causation in chemistry and thermodynamics are misplaced here, because his paper is about whether the Rayleigh-Benard mathematical model can exhibit top-down causation. Even if we discover that actual fluid dynamics exhibit strongly emergent top-down causal effects, that will only mean that the mathematical model is incorrect or incomplete.

    But the mathematical model is specified completely in terms of local quantities and interactions, despite B’s protestations to the contrary. The dynamical equations are DIFFERENTIAL equations. That means they are completely specified in terms of local interactions between infinitesimally separated points.

    Yes, boundary conditions are important: they act locally at the boundaries. Yes, there can be degeneracy in the solutions to the mathematical model–this only means that the model is an idealization. An ideal pencil balanced on its tip has an infinite degeneracy, but we don’t need to claim that top-down causes account for its falling this way rather than the other in real life. Yes, there are long-range forces–but the dynamics at any point depend only on the force (field strength) at that point.

    Actually I think that strongly emergent top-down causation cannot occur, in ANY classical model, because classical mechanics is always completely local. Would CB agree?

  7. Hi,

    I tried to post a comment yesterday, but apparently it did not come trough -or mr. Adminstrator has deleted it (only kidding…)

    However, all I wanted to say was that I agree when Eric says “Perhaps page 2 with his odd claim that nonlinearity implies you need a ‘nonlocal’ or ‘global’ description of the system. This is misleading, confused, and if shored up to be coherent, probably false. agree with this line “

    Yes, sir – I agree. But could you, please, tell briefly why you see that “misleading, confused and… probably false”. (Oh, this is almost like a poem or something. Wicked, as they say in England.)

  8. Anna-Mari:

    On page 2 he says:
    [In nonlinear systems] some
    particular global or nonlocal description is required taking into account that individual
    constituents cannot be fully characterized without reference to larger-scale structures of the
    system.

    I have a couple of problems with this. For one, it is unclear, so hard to evaluate (what is a global variable?). Let’s assume he means global in some spatial sense, as in distributed. But if this is what he means, consider the Hodgkin Huxely equations that capture the electrical behavior of neurons. There is no nonlocal or global variable in the HH equations. Mathematically, ou can have a single point in space that displays all the neuronal dynamics, the interesting nonlinearities.

    Also, beware of assuming that linear equations must be local (his above claim doesn’t imply this, but it is just something to be aware of): you can have nonlocal but linear Schrodinger equation.

    He then brings up the Hamiltonian as if that is essential to nonlinear systems, but the Hamiltonian is a specialized bit of advanced classical mechanics. The HH is nonlinear and is not equivalent to a Hamiltonian (in any obvious way, and not in the minds of any neuroscientist).

  9. Hi Eric,

    I am sorry it took so long to answer to your interesting reply. To be honest, I do not know much about these issues, and I am thus a way out of my league, as you would say. However, the impression I have is that this “non-linearity implies globality” is one of popular myths. People seem to be repeating this same “mantra” over and over again. But you seem to disagree (and so do some neural net modelers in their writings).

    However, a request fo clarification. Is your argument that since the specific non-linear mathematical equations do not have such variables that would be spatially (or whatever) “local” or “global”, it is not meaningful to argue that the non-linearity implies globality? But can it be argued, then, that the non-linearity implies locality either? Or is this precisely your point (and the reason for the “Ode to Negativity” written by E. Thomsom as I have started to call the “misleading, confusing… and probably false”- sentence)?

    I was also thinking that, whether it completely ruled out that there would be some other parts of certain mathematical model, in which for instance HH equations are playing role, would imply that HH equations + those other equations would justify the argument from non-linearity to globality/locality? I have no idea what these equations could be… I am just playing with the idea.

    a

  10. Anna-Mari: my point is that linearity/nonlinearity is orthogonal to global/local. You can have all four combinations of the two divisions. For instance, you could add to HH a new equation that did have nonlocality built in (and that equation could be linear or nonlinear).

    Note this confusion seems to have important consequences. For one, it appears he fails to notice that his star pupil, the convection equations, have no global variables: everything is local in that classical model.

  11. Eric… What an earth is “the convection equations”? I am sorry (and a bit embarrassed), but I really do not know. Should I know? Help…
    What are these equations/ what are they used for?

  12. Eric… What an earth are “the convection equations”? I am sorry (and a bit embarrassed), but I really do not know. Should I know? Help…
    What are these equations/ what are they used for?

  13. They are the equations that he uses in the paper as the model system for rigorously studying the question of top-down causation. They describe fluid flow in the presence of head on the boundaries (sometimes you get very interesting flow fields, such as circular ‘cells’ of cycling water). It’s all in his paper.

  14. ..

  15. Eric, thanks for the clarification. Very kind of you. I have to admit that I tried to read the Bishop-paper. But (as you mentioned in your “Ode to Negativity”) the mathematical “jargon” makes the paper very difficult to read for a reader without any mathematical background. Thus I did read the first sentences and then I just started think that “isn´t that a nice dot in that equation”- things… But, since we are apparently sinking into it`s world anyway, I´ll try to read it again.

    However, you say that ” For one, it appears he fails to notice that his star pupil, the convection equations, have no global variables: everything is local…” Ok, but why is everything “local” in that model?

  16. Hi Anna-Mari–
    I’ll try to explain what it means that the “convection equations” in Bishop’s paper are local, since I also claimed that. The equations describe what happens at various points in space. If they are LOCAL it means that what happens at point X1 only depends on what is happening very close to X1, not on what is happening far way at X2. The dynamics in the equation are described in terms of derivatives, which are differences between quantities at points that are only infinitesimally separated, i.e. very close.

    Now, it sometimes SEEMS like distant things are interacting in a classical model, like with Bishop’s long range forces. So, for example, a charge q2 at X2 might pull on another charge q1 far away at X1. But to be precise you have to say that q2 creates a field at X1 and q1 feels that field which is right there at X1. This is not just semantics, because if you wiggle q2, q1 cannot feel any effect of that wiggling until a little wave has propagated through the field to get to X1. So, even long range forces propagate their effects LOCALLY.

    Another way that Bishop makes it SOUND like there is non-locality when there is none in his model, is when he talks about temperature as “instantaneously” reacting to changes in the velocities of particles. I think in the equations T is a field, meaning it has a value at every point in space. But if we talk about a temperature T for the whole system, as Bishop seems to do, then it will be defined as something like the average kinetic energy of the particles in the system. This is a mathematical idealization, or approximation. So, when you change the kinetic energy of a particle in the system, say by kicking it really hard, the average energy will also go up “instantaneously”–not because of some spooky global influence, but simply because we defined T to be the average of a bunch of values that are spread out in space. There is no actual global entity in the system corresponding to some global T; T is just an average.

    To reiterate: the dynamics of the system are determined by the local particle energies, or local temperature at each point. If we write down a model where the average T over the whole system somehow influences the behavior of the system directly, then that model is an approximation to the real situation as understood in classical physics, where all influences are local.

    It’s the same for the other things that Bishop cites as “nonlocal,” like boundary conditions. Boundary conditions are “global properties” of the system, like the shape of the box holding the gas or fluid. But the boundary only effects the gas by pushing on it locally at the walls of the box.

    I claimed that all classical physics is local, even though when things get nonlinear people tend to start talking about global effects. In quantum mechanics, on the other hand, there can be GENUINE non-locality.
    Hope this helps.

  17. Thanks, Mike. To be fair,Bishop does try to address these concerns in the following (page 6):

    Moreover, there are two basic kinds of forces which act on fluids. The first group are
    long-range forces–such as gravity, electromagnetism (when fluids also carry a charge), so-called
    fictitious forces like centrifugal forces (when fluid motion takes place with respect to an
    accelerating frame)–called body or volume forces. Such forces act on all elements of a fluid, such
    that these forces act equally on all matter within a given volume of fluid. The second group are
    short-range forces of molecular origin and are appreciable only at distances on the order of the
    separation of molecules in the fluid. These latter forces are called surface forces because they
    mainly act on a thin layer adjacent to the boundary of a fluid element, where the thickness of the
    layer is equal to the depth the forces penetrate. Examples of such forces would be contact forces
    due to momentum transport across a common boundary between two fluid elements or forces
    arising from short-range interactions among molecules on the two sides of the common
    boundary.

    Both kinds of forces are taken into account in the hydrodynamic equations above such
    that the dynamics of fluids is not merely that of nearest neighbor interactions among fluid
    elements.

    The major problem I have with his claims is that all of the ‘global’ forces are known to operate via local interactions between molecules (walls of a volume) or fields of force that affect molecules when they ‘touch’ them (e.g., gravity).

    On page 16 he makes another case:

    Furthermore, although there is a microscopic approach to the fundamental conserved
    quantities of fluid systems (e.g., particle number, energy and momentum) analogous to the
    hydrodynamic approach discussed in §3, this kinetic approach still makes irremovable references
    to such nonlocal and system-wide features as conservation laws, symmetries and dynamical
    modes of the system as a whole in order to understand the behavior of a test particle (Pomeau
    and Résibois 1975). Collective features of the system still play an ineliminable, crucial
    determinating role in the dynamics of system constituents even from the kinetic perspective.

    I’m not sure what to make of this paragraph. Are conservation laws and symmetries nonlocal? I’m frankly not sure what to make of that claim.

  18. I would argue that the quote from page 16 is still smoke and mirrors. Conservation of matter-energy or momentum applies locally in all our physical theories including quantum ones. We could invent a new imaginary theory in which teleportation of matter was allowed, and say that matter is conserved globally; but this convection model is certainly not like that. In the convection model fluid that leaves a region around X1 can only do so by entering a neighboring region.

    I just checked Bishops’ reference about ineliminable global modes (forwarded to me by Eric), and if I understand correctly it says (on page 68) that the coupling of global modes that Bishop refers to is “just a convenient way for describing the microscopic dynamics of the system in an approximate way.”

    Symmetry is trickier but I still say it’s a red herring. We use symmetry to constrain possible solutions when we don’t know all the initial conditions of a system, or when we can’t solve the complete equations. We talk about broken symmetry when all the interactions are symmetric but the actual state of the system is not. The pencil balanced on its tip is a concrete example with a broken rotational symmetry (ie the symmetry is broken after the pencil falls). Because we don’t know anything about the actual microscopic cause that tips the pencil one way or another, we treat all directions as equally likely.

    A system’s symmetry is global just like the shape of the box is global. But the effects of a symmetry in a classical system are mediated by local effects, just like the walls of the box exert their effects locally.

    I don’t feel I’ve made this perfectly clear, but then I don’t think Bishop used symmetry in any specific way that I could respond to. He just declared that it’s a global property that affects dynamics. I’m asserting that rather than being “ineliminable,” as he claims, the effects of symmetry actually are reducible to local interactions in principle.

    This should be clear if you just imagine that all the positions and velocities of all the fluid particle and the “wall particles” are given, then in principle their future positions are determined for all time by the deterministic interactions among them (without reference to “global properties”) even if in practice we don’t know how to solve the equations.

  19. Thanks Mike!

  20. I would argue that the quote from page 16 is still smoke and mirrors. Conservation of matter-energy or momentum applies locally in all our physical theories including quantum ones. We could invent a new imaginary theory in which teleportation of matter was allowed, and say that matter is conserved globally; but this convection model is certainly not like that. In the convection model fluid that leaves a region around X1 can only do so by entering a neighboring region.

    I just checked Bishops’ reference about ineliminable global modes (forwarded to me by Eric), and if I understand correctly it says (on page 68) that the coupling of global modes that Bishop refers to is “just a convenient way for describing the microscopic dynamics of the system in an approximate way.”

    Symmetry is trickier but I still say it’s a red herring. We use symmetry to constrain possible solutions when we don’t know all the initial conditions of a system, or when we can’t solve the complete equations. We talk about broken symmetry when all the interactions are symmetric but the actual state of the system is not. The pencil balanced on its tip is a concrete example with a broken rotational symmetry (ie the symmetry is broken after the pencil falls). Because we don’t know anything about the actual microscopic cause that tips the pencil one way or another, we treat all directions as equally likely.

    A system’s symmetry is global just like the shape of the box is global. But the effects of a symmetry in a classical system are mediated by local effects, just like the walls of the box exert their effects locally.

    I don’t feel I’ve made this perfectly clear, but then I don’t think Bishop used symmetry in any specific way that I could respond to. He just declared that it’s a global property that affects dynamics. I’m asserting that rather than being “ineliminable,” as he claims, the effects of symmetry actually are reducible to local interactions in principle.

    This should be clear if you just imagine that all the positions and velocities of all the fluid particle and the “wall particles” are given, then in principle their future positions are determined for all time by the deterministic interactions among them (without reference to “global properties”) even if in practice we don’t know how to solve the equations.

  21. Hi Mike and Eric,

    Thank you so much for these posts. They are extremely clarifying, and I really do appreciate this. Thanks.
    I still have difficulties to understand this: ”The equations describe what happens at various points in space. If they are LOCAL it means that what happens at point X1 only depends on what is happening very close to X1, not on what is happening far way at X2. ” So, is the “local” here meant to be a sort of physical property described by these equations or is it a property of equations? I do not even know, whether this is actually a meaningful question…  I guess I am just trying to ask, whether it is the structure of the world (so to speak) that makes the question of non-linearity and global/local- issue “orthogonal” as Eric puts it, or whether it is the structure mathematical models. Does this make any sense?

  22. Hi Anna-Mari,
    That’s an important distinction you’re making, about whether one is talking about a model or the world. I mean, strictly speaking we can only talk about our various candidate models, but sometimes we know in advance that our model is only approximating the real situation. I think Bishop forgets this distinction when he talks about temperature responding instantaneously to particle velocities: there temperature is average velocity, so it is a convenient alternative to listing all the individual velocities. It doesn’t represent some new entity in the world that communicates with the particles, as Bishop seems to think. It’s pretty clear this is a mistake when it’s a simple example like T=Average(v). When they start talking about “global mode couplings” and whatnot it’s easy to get carried along by a tsunami of enthusiasm and jargon–but remember that in classical physics it’s all reducible to local interactions in principle.
    In the sentence you quoted from me, I think I would answer that “local” refers to a physical property of the hypothetical world represented by those equations. It’s a world (not the “real” world) where causal influences can’t jump across space. You could also call the equations themselves local, but that would be a loose way of talking (sorry I did it and confused you!). I say this because “locality” implicitly relies on a concept of “space,” which is not present in the equations unless we interpret the equations as representing a “physical world.”
    When Eric says non-linearity and non-locality are “orthogonal,” I think he is saying that we can conceive of mathematical models that are linear and local, linear and non-local, non-linear and local, or non-linear and non-local; so the two properties are not logically related. That is, non-linearity does not imply non-locality, and so on. So I guess we should say that the (lack of) relationship between locality and linearity is evident from our mathematical models, since the only way we have of talking about the world is in terms of our various candidate models of it. For instance, just declaring that the world is “non-linear” because “the whole is different from the sum of its parts” would be meaningless until you specify your model of what the parts are and how they should get added.
    To summarize: locality is a (hypothetical) physical property that might or might not be true about the real world, but we can only talk about locality in terms of particular mathematical models of possible worlds.
    Though every fundamental equation of classical physics is local (i.e. describes local physics), it is now established that our real world physics (as described by the quantum model of the world) is non-local. It seems to me that if Bishop wants to find true strong emergence and irreducible global effects, he should be looking at quantum models. He is wasting his time with the classical models, however non-linear they may be.

  23. I have nothing to add. THe only way I can approve comments is by adding my own! GRRRR.

  24. Thanks for this very clear, informative and clarifying post, Mike. Thanks, a

  25. Hi,

    I cannot stop thinking about this. I know it is a bit weird (and not a very “girly” thing to do), but people do have strange hobbies.

    Thus, one more question. Let´s assume that Bishop would be talking about – which he obviously is not – the so called “computational emergence” without any metaphysical commitments. Would you still think that his conclusions must be false?

  26. I have a hard time not thinking about these issues myself, at least as they relate to consciousness. I guess it’s not very girly, and I know it’s not very good for productivity at work…but what can you do?

    I’m intrigued by your question, but I don’t know what this “so called computational emergence” is. Can you define it or suggest a place to read a bit about it? Does it refer to when a deterministic computer running a simple algorithm generates unpredictable chaotic behavior, or something like that?

    Once we get that straight we should also specify what conclusion of Bishop’s we want to re-evaluate. I mean, if you’re asking if one can use “global” variables to describe local dynamics, the answer is yes. I have no problem with using labels that refer to distributed patterns–until they slip into metaphysical commitments, like saying that the global dynamic is “irreducible.” It’s very convenient to be able to talk about patterns like waves and vortices and Lorentz attractors and oscillatory modes etc, even though we know those phenomena are in principle all (classically) completely explicable in terms of local dynamics.

    Well, not sure if I answered your question or some other question…

    Cheers
    Mike

  27. Again, nothing to add. Only way to publish Mike’s post is to do this.

    Perhaps we should look into getting move flexible blog software?

  28. Thanks, Eric. I understand what you mean – the usability of this blog is not the best possible one. However, let´s see what mr. Master of the Brains (and the Known Universe) thinks about this.

  29. I have done some “googling” (is this a correct verb in English? In Finnish we just say that we are “googling” i.e. “googlataan” something, when we are using Google in order to find some stuff.) I found this one with some definitions of computational and theoretical emegence:

    http://www.nbi.dk/~emmeche/coPubl/97e.EKS/emer.cutout.html

    Since I cannot really evaluate the quality of paper, my evaluation should not be trusted. But the paper seems ok to me. 

    The second issue. I just did not find the words, but apparently you can read other people`s mind, since this was precisely what I was trying to ask: ”I mean, if you’re asking if one can use “global” variables to describe local dynamics, the answer is yes. I have no problem with using labels that refer to distributed patterns–until they slip into metaphysical commitments, like saying that the global dynamic is “irreducible”".

    Do you, then, think that it is possible (in principle) to strip the metaphysics off and keep some notion of emergence such as the computational one?

    Could this be done in that Bishop-case, or are his examples still basket cases, since they are all examples of physically defined in terms of local dynamics? And there is nothing that could help him, because his cases are so metaphysically loaded? I wish I could express myself a bit clearer, but I am completely blind here. 

     

  30. There is a typo with the earlier link, this one should work:

    http://www.nbi.dk/~emmeche/coPubl/97e.EKS/emerg.cutout.html

  31. I have no idea why the link is not working, so I´ll try to add it again.

    http://www.nbi.dk/~emmeche/coPubl/97e.EKS/emerg.cutout.html

  32. I have also wondered why the comments have to moderated here, they aren’t at the brainhammer and it does tend to make the conversation better…but I think there must be a reason for it…I was looking at some of the stats for this blog and it looks like there is a lot of spam that comes this way (in the form of weird trackbacks and random/bizzare comments from people who are in no way interested in the post, so maybe the moderation is necessary?

  33. Hi everybody,

    and apologies for this spamming. But I`d like to add one thing and say it explicitly. I am not a very fond of these downward-causation- arguments (computational or not), and in general I have very sceptical attitude with them. However, in many cases I just cannot argue against them, because I do not understand the structure of arguments. 

    And I know that people should not, in general, talk about their feelings, but I have this “feeling”. It seems to me that in many cases when people are championing their “here-is-an-example-of-downward-causation-and-I-can-illustrate-it-by-mathematics” they are actually confusing the properties of those mathematical models with the metaphysical questions. It seems to me that they are really arguing for some strange sort of supervenience, not emergentism. That paper in link is a good example of that.

    But let me emphasize; this is just an instinct, not an argument. However, I guess that if we take a good look of the variables used in the example-equations and so on, it should reveal at least something about this.
    This is the reason why I have been asking all those questions from Mike and Eric.  

    I can let the emergentists to have their non-determinable, computational properties, but I just wish a bit clarity with the epistemological and metaphysical questions from their side. And as Maestro (Fodor) once wrote: ”this is not negotiable. If this is wrong, then everything else I believe is wrong, and that´`s the end of the world”.

     

     

  34. Richard,

    I guess the moderation as such is a very welcome and good thing to have for the reasons you mentioned. But the problem is that the accepting comments- procedure is not very well-designed. An engineer has been busy, I guess. If one could accept the comments just by clicking a button, and not by adding another comment, this blog would be perfect. 

    a

  35. Oh, I see…yeah thatwould be nice…one thing that you can do is to log in and then reply to the comment from the ‘quick blog’ page and then your comment will be directly published…but this will only work for those of us who contribute to the blog…

    By the way, I think I agree with your ‘feeling’