Recognising Top-Down Causation by George F. R. Ellis

" a very old dream, and one that is probably unattainable both because of Godel's theorem"

Gödel's incompleteness theorems are often invoked as an argument against the possibility of complete and consistent axiom set from which all interactions at all scales of physical reality can be derived. The problem is, the incompleteness theorem apply to the formulation meta-mathematical statements about systems (arithmetic principally). But one has to remember that while, aside from basic rules of composition, there are constraints to the making of such meta-mathematical statements, theorems, (nothing prevents false statements or statements that can't be derived from any given finite axiom set), physical reality strictly constrains any system so that it must be consistent with the fundamental laws that govern forces and other interactions. So does Gödel's incompleteness theorems really preclude any possible answer to Hilbert's 6th problem?

If the Universe is made of a finite set of fundamental objects which combine in accordance to a finite set of laws that a finite number of fundamental interactions to produce physical reality, then it follows that Gödel's first incompleteness theorem is, at least in its present form, wrong when applied to reality. Also, if you believe that the fundamental components and laws are a consistent and that the Universe is a coherent system, then a physical interpretation of Gödel's second incompleteness theorem must also be wrong.

"in what way do these axioms and theorems exist, and where do they exist? Are they Platonic forms for example?"

We need to distinguish the axiom from the fundamental aspects of reality they would stand for. And by definitions, axioms cannot be proven. They are merely defined. Once that is done, the axiomatic system may be put to the test. If the axiomatic system is complete and consistent, then all that interactions should be derivable from it. It should also enable the emergences of falsifiable predictions.

" what decides the form they have? (there are various possible forms of logic: who chose this one?)"

That is the tricky part. Any choice must be made based on a number of assumptions. There can be a number of viable axiomatic systems that may be used, but whatever the choice, it must be self-consistent an all interactions must be either derivable from or reducible to it.

"how do they have the power to create any physical entity whatever? Actually axiomatic systems are rather limited in their powers and in their ability to represent reality."

If the Universe is found to be both consistent and complete, that is, the fundamental particles and the laws that govern them are consistent (consistency) and all that they produce remains part of the Universe (completeness), then all physical processes are emergent. It can then be shown that it is possible to create an axiomatic system that represent the fundamental aspects of reality and that representation of all interactions can be derived within such axiomatic system. If the Universe is a consistent and complete, then axiomatic representation can certainly be powerful enough to represent it.

Though a work in progress, I believe that I have shown that an hypothetical universe that is comparable to our Universe in complexity can emerge from an simple axiomatic set. My essay, titled "Questioning the Assumption that Space is Continuous" shows one way that can be done (my essay is based on a larger work, part of which can be freely).

Correction. I meant to write:

[...]But one has to remember that while, aside from basic rules of composition, there are ***no*** constraints to the making of such meta-mathematical statements,[...]

[corrected] Please ignore earlier reply.

@ Prof. Ellis

As a follow-up to our exchange.

" a very old dream, and one that is probably unattainable both because of Godel's theorem"

Gödel's incompleteness theorems are often invoked as an argument against the possibility of a complete and consistent axiom set from which all interactions at all scales of physical reality can be derived. The problem is, the incompleteness theorems apply to the formulation of meta-mathematical statements about systems (arithmetic principally). But one has to remember that, aside from basic rules of composition, there are no constraints to the making of such meta-mathematical statements, theorems, (nothing prevents false statements or statements that can't be derived from any given finite axiom set).

Physical reality, on the other hand, strictly constrains any phenomena so that it must be consistent with the fundamental laws that govern forces and other interactions. So does Gödel's incompleteness theorems really preclude any possible answer to Hilbert's 6th problem?

If the Universe is made of a finite set of fundamental objects which combine in accordance to a finite set of laws that a finite number of fundamental interactions to produce physical reality, then doesn't it follows that Gödel's first incompleteness theorem is, at least in its present form, wrong when applied to reality?

Also, if you believe that the fundamental components and laws are a consistent and that the Universe is a coherent system, then shouldn't any physical interpretation of Gödel's second incompleteness theorem also be wrong?

"in what way do these axioms and theorems exist, and where do they exist? Are they Platonic forms for example?"

We need to distinguish the axioms from the fundamental aspects of reality they would stand for. And by definitions, axioms cannot be proven. They are merely defined. Once that is done, the axiomatic system may be put to the test. If the axiom set and rule set that makes the axiomatic system are complete and consistent, then all that interactions should be derivable from it. It should also enable the emergence of falsifiable predictions.

" what decides the form they have? (there are various possible forms of logic: who chose this one?)"

That is the tricky part. Any choice must be made based on assumptions. There can be a number of viable axiomatic systems that may be used, but whatever the choice, it must be self-consistent an all interactions must be either derivable from or reducible to it.

"how do they have the power to create any physical entity whatever? Actually axiomatic systems are rather limited in their powers and in their ability to represent reality."

If the Universe is found to be both consistent and complete, that is, the fundamental objects and the laws that govern them are consistent (consistency) and all that they produce remains part of the Universe (completeness), then all physical processes are emergent. It can then be shown that it is possible to create an axiomatic system that represents the fundamental aspects of reality and that representations of all interactions can be derived within such axiomatic system. If the Universe is a consistent and complete, then wouldn't it follow that an axiomatic system that is powerful enough to describe it can be devised?

Though a work in progress, I believe that I have shown that an hypothetical universe that is comparable to our Universe in complexity can emerge from an simple axiomatic set. My essay, titled "Questioning the Assumption that Space is Continuous" shows one way that can be done (my essay is based on a larger work, part of which can be freely).

Dear George:

Following up on my earlier comments, there are additional physical and mechanistic arguments that support your statement -

" ...the foundational assumption that all causation is bottom up is wrong, even in the case of physics......... The key feature is that the higher level dynamics is effectively decoupled from lower level laws and details of the lower level variables:......you don't have to know those details in order to predict the higher level behavior."

The bottom up causation is used in standard cosmology to describe the universal reality based on the quantum reality exhibited by individual particles/fields. However, quantum reality represents only partial reality due the quantum measurement problem. A classical measuring instrument interprets the quantum phenomena (V~C) from a Newtonian (V~0) frame of reference, hence the quantum reality represents a truncated partial reality resulting in the observed weirdness and inconsistencies. The quantum phenomenon being observed occurs in a dilated space-time due to V~C, while the Newtonian space-time frame of reference of the observer remains fixed and undilated due to V~0. In order to describe the non-truncated wholesome universal reality, a top-down causation approach such as the one described in my paper - " From Absurd to Elegant Universe", is essential that satisfies laws of conservation of mass, energy, space-time, and momentum via proper inclusion of the relativistic effects. Paradoxes of quantum measurements and quantum reality (entanglement, tunneling, multiverses, multi-dimensions and anti-matter etc.) are artifacts of the quantum observational limitations imposed by the fixed space-time and not satisfying the overall conservation laws at the universe level. The top-down causation approach allows universal connectivity and non-locality via governing eternal and omnipresent conservation laws throughout the universe, which are missed out due to the consideration of only local or discrete realities of particles/fields in fixed space-time in the bottom-up approach.

And yes, bodies and brains can be created as well as annihilated by the top-down causation. As explained and described in my paper, both the creation and dilation of matter are predicted by the top-down causation model without the need for any nucleo-synthesis or anti-matter concepts used in the standard model.

The seriousness of the impact of the top-down causation should not be underscored. Without the top-down causation consideration, it is impossible to determine the universal wrongness or correctness of any assumption or theory. From the bottom-up causation, only a partial or local, and not universal, appropriateness of any assumption/theory can be estimated. For this very reason, the widely successful bottom up quantum theory at worldly level fails to predict 96% (dark matter and dark energy) of the wholesome universe.

Sincerely,

Avtar Singh

Daniel

Agreed. Any such concepts as incompleteness, etc are a reflection of our failure to comprehend all that existed, not a feature of physical reality. Which existed in a definite form, as at any point in time, and is, by definition, a sequence which is being driven by the lowest level of that which it comprises.

Paul

George/JCN/John

All the above may be correct from the perspective being taken (ie non physical). But, at the physical level, there is no influence on the next state which will exist (commonly known as future), because it does not exist. What happens is that a state occurs which is different from what which would otherwise have occurred. Nothing has been changed, physically, because nothing existed physically to change. In terms of sequence, what might be seen as 'oscillation', 'reaction', etc, is just re-occurrence. For example: A B C B D, is not, physically, some form of 'return' to B, but a re-occurrence of B. And for those who would ask the next question, what if it was A B C B D D D E. The answer is that D continued to exist for more than one point in time, that being, by definition, the level at which the sequence is fully differentiatable, because it is the fastest at which any change occurs, and D was a state which did not alter at that speed.

Paul

In thinking about this I then ponder whether random networks subjected to some sort of selection process can then evolve into a form suggested here. This is in a manner of thinking a sort of Darwinian process. A random network might compared to some random noise or white noise system, but where given some sample of possible random networks subjected to a culling process plus some "survival criterion" results in networks which are less random and output what might be called pink noise.

Thanks for the reference.

Cheers LC

Dear George Ellis,

A very interesting read. In a reply to Paul you note that "reality is unclear" at the particle level because of uncertainty, wave-particle duality, and entanglement. In this sense any change in understanding of these aspects of reality might be expected to have some effect on the conception of 'the bottom' (although equivalence classes might not change). For this reason I invite you to read and hopefully comment on my current essay, The Nature of the Wave Function.

At the other end of the spectrum, in a comment to jcns, you bring 'meaning and purpose' into the picture. This brings up the question, "where is the top?". Do you make an assumption here, or is the top an open ended concept?

I agree that most discussions of emergence do NOT treat 'top down causation' and you are to be commended for doing so.

Edwin Eugene Klingman

"In a reply to Paul you note that "reality is unclear" at the particle level because of uncertainty, wave-particle duality, and entanglement"

Indeed, to which I have responded with the point that this cannot be so, otherwise there would be no physical existence, which there is, and no alteration to that, which there is. Whatever reality 'ultimately' is, which we can never know, because we too are part of it, what we certainly do know is that there is 'something out there' ('out' being extrinsic to sensory detection systems)and it alters. The whole process of sensory detection(ie seeing, hearing, etc) involves the physical receipt of physically existent phenomena (eg light, noise, vibration), which are themselves the result of an interaction between other physically existent phenomena (one of which we tend to label the reality). That is the fundamental physics.

So physical reality obviously occurs in a specific physically existent state. It does not exist in some "unclear" manner. The issue is our inability to identify that. The sensory systems evolved to ensure survival of organisms, not the sensing of the very constitution of reality ('the bottom'). The Copenhagen interpretation, and any other theory that assumes there is no 'bottom', or that sensing affects the 'bottom', is invalid. In the latter case, it is sheer nonsense. Not only do organisms not receive reality anyway, when sensing, by definition, reality has already occurred for them to be able to sense it!

The question then becomes, having swept away metaphysical presumptions and invalid theories, what constitutes the 'bottom'? My definition, and I am perfectly happy with improvements thereto-just no the incorrect assertion that there is not one, is: " the physically existent state which occurs as at any given point in time, is a function of the particular state of the properties of the elementary particles involved, and their spatial position, as at that point in time"

Paul

George,

I'm afraid that you (and everybody else, for that matter) confuse causality with reason.

If we understand something only if we can explain it as the effect of some cause, and understand this cause only if we can explain it as the effect of a preceding cause, then this chain of cause-and-effect either goes on ad infinitum, or it ends at some primordial cause which, as it cannot be reduced to a preceding cause, cannot be understood by definition.

Causality therefore ultimately cannot explain anything. If, for example, you invent Higgs particles to explain the mass of other particles, then you'll eventually find that you need some other particle to explain the Higgs, a particle which in turn also has to be explained etcetera.

If you press the A key on your computer keyboard, then you don't cause the letter A to appear on your computer screen but just switch that letter on with the A tab, just like when you press the heck, you don't cause the door to open, but just open it. Similarly, if a let a glass fall out of my hand, then I don't cause it to break as it hits the floor, I just use gravity to smash the glass so there's nothing causal in this action.

Though chaos theory often is thought to say that the antics of a moth at one place can cause a hurricane elsewhere, if an intermediary event can cancel the hurricane, then the moth's antics only can be a cause in retrospect, if the hurricane actually does happens, so it cannot cause the hurricane at all. Though events certainly are related, they cannot always be understood in terms of cause and effect.

The flaw at the heart of Big Bang Cosmology is that in the concept of cosmic time (the time passed since the mythical bang) it states that the universe lives in a time continuum not of its own making, that it presumes the existence of an absolute clock, a clock we can use to determine what in an absolute sense precedes what.

This originates in our habit in physics to think about objects and phenomena as if looking at them from an imaginary vantage point outside the universe, as if it is legitimate scientifically to look over God's shoulders at His creation, so to say.

However, a universe which creates itself out of nothing, without any outside interference does not live in a time continuum of its own making but contains and produces all time within: in such universe there is no clock we can use to determine what precedes what in an absolute sense, what is cause of what.

For a discussion why big bang cosmology describes a fictitious universe, see my essay 'Einstein's Error.'

Anton

Anton

I am not going to make a judgement on the validity of your general point, but will alight on "then this chain of cause-and-effect either goes on ad infinitum, or it ends at some primordial cause which, as it cannot be reduced to a preceding cause, cannot be understood by definition".

Now, there are two issues here:

1 Cause must involve physically existent phenomena. In simple language, cause is not something which is somehow 'separate' from physical existence (and I am not implying you are saying that). So it is definitive and knowable, and must have correspondence with physically existent phenomena.

2 We are concerned with knowledge of reality, not reality. In other words, assuming a valid closed system can be identified (which it can-sensory detection in all organisms), then there is a 'limit/confine', within which all is, potentially, knowable (only practical problems in the sensory detection process prevent this from being so, not metaphysical considerations). There is a valid limit to the knowledge that is potentially available to us. The confusion is in not understanding that we are ultimately dealing with knowledge of the actuality, not the actuality.

Paul

Paul,

You have repeated your beliefs on FQXi probably more often than any one else. My question was addressed to George Ellis, who has not flooded FQXi with his opinions, and whose thread this is.

Paul,

What is or happens within a perfectly closed system has no physical reality to someone outside of it: it does not belong to his universe, is unobservable so he cannot say anything about it. The same goes for the second law of thermodynamics: if a system is perfectly closed, that is, if there's no physical communication possible with what's inside of it, then it doesn't even make sense to ask how much entropy it contains. As in a self-creating universe the observation interaction affects the observed, there is no absolute, i.e., objectively observable reality at the origin of our observations. It isn't that our observation is imperfect; the point is that in a universe where particles create one another, their properties are as much the effect as the cause of their interactions so the observation interaction unavoidably affects the nature of the thing to be observed. Here we cannot really distinguish between the properties of a fundamental particle and their expression. In such universe there is no reality separate from its observation, though imperfect observational equipment or methods of course blur observations.

Anton

Dear George

(As a courtesy to Professor Ellis, and to keep discussions focused I hope other posters will not respond to this on his page unless he does.)

You make a convincing case for being wary of simplistic down-up causation. Your arguments make sense but only in the context of present-day physics which is far from being a harmonious conceptual whole where one theory applies both to the very large and the very small - please see my present fqxi essay Fix Physics! about that. I am conviced that if such a simple theory of everything were to be found, causation would be always local and linear at the smallest scales and the effects of large systems will be the resultant of effects transmitted locally and causally down to the local level and vice-versa simultaneously in a balanced way:

Think of a ripple tank where one 'simple local' point sends out waves to a 'complex system' consisting of points on a surrounding perimeter. Anywhere in the space between the 'local or down point' and those of a larger 'higher complex perimeter' system the resulting interference pattern will be caused by both systems simultaneously. Here is my tentative approach to such a ToE Beautiful Universe Theory .

With best wishes from Vladimir

Well said Edwin.

Paul, has a gift for systematic analysis of statements by physicists. This may be put to very good use for example in writing a monograph on how historically various physicists changed their own positions on subjects such as SR , the ether, time, etc. That would be really interesting.

Cheers to both of you

Vladimir