Dear Tommaso Bolognesi,
I have printed your response. I am impressed. Your response is not in agreement with me; but, that is a minor point. Your response was directed at my questions and even referred to my own essay. I appreciate your time and effort in putting your response together. I will follow the leads you referrenced. I will respond when I put something together worth your time.
James
Tommaso,
Thanks for a fascinating and extremely well constructed essay. Since Wolfram is scheduled to speak at ICCS in Boston this summer, I think it might be interesting to see how your multi-level hierarchy compares to Bar-Yam's multiscale variety -- hierarchies of emergence vs. lateral distribution of information.
Interesting conceptual equation, "spacetime geometry = order number." Suppose one were to make another equation: "order = organization feedback." Then one would get -- substituting terms in my equation for yours -- the theme of my ICCS 2006 paper ("self-organization in real and complex analysis") that begs self-organization of the field of complex numbers, z, in the closed algebra of C.
One more comment (though I could go on; your paper is rich in quotable points), concerning global and local (4.1) time-dependent relations among point particles. Research in communication network dynamics (e.g., Braha--Bar-Yam 2006, Complexity vol 12) shows often radical shifts in hub to node connectivity on short time intervals while time in the aggregate shows that the system changes very little. Taking point particles as network nodes, perhaps something the same or similar is happening.
Good luck in the contest. (I also have an entry.) I expect that you will rank deservedly high.
All best,
Tom
Dear Tom,
thanks for the positive comments. Following your links I reached the Robert Laughlin's 2005 book 'A Different Universe: Reinventing Physics from the Bottom Down', in which the role of emergence in theoretical physics is given an important role. Good to hear; another book on the pile!
In the equation 'spacetime geometry = order plus number', introduced by people in the Causal Set programme, 'number' simply refers to counting the number of events in a region of the causal set, which is then equated to the volume of that region. And 'order' is the partial order among events. You mention self-organization in the context of the field of complex numbers, and this does not seem much related to 'number' in the above sense (if this is what you meant to suggest). But of course I am curious about everything that has to do with self-organization.
Usually a self-organizing system is conceived as a moltitude of simple active entities. Does this happen in your ICCS 2006 paper?
One peculiarity of the 'ant-based' (or Turing-machine-like) approach dicussed in my essay is that you actually have only ONE active entity -- the 'ant' -- and expect everything else to emerge, including the moltitude of interacting particles or entities that one normally places at the bottom of the hierarchy of emergence.
Ciao. Tommaso
Dear Tommaso,
Thank you for your essay. You write a lot about an emergence and computation, chaos, self-organization and automata. All the elements I have touched in my essay because they are closely connected to the evolution of spacetime concept.
E.g. you write: "Computations may exist even without computers". It seems to have something in common with Computational LQG by Paola Zizzi. In my essay I have even quoted Paola.
My own view is that the universe is a dissipative coupled system that exhibits self-organized criticality. The structured criticality is a property of complex systems where small events may trigger larger events. This is a kind of chaos where the general behavior of the system can be modeled on one scale while smaller- and larger-scale behaviors remain unpredictable. The simple example of that phenomenon is a pile of sand.
When QM and GR are computable and deterministic, the universe evolution (naturally evolving self-organized critical system) is non-computable and non-deterministic. It does not mean that computability and determinism are related. Roger Penrose proves that computability and determinism are different things.
Let me try to summarize: the actual universe is computable at the Lyapunov time so it is digital but its evolution is non-computable so it remains at the same time analog (the Lyapunov time is the length of time for a dynamical system to become chaotic).
Your work seems to be the trial to develop the computable model of the universe at the Lyapunov time. Good luck!
Jacek
Ciao Tommaso,
Yes, I do mean to suggest that the non-ordered set, z (the universal set of complex numbers) is organized to allow -- not a partial order of events -- but a well-ordered sequence in the specified domain of topology and scale, with analytic continuation over n-dimension manifolds. It is nontrivial that this is accomplished without appeal to Zorn's lemma (axiom of choice). And time is given a specifically physical definition. I followed up at ICCS 2007 with a nonmathematical paper ("Time, change and self organization") that incorporated and expanded on some of these results.
You pick up right away, the difference between the hierarchical distribution of information, and multiscale variety. I am thinking that your "multitude of entities" may be dual to the "ant" analogy, because with activities occuring at varying rates at different scales, new hierarchies may form and feed back to the system dynamics.
You know, Boston is very beautiful in the summer. :-)
All best,
Tom
Hi again Tommaso,
Just to let you know I dropped you a comment on Feb. 18, 2011 @ 21:07 GMT concerning the data vs. code question, just in case you hadn't seen it.
Best.
Dear Tommaso,
Welcome to the essay contest. This essay contradicts quantum mechanics: How your digital/computational universe conjecture theory manages the Heisenberg uncertainty? For this purpose your digital computer must know the definite, absolute information about the position and momentum of every particle. Moreover, this ''computer'' must know all quantum information with absolute precision before events occurs - it is forbidden by quantum mechanics. Also, to perform such processing, the exchange of information and the work of computer must be faster that light. How your digital computation theory explains the EPR paradox and nonlocality?
I can prove a theory false by simply finding one example in which the theory does not hold. Let us analyze your statement: ''all the complexity we observe in the physical universe, from subatomic particles to the biosphere, is a manifestation of the emergent properties of a digital computation that takes place at the smallest spacetime scale''.
I can show you a place where the digital/computational universe conjecture theory is wrong: 1) At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite. Thus, at the center of a black hole a digital computation is not possible because spacetime curvature becomes infinite. You see, there are places and phenomena which exist without need in the digital computation. Since I found at least one place where the digital computation can not exist, it is a proof that this theory is wrong.
Besides, to process an event the digital computation needs the exchange of information. Inside of the black hole (event horizon) all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape. Since the signal can neither escape from a black hole nor move inside of a black hole, it means the exchange of information is not possible. Since the exchange of information near the event horizon is not possible, it mean that digital computation also is not possible. Pay attention that the digital computation is not possible even outside of the Black Hole, near the event horizon because the exchange of information is forbidden.
The essay is inconsistent; I found propositions which contradict each other. For example: ''There exists a tiniest scale at which the fabric of spacetime appears as a pomegranate, made of indivisible atoms, or seeds''. ''all the complexity we observe in the physical universe, is a manifestation of the emergent properties of a digital computation that takes place at the smallest spacetime scale''.
Suppose that at the level of indivisible atoms a universal computation keeps running and manage the external physical processes. There appears a question: who/what manage this ''digital computer' and the work of the indivisible atoms? It means the existence of the deeper background structure which process and manage the activity of "indivisible" atoms this ''digital computer''. If the universal computation sits at the bottom of a multi-level hierarchy of emergence then where sits the computation which manage ''the universal computation''? Thus, the idea of the digital/computational universe conjecture contradicts to the idea of indivisible atoms.
In conclusion, I agree with you that Reality is ultimately digital, but the digital/computational universe conjecture theory is wrong and inconsistent.
Sincerely,
Constantin
The previous post is my post, by Constantin Leshan. The login does not hold.
Soncerely,
Constantin Leshan
Hi Tommaso
My rate is done and you got a good grade. A very well written essay. I agree with the essence of it as I hope you could verify on my essay, even that the style of my writing is quite different.
Now having said that, I would say:
I agree our universe is made from some simple basic cellular automata and most things are emergent phenomena.
I don't agree to identify those automata to space-time and see particles and every thing else emerge from there.
My position is quite the opposite. I identify the basic automata with particles and see space and time derived from the interaction. Unfortunatly I haven't done concrete definitions and experimentation with my approach.
I feel my approach may have the problem of having more complex automata but might be easier to codify relativity in there.
Could you comment ?
Regards
Juan Enrique Ramos Beraud
Hi Juan Enrique,
Tommaso Bolognesi's essay contradicts quantum mechanics: How the digital/computational universe conjecture theory manages the motion of particle and Heisenberg uncertainty? For this purpose this digital computer must know the definite, absolute information about the position and momentum of every particle. Moreover, this ''computer'' must know all quantum information with absolute precision before events occurs - it is forbidden by quantum mechanics. Also, to perform such processing, the exchange of information and the work of computer must be faster that light. How your digital computation theory explains the EPR paradox and nonlocality?
I can prove a theory false by simply finding one example in which the theory does not hold. Let us analyze your statement: ''all the complexity we observe in the physical universe, from subatomic particles to the biosphere, is a manifestation of the emergent properties of a digital computation that takes place at the smallest spacetime scale''.
I can show you a place where the digital/computational universe conjecture theory is wrong: 1) At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite. Thus, at the center of a black hole a digital computation is not possible because spacetime curvature becomes infinite. You see, there are places and phenomena which exist without need in the digital computation. Since I found at least one place where the digital computation can not exist, it is a proof that this theory is wrong.
Besides, to process an event the digital computation needs the exchange of information. Inside of the black hole (event horizon) all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape. Since the signal can neither escape from a black hole nor move inside of a black hole, it means the exchange of information is not possible. Since the exchange of information near the event horizon is not possible, it mean that digital computation also is not possible. Pay attention that the digital computation is not possible even outside of the Black Hole, near the event horizon because the exchange of information is forbidden.
The essay is inconsistent; I found propositions which contradict each other. For example: ''There exists a tiniest scale at which the fabric of spacetime appears as a pomegranate, made of indivisible atoms, or seeds''. ''all the complexity we observe in the physical universe, is a manifestation of the emergent properties of a digital computation that takes place at the smallest spacetime scale''.
Suppose that at the level of indivisible atoms a universal computation keeps running and manage the external physical processes. There appears a question: who/what manage this ''digital computer' and the work of the indivisible atoms? It means the existence of the deeper background structure which process and manage the activity of "indivisible" atoms this ''digital computer''. If the universal computation sits at the bottom of a multi-level hierarchy of emergence then where sits the computation which manage ''the universal computation''? Thus, the idea of the digital/computational universe conjecture contradicts to the idea of indivisible atoms.
In conclusion, I agree with you that Reality is ultimately digital, but the digital/computational universe conjecture theory is wrong and inconsistent.
Sincerely,
Constantin
Dear Constantin,
would it be wise to say that Quantum Field Theory is wrong because it does not predict the existence of unicellular organisms?
This is not meant to be provocative, but only to express what I believe is the 'delicate' status of any conjectured theory of everything (QFT not even pretending to be one). Any such conjecture should maximize the number of explained physical phenomena while minimizing the machinery of the explanations, for example by getting rid of universal constants such as c and G, which should be derived, not assumed.
I believe that the digital/computational reality conjecture (I wrote 'conjecture', not 'theory'), could hardly be beaten in terms of simplicity -- any kid can understand and reproduce the steps of, say, a deterministic Turing machine moving on a binary tape, or on a graph -- and this is already a great incentive for investigating it. But it is equally clear that the number of 'proof obligations' assigned to the conjecture is explosive, offering much room to criticism, until these are not discharged.
Then, looking at the long list of TODO's , let me first summarize the good news, and tick the phenomena that occur in spacetime, that the conjecture can comfortably explain, via emergence in computation (see also essay and references):
- random-like behaviors;
- periodicity, and co-existence of regular-periodic and random-like structures;
- self-replication;
- localized periodic structures that interact with one another, similar to particle scattering diagrams.
All these can be observed in cellular automata as well as in algorithmic causal sets.
What I find almost miraculous is that we get these features for free, that is, without coding anything of physical flavor into those simple models of computation. And I do hope that you agree in considering the above as fundamental PHYSICAL phenomena, in the broad sense that they characterize qualitatively our universe, as we perceive it.
I would not endorse any ToE proposal that does not perform VERY well at these tasks -- first qualitatively, and then, of course, also quantitatively. In my essay I additionally suggest that these properties, in duly varied forms, should manifest very early in the history of the universe.
I realize that this conjecture represents a radical shift of perspective, in open violation with a principle supported by many scientists (e.g. Carlo Rovelli), also expressed somewhere in these blogs, that science always progresses incrementally, by smooth improvements of the best existing theories. To say that this has always been, and will ever be the case, is quite a strong statement (proposal for the next FQXi Contest: 'Is the History of Physics Discrete or Continuous'?). But, if the 'continuous' solution is preferred, it would be certainly wise to widen the domain of theories to be considered for improvement or integration, including not only SR, GR and QM, but also Complex Systems, Self-Organization, and, or course, Darwin.
I have taken a larger tour than you probably expected. You raise specific points and I do want to answer them as punctually as possible. Take this as a preamble. I'll be back.
Bye for now
Tommaso
Constantin (and Juan-Enrique), I have given a first answer to your objections up in the blog where you raised them first. The rest of my replies comes hopefully tomorrow. Look for it by scrolling up to that same place. Thanks. Tommaso.
SECOND PART of my answer.
(The ultimate bottom)
You find a contradiction between placing indivisible atoms of spacetime at the bottom of reality, and the need for a digital computer that runs the evolution of this collection of atoms. You seem annoyed by the fact that such a digital computer would represent a 'deeper background structure' beneath the level of these indivisible spacetime atoms, requiring perhaps even an operator (you ask 'who/what manages this digital computer'?): discrete spacetime would no longer be the very 'bottom' of the universe. The answer is simple: I do NOT postulate the existence of such a computer, in the basement or elsewhere, as clearly written at the bottom of page 1 in my essay. An algorithm, as well as a differential equation, is simply a formal way to describe dynamics. No need for hardware.
(Computation and curvature)
You write that 'at the center of a black hole, a digital computation is not possible because spacetime curvature becomes infinite'. I completely agree that your PC (or even my Mac!) would start having computing problems a while after crossing a black hole horizon. But, again, we are not talking about hardware, we are abstractly talking about computation. Better: computations on graphs. The variety of structures and phenomena that one can obtain out of algorithmically evolving graphs is formidable. A cheap proof of this, if you wish, is that when you describe phenomena such as those involving black holes, you tend to visualize things precisely in terms of points and arrows, which is what directed graphs are made of...
By the way, a very good 1999 paper by Margenstern and Morita proves that, in the context of cellular automata, spatial (negative) curvature offers indeed a great computational advantage over flat space (M. Margenstern, K. Morita, 'A Polynomial Solution for 3-SAT in the Space of Cellular Automata in the Hyperbolic Plane', Journal of Universal Computer Science, vol. 5, no. 9, Springer, 1999, pp. 563-573). Amazing.
However, to me, the appropriate question is not whether a computation is possible inside a black hole, but, rather, what IS a black hole, how does it look like or manifest, in a graph-based, computational spacetime. I don't know. But simple concepts such as sink node (one with only incoming arcs), or strongly connected components are available that may help. Curvature can also be defined for (planar) graphs, called 'combinatorial curvature'. It is only finite, but possibly unbounded, if you grow the number of faces sharing the inspected node, as it can indeed happen in some of my algorithmic causal sets.
(Quantum effects)
If I had good answers for these problems, they would have appeared very early in the essay. Stephen Wolfram has some potentially useful suggestions for entanglement (NKS book, ch. 9). I have long discussed the quantum effects issue with Alex Lamb, who is also participating to this Contest , and he half-managed to convince me that a form of nonlocality could be achieved if we imagine the algorithmic graph rewriting to take place directly on the causal set, rather than on an underlying spatial support, as I've done so far.
But the more general question is: are we going to eventually apply the standard QM techniques and compose instances of discrete spacetime in a gravitational path integral -- a sum over histories? Perhaps... but later. In doing so, we could follow, for example, the work of Renate Loll and collaborators, who take sums of causal dynamic triangulations (CDT) of spacetimes, and investigate consequences such as emergent spacetime dimension. But I am reluctant to do this, at least before having fully explored the potential of a classical approach to emergence in discrete, computational spacetime. Exciting phenomena such as those illustrated at Figures 3 - 5 of my essay would probably be obscured by a QM treatment.
Finally, while I have no problems in conceiving 'computations' without 'computers', I am more skeptical about defining 'observations' without 'observers', and QM effects do depend on rather intrusive observers, engaging in interactions that affect both the observed and the observer subsystem. In a tiny, discrete, newborn universe that has just reached the size of say 33 elements -- counting edges, nodes, faces, or simplices -- is there enough room for this interaction? Is there room for an observer? (an INTERNAL observer, that is). Maybe quantum effects, and perhaps even relativistic ones, unfold only at a later stage, when entities emerge that can play the role of (proto-)observers. But this is only wild speculation.
Second part of answer has been appended above.
Dear Tommaso,
My remark concerns your as well as other purely 'computational approaches' to physics.
What troubles me about them is that they fail to address the nature of physical reality: as I discussed elsewhere, theory of computability came out of logic and has never been concerned with this question.
At the same time, physics is the central natural science, and if it does not address the above question, as it has tried to do so far, we are left with no science addressing it.
Dear Tommaso:
I think my previous question - or the answer for it- got lost with the answer from an for Constantin.
I think your essay is great and your proposal of identifying space time "atoms" with a cellular automata yet to be debugged and understood is plausible. From experiments - or simulations- like the ones presented in "new kind of science" and in your essay we see "particles" and all sorts of things emerge. We could even find quantum mechanics emerging from there.
As you say, the automata are not yet "seen" and not debugged.
I think - as I propose in my essay- it might also be plausible to search the basic automata on the particles or sub particles instead of in space-time. I identify the basic automata with particles and see space and time derived from the interaction. Unfortunatly I haven't done concrete definitions and experimentation.
I feel my approach may have the problem of having more complex automata but might be easier to codify relativity and quantum mechanics in there.
Now, again, could you comment on the different approaches?. I do believe in an algorithmic universe, as many others -like Hector Zenil- do.
Regards
Dear Juan Enrique Ramos Beraud,
You supports Tommaso' essay because you have the same essay ''Universe is a computer'' with the similar statements and errors. If you want I can review your essay and show you a lot of flaws in your essay.
Sincerely,
Constantin
Dear Tommaso,
Your answers are unconvincing and wrong. Moreover, I suspect that you are trying to suppress my questions by the stream of senseless information. It is impossible to find the answers for these questions because this theory is fundamentally wrong.
Let us begin again with quantum mechanics. Your essay states that all the complexity we observe, from subatomic particles to the biosphere, is a manifestation of the emergent properties of a digital computation that takes place at the smallest spacetime scale. How this digital computation can explain the simple motion of free particle, the Heisenberg uncertainty? For this purpose this digital computation must know the absolute information position-momentum about every particle before events occurs, that is forbidden by quantum mechanics.
And I don't see any answer for this problem; your words about Quantum effects, Stephen Wolfram, Renate Loll explain nothing; It is a stream of senseless information. You cannot explain it by definition; it is a fundamental flaw in this theory.
The next flaw about black holes: I found at least one place where the digital computation can not exist, it is a proof that this theory is wrong.
And your answer is senseless: ''I completely agree that your PC (or even my Mac!) would start having computing problems a while after crossing a black hole horizon. But, again, we are not talking about hardware, we are abstractly talking about computation''. Do you think your spatial atoms will be able to process information inside of black hole, in singularity? Inside of the Black Hole the exchange of information is not possible, therefore the digital computation cannot work. Since I found at least one phenomenon/place that exist without need in the digital computation, it is a proof this theory is wrong.
Another argument also is not valid: ''By the way, a very good 1999 paper by Margenstern and Morita proves that, in the context of cellular automata, spatial (negative) curvature offers indeed a great computational advantage over flat space''. They refer about the usual curvature but not infinite curvature, singularity.
Thus, this theory is fundamentally wrong.
Regards,
Constantin
Constantin:
If you find my essay wrong, it's own thread is the place to comment it, and yes I would love the criticism.
Tommaso:
I would like some comments any way.
Yours.
Juan Enrique Ramos Beraud
Dear Tommaso
After recovering from my cataract operations I re-read your essay, and enjoyed the lovely photo of the pomegranate and the beautiful causal set plots. I also read the paper by Reid that you referred to. I still do not understand several aspects of causal sets. With my limited understanding of the technicalities involved I will try to express my reaction to the concept as applied to physics: You started by discussing automata and I could follow the logic of causality between nodes following a simple algorithm as in Wolfram's NKS. I have no access to the printed references of your other papers and could not understand the Termite simulations.
Generally I think complications occur when applying the automata concept to physics. GR and Quantum mechanics are accepted as they are now formulated, and the simplicity of a node structure has to be abandoned to accommodate their physically unrealistic and mutually incongruous methodologies. The resulting causal sets are bloated beyond necessity. In my earlier 2005 Beautiful Universe theory on which my present fqxi paper is based, both GR and QM have to be reverse-engineered and some complications discarded before my simple dielectric node-interactions are applied. Hope this makes some sort of sense!
Best wishes from Vladimir
