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Particle emergence and evolution in trivalent network computations

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Posted by: Tommaso Bolognesi

Particle emergence and evolution in trivalent network computations

The universe exhibits symmetry and complexity.
Symmetry appears as a key shaping factor, and inspires the search for ultimate laws of physics: these should expose the symmetry observed in nature, and be themselves mathematically elegant. (Example: Lisi's most recent E8-Theory of elementary particles.)

The principle of minimality, or Occam's razor, is another inspiring principle in science, and the search for symmetry in the universe can itself be seen under this light.
But another effective way to achieve minimality in the explanation of dynamic phenomena is via the powerful notion of emergence: constant, regular/symmetric, complex, even chaotic dynamics can be obtained from iterating minimal sets of simple rules. (Example: the artificial particles emerging from the computations of elementary cellular automaton Rule 110.)

Finally, natural evolution, through self-replication, random mutation and natural selection, is a key mechanism for explaining the emergence of complexity in nature, and although its traditional scope is the biosphere, some have boldly suggested it might also be relevant to particle physics. Interestingly, symmetry itself, e.g. in a flower or a savanna runner, appears as the result of an evolutionary process.

If an ultimate theory of reality (a ToE) is at reach, we expect it to reflect and combine minimality, emergence, evolution, symmetry (and beauty).

Out of countless possible approaches, here is an outline of one radical way to do this, that I have started exploring, and which I post here hoping to have some feedback or useful pointers.

1.
Physical space is modeled by, or actually assumed to be, a conceptually elementary, discrete, finite, dynamic structure, that grows unbounded; following Wolfram, I choose undirected trivalent graphs, and very few elementary, trial initial configurations for them.

2.
The dynamics of this space is governed by the local, deterministic, iterated application of a minimal, complete set of graph rewrite rules, as considered also in Loop Quantum Gravity, and by a simple rule for the moves of the control point, in analogy with (n-dimensional) Turing machines.

3.
The computations of the above formal system should exhibit the emergence of particles, that is, persistent, coherent structures able to preserve/replicate themselves. Particles and space are the same fabric.

4.
Particles should in turn appear to interact in complex ways -- complex enough to
(i) support universal (e.g. Turing complete) computations, and
(ii) manifest emergent phenomena of mutation, selection, evolution.

5.
Finally, particle evolution may be expected to traverse a stepwise progression of stable configurations, perhaps up to matching the complex symmetry of the E8-based theory.

Items 3, 4 and 5 represent progressively ambitious goals, and the pure achievement of goal 3 would be a major result in itself.

A few comments on the above plan.

Unlabeled, dynamic trivalent networks are assumed as an infinitely accurate model of the exploding universe. Since the 'universal computation' operates at Plank scales, a gap of several orders of magnitude separates the largest models that can be grown by current computing technology from the smallest quantities measurable by current experimental-physics equipment. One way to mitigate this technological gap problem, with its negative impact on the possibility to make testable predictions, is to rely on the following assumption.

('Teilhard' postulate). The fundamental mechanisms permeating the universe at the scales of our most direct experience, should manifest themselves, in duly varied forms, at all scales, and since the very beginning.

If atoms and galaxies emerge as persistent objects, distinguished from their background, then some persistent objects should also emerge soon after the big bang, at ultra-low scales. If random mutation and selection drive evolution in the biosphere, then they should also operate at the level of subatomic particles.
A most extreme version of this idea was passionately advocated by the french paleontologist and philosopher Teilhard de Chardin in his book 'The Phenomenon of Man', where he suggested that a rudimentary form of consciousness must permeate the 'internals' of matter even in its primitive forms. (Under the computational universe view, one may argue that self-reference, which appears as intimately related with computational universality in formal systems, might be a precursor of self-consciousness, and represent another all-pervasive feature.)

Of course the 'Teilhard' postulate may turn out to be wrong. Yet, the optimistic view that the universe be born intelligible and beautiful, and that its evolution be ultimately driven by an algorithm that could be understood by virtually anyone, boosts interesting research.

The main reason for considering the outlined plan as not excessively unrealistic comes from appreciating the full power of emergence, and the lesson from elementary cellular automata. While these automata cannot be taken as a realistic, direct substratum for the physical universe, they clearly indicate that particles, self-reproduction and pseudo-randomness -- three fundamental ingredients for cooking complexity -- can emerge from the computations of an elementary formal system. I believe this is one of the most important lessons from NKS.

Graph-based models such as spin networks, or just plain undirected, unlabeled trivalent graphs, appear as more flexible and plausible candidates for a computational ToE than CA's. And although particles have not yet convincingly emerged from dynamic trivalent network experiments so far, I am quite excited about the results I have obtained during the last year. In my experiments with a specific trivalent network mobile automaton (see NKS'07 conference) I could not yet spot particles, but I did find a number of other interesting things -- most notably, a computation (code 4-17-8) that appears as the perfect randomization of a trivial, visit-and-grow procedure.
I cannot yet compete with ECA 110, but what I have found appears to me as the equivalent of ECA 30; and one of the NKS assumptions is that pseudo-randomness, as found in the latter, is a sign of computational universality, as achieved by the particles in the former.

(Find the full details of the 'trinet' mobile automaton in the technical report: http://puma.isti.cnr.it/download.ph...2007-TR-016.pdf ;
see also the demo at http://demonstrations.wolfram.com/P...woRewriteRules/ .)

And once we see particles emerge from trinets, we are left with an even more challenging objective: to spot in their dynamics the emergence of natural evolution mechanisms. Too ambitious?
No phenomena resembling the far-reaching, robust evolutionary processes of the biosphere have been explicitly observed in CA computations so far, at least to my knowledge, although one might speculate that something similar obscurely happens during the initial, random-like phases of some class 4 computation.
However, some optimism is justified, in light of the minimality of the mechanisms sufficient for triggering and sustaining a whole evolution process, as well illustrated, e.g., by R. Dawkins.


Posted by: RLamy

I'm glad to see someone is tackling what I consider the most interesting part of Wolfram's book. There is however one point of your program with which I disagree: I don't think a Turing-machine-like system is a very good candidate for a model of physics.

To have identifiable particles, the system must have a locality property, in the sense that when a site is updated, its new state should depend only on the state of neighbouring sites at the time of its previous update. Amongst your systems, those that could be physics-like are necessarily those that can travel arbitrarily far between consecutive updates of the same site, which means that there is absolutely no guarantee of locality (one would rather expect a completely chaotic behaviour, in fact). There remains the possibility that the interaction of particles with a random background produces a stochastic effective locality, but this would be an emergent property, and probably quite difficult to assess.

In contrast, CA-like systems (iterated local maps, for a suitable definition of "local") have locality built-in and the existence of particles in them tends to be rather easily assessed.


Posted by: Tommaso Bolognesi

The trinet algorithms use indeed the Turing-machine-like approach that Wolfram calls 'network mobile automaton'; sites are updated one at a time, with the control head moving in a sort of (deterministic) brownian motion, rather than being updated in synchronous parallelism, as done with CAs.

Two reasons for this choice are:

1 - Updating one site -- a tiny portion of the graph, involving only one or two nodes -- is cheaper, more 'natural' , or primitive, than updating all of them simultaneously: Occam's principle of minimality suggests to avoid a global clock.

2 - The notion of physical time that emerges from network mobile automata is extremely interesting to me, especially in light of the fair, random-like computation 4-17-8. There is an external time -- objective time, or God's time--, which corresponds to the steps/ticks of the algorithm and is not directly accessible to us. (Perhaps we should not even call it 'time'.) Then there is the 'real' physical time -- internal, subjective, relative time -- the one perceived by observers (ultimately, by humans) that are part of the universe itself, and that are located in a specific place inside it. These concepts can be made quite precise, in the context of network mobile automata, and are not purely philosophical. They should for example lead to the prediction of some physical constant.
On the contrary, in CAs there seems to be only one, rather obvious notion of time, and no way to conceive a relativistic view -- at least, not at the most fundamental level.

You are right in observing that in trinet mobile automata the neighborhood of a site X is very likely to change between two consecutive updates of X; this does violate your (admittedly strong) notion of locality.
But then you say that identifiable particles can only emerge if the system has this strong locality property.
I understand that this requirement may promote the emergence of directly observable particles, and ECA 110 illustrates this fact quite well. But this type of direct observation may not be the proper one for a fundamental physics (at least, one addressed to humans): these particles are visible to an external observer, under an external, global time -- they are in God's eye, and move in God's time.
What we need instead is observer-dependent particles, that move in observer-time. I agree that this is harder.

The problem with computer experiments is that they make it easy to play God, and hard to play human.

Another (related) argument in favour of particle emergence even without synchronous updates comes from the notion of compressed computation. The computations of ECA 110 can be simulated by a suitable Turing Machine; you do not see particles in the full trace of the TM (stacking tape snapshots), but when the stack is properly compressed, particles become visible.
Here compression plays somehow the role of an observational filter, or converter from external/objective to internal/subjective view.

If particles ever emerge from trinet mobile automata, and I hope they will (trinions?), they would manifest themselves in properly filtered instances of the dynamic graphs; we need smart complexity indicators, hopefully reflecting the idea of observing dynamic graphs from inside...

In any case, your comments are very interesting and stimulating. In particular, I wonder whether you have in mind (or in paper?) some graph rewriting system based on a CA-like synchronous update policy, in which, according to what you say, particles would emerge more easily/visibly.


Posted by: tomjones

So in your simulation how would you know wether some aspect of your graph network represents a particle or not? Of course you can make any assignment you want but do you really believe that you'll get all the richness of the world around us from such a model? Further more it seems to me there are more basic elements that would need to be in place in your model before particles would emerge. For example a constant speed of light, gravity...

Thanks


Posted by: PaulR

I think there is considerable merit in Tommaso's ideas subject to one critical variation.

This variation is necessary because the idea of a "particle" is the most difficult one, for elementary physics. Any theory that starts with a particle fails to explain "where did it come from?" and "what is it made of”?
An alternative approach is available which maintains the elegance and symmetry principles and incorporates the ideas of emergence of complexity by evolution from simplicity, via basic mechanisms which can be modelled by CAs.
The critical variation is to understand basic particles as being complex patterns of insubstantial elementary nodes, which are merely fluctuations in the zero energy space. To put this another (more controversial) way, there is no such thing as a particle, only interactions of patterns.
This approach makes it easier to understand some of the characteristics of the smallest scale quantum world, such as tunnelling, randomness, diffraction, wave-particle duality. And it also appears to be scaleable up to the largest phenomena.
The attached PDF file tries to illustrate this approach verbally. I think it ties right in with Tommaso's approach, which is very promising.


Posted by: Tommaso Bolognesi

Wolfram suggests that a particle might be a local non planarity in an otherwise planar graph, or a specific pattern (a subgraph) that, due to the rewriting game, appears to move across an otherwise regular grid. These are just examples; but it may also be that particles manifest in more subtle ways, especially when adopting the 'internal observer' viewpoint discussed earlier.

In general, however, once the proper observational viewpoint is established, and corresponding diagrams are produced, a particle should be anything that my 8-year old daughter could spot without hesitation. There should be a background and a clearly identifiable something that springs out of it and moves. There are probably many ways in which this can happen, and one of the good lessons of NKS is to run experiments without predefined expectations. I am pretty sure that nobody has ever imagined the corkscrew particle of ECA 110 before actually seeing it.

You may be right: other meaningful phenomena might emerge before particles, but even forces are mediated by them, so it seems reasonable to expect particles, in very elementary forms, to be among the first actors to come up on stage.

In ECAs, the speed of light is the 45 degree angle. An upper limit for the transmission of information is also readily obtained in all confluent rewrite systems: once you arrange the rewrite events in a partial order, you have a discrete spacetime in which a 'light cone' concept is immediately available. These ideas are discussed in the NKS book, and were nicely illustrated by Oyvind Tafjord at NKS 2004 (find his slides here: http://www.wolframscience.com/confe.../presentations/).
Of course, this is still rather abstract, and precise numeric predictions could only be made after many more assumptions and findings.

Do I really believe that all the complexity of the world around us can emerge from such a model?
No.
I believe the model should be simpler than the trinet mobile automaton, although it might still end up involving dynamic trinets. For example, I am currently playing with two things: the program/rule, which is fixed, and a graph, which changes. It would be great to have one thing only: a graph that represents both space and the program that operates on it(self). One is simpler than two. Emergence might be even more creative, in that setting!

My personal opinion is that, once the process of looking for increasingly simple and unifying explanations has been started, and rather encouraging intermediate results have been achieved (such as recognizing that a falling apple and an orbiting moon follow the same law), it would be unwise not to push it to the limit, and look for the smallest conceivable law. The computational-Universe assumption seems to offer a great opportunity to achieve such minimality, with 'law' replaced by 'rule'.


Posted by: RLamy

Originally posted by Tommaso Bolognesi
1 - Updating one site -- a tiny portion of the graph, involving only one or two nodes -- is cheaper, more 'natural' , or primitive, than updating all of them simultaneously: Occam's principle of minimality suggests to avoid a global clock.

Ah, but there is a global clock in your system: the sequence of elementary simulation steps provides a total ordering of update events. In CAs, locality limits the impact of the global clock: for an observer inside the CA, what happens now 1000 cells away has no relevance and will only perhaps matter in 500 time steps. The observer will probably even never be able to know what exactly happened at what time. In mobile automata, one has to rely on emergent locality to get the same effect.

The systems this argument actually favors aren't mobile automata but multiway systems. Or, as Wolfram argues p.504 and following, systems with invariant causal networks.

2 - The notion of physical time that emerges from network mobile automata is extremely interesting to me, especially in light of the fair, random-like computation 4-17-8. There is an external time -- objective time, or God's time--, which corresponds to the steps/ticks of the algorithm and is not directly accessible to us. (Perhaps we should not even call it 'time'.) Then there is the 'real' physical time -- internal, subjective, relative time -- the one perceived by observers (ultimately, by humans) that are part of the universe itself, and that are located in a specific place inside it. These concepts can be made quite precise, in the context of network mobile automata, and are not purely philosophical. They should for example lead to the prediction of some physical constant.
On the contrary, in CAs there seems to be only one, rather obvious notion of time, and no way to conceive a relativistic view -- at least, not at the most fundamental level.


I guess that the proper way to look at this is to examine causal networks where edges corresponding to redundant information are removed. This can yield interesting results even for ECAs. To take a trivial example, the identity map, rule 204, yields in this scheme a causal network with a linear chain for each cell. In the general case, there is probably no unique way to define the network, but I suspect that every possible choice will have the same qualitative features.

I think you can easily check for locality in your automata by assessing whether the number of nodes in the causal network at a distance t from a given node is bounded by a polynomial.

The problem with computer experiments is that they make it easy to play God, and hard to play human.

Very well said! Actually, I don't know of any convincing attempt to understand what an NKS-system looks like when seen from the inside. Perhaps we should build our intuition on this point using easily visualized systems, before tackling systems where we can't use the tremendous pattern recognition capabilities of our visual cortex.




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