Reality Is Ultimately Digital, and Its Program Is Still Undebugged by Tommaso Bolognesi

Hi Don,

1) Thank you.

2) You refer to the JOUAL 2009 conference . Four of the six regular papers presented at the event are now published in Complex Systems . I could add that one of those authors - Alex Lamb - has just submitted an interesting essay at this contest, which matches very well, again, the JOUAL focus! Go take a look.

3) That's what I call the 'Teilhard conjecture' (after T. de Chardin). We are still very far from its experimental validation, but if it turned out to be false, all the experiments I am running on computational, causet-based big bangs would be, mostly, wasted cpu time...

4) I fully agree.

Dear James Putnam,

your post triggers a number of reactions, probably (and unfortunately) more than I can put in a post here.

The first general point I need to clarify is that, in an attempt to be concise in writing the essay, I adopted a style, especially in the opening that you quote, which may indeed sound more 'assertive' than that of a stardard scientific paper. On the other hand, I believe that a bit of 'assertiveness' may be helpful for stimulating discussions, in a context such as the FQXi forum.

And in the sequel of the essay, in particular in Section 3 - 'Experimental validation', I do put my views in the right perspective.

I did not feel like using more space just for supporting the validity of the idea of working with discrete models such as causal sets, in light of the aboundance of solid papers that share that view as a very reasonable working hypothesis, to say the least.

You ask: By which means does a discrete spacetime grow?

Rideout and Sorkin [Phys. Rev. D 61, 024002, 2000] discuss classical dynamics for causal set growth, using *probabilistic* techniques.

Out of the several ways I have explored (by simulations) for obtaining causal sets by *deterministic algorithms*, the one that I personally consider most attractive consists in letting a 'stateless ant' walk on a trivalent graph G while applying, step by step, one out of two possible graph rewrite rules (known also in Loop Quantum Gravity, and used by Smolin, Markopoulou & friends). G can be equated to a growing space, while spacetime corresponds to the causal set of the computation being performed on it (the relevant references are [1-5], [8], [14] and [17]).

One of the two graph rewrite rules introduces a new node in G, so this rule would be responsible for the growth of space. But spacetime (the causal set) grows at *every* rewrite rule application, since:

1 rewrite rule application = 1 computation step = 1 node (event) added to the causal set (spacetime).

In this respect, my approach is indeed in contrast with the following statement from your essay:

"The universe evolves, but not because simplicity can generate complexity. Complexity can come only from pre-existing complexity. The greatest possible effects of complexity in the universe exist right from its start in a potential state."

I tend to disagree on that, based on the phenomenon of deterministic chaos, or algorithmic randomness. The best example of this is perhaps Wolfram's elementary cellular automaton n. 30: in spite of the elementary initial condition and the very simple rule (coded by a boolean function of three variables), the computation dynamics exhibit surpring pseudo-random character, as if information were continuously injected in the process from outside.

I like to believe (ideology again!) that our universe started from nothing, or almost nothing, and that space, spacetime, and complexity did increase: they were not 'already there' at the beginning, unless you mean that all the complexity of the mentioned rule 30 computation is 'potentially' present in the few bits that code its initial condition and boolean function.

I remember a workshop at the Phys. Dept. of the Padova Univ. (Jan 15, 2008) with lively discussions on String Theory vs. Loop Quantum Gravity. During the panel, Gabriele Veneziano and Carlo Rovelli did agree on one thing: they both were unable to point out a crucial validation/falsification experiment for their respective theories. I believe I am in good company in claiming that, in physics, both imaginative hypotheses and accurate experimental verification are necessary. If you call the former 'ideological', then I am afraid my essay has a lot of ideology in it. And, although I also provide simulation results (more in the references) that suggest interesting analogies with physical phenomena (e.g. the emergence of interacting objects!), my research on causal sets (as well as that of many others) is still very far from precise numerical predictions.

Since this is getting long, I answer to the remark on the self-modifying program in the next post. Looking forward to your comments after reading the essay. Thanks for your stimulating remarks!

Tommaso

Dear James,

you quote my essay:

"Perhaps it is a self-modifying program: code and manipulated data might coincide. ..."

and ask:

Self? In other words by mechanical magic?

The funny thing is that I had removed this line from the quasi-final version of the essay, because I did not have enough space for expanding on it. But then I put it back, being ready to accept questions or criticism. Thank you for giving me an opportunity to explain.

The idea of a self modifying program is, again, an attempt to satisfy the requirement of minimality. While I support the computational universe idea, what I find a bit annoying is the separation between (i) a (fixed) program P and (ii) the data D that it manipulates. Under this view, D represents our Reality, while P would be the rule that governs it, without enjoying itself the status of a Real entity. They are two things, and one of them is even 'unreal'. Two is bigger than one. If the program operates on itself, we would have only one thing: P = D = Reality. That would be more elegant. I believe that the Mathematical Universe idea by Max Tegmark also achieves this unity: there's only one thing, namely a mathematical structure.

By the way, the concept of a self-modifying program is quite familiar in computer science, e.g. in logic programming (in the Prolog language etc.). Furthermore, self-reference is a recurrent concept when dealing with formal systems (Goedel's theorem), computation (universal Turing machines), not to mention consciousness. I would not be surprised at all if it played a crucial role in an ultimate, computational theory of physics.

If you claim that there is something magic in a program that modifies itself (= Reality), then I'd expect you to claim the same for a program that modifies 'external' data (= Reality). In my opinion, there is no more magic in a program that runs our Reality, than in a set of differential equations that does essentially the same thing.

Cheers. Tommaso

PS

So far I've done only few experiments on self-modifying Turing machines, without exciting results. In all the experiments mentioned in the essay, data and program are separated, and the latter is fixed.

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 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.