## Round Table

Experiments with emergence in models of computation: a new kind of physics?

## Participants

*Vieri Benci*

*Applied Mathematics Dept., Pisa University*

*Hans Thomas Elze*

Physics Dept., Pisa University

*Renate Loll*

Institute for Theoretical Physics, Utrecht University

*Juergen Schmidhuber*

IDSIA - Dalle Molle Institute for Artificial Intelligence, Lugano

*Stephen Wolfram*

Wolfram Research

Moderator:

*Tommaso Bolognesi*- CNR/ISTI, Pisa

## Motivation

The round table (as well as the whole JOUAL Workshop) is meant to establish some link between two rather different communities.One one hand, there is a relatively sparse but growing group of researchers and enthusiast practitioners, identifying themselves by keywords such as 'Digital Physics' and 'NKS' (New Kind of Science), often with roots in computer science or complex systems more than in quantum mechanics or general relativity, that endorse a radical, computational view at the physical universe. For them, the ultimate, unifying laws of physics might take the form of a simple computer program. Consequently, they mine the computational universe with an attitude somewhat similar to that of an entomologist, in search for such programs.

On the other hand, theories of more genuine and standard physical nature address the problem of a unified theory (say, a theory of quantum gravity) based on more consolidated and provably effective tools and techniques; these people work with manifolds, fields, symmetry groups, Lagrangians and Hamiltonians, path integrals, and expect the unifying laws of physics to take the form of differential equations.

Optimistically, two results of this meeting might be:

1. Providing a stronger basis, in terms of existing physical theories, to the computational experiments carried on, often in a fully abstract way, by people in the first community, and suggesting alternative, computational experiments.

2. Assessing and perhaps strengthening the role that emergent properties of simple program computations (e.g. pseudo-randomness, pseudo-particles, fractals/nesting) might play in the context of current physical theories, in quantum gravity or elsewhere.

## Questions

- Could all the complexity we observe in the physical universe emerge by just iterating a few simple state transition rules, and be virtually reproducible by running a few lines of code?

- Which are the concepts/phenomena from physics that computational models and their emergent properties are more likely / less likely to successfully capture, ? (Gravity, quantum behavior, particle/wave duality, ...)

- Which kind of programs running on which type of computational device could in principle provide a concise description of quantum physics?

- Which discrete models from physics (and from quantum gravity) best lend themselves to computational experiments on emergence?

- What is the importance attributed by physicists to emergence in computation, as illustrated by the moving structures (particles, gliders) of cellular automata such as Wolfram's Rule 110 or Conway's Game of Life? Is it just a bizarre, irrelevant coincidence? A useful metaphor? A key to a deeper theory of physics?

- How do different theories (Digital Physics, NKS, Loop Quantum Gravity, Causal Dynamical Triangulation, Causal Sets ...) picture the 'baby universe'? How simple do they allow it to be? Are these pictures compatible? Is there a state zero?

- Does current work on possible deterministic foundations for quantum mechanics (by G. 't Hooft) legitimate the (deterministic) computational universe picture?

- How can algorithmic information theory guide the quest for simple explanations of the world in the sense of Occam's razor?

- Are graph-rewrite systems more 'physical' than cellular automata? Is sequential updating (as in Turing machines) more 'physical' than parallel updating (CAs). Or, would all Turing-complete models yield the same physics? Do causal sets play a role here?

- Is it conceivable that the simple evolutionary mechanisms operating in the biosphere be also active in particle physics? How could this be possibly taken into account in current theories of quantum gravity or digital physics? Should the 'program' be able to modify itself?

## Some inspiring quotes

J. A. Wheeler, Foreword of J. D. Barrow, P. C. W. Davies, C. L. Harper (eds.) Science and Ultimate Reality - Quantum Theory, Cosmology and Complexity, Cambridge Univ. Press, 2004.

*'Like many of the authors of this book, I remain convinced that some deeper reason for quantum mechanics will one day emerge, that eventually we will have an answer to the question "How come the quantum"?*

R. P. Feynman, The Character of Physical Law, November 1964 Cornell Lectures.

*‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’*

- G. 't Hooft, Determinism beneath quantum mechanics - arXiv:quant-ph/0212095v1 - 2002

*'Beneath Quantum Mechanics, there may be a deterministic theory with (local) information loss. This may lead to a sufficiently complex vacuum state, and to an apparent non-locality in the relation between the deterministic ("ontological") states and the quantum states, of the kind needed to explain away the Bell inequalities. Theories of this kind would not only be appealing from a philosophical point of view, but may also be essential for understanding causality at Planckian distance scales.'*

- Ed Fredkin, Five big questions with pretty simple answers - IBM J. Res. & Dev., Vol. 48, N. 1, Jan 2004

*'... what we have so far learned about digital informational processes seems to imply that many accepted concepts and laws of physics are informational impossibilities. All of these conflicts are resolved if the finite nature (FN) assumption is valid. Finite nature [Fredkin 1992] encompasses the following assumptions:*

* At some scale, space, time and state are discrete.

* The number of possible states of every finite volume of space-time is finite.

* There are no infinities, infinitesimals, or locally generated random variables.

* The fundamental process of physics must be a simple deterministic digital process.'

[...]

When we say that we have a computer model of some system, we normally mean that a subset of the data in the computer can be mapped onto the system being modeled.

[...]

We might be able to demonstrate that an ordinary computer model of physics is sufficient, but we cannot normally show that it is necessary. The reason is that any and all models of finite nature can be replaced by equivalent computational models based on any universal computer.

[...]

DM (Digital Mechanics) implies that there is a computer-like model that has a bijective mapping, one to one, from states and function in the real world to states and function in the model. This imposes absolute requirements that the computer-like model be spatially organized like cellular automata, be reversible, and be computation-universal.

[...]

The beauty of the 'one-to-one mapping onto' restriction is that it delivers us from the apparent tyranny of computation universality. It is unlikely that there will be more than one such correct model...

* At some scale, space, time and state are discrete.

* The number of possible states of every finite volume of space-time is finite.

* There are no infinities, infinitesimals, or locally generated random variables.

* The fundamental process of physics must be a simple deterministic digital process.'

[...]

When we say that we have a computer model of some system, we normally mean that a subset of the data in the computer can be mapped onto the system being modeled.

[...]

We might be able to demonstrate that an ordinary computer model of physics is sufficient, but we cannot normally show that it is necessary. The reason is that any and all models of finite nature can be replaced by equivalent computational models based on any universal computer.

[...]

DM (Digital Mechanics) implies that there is a computer-like model that has a bijective mapping, one to one, from states and function in the real world to states and function in the model. This imposes absolute requirements that the computer-like model be spatially organized like cellular automata, be reversible, and be computation-universal.

[...]

The beauty of the 'one-to-one mapping onto' restriction is that it delivers us from the apparent tyranny of computation universality. It is unlikely that there will be more than one such correct model...