Abstract

There's Plenty of Room at the Bottom, said the title of Richard Feynman's 1959 seminal conference at the California Institute of Technology. Fifty years on, nanotechnologies have led computer scientists to pay close attention to the links between physical reality and information processing. Not all the physical requirements of optimal computation are captured by traditional models--one still largely missing is reversibility. The dynamic laws of physics are reversible at microphysical level, distinct initial states of a system leading to distinct final states. On the other hand, as von Neumann already conjectured, irreversible information processing is expensive: to erase a single bit of information costs ~3 × 10ź21 joules at room temperature. Information entropy is a thermodynamic cost, to be paid in non-computational energy dissipation. This paper addresses the problem drawing on Edward Fredkin's Finite Nature hypothesis: the ultimate nature of the universe is discrete and finite, satisfying the axioms of classical, atomistic mereology. The chosen model is a cellular automaton (CA) with reversible dynamics, capable of retaining memory of the information present at the beginning of the universe. Such a CA can implement the Boolean logical operations and the other building bricks of computation: it can develop and host all-purpose computers. The model is a candidate for the realization of computational systems, capable of exploiting the resources of the physical world in an efficient way, for they can host logical circuits with negligible internal energy dissipation.

Highlights

  • Abstract ‘‘There’s Plenty of Room at the Bottom’’, said the title of Richard Feynman’s 1959 seminal conference at the California Institute of Technology

  • The framework is a proper implementation of what computational physicist Edward Fredkin has called Finite Nature hypothesis: Finite Nature is a hypothesis that every quantity of physics, including space and time, will turn out to be discrete and finite; that the amount of information in any small volume of space–time will be finite and equal to one of a small number of possibilities. [...] Finite Nature implies that the basic substrate of physics operates in a manner similar to the workings of certain specialized computers called cellular automata (Fredkin 1993: 117)

  • By producing our /-rule-based cellular automaton (CA), we put forward a new CA that satisfies natural constraints from the ontology of physics and may well serve as a model to understand the duality of physical processes and information

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Summary

Cellular Automata and the Physics of Information

Cellular Automata (CA) are mathematical representations of complex dynamical systems whose macro-behaviour is determined by non-linear relations among its micro-constituents. Several features make CA appealing to information scientists They simulate a variety of adaptive processes: from urban evolution (Batty 2005), to Ising models (Creutz 1986), neural networks (Franceschetti et al 1992), and turbulence phenomena (Chen et al 1983). The framework is a proper implementation of what computational physicist Edward Fredkin has called Finite Nature hypothesis: Finite Nature is a hypothesis that every quantity of physics, including space and time, will turn out to be discrete and finite; that the amount of information in any small volume of space–time will be finite and equal to one of a small number of possibilities. There’s Plenty of Boole at the Bottom: A Reversible CA

A Digital Universe
Weak and Strong Reversibility
Niceties
Information Entropy
Universal Computation
Duplication
Delays
Conclusions
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