Billiard-ball computer

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Fredkin and Toffoli Gate Billiard Ball Model
Fredkin and Toffoli Gate Billiard Ball Model

A billiard ball computer as in [1] is an idealized model of a computing machine based on Newtonian dynamics. Instead of using electronic signals like a conventional computer, it relies on the motion of spherical billiard balls in a friction-free environment made of buffers against which the balls bounce perfectly. It was devised to provide context to the Halting problem and similar results in computability. A paradox seems to arise as a consequence of the existence of this ideal machine, since it shows that it is possible to construct a system from billiard balls where there exists no algorithm to predict whether the system will provide an "output" for any given "input", apparently contradicting the expectation that the Newtonian motion of the balls is deterministic.

The billiard ball model was proposed in 1982 in a seminal paper[2] of Edward Fredkin and Tommaso Toffoli. The work on this and similar models was continued by the MIT Information Mechanics group and has strong relations with the present Amorphous computing group at MIT or the Quantum Mechanical Hamiltonian Model of Paul Beniof. Presently there are a few research lines related to these kind of models in what it is known as unconventional computing.

When the number of objects (such as billiard balls) in a system becomes large, we need new principles like the entropy or temperature [3] relations. And when the multitude of particles are able to react and change (not only in position and momentum) then new behaviours arise. The Amorphous computing paradigm prepares the engineering principles to observe, control, organize, and exploit the coherent and cooperative behaviour of programmable multitudes. It is a new paradigm of architecture on. The Unconventional [3] [4] and Biologically-inspired computing paradigms use asynchronous and decentralized agents and include the model of cellular automats. Recent works related to the billiard ball model are the particle-based model [5][6] [7] and the reaction and diffusion of chemical species [8].

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  1. ^  Penrose, R. The Emperor's New Mind. Oxford University Press. 1989
  2. ^  Fredkin, Toffoli, Int. J. Theor. Phys. 21 (1982), 219-253. http://www.digitalphilosophy.org/download_documents/ConservativeLogic.pdf describes the Billiard-Ball model
  3. ^  Unconventional computation Conference 2007 , http://cnls.lanl.gov/uc07/
  4. ^  Information Mechanics and Unconventional computating, http://www.interquanta.biz/im/
  5. ^  "Particle-based Methodology for Representing Mobile Ad-Hoc Networks", InterSense 2006 Conference Nice ACM Press New York
  6. ^  "Special issue on particle based modelling methods applied in biology", Issue 7 May 2001, ACM
  7. ^  "Physics-Based Models to Support Test and Evaluation, S. Blankenship & F. Mello, High Performance Computing Workshop 1998" http://www.dtc.army.mil/hpcw/1998/blanken/blanken.html
  8. ^  the Gray-Scott model of a chemical reaction. http://www-swiss.ai.mit.edu/projects/amorphous/GrayScott/