• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
A billiard-ball computer, a type of conservative logic circuit, is an idealized model of a reversible mechanical computer based on Newtonian dynamics, proposed in 1982 by Edward Fredkin and Tommaso Toffoli.
Science done based on an idealized model does not make much sense, specific based on a rather speculative subject.
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.
The environment is never friction-free. Bouncing is also never friction free. Both involve energy loss, which makes the process irreversible.
It was devised to investigate the relation between computation and reversible processes in physics.
Operating a computer always involves energy.

### 1. Simulating circuits with billiard balls

This model can be used to simulate Boolean circuits in which the wires of the circuit correspond to paths on which one of the balls may travel, the signal on a wire is encoded by the presence or absence of a ball on that path, and the gates of the circuit are simulated by collisions of balls at points where their paths cross.
Okay.
In particular, it is possible to set up the paths of the balls and the buffers around them to form a reversible Toffoli gate, from which any other Boolean logic gate may be simulated.
The definition of a reversible gate is required.
Therefore, suitably configured billiard-ball computers may be used to perform any computational task.
This statement is too strong, without any true evidence.

### 2. Simulating billiard balls in other models of computation

It is possible to simulate billiard-ball computers on several types of reversible cellular automaton, including block cellular automata and second-order cellular automata.
If block cellular automata operation is reversible I leave an open question. Any way if it involves copying (see https://en.wikipedia.org/wiki/Reversible_cellular_automaton) , such a copying operation involves energy (large or small), but that makes the operation irreversible.

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Created: 11 January 2022

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