Local and global models of physics and computation

Abstract

Classical computation is essentially local in time, yet some formulations of physics are global in time. Here, I examine these differences and suggest that certain forms of unconventional computation are needed to model physical processes and complex systems. These include certain forms of analogue computing, massively parallel field computing and self-modifying computations.

Keywords:

• unconventional computation
• Newtonian schema
• principle of least action
• field computing
• complex systems
• self-modifying code

Acknowledgements

My thanks to Angelika Sebald for highlighting the important distinction between statistical ensembles and growing systems.

Notes

1 Here, I give only a thumbnail sketch of the approaches, extracting the essence that affects the computational argument. For a more rigorous discussion, see a good textbook on classical mechanics, such as Goldstein (1980).

2 More correctly, of stationary action.

3 Higher order differential equations can be expressed as first-order equations by introducing more variables. For example, can be expressed in normal form with two equations: .

4 A robust numerical integration would use a more sophisticated numerical method than this. However, this simplistic algorithm illustrates the basic underlying computational principle.

5 A rule such as can be read as “ has 8 legs if is a spider”, and can be read as “archy is an insect”.

This work was partly funded by the EU FP7 FET Coordination Activity TRUCE (Training and Research in Unconventional Computation in Europe), project reference number 318235.