When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169): September 8, 2014 ©2014 by The Royal Society

Representation in physics. Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Parallel evolution of theory and experiment. Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

A ‘good enough’ commuting diagram for an experiment to test a theory. Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Reversing the modelling relation within science: (a) a fully commuting diagram for physical and abstract evolution, based on a modelling relation only. Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Technology reversing the modelling relation: p, T and H are found such that these conditions hold. Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

(a) Embedding an abstract problem ms into an abstract machine description mp using embedding Δ, then encoding into p. Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Physical computation, with layers of refinement R on top for base ten (decimal) addition (‘dec add’), binary addition (‘binary add’) and assembly language addition (‘asm add’). Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

(a) Two separate physical systems, p and s. Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

System s running as a simulator for system p, constructed as a compute cycle nested within a predict cycle: (a) the predict cycle using C(p) to find the abstract prediction for the evolution of system p; (b) embedding C(p) in the simulator model dynamics, C... Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

A system simulating itself (compare with figure 8c). Clare Horsman et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society