when does a physical system compute? by clare horsman, susan stepney, rob c. wagner, and viv kendon...

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When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8, 2014 ©2014 by The Royal Society

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Page 1: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

When does a physical system compute?

by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon

Proceedings AVolume 470(2169):20140182

September 8, 2014

©2014 by The Royal Society

Page 2: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

Representation in physics.

Clare Horsman et al. Proc. R. Soc. A 2014;470:20140182

©2014 by The Royal Society

Page 3: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

Parallel evolution of theory and experiment.

Clare Horsman et al. Proc. R. Soc. A 2014;470:20140182

©2014 by The Royal Society

Page 4: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

A ‘good enough’ commuting diagram for an experiment to test a theory.

Clare Horsman et al. Proc. R. Soc. A 2014;470:20140182

©2014 by The Royal Society

Page 5: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

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;470:20140182

©2014 by The Royal Society

Page 6: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

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;470:20140182

©2014 by The Royal Society

Page 7: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

(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;470:20140182

©2014 by The Royal Society

Page 8: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

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;470:20140182

©2014 by The Royal Society

Page 9: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

(a) Two separate physical systems, p and s.

Clare Horsman et al. Proc. R. Soc. A 2014;470:20140182

©2014 by The Royal Society

Page 10: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

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;470:20140182

©2014 by The Royal Society

Page 11: When does a physical system compute? by Clare Horsman, Susan Stepney, Rob C. Wagner, and Viv Kendon Proceedings A Volume 470(2169):20140182 September 8,

A system simulating itself (compare with figure 8c).

Clare Horsman et al. Proc. R. Soc. A 2014;470:20140182

©2014 by The Royal Society