Assumptions of Physics - From Classical Mechanics to Field Theory

13:13 How do you define volume in an infinite dimensional phase space on a finite whiteboard? 

1:05:39 I enjoyed listening to this discussion. Thanks to everyone who took part. 

I was thinking about causal sets as modeling those second countable collections of empirically verifiable statements. That may not be how Sorkin sees it though! See Geometry from order: causal sets. 

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See also this discussion with Urs Schreiber on Gauge fields and configuration spaces at 44:33.

The earlier discussion he referred to on differential geometry and compact spaces is at 17:05 

He's saying that you do not want to restrict physics to describing only compact spaces. But you do want to restrict observations to compact spaces. At 26:03 you can get a coherent notion of field configuration spaces in a topos.

35:37 William Lawvere's early career in physics. See also Vladimir Voevodsky - What if Current Foundations of Mathematics are Inconsistent. 

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