"The Probing of, Approximation to and Idealization of Structure" for Foundations

[Guy_Walters]

Hey,

Over the past six years I have worked with Lucien Hardy at Perimeter in Waterloo and Prakash Panangaden at McGill. This paper is the culmination of thoughts on physics gleaned from that work.

 

On Introducing into the Foundations of Physics the Notions of "The Probing of, Approximation to and Idealization of Structure"

 

or try this link

On Introducing into the Foundations of Physics the Notions of "The Probing of, Approximation to and Idealization of Structure"

 

or this link

On Introducing into the Foundations of Physics the Notions of "The Probing of, Approximation to and Idealization of Structure"

 

 

Preamble:

After completing the requirements for an MSc in Computer Science at McGill University, I have attempted to formulate a novel view which places certain computational and mathematical concepts into the foundations of phycis. The following paper is deeply inspired by Panangaden, Keyes, Blute, Hardy and Ivanov's work as well as Lawvere's functorial semantics. Specifically, it takes an evolving universe as a Domain map with a Scott topology and further abstracts this to continuous functors so that a universe is evolving continuously over all structures. This is based on a tentative belief in a realist causal structure where the order relation is also seen as composition in a category. Attention is given to indefinite causal structure by looking at the Fischer impossibility result as an indication that, while Set is untenable for speaking about the universe, it is possibly natural for the universe to approximate the category of sets when the rich interplay of signalling systems is seen as a consensus protocol. This is all given a local semantics in that all knowledge is understood as derived from morphisms in a local lab. The morphisms in the history of the universe are mapped to local morphisms by a functor and a domain map.

 

Best,

 

Ben

Edited March 2, 2011 by Guy_Walters