FOM: Thesis M

[Kanovei]

>Date: Mon, 09 Nov 1998 12:50:28 -0500
>From: Joe Shipman <shipman at savera.com>

>   Thesis M (for 'mechanical'): The behavior of any discrete physical
>  system evolving according to local mechanical laws is recursive.
> Yes, key words "discrete" and "local"

*behavior* and *recursive* are also a good words. 
In the formulation above, thesis M is \Sigma_3, that is, 

(for any system)(there is Goedel number)(for any moment of time)

This makes M physically meaningless, at least 
1) far different from usual laws of physics which are Pi_1,
2) having no meaning also because the development of the 
universe may not allow infinitely long time, or, in other words, 
inf. many steps, which is necessary for any sort of understanding 
of the thesis that something is recursive. 

I would suggest a more meaningful form: 

FM: The behavior of any discrete physical
system, evolving according to local mechanical laws, 
in the course of time period T, is recursive with 
Goedel number much less than both T and the description 
of the system (including essential boundary conditions).

This moves the thesis back to \Pi_1. The meaning of 
*much less* can be determined via e.g. the Ackermann 
function or some other similar way. 

V.Kanovei