Re: Are proofs equivalent to dovetailing computations?

On 8/24/2019 1:35 PM, Jason Resch wrote: That seems more like the arithmetical explanation of the quantum indeterminacy. The thermodynamics would be more related to some identification of the length of a finite computation and its code. A short code leading to a long computatio

Re: Are proofs equivalent to dovetailing computations?

On Sat, Aug 24, 2019 at 4:52 AM Bruno Marchal wrote: > > On 24 Aug 2019, at 00:23, Jason Resch wrote: > > > > On Sat, Aug 17, 2019 at 5:17 AM Bruno Marchal wrote: > >> >> On 16 Aug 2019, at 19:06, Jason Resch wrote: >> >> Would Chaitin's constant also qualify as a compact description of the >>

Re: Are proofs equivalent to dovetailing computations?

> On 24 Aug 2019, at 00:23, Jason Resch wrote: > > > > On Sat, Aug 17, 2019 at 5:17 AM Bruno Marchal > wrote: > >> On 16 Aug 2019, at 19:06, Jason Resch > > wrote: >> Would Chaitin's constant also qualify as a compact description of the

Re: Are proofs equivalent to dovetailing computations?

On Sat, Aug 17, 2019 at 5:17 AM Bruno Marchal wrote: > > On 16 Aug 2019, at 19:06, Jason Resch wrote: > > Would Chaitin's constant also qualify as a compact description of the > universal dovetailing (though being a single real number, rather than a set > of rational complex points)? > > > It do

Re: Are proofs equivalent to dovetailing computations?

> On 19 Aug 2019, at 03:25, Russell Standish wrote: > > On Sat, Aug 17, 2019 at 12:17:38PM +0200, Bruno Marchal wrote: >> >> You cannot identify a computation and a representation of that computation. >> So >> the answer is no: the blockhead or the infinite look-up table does not >> process

Re: Are proofs equivalent to dovetailing computations?

On Sat, Aug 17, 2019 at 12:17:38PM +0200, Bruno Marchal wrote: > > You cannot identify a computation and a representation of that computation. So > the answer is no: the blockhead or the infinite look-up table does not process > a computation. That is incorrect. Lookup tables _are_ computations,

Re: Are proofs equivalent to dovetailing computations?

> On 16 Aug 2019, at 19:06, Jason Resch wrote: > > > > On Wed, Aug 14, 2019 at 5:02 AM Bruno Marchal > wrote: > >> On 12 Aug 2019, at 23:36, Jason Resch > > wrote: >> >> In "The Universal Numbers. From Biology to Physics" Bruno writes >

Re: Are proofs equivalent to dovetailing computations?

Chaitin numbers of course can also be extended to the computational hierarchy (oracles, Turing jump iterations of the halting problem): Super-Ω https://en.wikipedia.org/wiki/Chaitin%27s_constant#Super_Omega https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2011.0319 @philipthrift On Fri

Re: Are proofs equivalent to dovetailing computations?

On Fri, Aug 16, 2019 at 6:31 PM Russell Standish wrote: > On Fri, Aug 16, 2019 at 12:06:32PM -0500, Jason Resch wrote: > > > > Thanks for the background and explanation. Is it the case then that any > > undecidable (creative?) set is a compact description of universal > dovetailing? > > Would Ch

Re: Are proofs equivalent to dovetailing computations?

On Fri, Aug 16, 2019 at 12:06:32PM -0500, Jason Resch wrote: > > Thanks for the background and explanation.  Is it the case then that any > undecidable (creative?) set is a compact description of universal > dovetailing?  > Would Chaitin's constant also qualify as a compact description of the >

Re: Are proofs equivalent to dovetailing computations?

On Wed, Aug 14, 2019 at 5:02 AM Bruno Marchal wrote: > > On 12 Aug 2019, at 23:36, Jason Resch wrote: > > In "The Universal Numbers. From Biology to Physics" Bruno writes > > "The universal dovetailing can be seen as the proofs of all true Sigma_1 > propositions there exists x,y,z such that P_x(

Re: Are proofs equivalent to dovetailing computations?

> On 12 Aug 2019, at 23:36, Jason Resch wrote: > > In "The Universal Numbers. From Biology to Physics" Bruno writes > > "The universal dovetailing can be seen as the proofs of all true Sigma_1 > propositions there exists x,y,z such that P_x(y) = z, with some sequences of > such propositions m

Re: Are proofs equivalent to dovetailing computations?

On Tue, Aug 13, 2019 at 02:41:09AM -0700, Philip Thrift wrote: > > If only there were a dovetailer to multiplex all one's duties. :) They made a movie about that, starring Tom Hanks IIRC. Can't tremeber the title, though... -- --

Re: Are proofs equivalent to dovetailing computations?

If only there were a dovetailer to multiplex all one's duties. :) @philipthrift On Tuesday, August 13, 2019 at 4:08:28 AM UTC-5, Bruno Marchal wrote: > > Jason, > > Interesting and important questions. Unfortunately today I have family > duties … , > I will answer in the evening or tomorrow. (

Re: Are proofs equivalent to dovetailing computations?

Jason, Interesting and important questions. Unfortunately today I have family duties … , I will answer in the evening or tomorrow. (Same for possible other posts), Best, Bruno > On 12 Aug 2019, at 23:36, Jason Resch wrote: > > In "The Universal Numbers. From Biology to Physics" Bruno writ

Re: Are proofs equivalent to dovetailing computations?

On Mon, Aug 12, 2019 at 4:36 PM Jason Resch wrote: > In "The Universal Numbers. From Biology to Physics" Bruno writes > > "The universal dovetailing can be seen as the proofs of all true Sigma_1 > propositions there exists x,y,z such that P_x(y) = z, with some sequences > of such propositions mim