Re: Are there real numbers that cannot be defined?

ISTM that the 8000th BB number is unknowable, rather than uncomputable. As Bruno said, there is a program that outputs the 8000th BB number, but we can never know that this program is the correct one. Cheers On Sun, Mar 03, 2019 at 12:28:54PM -0500, John Clark wrote: > > > On Sun, Mar 3, 2019

Re: Are there real numbers that cannot be defined?

On Mon, Mar 4, 2019 at 9:13 AM Bruce Kellett wrote: > On Mon, Mar 4, 2019 at 8:58 AM Brent Meeker wrote: > >> On 3/3/2019 1:37 PM, John Clark wrote: >> >> On Sun, Mar 3, 2019 at 2:52 PM Philip Thrift >> wrote: >> >> *> If a program "represents" a real number (e.g. in the spigot sense), >>>

Re: Are there real numbers that cannot be defined?

On Mon, Mar 4, 2019 at 8:58 AM Brent Meeker wrote: > On 3/3/2019 1:37 PM, John Clark wrote: > > On Sun, Mar 3, 2019 at 2:52 PM Philip Thrift > wrote: > > *> If a program "represents" a real number (e.g. in the spigot sense), >> then that could be said to "define" it.* > > > But for most Real

Re: Are there real numbers that cannot be defined?

On Sunday, March 3, 2019 at 3:38:18 PM UTC-6, John Clark wrote: > > On Sun, Mar 3, 2019 at 2:52 PM Philip Thrift > wrote: > > *> If a program "represents" a real number (e.g. in the spigot sense), >> then that could be said to "define" it.* > > > But for most Real Numbers there is no such

Re: Are there real numbers that cannot be defined?

On 3/3/2019 1:37 PM, John Clark wrote: On Sun, Mar 3, 2019 at 2:52 PM Philip Thrift > wrote: /> If a program "represents" a real number (e.g. in the spigot sense), then that could be said to "define" it./ But for most Real Numbers there is no such

Re: Are there real numbers that cannot be defined?

On Sun, Mar 3, 2019 at 2:52 PM Philip Thrift wrote: *> If a program "represents" a real number (e.g. in the spigot sense), then > that could be said to "define" it.* But for most Real Numbers there is no such program. * > But what does it mean for a real number to be "defined"?* If you can

Re: Recommend this article, Even just for the Wheeler quote near the end

On Sunday, March 3, 2019 at 1:43:58 PM UTC-6, Brent wrote: > > > > On 3/3/2019 4:52 AM, Philip Thrift wrote: > > >> > Here's an example David Wallace presents (as an "outlandish" possibility): > Suppose in *pi *(which is computable, so has a *program* (a spigot one, > in fact) that produces

Re: Are there real numbers that cannot be defined?

On Sunday, March 3, 2019 at 11:29:32 AM UTC-6, John Clark wrote: > > > > On Sun, Mar 3, 2019 at 9:26 AM Bruno Marchal > wrote: > >> >> >> The 8000th Busy Beaver Number can be named but not calculated even >>> theoretically, >> >> >> *> The busy beaver function is not computable, but on each

Re: Recommend this article, Even just for the Wheeler quote near the end

On Sunday, March 3, 2019 at 7:58:01 AM UTC-6, Philip Thrift wrote: > > > > On Sunday, March 3, 2019 at 7:32:00 AM UTC-6, Lawrence Crowell wrote: > > Bringing Gödel into physics is treading on a mine field as it is. Believe >> me, most physicists react in horror at the mere suggestion of this. I

Re: Recommend this article, Even just for the Wheeler quote near the end

On 3/3/2019 4:52 AM, Philip Thrift wrote: Here's an example David Wallace presents (as an "outlandish" possibility): Suppose in *pi *(which is computable, so has a /program/ (a spigot one, in fact) that produces its digits. Suppose somewhere in that stream of digits is the Standard Model

Re: When Did Consciousness Begin?

On 3/3/2019 3:45 AM, Bruno Marchal wrote: On 1 Mar 2019, at 23:21, Brent Meeker wrote: On 3/1/2019 7:04 AM, Bruno Marchal wrote: The “minimal” consciousness require only a weak notion of self. It does not require memory, nor any sense. It is a highly dissociated state of consciousness.

Re: When Did Consciousness Begin?

On 3/3/2019 3:34 AM, Bruno Marchal wrote: On 1 Mar 2019, at 21:36, Brent Meeker > wrote: On 3/1/2019 7:08 AM, Bruno Marchal wrote: On 28 Feb 2019, at 22:47, Brent Meeker > wrote: On 2/28/2019 1:17 PM, Philip Thrift wrote:

Re: Are there real numbers that cannot be defined?

On Sun, Mar 3, 2019 at 9:26 AM Bruno Marchal wrote: > > >> The 8000th Busy Beaver Number can be named but not calculated even >> theoretically, > > > *> The busy beaver function is not computable, but on each individual n, > it is computable theoretically, * > No it is not, not if n= 7918, to

Re: Are there real numbers that cannot be defined?

On Sun, Mar 3, 2019 at 3:25 AM Philip Thrift wrote: The 8000th Busy Beaver Number can be named but not calculated even >> theoretically, but most Real Numbers can't even be uniquely named with >> ASCII characters, not even with an infinite number of them. >> >> > > *The "computable" real numbers

Re: Recommend this article, Even just for the Wheeler quote near the end

On Sunday, March 3, 2019 at 8:54:42 AM UTC-6, Bruno Marchal wrote: > > > On 3 Mar 2019, at 15:32, Philip Thrift > > wrote: > > > > On Sunday, March 3, 2019 at 6:52:41 AM UTC-6, Philip Thrift wrote: >> >> >> >> On Sunday, March 3, 2019 at 5:58:17 AM UTC-6, Bruno Marchal wrote: >>> >>> >>> On 1

Re: HoTT: The programing language of space

> On 3 Mar 2019, at 14:42, Philip Thrift wrote: > > > > On Sunday, March 3, 2019 at 6:32:50 AM UTC-6, Bruno Marchal wrote: > >> On 1 Mar 2019, at 22:57, Philip Thrift > >> wrote: >> >> >> >> On Friday, March 1, 2019 at 3:19:21 PM UTC-6, Philip Thrift wrote: >> >> >> On Friday, March 1,

Re: Recommend this article, Even just for the Wheeler quote near the end

> On 3 Mar 2019, at 14:32, Lawrence Crowell > wrote: > > I wrote quite a bit here in green color. I will look at this at ease. Thanks for the attempts. I have to re-study Gleason theorem. I am already re-assured that we would get the Born Rule in the time-independent setting, but even

Re: Recommend this article, Even just for the Wheeler quote near the end

> On 3 Mar 2019, at 15:32, Philip Thrift wrote: > > > > On Sunday, March 3, 2019 at 6:52:41 AM UTC-6, Philip Thrift wrote: > > > On Sunday, March 3, 2019 at 5:58:17 AM UTC-6, Bruno Marchal wrote: > >> On 1 Mar 2019, at 19:32, Philip Thrift > wrote: >>> >>> >>> Reading all the above in

Re: Recommend this article, Even just for the Wheeler quote near the end

> On 3 Mar 2019, at 13:52, Philip Thrift wrote: > > > > On Sunday, March 3, 2019 at 5:58:17 AM UTC-6, Bruno Marchal wrote: > >> On 1 Mar 2019, at 19:32, Philip Thrift > >> wrote: >>> >>> >>> Reading all the above in the context of >>> >>> Naturalness and Emergence >>> David Wallace >>>

Re: Recommend this article, Even just for the Wheeler quote near the end

On Sunday, March 3, 2019 at 6:52:41 AM UTC-6, Philip Thrift wrote: > > > > On Sunday, March 3, 2019 at 5:58:17 AM UTC-6, Bruno Marchal wrote: >> >> >> On 1 Mar 2019, at 19:32, Philip Thrift wrote: >> >>> >>> >>> Reading all the above in the context of >>> >>> *Naturalness and Emergence* >>>

Re: Are there real numbers that cannot be defined?

> On 3 Mar 2019, at 03:27, John Clark wrote: > > > On Fri, Mar 1, 2019 at 4:23 PM Lawrence Crowell > mailto:goldenfieldquaterni...@gmail.com>> > wrote: > > > There are numbers that have no description in a practical sense. The > > numbers 10^{10^{10^{10}}} and 10^{10^{10^{10^{10 have a

Re: Recommend this article, Even just for the Wheeler quote near the end

On Sunday, March 3, 2019 at 7:32:00 AM UTC-6, Lawrence Crowell wrote: Bringing Gödel into physics is treading on a mine field as it is. Believe > me, most physicists react in horror at the mere suggestion of this. I have > this suspicion however that quantum measurement is a a sort of Gödel

Re: HoTT: The programing language of space

On Sunday, March 3, 2019 at 6:32:50 AM UTC-6, Bruno Marchal wrote: > > > On 1 Mar 2019, at 22:57, Philip Thrift > > wrote: > > > > On Friday, March 1, 2019 at 3:19:21 PM UTC-6, Philip Thrift wrote: >> >> >> >> On Friday, March 1, 2019 at 3:09:23 PM UTC-6, Lawrence Crowell wrote: >>> >>> The

Re: Recommend this article, Even just for the Wheeler quote near the end

I wrote quite a bit here in green color. On Sunday, March 3, 2019 at 6:23:04 AM UTC-6, Bruno Marchal wrote: > > > On 1 Mar 2019, at 19:55, Lawrence Crowell > wrote: > > On Friday, March 1, 2019 at 8:49:54 AM UTC-6, Bruno Marchal wrote: >> >> >> On 1 Mar 2019, at 01:42, Lawrence Crowell >>

Re: Recommend this article, Even just for the Wheeler quote near the end

On Sunday, March 3, 2019 at 5:58:17 AM UTC-6, Bruno Marchal wrote: > > > On 1 Mar 2019, at 19:32, Philip Thrift > > wrote: > >> >> >> Reading all the above in the context of >> >> *Naturalness and Emergence* >> David Wallace >> February 20, 2019 >>

Re: HoTT: The programing language of space

> On 1 Mar 2019, at 22:57, Philip Thrift wrote: > > > > On Friday, March 1, 2019 at 3:19:21 PM UTC-6, Philip Thrift wrote: > > > On Friday, March 1, 2019 at 3:09:23 PM UTC-6, Lawrence Crowell wrote: > The question is whether HoTT is also the language of entanglement. > > LC > > > > All

Re: Recommend this article, Even just for the Wheeler quote near the end

> On 1 Mar 2019, at 19:55, Lawrence Crowell > wrote: > > On Friday, March 1, 2019 at 8:49:54 AM UTC-6, Bruno Marchal wrote: > >> On 1 Mar 2019, at 01:42, Lawrence Crowell > > wrote: >> >> >> >> On Monday, February 25, 2019 at 9:42:01 AM UTC-6, Bruno Marchal wrote: >> >>> On 25 Feb 2019,

Re: Recommend this article, Even just for the Wheeler quote near the end

> On 1 Mar 2019, at 19:32, Philip Thrift wrote: > > > > On Friday, March 1, 2019 at 8:53:00 AM UTC-6, Bruno Marchal wrote: > >> On 1 Mar 2019, at 09:20, Philip Thrift > >> wrote: >> >> >> >> On Thursday, February 28, 2019 at 6:42:07 PM UTC-6, Lawrence Crowell wrote: >> >> >> On Monday,

Re: When Did Consciousness Begin?

> On 1 Mar 2019, at 23:21, Brent Meeker wrote: > > > > On 3/1/2019 7:04 AM, Bruno Marchal wrote: >> >> The “minimal” consciousness require only a weak notion of self. It does not >> require memory, nor any sense. It is a highly dissociated state of >> consciousness. It is quite different

Re: When Did Consciousness Begin?

> On 1 Mar 2019, at 21:36, Brent Meeker wrote: > > > > On 3/1/2019 7:08 AM, Bruno Marchal wrote: >> >>> On 28 Feb 2019, at 22:47, Brent Meeker >> > wrote: >>> >>> >>> >>> On 2/28/2019 1:17 PM, Philip Thrift wrote: The best current philosopher

Re: A Program to Compute Gödel-Löb Fixpoints

> On 2 Mar 2019, at 10:26, Philip Thrift wrote: > > > > A Program to Compute Gödel-Löb Fixpoints > Melvin Fitting [ http://melvinfitting.org/ ] > > https://www.researchgate.net/publication/285841645_A_program_to_compute_Godel-Lob_fixpoints > > > A loose motivation for much of Melvin

Re: Are there real numbers that cannot be defined?

On Saturday, March 2, 2019 at 8:28:01 PM UTC-6, John Clark wrote: > > > On Fri, Mar 1, 2019 at 4:23 PM Lawrence Crowell > wrote: > > > There are numbers that have no description in a practical sense. The >> numbers 10^{10^{10^{10}}} and 10^{10^{10^{10^{10 have a vast number of >> numbers