Re: Are there real numbers that cannot be defined?

On Tuesday, March 5, 2019 at 12:23:28 AM UTC-6, Bruce wrote: > > On Tue, Mar 5, 2019 at 4:55 PM Russell Standish > wrote: > >> On Tue, Mar 05, 2019 at 02:22:05PM +1100, Bruce Kellett wrote: >> > On Tue, Mar 5, 2019 at 2:03 PM Russell Standish > > wrote: >> > >> > You cannot represent n as a

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 4:55 PM Russell Standish wrote: > On Tue, Mar 05, 2019 at 02:22:05PM +1100, Bruce Kellett wrote: > > On Tue, Mar 5, 2019 at 2:03 PM Russell Standish > wrote: > > > > You cannot represent n as a finite string for an arbitrary real > number > > n. But you can for an

Re: Are there real numbers that cannot be defined?

On Tue, Mar 05, 2019 at 02:22:05PM +1100, Bruce Kellett wrote: > On Tue, Mar 5, 2019 at 2:03 PM Russell Standish wrote: > > On Tue, Mar 05, 2019 at 12:06:00PM +1100, Bruce Kellett wrote: > > > > My problem with your idea that the function: "(n-1)+1" is a valid > computational >

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 2:03 PM Russell Standish wrote: > On Tue, Mar 05, 2019 at 12:06:00PM +1100, Bruce Kellett wrote: > > > > My problem with your idea that the function: "(n-1)+1" is a valid > computational > > algorithm for n is that it makes all real numbers also computable, but > the > > no

Re: Are there real numbers that cannot be defined?

On Tue, Mar 05, 2019 at 12:06:00PM +1100, Bruce Kellett wrote: > > My problem with your idea that the function: "(n-1)+1" is a valid > computational > algorithm for n is that it makes all real numbers also computable, but the > notion of Turing computability applies only to the integers. We do no

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 11:50 AM Russell Standish wrote: > On Tue, Mar 05, 2019 at 10:42:00AM +1100, Bruce Kellett wrote: > > On Tue, Mar 5, 2019 at 10:25 AM Russell Standish > wrote: > > > > On Mon, Mar 04, 2019 at 05:31:00PM -0500, John Clark wrote: > > > On Mon, Mar 4, 2019 at 11:04 AM

Re: Are there real numbers that cannot be defined?

On Tue, Mar 05, 2019 at 10:42:00AM +1100, Bruce Kellett wrote: > On Tue, Mar 5, 2019 at 10:25 AM Russell Standish > wrote: > > On Mon, Mar 04, 2019 at 05:31:00PM -0500, John Clark wrote: > > On Mon, Mar 4, 2019 at 11:04 AM Bruno Marchal wrote: > > > > > >         >> I don't

Re: Are there real numbers that cannot be defined?

On Mon, Mar 04, 2019 at 06:48:19PM -0500, John Clark wrote: > > On Mon, Mar 4, 2019 at 6:25 PM Russell Standish wrote: >   > > > OK, so what about the program "print X+1", where X is the expansion of > the number BB(8000)-1? > > > Well what about it? If you don't know what BB(8000) is,

Re: Are there real numbers that cannot be defined?

On Mon, Mar 4, 2019 at 6:25 PM Russell Standish wrote: > > > *OK, so what about the program "print X+1", where X is the expansion of > the number BB(8000)-1?* > Well what about it? If you don't know what BB(8000) is, and you don't and neither does God, then neither of you will ever know what BB

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

On 3/4/2019 3:54 AM, Bruno Marchal wrote: On 3 Mar 2019, at 20:43, Brent Meeker > 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 /p

Re: Are there real numbers that cannot be defined?

On Tue, Mar 5, 2019 at 10:25 AM Russell Standish wrote: > On Mon, Mar 04, 2019 at 05:31:00PM -0500, John Clark wrote: > > On Mon, Mar 4, 2019 at 11:04 AM Bruno Marchal wrote: > > > > > > >> I don't follow you. If the 8000th BB number is unknowable > then it is > > certainly uncom

Re: Are there real numbers that cannot be defined?

On Mon, Mar 04, 2019 at 05:31:00PM -0500, John Clark wrote: > On Mon, Mar 4, 2019 at 11:04 AM Bruno Marchal wrote: > > > >> I don't follow you. If the 8000th BB number is unknowable then it > is > certainly uncomputable > > > > That is not true. All natural number n are co

Re: Are there real numbers that cannot be defined?

On Mon, Mar 4, 2019 at 11:04 AM Bruno Marchal wrote: >> I don't follow you. If the 8000th BB number is unknowable then it is >> certainly uncomputable > > > *> That is not true. All natural number n are computable. The program is > “output n”.* > I think you're being silly. You're saying if you

Re: Are there real numbers that cannot be defined?

On Monday, March 4, 2019 at 12:00:05 PM UTC-6, John Clark wrote: > > > > And proof is not truth. > ... > > John K Clark > > > >> Of course *truth == proof *in the land of radical intuitionists-constructivists. (And what is proof anyway?) From: Doren Zeilberger To: Scott Aaronson [ http://

Re: When Did Consciousness Begin?

On 3/4/2019 3:45 AM, Bruno Marchal wrote: Unconsciousness is an illusion of consciousness … It should be obvious that “being unconscious” cannot be a first person experience, for logical reason. To die is not a personal event. That happens only to the others. I agree.  Except I don't supp

Re: When Did Consciousness Begin?

On 3/4/2019 3:45 AM, Bruno Marchal wrote: I have had two relatives die of Alzheimers and they lost their identity gradually as they lost memory. They lost they memory. Not their identity, but the apprehension of their identity. If not, when you ask where they are in the hospital, the nurs

Re: When Did Consciousness Begin?

On 3/4/2019 3:32 AM, Bruno Marchal wrote: On 3 Mar 2019, at 20:15, Brent Meeker > wrote: 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 2

Re: Are there real numbers that cannot be defined?

On Mon, Mar 4, 2019 at 7:56 AM Bruno Marchal wrote: > *> BB(7918) is just a number, say k, and the program “print k” will do.* > Unless God wrote the program the output would just be "k" or perhaps "BB(7918)". And as I said before unlike most Real Numbers Busy Beaver Numbers can be named but ju

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

> On 4 Mar 2019, at 15:13, Philip Thrift wrote: > > > > On Monday, March 4, 2019 at 5:54:24 AM UTC-6, Bruno Marchal wrote: > >> On 3 Mar 2019, at 20:43, Brent Meeker > >> wrote: >> >> >> >> On 3/3/2019 4:52 AM, Philip Thrift wrote: >>> >>> >>> Here's an example David Wallace presents (a

Re: Are there real numbers that cannot be defined?

> On 4 Mar 2019, at 14:24, John Clark wrote: > > On Sun, Mar 3, 2019 at 6:38 PM Russell Standish > wrote: > > > ISTM that the 8000th BB number is unknowable, rather than uncomputable. > > I don't follow you. If the 8000th BB number is unknowable then it is > cer

Re: Are there real numbers that cannot be defined?

> On 4 Mar 2019, at 11:35, Lawrence Crowell > wrote: > > 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}}} an

Re: Are there real numbers that cannot be defined?

> On 4 Mar 2019, at 00:37, Russell Standish wrote: > > 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. Yes. Clark mention an interestin

Re: Are there real numbers that cannot be defined?

> On 3 Mar 2019, at 22:58, 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 "

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

On Monday, March 4, 2019 at 5:54:24 AM UTC-6, Bruno Marchal wrote: > > > On 3 Mar 2019, at 20:43, Brent Meeker > > 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,

Re: Are there real numbers that cannot be defined?

On Sun, Mar 3, 2019 at 6:38 PM Russell Standish wrote: *> ISTM that the 8000th BB number is unknowable, rather than uncomputable.* I don't follow you. If the 8000th BB number is unknowable then it is certainly uncomputable but if it's uncomputable then it's only *probably* unknowable because yo

Re: Are there real numbers that cannot be defined?

> On 3 Mar 2019, at 20:52, Philip Thrift wrote: > > > > 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 b

Re: Are there real numbers that cannot be defined?

> On 3 Mar 2019, at 18:28, 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 i

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

> On 3 Mar 2019, at 20:49, Lawrence Crowell > wrote: > > 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 ph

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

> On 3 Mar 2019, at 20:43, Brent Meeker 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 its digits.

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

> On 3 Mar 2019, at 16:46, Philip Thrift wrote: > > > > 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,

Re: When Did Consciousness Begin?

> On 3 Mar 2019, at 20:23, Brent Meeker wrote: > > > > 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 no

Re: When Did Consciousness Begin?

> On 3 Mar 2019, at 20:15, Brent Meeker wrote: > > > > 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 Meeke

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 tha