We Are Legion We Are Bob Bobiverse Book 1

[John Clark]

When I was younger I read a lot of science fiction, I don't do it so much anymore and technically I didn't do it this time either but I did listen to a audio book called "We Are Legion We Are Bob" it's the first book of the Bobiverse trilogy and I really enjoyed it. You can get a free 5 minute sample of the book here:

We Are Legion (We Are Bob): Bobiverse, Book 1 

It tells the story of Bob, a young man who has just sold his software company for a crazy amount of money and decides that after a decade of hard work he's going to spent the rest of his life just goofing off. On a whim he signs with a Cryonics company to have his head frozen after his death and then just hours later while crossing the street to go to a science fiction convention is hit by a car and dies. Five subjective seconds later he wakes up and finds that a century has passed and he's been uploaded into a computer. This is all in the opening chapter.

Parts of the story are unrealistic but parts of it are not, I think it was Isaac Asimov who said it's OK for a science fiction writer to violate the known laws of physics but only if he knows he's doing it, and when Dennis Taylor, the creator of Bob universe, does it at one point with faster than light communication it's obvious that he knowns it. And I can't deny it makes for a story that is more fun to read. I have now read (well listened) to all 3 Bob books and, although parts are a little corny and parts a little too Star Trek for my taste, on the whole I greatly enjoyed them all. They're a lot of fun.

The only other novel I can think of that treats the subject of uploading with equal intelligence is "The Silicon Man".

The Silicon Man by Charles Platt

John K Clark

[Bruce Kellett]

Consider any of the earlier novels by Greg Egan, the Australian hard science fiction write based in Perth, WA: particularly "Permutation City" (1994).

Bruce 

[Brent Meeker]

And you can learn a lot about black holes from Egan's website.  He does serious visual simulation too.  I've read several of his novels, including "Permutation City" but I liked his short story collection "Axiomatic" best.

Brent

[Bruce Kellett]

On Fri, Jul 26, 2019 at 1:12 PM 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

On 7/25/2019 8:02 PM, Bruce Kellett wrote:

On Fri, Jul 26, 2019 at 12:48 PM John Clark <johnk...@gmail.com> wrote:

When I was younger I read a lot of science fiction, I don't do it so much anymore and technically I didn't do it this time either but I did listen to a audio book called "We Are Legion We Are Bob" it's the first book of the Bobiverse trilogy and I really enjoyed it. You can get a free 5 minute sample of the book here:

We Are Legion (We Are Bob): Bobiverse, Book 1 

The only other novel I can think of that treats the subject of uploading with equal intelligence is "The Silicon Man".

The Silicon Man by Charles Platt

John K Clark

Consider any of the earlier novels by Greg Egan, the Australian hard science fiction write based in Perth, WA: particularly "Permutation City" (1994).

And you can learn a lot about black holes from Egan's website.  He does serious visual simulation too.  I've read several of his novels, including "Permutation City" but I liked his short story collection "Axiomatic" best.

Brent

It is a long time since I read "Axiomatic". But glancing at the book again now, I see that at least one of the stories might be relevant to current discussions: "Closer". The blurb on the back reads "Michael and Siran are happy together, but as people they are very different. In an attempt to understand each other better they switch bodies and minds -- but you can have too much of a good thing."

Or "The Safe Deposit Box": "A man wakes up each day with a new body: a body that belongs to someone else."

Bruce

[Russell Standish]

On Thu, Jul 25, 2019 at 10:47:46PM -0400, John Clark wrote:
>
> The only other novel I can think of that treats the subject of uploading with
> equal intelligence is "The Silicon Man".
>
> The Silicon Man by Charles Platt
>

There's a movie "Abre los oyos" (Open your eyes) that deals with this
subject that I thought was quite good.


--

----------------------------------------------------------------------------
Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow hpc...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au
----------------------------------------------------------------------------

[Lawrence Crowell]

I had this idea of a science fiction story of where minds are stored in machines in order to "eternally" punish them. The idea is that if a million seconds in the simulated world is a second in the outer world then one can in effect construct a near version of eternal hell-fire. The setting is a world governed by complete terror. Then Egan came out with Permutation city, which explores a similar set of ideas.  

The problem with the idea of putting minds into machines is that machines can run recursive functions or algorithms, but in a number system such as Peano's we make the inductive leap that the successor of any number can't be the same number or zero in all (infinite number) cases. We can make an inference from a recursively enumerable set. I would then think that the idea of putting minds into machines, or robotic consciousness, is at this time an unknown, maybe an unknowable, proposition.

LC

[John Clark]

All that assumes that infinity exists for any meaningful use of the word “exists” and as far as I know nobody has ever found a infinite number of anything. Mathematics can write stories about the infinite in the language of mathematics but are they fiction or nonfiction?

John k Clark

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[Lawrence Crowell]

On Saturday, July 27, 2019 at 8:38:12 AM UTC-5, John Clark wrote:

All that assumes that infinity exists for any meaningful use of the word “exists” and as far as I know nobody has ever found a infinite number of anything. Mathematics can write stories about the infinite in the language of mathematics but are they fiction or nonfiction?

John k Clark

Infinity is not a number in the usual sense, but more a cardinality of a set. Infinity has been a source of trouble for some. I work with Hilbert spaces that have a form of construction that is finite, but where the finite upper limit is not bounded ---- it can always be increased. This is because of entropy bounds, such as the Bekenstein bound for black holes and Bousso bounds on AdS, that demands a finite state space for local physics. George Cantor made some set theoretic sense out of infinities, even a hierarchy of them. This avoids some difficulties. However, I think that mathematics in general is not as rich if you work exclusively in finitude. Fraenkel-Zermelo set theory even has an axiom of infinity. The main point is with axiomatic completeness, and mathematics with infinity is more complete. 

Richard Feynman talked about Greek mathematics, the axiomatic formal systems of mathematics, and Babylonian mathematics that is set up for practical matters. I have no particular preference for either, and think it is interesting to switch hats.

LC

 

On Sat, Jul 27, 2019 at 7:36 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Thursday, July 25, 2019 at 10:02:39 PM UTC-5, Bruce wrote:

On Fri, Jul 26, 2019 at 12:48 PM John Clark <johnk...@gmail.com> wrote:

When I was younger I read a lot of science fiction, I don't do it so much anymore and technically I didn't do it this time either but I did listen to a audio book called "We Are Legion We Are Bob" it's the first book of the Bobiverse trilogy and I really enjoyed it. You can get a free 5 minute sample of the book here:

We Are Legion (We Are Bob): Bobiverse, Book 1 

It tells the story of Bob, a young man who has just sold his software company for a crazy amount of money and decides that after a decade of hard work he's going to spent the rest of his life just goofing off. On a whim he signs with a Cryonics company to have his head frozen after his death and then just hours later while crossing the street to go to a science fiction convention is hit by a car and dies. Five subjective seconds later he wakes up and finds that a century has passed and he's been uploaded into a computer. This is all in the opening chapter.

Parts of the story are unrealistic but parts of it are not, I think it was Isaac Asimov who said it's OK for a science fiction writer to violate the known laws of physics but only if he knows he's doing it, and when Dennis Taylor, the creator of Bob universe, does it at one point with faster than light communication it's obvious that he knowns it. And I can't deny it makes for a story that is more fun to read. I have now read (well listened) to all 3 Bob books and, although parts are a little corny and parts a little too Star Trek for my taste, on the whole I greatly enjoyed them all. They're a lot of fun.

The only other novel I can think of that treats the subject of uploading with equal intelligence is "The Silicon Man".

The Silicon Man by Charles Platt

John K Clark

Consider any of the earlier novels by Greg Egan, the Australian hard science fiction write based in Perth, WA: particularly "Permutation City" (1994).

Bruce 

I had this idea of a science fiction story of where minds are stored in machines in order to "eternally" punish them. The idea is that if a million seconds in the simulated world is a second in the outer world then one can in effect construct a near version of eternal hell-fire. The setting is a world governed by complete terror. Then Egan came out with Permutation city, which explores a similar set of ideas.  

The problem with the idea of putting minds into machines is that machines can run recursive functions or algorithms, but in a number system such as Peano's we make the inductive leap that the successor of any number can't be the same number or zero in all (infinite number) cases. We can make an inference from a recursively enumerable set. I would then think that the idea of putting minds into machines, or robotic consciousness, is at this time an unknown, maybe an unknowable, proposition.

LC

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[Philip Thrift]

If an actual "black hole" (relativistic) computer existed, it would effectively compute an infinite number of operations in finite time.

One could have, in effect, an infinite-time Turing machine.

https://arxiv.org/abs/math/9808093

We extend in a natural way the operation of Turing machines to infinite ordinal time.

But all this is fiction. 

"In the 1980s, Hartry Field started a project in the philosophy of mathematics discussing mathematical fictionalism, the doctrine that all mathematical statements are merely useful fictions, and should not be taken to be literally true. More precisely, Field holds that the existence of sets may be denied, in opposition to Quine and Putnam." [Wikipedia]

@philipthrift

[John Clark]

On Sat, Jul 27, 2019 at 2:42 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

>  I think that mathematics in general is not as rich if you work exclusively in finitude. Fraenkel-Zermelo set theory even has an axiom of infinity. The main point is with axiomatic completeness, and mathematics with infinity is more complete.

I wonder If "more complete" just means more opportunity to write stories in the language of mathematics that have no plot holes but are nevertheless fictional; just as a fantasy novel by JK Rowling is still fictional even if she maintains perfect internal consistency within her story that is written in the language of English. For example take Euclid's proof that there is no largest Prime Number, it's a beautiful mathematical story and it has no plot holes, but is the story true?

Unless it turns out we were very very wrong about General Relativity and Quantum Mechanics I don't believe the universe has the computational resources to calculate the 10^(10^9)^(10^9) prime number, not even if the universe is infinite in extent because it is expanding and accelerating. So if the word has any meaning how can the 10^(10^9)^(10^9) prime number be said to "exist"?

John K Clark

[Bruno Marchal]

On 27 Jul 2019, at 20:42, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, July 27, 2019 at 8:38:12 AM UTC-5, John Clark wrote:

All that assumes that infinity exists for any meaningful use of the word “exists” and as far as I know nobody has ever found a infinite number of anything. Mathematics can write stories about the infinite in the language of mathematics but are they fiction or nonfiction?

John k Clark

Infinity is not a number in the usual sense, but more a cardinality of a set. Infinity has been a source of trouble for some. I work with Hilbert spaces that have a form of construction that is finite, but where the finite upper limit is not bounded ---- it can always be increased. This is because of entropy bounds, such as the Bekenstein bound for black holes and Bousso bounds on AdS, that demands a finite state space for local physics. George Cantor made some set theoretic sense out of infinities, even a hierarchy of them. This avoids some difficulties. However, I think that mathematics in general is not as rich if you work exclusively in finitude. Fraenkel-Zermelo set theory even has an axiom of infinity. The main point is with axiomatic completeness, and mathematics with infinity is more complete. 

Mechanism provides an ontological finitism (what exists are only 0, s(0), s(s(0)), …), but it explains why those finite objects will believe correctly in some phenomenological infinite (already needed to get an idea of what “finite” could mean.

The infinite is phenomenologically real, but has no ontology.

No first order logical theories can really define the difference between finite and infinite. Even ZF, despite its axiom of infinity is not able to do that, in the sense that it too has non standard model, in which we can have a finite number greater than all the “standard” natural numbers 0, s(0) …

I am not sure why you say that adding an axiom of infinity makes a theory more complete. There are sense it which it only aggravate incompleteness. 

Once a theory is rich enough to define and prove the existence of a universal machine, that theory becomes essentially undecidable (which means that not only it is undecidable, but it is un-completable: all the effective consistent extensions are undecidable.

Bruno

Richard Feynman talked about Greek mathematics, the axiomatic formal systems of mathematics, and Babylonian mathematics that is set up for practical matters. I have no particular preference for either, and think it is interesting to switch hats.

LC

 

On Sat, Jul 27, 2019 at 7:36 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Thursday, July 25, 2019 at 10:02:39 PM UTC-5, Bruce wrote:

On Fri, Jul 26, 2019 at 12:48 PM John Clark <johnk...@gmail.com> wrote:

When I was younger I read a lot of science fiction, I don't do it so much anymore and technically I didn't do it this time either but I did listen to a audio book called "We Are Legion We Are Bob" it's the first book of the Bobiverse trilogy and I really enjoyed it. You can get a free 5 minute sample of the book here:

We Are Legion (We Are Bob): Bobiverse, Book 1 

It tells the story of Bob, a young man who has just sold his software company for a crazy amount of money and decides that after a decade of hard work he's going to spent the rest of his life just goofing off. On a whim he signs with a Cryonics company to have his head frozen after his death and then just hours later while crossing the street to go to a science fiction convention is hit by a car and dies. Five subjective seconds later he wakes up and finds that a century has passed and he's been uploaded into a computer. This is all in the opening chapter.

Parts of the story are unrealistic but parts of it are not, I think it was Isaac Asimov who said it's OK for a science fiction writer to violate the known laws of physics but only if he knows he's doing it, and when Dennis Taylor, the creator of Bob universe, does it at one point with faster than light communication it's obvious that he knowns it. And I can't deny it makes for a story that is more fun to read. I have now read (well listened) to all 3 Bob books and, although parts are a little corny and parts a little too Star Trek for my taste, on the whole I greatly enjoyed them all. They're a lot of fun.

The only other novel I can think of that treats the subject of uploading with equal intelligence is "The Silicon Man".

The Silicon Man by Charles Platt

John K Clark

Consider any of the earlier novels by Greg Egan, the Australian hard science fiction write based in Perth, WA: particularly "Permutation City" (1994).

Bruce 

I had this idea of a science fiction story of where minds are stored in machines in order to "eternally" punish them. The idea is that if a million seconds in the simulated world is a second in the outer world then one can in effect construct a near version of eternal hell-fire. The setting is a world governed by complete terror. Then Egan came out with Permutation city, which explores a similar set of ideas.  

The problem with the idea of putting minds into machines is that machines can run recursive functions or algorithms, but in a number system such as Peano's we make the inductive leap that the successor of any number can't be the same number or zero in all (infinite number) cases. We can make an inference from a recursively enumerable set. I would then think that the idea of putting minds into machines, or robotic consciousness, is at this time an unknown, maybe an unknowable, proposition.

LC

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[Lawrence Crowell]

Black holes are limited to the amount of information they contain by the Bekenstein bound. Also the duration of a black hole is T ~ M^3. So an observer of the outside world would not encounter an infinite Cauchy sequence of null rays at the inner event horizon. The idea of the infinite task or hyper-Turing machine is interesting, but it may only adjust the Chaitin halting probability for any given algorithm closer to 0 or 1, but not absolutely determine halting or non-halting status.

LC

[Lawrence Crowell]

On Sunday, July 28, 2019 at 5:09:56 AM UTC-5, Bruno Marchal wrote:

On 27 Jul 2019, at 20:42, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, July 27, 2019 at 8:38:12 AM UTC-5, John Clark wrote:

All that assumes that infinity exists for any meaningful use of the word “exists” and as far as I know nobody has ever found a infinite number of anything. Mathematics can write stories about the infinite in the language of mathematics but are they fiction or nonfiction?

John k Clark

Infinity is not a number in the usual sense, but more a cardinality of a set. Infinity has been a source of trouble for some. I work with Hilbert spaces that have a form of construction that is finite, but where the finite upper limit is not bounded ---- it can always be increased. This is because of entropy bounds, such as the Bekenstein bound for black holes and Bousso bounds on AdS, that demands a finite state space for local physics. George Cantor made some set theoretic sense out of infinities, even a hierarchy of them. This avoids some difficulties. However, I think that mathematics in general is not as rich if you work exclusively in finitude. Fraenkel-Zermelo set theory even has an axiom of infinity. The main point is with axiomatic completeness, and mathematics with infinity is more complete. 

Mechanism provides an ontological finitism (what exists are only 0, s(0), s(s(0)), …), but it explains why those finite objects will believe correctly in some phenomenological infinite (already needed to get an idea of what “finite” could mean.

The infinite is phenomenologically real, but has no ontology.

No first order logical theories can really define the difference between finite and infinite. Even ZF, despite its axiom of infinity is not able to do that, in the sense that it too has non standard model, in which we can have a finite number greater than all the “standard” natural numbers 0, s(0) …

I am not sure why you say that adding an axiom of infinity makes a theory more complete. There are sense it which it only aggravate incompleteness. 

Once a theory is rich enough to define and prove the existence of a universal machine, that theory becomes essentially undecidable (which means that not only it is undecidable, but it is un-completable: all the effective consistent extensions are undecidable.

Bruno

I am not a set theory maven particularly. I only know the basic things and some aspects of advanced topics I have read. The recursive function is to take 0 and "compute" s(0) and then ss(0) and so forth. The entire set is recursively enumerable and the idea that given 0 and computing s(0) one has ss^n(0) = s^{n+1}(0) is induction. That this leads to a countably infinite set is recursively enumerable and that is not something one can "machine compute." I think this is this "extension."

LC

 

Richard Feynman talked about Greek mathematics, the axiomatic formal systems of mathematics, and Babylonian mathematics that is set up for practical matters. I have no particular preference for either, and think it is interesting to switch hats.

LC

 

On Sat, Jul 27, 2019 at 7:36 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Thursday, July 25, 2019 at 10:02:39 PM UTC-5, Bruce wrote:

On Fri, Jul 26, 2019 at 12:48 PM John Clark <johnk...@gmail.com> wrote:

When I was younger I read a lot of science fiction, I don't do it so much anymore and technically I didn't do it this time either but I did listen to a audio book called "We Are Legion We Are Bob" it's the first book of the Bobiverse trilogy and I really enjoyed it. You can get a free 5 minute sample of the book here:

We Are Legion (We Are Bob): Bobiverse, Book 1 

It tells the story of Bob, a young man who has just sold his software company for a crazy amount of money and decides that after a decade of hard work he's going to spent the rest of his life just goofing off. On a whim he signs with a Cryonics company to have his head frozen after his death and then just hours later while crossing the street to go to a science fiction convention is hit by a car and dies. Five subjective seconds later he wakes up and finds that a century has passed and he's been uploaded into a computer. This is all in the opening chapter.

Parts of the story are unrealistic but parts of it are not, I think it was Isaac Asimov who said it's OK for a science fiction writer to violate the known laws of physics but only if he knows he's doing it, and when Dennis Taylor, the creator of Bob universe, does it at one point with faster than light communication it's obvious that he knowns it. And I can't deny it makes for a story that is more fun to read. I have now read (well listened) to all 3 Bob books and, although parts are a little corny and parts a little too Star Trek for my taste, on the whole I greatly enjoyed them all. They're a lot of fun.

The only other novel I can think of that treats the subject of uploading with equal intelligence is "The Silicon Man".

The Silicon Man by Charles Platt

John K Clark

Consider any of the earlier novels by Greg Egan, the Australian hard science fiction write based in Perth, WA: particularly "Permutation City" (1994).

Bruce 

I had this idea of a science fiction story of where minds are stored in machines in order to "eternally" punish them. The idea is that if a million seconds in the simulated world is a second in the outer world then one can in effect construct a near version of eternal hell-fire. The setting is a world governed by complete terror. Then Egan came out with Permutation city, which explores a similar set of ideas.  

The problem with the idea of putting minds into machines is that machines can run recursive functions or algorithms, but in a number system such as Peano's we make the inductive leap that the successor of any number can't be the same number or zero in all (infinite number) cases. We can make an inference from a recursively enumerable set. I would then think that the idea of putting minds into machines, or robotic consciousness, is at this time an unknown, maybe an unknowable, proposition.

LC

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[spudb...@aol.com]

I am suspecting that someone who works with Hilbert space, might see themselves as Hugh Everett friendly? Throw in Bryce DeWitt and John A. Wheeler too. 

-----Original Message-----
From: Lawrence Crowell <goldenfield...@gmail.com>
To: Everything List <everyth...@googlegroups.com>
Sent: Sun, Jul 28, 2019 5:42 pm
Subject: Re: We Are Legion We Are Bob Bobiverse Book 1

On Sunday, July 28, 2019 at 5:09:56 AM UTC-5, Bruno Marchal wrote:

To view this discussion on the web visit https://groups.google.com/d/ msgid/everything-list/ 1c518015-9dc2-47a8-968c- 3b6c8eed1594%40googlegroups. com.

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.

[Lawrence Crowell]

On Sunday, July 28, 2019 at 5:22:39 PM UTC-5, spudb...@aol.com wrote:

I am suspecting that someone who works with Hilbert space, might see themselves as Hugh Everett friendly? Throw in Bryce DeWitt and John A. Wheeler too. 

I am fairly agnostic about quantum interpretations. They are auxiliary postulates or physical axioms that appear to have no falsifiable content. 

LC 

 

https://groups.google.com/d/msgid/everything-list/633a983a-30bb-4cc7-bcd4-5eac8636b699%40googlegroups.com

.

[Philip Thrift]

On Sunday, July 28, 2019 at 4:42:40 PM UTC-5, Lawrence Crowell wrote:

On Sunday, July 28, 2019 at 5:09:56 AM UTC-5, Bruno Marchal wrote:

On 27 Jul 2019, at 20:42, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, July 27, 2019 at 8:38:12 AM UTC-5, John Clark wrote:

All that assumes that infinity exists for any meaningful use of the word “exists” and as far as I know nobody has ever found a infinite number of anything. Mathematics can write stories about the infinite in the language of mathematics but are they fiction or nonfiction?

John k Clark

Infinity is not a number in the usual sense, but more a cardinality of a set. Infinity has been a source of trouble for some. I work with Hilbert spaces that have a form of construction that is finite, but where the finite upper limit is not bounded ---- it can always be increased. This is because of entropy bounds, such as the Bekenstein bound for black holes and Bousso bounds on AdS, that demands a finite state space for local physics. George Cantor made some set theoretic sense out of infinities, even a hierarchy of them. This avoids some difficulties. However, I think that mathematics in general is not as rich if you work exclusively in finitude. Fraenkel-Zermelo set theory even has an axiom of infinity. The main point is with axiomatic completeness, and mathematics with infinity is more complete. 

Mechanism provides an ontological finitism (what exists are only 0, s(0), s(s(0)), …), but it explains why those finite objects will believe correctly in some phenomenological infinite (already needed to get an idea of what “finite” could mean.

The infinite is phenomenologically real, but has no ontology.

No first order logical theories can really define the difference between finite and infinite. Even ZF, despite its axiom of infinity is not able to do that, in the sense that it too has non standard model, in which we can have a finite number greater than all the “standard” natural numbers 0, s(0) …

I am not sure why you say that adding an axiom of infinity makes a theory more complete. There are sense it which it only aggravate incompleteness. 

Once a theory is rich enough to define and prove the existence of a universal machine, that theory becomes essentially undecidable (which means that not only it is undecidable, but it is un-completable: all the effective consistent extensions are undecidable.

Bruno

I am not a set theory maven particularly. I only know the basic things and some aspects of advanced topics I have read. The recursive function is to take 0 and "compute" s(0) and then ss(0) and so forth. The entire set is recursively enumerable and the idea that given 0 and computing s(0) one has ss^n(0) = s^{n+1}(0) is induction. That this leads to a countably infinite set is recursively enumerable and that is not something one can "machine compute." I think this is this "extension."

LC

Of course in programming "infinite structures" are not uncommon:

e.g.

SMT Solving for Functional Programming over Infinite Structures

Bartek Klin, Michał Szynwelski

University of Warsaw

https://www.mimuw.edu.pl/~szynwelski/nlambda/nlambda.pdf

We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets are represented by logical formulas that define them, and an external satisfiability modulo theories (SMT) solver is regularly run by the interpreter to check their basic properties.

Our goal is a set of programming idioms that would hide from the programmer as much as it is possible the fact that she or he is dealing with infinite sets presented by first-order formulas rather than with finite sets presented by enumerating their elements.

The language is implemented as a Haskell module.

@philipthrift

 

 

[Bruno Marchal]

On 28 Jul 2019, at 23:42, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Sunday, July 28, 2019 at 5:09:56 AM UTC-5, Bruno Marchal wrote:

On 27 Jul 2019, at 20:42, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, July 27, 2019 at 8:38:12 AM UTC-5, John Clark wrote:

All that assumes that infinity exists for any meaningful use of the word “exists” and as far as I know nobody has ever found a infinite number of anything. Mathematics can write stories about the infinite in the language of mathematics but are they fiction or nonfiction?

John k Clark

Infinity is not a number in the usual sense, but more a cardinality of a set. Infinity has been a source of trouble for some. I work with Hilbert spaces that have a form of construction that is finite, but where the finite upper limit is not bounded ---- it can always be increased. This is because of entropy bounds, such as the Bekenstein bound for black holes and Bousso bounds on AdS, that demands a finite state space for local physics. George Cantor made some set theoretic sense out of infinities, even a hierarchy of them. This avoids some difficulties. However, I think that mathematics in general is not as rich if you work exclusively in finitude. Fraenkel-Zermelo set theory even has an axiom of infinity. The main point is with axiomatic completeness, and mathematics with infinity is more complete. 

Mechanism provides an ontological finitism (what exists are only 0, s(0), s(s(0)), …), but it explains why those finite objects will believe correctly in some phenomenological infinite (already needed to get an idea of what “finite” could mean.

The infinite is phenomenologically real, but has no ontology.

No first order logical theories can really define the difference between finite and infinite. Even ZF, despite its axiom of infinity is not able to do that, in the sense that it too has non standard model, in which we can have a finite number greater than all the “standard” natural numbers 0, s(0) …

I am not sure why you say that adding an axiom of infinity makes a theory more complete. There are sense it which it only aggravate incompleteness. 

Once a theory is rich enough to define and prove the existence of a universal machine, that theory becomes essentially undecidable (which means that not only it is undecidable, but it is un-completable: all the effective consistent extensions are undecidable.

Bruno

I am not a set theory maven particularly. I only know the basic things and some aspects of advanced topics I have read. The recursive function is to take 0 and "compute" s(0) and then ss(0) and so forth. The entire set is recursively enumerable and the idea that given 0 and computing s(0) one has ss^n(0) = s^{n+1}(0) is induction. That this leads to a countably infinite set is recursively enumerable and that is not something one can "machine compute." I think this is this "extension.”

The set N = {0, 1, 2, …} is trivially recursively enumerable (can be generated by a digital machine/program). It is the range of the identity function. 

Once a function is computable, or once a set can be computably generated, we usually say that the function (an infinite object) is (partially) computable, or that the set is (semi)-computable. A function can be said to compute its extension.

A function is NOT computable when there is no algorithm capable of giving output on some input where it is defined.

I have shown that the function deciding if a code compute a total or a strictly partial function is (highly) not computable, although well defined if we accept the excluded principle (as we do in classical (non intuitionist) computer science, and as we have to do when we do theology, given that a theology is a highly non constructive notion (provably so for the theology of a machine (by definition: the study of the true propositions (and subset of true propositions) on the machine, provable or not by that machine).

Bruno

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[Bruno Marchal]

On 29 Jul 2019, at 03:03, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Sunday, July 28, 2019 at 5:22:39 PM UTC-5, spudb...@aol.com wrote:

I am suspecting that someone who works with Hilbert space, might see themselves as Hugh Everett friendly? Throw in Bryce DeWitt and John A. Wheeler too. 

I am fairly agnostic about quantum interpretations. They are auxiliary postulates or physical axioms that appear to have no falsifiable content. 

Everett does not talk about interpretation, but about a new formulation, or new theory. That new theory which is the old Copenhagen one, but with the postulate collapse deleted.

I agree, this are different theories, before suggesting different type of interpretation (differing along the lines dividing monism (Everett) and dualist (Copenhagen).

Everett ides is the idea that a physicist obey to quantum mechanics too. Eventually this lead to a “relative state interpretation” of the same kind of the “relative computational state” in arithmetic.

With mechanism, quantum mechanics is how the digital number reality looks from inside,by machines which are supported by infinitely many computations (which are relatively executed in virtue of pure number theoretical relations (indeed the so called sigma_1).

Everett eliminates the wave collapse postulate, but with mechanism, the wave itself is eliminated, and must be recovered through the geometry and topology associated with the material/observable modes of the universal machine (those given by Theaetetus and variants applied to Gödel’s beweisbar (provability) postulate. That gives already the quantum logics needed where they were expected). Quantum mechanics becomes a “theorem” in the universal machine's theory of consciousness and matter.

Bruno

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[Lawrence Crowell]

On Monday, July 29, 2019 at 5:34:39 AM UTC-5, Bruno Marchal wrote:

On 28 Jul 2019, at 23:42, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Sunday, July 28, 2019 at 5:09:56 AM UTC-5, Bruno Marchal wrote:

On 27 Jul 2019, at 20:42, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, July 27, 2019 at 8:38:12 AM UTC-5, John Clark wrote:

All that assumes that infinity exists for any meaningful use of the word “exists” and as far as I know nobody has ever found a infinite number of anything. Mathematics can write stories about the infinite in the language of mathematics but are they fiction or nonfiction?

John k Clark

Infinity is not a number in the usual sense, but more a cardinality of a set. Infinity has been a source of trouble for some. I work with Hilbert spaces that have a form of construction that is finite, but where the finite upper limit is not bounded ---- it can always be increased. This is because of entropy bounds, such as the Bekenstein bound for black holes and Bousso bounds on AdS, that demands a finite state space for local physics. George Cantor made some set theoretic sense out of infinities, even a hierarchy of them. This avoids some difficulties. However, I think that mathematics in general is not as rich if you work exclusively in finitude. Fraenkel-Zermelo set theory even has an axiom of infinity. The main point is with axiomatic completeness, and mathematics with infinity is more complete. 

Mechanism provides an ontological finitism (what exists are only 0, s(0), s(s(0)), …), but it explains why those finite objects will believe correctly in some phenomenological infinite (already needed to get an idea of what “finite” could mean.

The infinite is phenomenologically real, but has no ontology.

No first order logical theories can really define the difference between finite and infinite. Even ZF, despite its axiom of infinity is not able to do that, in the sense that it too has non standard model, in which we can have a finite number greater than all the “standard” natural numbers 0, s(0) …

I am not sure why you say that adding an axiom of infinity makes a theory more complete. There are sense it which it only aggravate incompleteness. 

Once a theory is rich enough to define and prove the existence of a universal machine, that theory becomes essentially undecidable (which means that not only it is undecidable, but it is un-completable: all the effective consistent extensions are undecidable.

Bruno

I am not a set theory maven particularly. I only know the basic things and some aspects of advanced topics I have read. The recursive function is to take 0 and "compute" s(0) and then ss(0) and so forth. The entire set is recursively enumerable and the idea that given 0 and computing s(0) one has ss^n(0) = s^{n+1}(0) is induction. That this leads to a countably infinite set is recursively enumerable and that is not something one can "machine compute." I think this is this "extension.”

The set N = {0, 1, 2, …} is trivially recursively enumerable (can be generated by a digital machine/program). It is the range of the identity function. 

Once a function is computable, or once a set can be computably generated, we usually say that the function (an infinite object) is (partially) computable, or that the set is (semi)-computable. A function can be said to compute its extension.

A function is NOT computable when there is no algorithm capable of giving output on some input where it is defined.

I have shown that the function deciding if a code compute a total or a strictly partial function is (highly) not computable, although well defined if we accept the excluded principle (as we do in classical (non intuitionist) computer science, and as we have to do when we do theology, given that a theology is a highly non constructive notion (provably so for the theology of a machine (by definition: the study of the true propositions (and subset of true propositions) on the machine, provable or not by that machine).

Bruno

Numbers are computable, but the entire set Z of integers is not. The conscious being or human makes the inductive leap from the successors of 0 that the set of integers is an infinite set.

LC 

[Lawrence Crowell]

The paper looks rather dense, but I save it and maybe I will get to it at some point. It though looks as if they have implemented something that appears to give infinite strings. I doubt this acts as a hyper-Turing machine.

LC

[Lawrence Crowell]

On Monday, July 29, 2019 at 5:47:16 AM UTC-5, Bruno Marchal wrote:

On 29 Jul 2019, at 03:03, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Sunday, July 28, 2019 at 5:22:39 PM UTC-5, spudb...@aol.com wrote:

I am suspecting that someone who works with Hilbert space, might see themselves as Hugh Everett friendly? Throw in Bryce DeWitt and John A. Wheeler too. 

I am fairly agnostic about quantum interpretations. They are auxiliary postulates or physical axioms that appear to have no falsifiable content. 

Everett does not talk about interpretation, but about a new formulation, or new theory. That new theory which is the old Copenhagen one, but with the postulate collapse deleted.

I agree, this are different theories, before suggesting different type of interpretation (differing along the lines dividing monism (Everett) and dualist (Copenhagen).

Everett ides is the idea that a physicist obey to quantum mechanics too. Eventually this lead to a “relative state interpretation” of the same kind of the “relative computational state” in arithmetic.

With mechanism, quantum mechanics is how the digital number reality looks from inside,by machines which are supported by infinitely many computations (which are relatively executed in virtue of pure number theoretical relations (indeed the so called sigma_1).

Everett eliminates the wave collapse postulate, but with mechanism, the wave itself is eliminated, and must be recovered through the geometry and topology associated with the material/observable modes of the universal machine (those given by Theaetetus and variants applied to Gödel’s beweisbar (provability) postulate. That gives already the quantum logics needed where they were expected). Quantum mechanics becomes a “theorem” in the universal machine's theory of consciousness and matter.

Bruno

MWI is a quantum interpretation because it makes an ontological statement on the nature of the wave function. Quantum mechanics by itself makes no inference on the existential nature of ψ. The MWI is ψ-ontological, which means it requires the wave function to be ontic or real. By way of contrast the Bohr interpretation is ψ-epistemic, which is to say the ψ is just an epistemological entity used to compute experimental outcomes; it has no reality.

LC

[Bruno Marchal]

We should always be clear about three forms of existence, and mechanism provides a way to make that clear:

1) You have what you assume to exist in the ontology.

Exemple: 0, 1, 2, … in an ontology which is sufficient and necessary, and cannot be completed.

2) Then you have the things who existence, can be derived directly in the theory, examples are the prime numbers, or the relative universal numbers, the combinators, the Turing machine, etc.

3) Then you have the phenomenologies: the things that the universal numbers will themselves postulate, either as tools or as possible ontological things added to their possible basic ontological commitment (the universal machine will debate this).

The axiom of infinity is a good example of this. It simplifies the life a lot, but with mechanism, its existence is phenomenological and not part of the ontology, nor are the real numbers, or even the negative numbers.

The choice of the ontology is not important, and the difference between 1) and 2) is not conceptually important. You can take the combinators as ontology (K, S, KK, KS, …) and then prove the existence of the natural numbers from there, or you can take the numbers as ontology, and prove the existence of the combinators from the numbers. That will not change anything in the “machine’s” theology, nor the machine’s physics. But it is important to distinguish 1) and 2) to fix the discourse. Mechanism needs just one universal machinery, and we get all the others from it.

Now, if you assume *any* universal machinery, (and classical logic, to remain simple), it is a theorem that 10^(10^9)^(10^9) prime number exists. That existence has nothing to do with the idea that a universe exists or not, and that we can represents such number in some way or not. In this case, you don’t even need the excluded third principle.

A universal machinery can always be specified by first order (non logical) axioms, which makes all the notion of existence definable in small amont of second order logic, or set theory.

We have many notion of existence in arithmetic.

ExP(x)  ontological existence (here existence is defined in the usual way of first order logic).

[]ExP(x) ontological existence accessible by the machine specifying the “[]”

[]Ex[]P(x) ontological constructive existence (the machine can prove the existence, and find how to build the existing object)

Then the same with [1], [2], [3], … [7], and even other related to the quantisation of the observable, which involved the variants of "[]<>” in front of the propositions and quantifier.

Bruno

John K Clark

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[Bruno Marchal]

?

All numbers in N, Q, and Z are computable. For the real numbers, it is different and more subtle, but usually we represent the (computable) real number by total computable functions from N to N.

N, Z, and Q are equivalent with respect of computability theory. They are all equivalent to V_w (V_omega), the set of rank smaller than w (omega, the least infinite ordinal), which is the theory of finite sets.

The conscious being or human makes the inductive leap from the successors of 0 that the set of integers is an infinite set.

They do that in set theory, not in arithmetic, except at the meta-level in case work on arithmetic (as opposed to work in arithmetic).

(Z, +, *)  and (Q, +, *) are representable in (N, +, *) , like the SK-combinators, and all universal machineries,  are representable in (N, +, *).

Bruno

LC 

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[Bruno Marchal]

On 29 Jul 2019, at 13:18, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Monday, July 29, 2019 at 5:47:16 AM UTC-5, Bruno Marchal wrote:

On 29 Jul 2019, at 03:03, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Sunday, July 28, 2019 at 5:22:39 PM UTC-5, spudb...@aol.com wrote:

I am suspecting that someone who works with Hilbert space, might see themselves as Hugh Everett friendly? Throw in Bryce DeWitt and John A. Wheeler too. 

I am fairly agnostic about quantum interpretations. They are auxiliary postulates or physical axioms that appear to have no falsifiable content. 

Everett does not talk about interpretation, but about a new formulation, or new theory. That new theory which is the old Copenhagen one, but with the postulate collapse deleted.

I agree, this are different theories, before suggesting different type of interpretation (differing along the lines dividing monism (Everett) and dualist (Copenhagen).

Everett ides is the idea that a physicist obey to quantum mechanics too. Eventually this lead to a “relative state interpretation” of the same kind of the “relative computational state” in arithmetic.

With mechanism, quantum mechanics is how the digital number reality looks from inside,by machines which are supported by infinitely many computations (which are relatively executed in virtue of pure number theoretical relations (indeed the so called sigma_1).

Everett eliminates the wave collapse postulate, but with mechanism, the wave itself is eliminated, and must be recovered through the geometry and topology associated with the material/observable modes of the universal machine (those given by Theaetetus and variants applied to Gödel’s beweisbar (provability) postulate. That gives already the quantum logics needed where they were expected). Quantum mechanics becomes a “theorem” in the universal machine's theory of consciousness and matter.

Bruno

MWI is a quantum interpretation because it makes an ontological statement on the nature of the wave function.

I use “MWI” as a synonym as “no assumption of collapse”. Then the theory is neutral on the nature of the wave. It can still become purely epistemological, as it is necessarily the case if we assume digital mechanism. There are still “many-histories”, but this are expected to be the same as the computations, which exists in arithmetic.

Quantum mechanics by itself makes no inference on the existential nature of ψ.

If Quantum Mechanics means the Copenhagen theory, then there is strong inference on the existential nature of Psi. There is a physical wave of some sort, and the human observation reduces it physically. It is a dualist theory, assuming that the ave describes some reality (testable by experiment) and that the observation acts on that reality, but is not part of that reality.

The MWI is ψ-ontological,

Not necessarily, as mechanism illustrates. In that case there is nothing but the natural numbers in the ontology, and the wave is purely epistemological, it describes the map of the consistent extension of the observer/universal-machine (in arithmetic).

which means it requires the wave function to be ontic or real. By way of contrast the Bohr interpretation is ψ-epistemic, which is to say the ψ is just an epistemological entity used to compute experimental outcomes; it has no reality.

I guess you mean “no physical reality”, but with Mechanism, there is no physical reality at all, except a special  sharable epistemological reality, that we can call “physical”, but is pure first person (plural) histories.

Here, we mix two difficulties, which is that 1) with mechanism, all physical terms get a new interpretation in terms of natural numbers (and set of natural numbers), 2) that even in the materialist (and thus non mechanist) frame, there is no unanimity of how to interpret the wave and the measurement operations.

With Mechanism, both Copenhagen and Everett admits purely epistemological interpretations.

Bruno

LC

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[John Clark]

On Mon, Jul 29, 2019 at 7:18 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> MWI is a quantum interpretation because it makes an ontological statement on the nature of the wave function. Quantum mechanics by itself makes no inference on the existential nature of ψ.

The square of the absolute value of nothing is nothing but Quantum Mechanics states that the square of the absolute value of the wave function is a probability and that's something, so it seems to me  Quantum Mechanics is saying the wave function is consistent with reality, it exists.

> The MWI is ψ-ontological, which means it requires the wave function to be ontic or real. By way of contrast the Bohr interpretation is ψ-epistemic, which is to say the ψ is just an epistemological entity used to compute experimental outcomes; it has no reality.

Bohr assumes the wave function collapses, MWI does not make that assumption. Bohr needs to explain how consciousness works as conscious observers have the ability to collapse the wave function, but MWI can ignore consciousness because it has nothing to do with it, MWI says conscious things obey the same laws of physics as things that are not conscious. Bohr needs to explain exactly what a "observation" is but all MWI needs to say is when something changes the universe splits.  MWI maintains that the Schrodinger equation means exactly what it says, Bohr insists on putting in a lot of caveats. MWI is cheap on assumptions but expensive in universes, Bohr is the opposite, take your pick. 

John K Clark
 

[John Clark]

On Mon, Jul 29, 2019 at 8:14 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

> Now, if you assume *any* universal machinery, (and classical logic, to remain simple), it is a theorem that 10^(10^9)^(10^9) prime number exists. 

If the entire Multiverse can not produce that number even in theory then that number can not effect the Multiverse either. The two things have nothing to do with each other.

> That existence has nothing to do with the idea that a universe exists or not, 

Then whatever "exists" means it can't be anything of the slightest importance.

John K Clark

[Lawrence Crowell]

The MWI is a specific interpretation, and it maintains an existence of the wave function. We local observers are only able to witness a pieces of it. This is in place of collapse. Either way one is left with an unsettled sense of how the collapse or this splitting is realized. With Bohr's Copenhagen interpretation the wave function is a device to calculate outcomes and then does this collapse, which really just means revealing a result. MWI splits the world, it continues to have a constancy. Bohr's CI is epistemic and MWI is ontic.

LC

 

LC

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[Bruno Marchal]

I see you take it that way. But that is not the original idea of Everett, who propose just a new formulation of quantum mechanics: the wave function. It is Copenhagen, with the difference that we never eliminate any branch/term in the (universal) wave function. That gives a monist theory, coherent with mechanism … at first sight. Eventually, the wave itself has to be eliminated (and recovered phenomenologically, to be consistent with digital mechanism).

Copenhagen add an axiom to this: not only the wave exists (in some sense at least), but it collapses when an observer does a measurement, which leads to a dualist theory where the observed and the observer obeys different logic/theory.

I p^refer to avoid the terming “MWI”, because the notion of “world” is a bit too much “metaphysical” to be used in serious metaphysics … Eventually, with mechanism, “worlds” are very abstract sets of “personally-equivalent” computations (in arithmetic).

and it maintains an existence of the wave function. We local observers are only able to witness a pieces of it. This is in place of collapse. Either way one is left with an unsettled sense of how the collapse or this splitting is realized.

With Everett, there is no collapse, and the “feeling of collapse” is explained naturally by the mechanist first person indeterminacy is self-multiplication, or self-superposition. When the Helsinki guy is duplicated into the Washington and Moscow guys, each resulting person feel like a collapse has occurred. The symmetrical 3p description of reality has become dissymmetrical for both (all) copies.

With Bohr's Copenhagen interpretation the wave function is a device to calculate outcomes and then does this collapse, which really just means revealing a result.

After EPR, Bohr agrees that the collapse cannot be a physical event, but then the is quite unclear on what could be the nature of the quantum reality, and this complexification has hidden Einstein’s discovery of “non locality” (made testable by Bell later).

MWI splits the world, it continues to have a constancy. Bohr's CI is epistemic and MWI is ontic.

As a logician; I insist that we have to be clear on the theories, before tacking their possible interpretations. I see two theories (actually three theories): 

1) Copenhagen:

   - wave

   - collapse

   - dualist theory of mind (not explicitly given)

2) Everett:

   - wave

   - monist theory of mind (more or less explicitly mechanist)

3) your servitor:

     - monist theory of mind (explicitly: digital mechanism, aka computationalism)

The theory “2)” assumes the wave, and derives a phenomenology of the collapse.

The theory “3)” assumes only elementary arithmetic and derives a phenomenology of both the wave and the collapse.

Only “3)” seems to me to explain both matter and consciousness, but “2)” is a natural intermediate between 2 and 3.

Why assume a multiverse when elementary arithmetic proves the existence of a highly structured multi-computation and the logical obligation to derive the mathematics of the machine’s observable from that structure?

Bruno

LC

 

LC

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