Re: We Are Legion We Are Bob Bobiverse Book 1

[Bruno Marchal]

> On 30 Jul 2019, at 01:29, Lawrence Crowell  
> wrote:
> 
> On Monday, July 29, 2019 at 8:00:31 AM UTC-5, Bruno Marchal wrote:
> 
>> On 29 Jul 2019, at 13:18, Lawrence Crowell > > 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 > 
>>> 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
> 
> 
> 
> The MWI is a specific interpretation,

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 

Re: We Are Legion We Are Bob Bobiverse Book 1

[Lawrence Crowell]

On Monday, July 29, 2019 at 8:00:31 AM UTC-5, Bruno Marchal wrote:
>
>
> On 29 Jul 2019, at 13:18, Lawrence Crowell  > 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  
>> 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
>
>
>
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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> You received this message because you are subscribed to the Google Groups 
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Re: We Are Legion We Are Bob Bobiverse Book 1

[John Clark]

On Mon, Jul 29, 2019 at 8:14 AM Bruno Marchal  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

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Re: We Are Legion We Are Bob Bobiverse Book 1

[John Clark]

On Mon, Jul 29, 2019 at 7:18 AM Lawrence Crowell <
goldenfieldquaterni...@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

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Re: We Are Legion We Are Bob Bobiverse Book 1

[Bruno Marchal]

> On 29 Jul 2019, at 13:18, Lawrence Crowell  
> 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 > > 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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Re: We Are Legion We Are Bob Bobiverse Book 1

[Bruno Marchal]

> On 29 Jul 2019, at 13:06, Lawrence Crowell  
> wrote:
> 
> On Monday, July 29, 2019 at 5:34:39 AM UTC-5, Bruno Marchal wrote:
> 
>> On 28 Jul 2019, at 23:42, 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 > 
>>> 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.

?

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 

Re: We Are Legion We Are Bob Bobiverse Book 1

[Bruno Marchal]

> On 27 Jul 2019, at 23:59, John Clark  wrote:
> 
> 
> On Sat, Jul 27, 2019 at 2:42 PM Lawrence Crowell 
> mailto:goldenfieldquaterni...@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”?


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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Re: We Are Legion We Are Bob Bobiverse Book 1

[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  > 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

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Re: We Are Legion We Are Bob Bobiverse Book 1

[Lawrence Crowell]

On Monday, July 29, 2019 at 5:27:55 AM UTC-5, Philip Thrift wrote:
>
>
>
> 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  
>>> 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
>

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

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Re: We Are Legion We Are Bob Bobiverse Book 1

[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  > 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  
>> 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 

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Re: We Are Legion We Are Bob Bobiverse Book 1

[Bruno Marchal]

> On 29 Jul 2019, at 03:03, Lawrence Crowell  
> 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



> 
> LC 
>  
> 
> -Original Message-
> From: Lawrence Crowell >
> To: Everything List >
> 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:
> 
>> On 27 Jul 2019, at 20:42, Lawrence Crowell > 
>> 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

Re: We Are Legion We Are Bob Bobiverse Book 1

[Bruno Marchal]

> On 28 Jul 2019, at 23:42, 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 > > 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




> 
> 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 > <>> 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 > wrote:
>> When I was younger

Re: We Are Legion We Are Bob Bobiverse Book 1

[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  
>> 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
 

>  
>

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Re: We Are Legion We Are Bob Bobiverse Book 1

[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 
 

>
> -Original Message-
> From: Lawrence Crowell >
> To: Everything List >
> 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:
>
>
> On 27 Jul 2019, at 20:42, Lawrence Crowell  
> 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  
> 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  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  
> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>
>
> 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

Re: We Are Legion We Are Bob Bobiverse Book 1

[spudboy100 via Everything List]

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 
To: Everything List 
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:


On 27 Jul 2019, at 20:42, Lawrence Crowell  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  
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  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 

Re: We Are Legion We Are Bob Bobiverse Book 1

[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  > 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  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  
>>>>> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>
>>>>>
>>>>> 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 
>>>>> scien

Re: We Are Legion We Are Bob Bobiverse Book 1

[Lawrence Crowell]

On Saturday, July 27, 2019 at 2:14:26 PM UTC-5, Philip Thrift wrote:
>
>
>
> On Saturday, July 27, 2019 at 1:42:43 PM UTC-5, Lawrence Crowell 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. 
>>
>> 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  
>>>>> 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  
>>>>>> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>
>>>>>>
>>>>>> 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 wit

Re: We Are Legion We Are Bob Bobiverse Book 1

[Bruno Marchal]

> On 27 Jul 2019, at 20:42, Lawrence Crowell  
> 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  > 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 > 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  
> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>
> 
> 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 
> <https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/169143>
> 
>

Re: We Are Legion We Are Bob Bobiverse Book 1

[John Clark]

On Sat, Jul 27, 2019 at 2:42 PM Lawrence Crowell <
goldenfieldquaterni...@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

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Re: We Are Legion We Are Bob Bobiverse Book 1

[Philip Thrift]

On Saturday, July 27, 2019 at 1:42:43 PM UTC-5, Lawrence Crowell 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. 
>
> 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  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  
>>>>> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>
>>>>>
>>>>> 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 
>>>>> second
>>>>> s 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 
>>>>> <https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/169143>
>>>>>
>>>>> John K Clark
>>>>>
>>>>
>>>> Consider any of the earlier novels by Greg Egan, the Australian hard 
>>>> science fiction write based in Perth, WA: particularl

Re: We Are Legion We Are Bob Bobiverse Book 1

[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  > 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  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  
>>>> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>
>>>>
>>>> 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 second
>>>> s 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 
>>>> <https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/169143>
>>>>
>>>> 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 Ega

Re: We Are Legion We Are Bob Bobiverse Book 1

[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


On Sat, Jul 27, 2019 at 7:36 AM Lawrence Crowell <
goldenfieldquaterni...@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  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
>>> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>
>>>
>>> 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 second
>>> s 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
>>> <https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/169143>
>>>
>>> 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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> .
>

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Re: We Are Legion We Are Bob Bobiverse Book 1

[Lawrence Crowell]

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  > 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  
>> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>
>>
>> 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 
>> <https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/169143>
>>
>> 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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Re: We Are Legion We Are Bob Bobiverse Book 1

[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 StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: We Are Legion We Are Bob Bobiverse Book 1

[Bruce Kellett]

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

> On 7/25/2019 8:02 PM, Bruce Kellett wrote:
>
> On Fri, Jul 26, 2019 at 12:48 PM John Clark  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
>> <https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>
>>
>> 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
>> <https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/169143>
>>
>> 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

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Re: We Are Legion We Are Bob Bobiverse Book 1

['Brent Meeker' via Everything List]

On 7/25/2019 8:02 PM, Bruce Kellett wrote:
On Fri, Jul 26, 2019 at 12:48 PM John Clark <mailto:johnkcl...@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

<https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>

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
<https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/169143>

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

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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
<https://www.amazon.com/We-Are-Legion-Bob-Bobiverse/dp/B01L082SCI/ref=tmm_aud_swatch_0?_encoding=UTF8==>

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
<https://www.amazon.com/Silicon-Man-Cortext-Charles-Platt/dp/169143>

John K Clark

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