Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 8 Nov 2018, at 12:42, Philip Thrift  wrote:
> 
> 
> 
> On Thursday, November 8, 2018 at 3:10:15 AM UTC-6, Bruno Marchal wrote:
> 
>> On 5 Nov 2018, at 18:05, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Friday, November 2, 2018 at 3:47:58 AM UTC-5, Bruno Marchal wrote:
>> 
>>> On 1 Nov 2018, at 19:59, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:
>>> 
>>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift > wrote:
>>> 
>>> > infinite time Turing machines are more powerful than ordinary Turing 
>>> > machines
>>> 
>>> That is true, it is also true that if dragons existed they would be 
>>> dangerous and if I had some cream I could have strawberries and cream, if I 
>>> had some strawberries.   
>>> 
>>> > How  "real" you think this is depends on whether you are a Platonist or a 
>>> > fictionalist.
>>> 
>>> No, it depends on if you think logical contradictions can exist, if they 
>>> can then there is no point in reading any mathematical proof and logic is 
>>> no longer a useful tool for anything.
>>> 
>>> John K Clark
>>> 
>>> 
>>> 
>>> Of course logics are fiction too. (They're just languages after all.)
>> 
>> 
>> There is a logical language, but that is different from a logical theory. It 
>> is important to distinguish the languages from the theories, and the 
>> theories from the models/interpretations.
>> 
>> Bruno
>> 
>> 
>> 
>>  
>> Logics correspond to type-theoretic programming languages.
> 
> ?
> 
> That would restrict the meaning of logic to the logic obtained by the 
> Curry-Howard morphism. There is no compelling reason to do that.
> 
> Bruno
> 
> 
> 
> I don't know. Even Hegel's logic is not immune:
> 
> https://ncatlab.org/nlab/show/Hegel%27s+%22Logic%22+as+Modal+Type+Theory
> 
> Hegel's "Logic" as Modal Type Theory
> 
> Abstract While analytic philosophy famously rejected the speculative 
> metaphysics of Hegel in favor of the analysis of concepts by means of 
> mathematical logic, in particular predicate logic, recent developments in the 
> foundations of mathematics via homotopy type theory offer a way to re-read 
> Hegel as having useful formal meaning not in predicate logic, but in ‘modal 
> type theory’. The essence of this suggestion has been made by Lawvere in 
> 1991, which however remains largely unnoticed. Here we aim to give a 
> transparent account of this perspective both philosophically as well as 
> category-theoretically. We then further expand on Lawvere’s formalization of 
> Hegel’s “Science of Logic” in terms of the categorical semantics given by 
> cohesive higher toposes. We discuss how there is a useful formalization of a 
> fair bit of modern fundamental physics, in fact of local gauge quantum field 
> theory, to be found here.


I appreciate Lawvere’s mathematics, but I am neutral on Hegel, and what he did 
is a part of the S4Grz1 logic, which concerns the subject, at the expense of 
the object. 

Some author makes good quality work, being rather clear, notably, but in doing 
so they help me to better understand why I do not follow them, or why their 
work cannot be applied in the frame of my basic hypotheses. In the case of 
Hegel and Leibniz, I appreciate their early work, in the case of Wittgenstein, 
I prefer his late work. 

Bruno



> 
>  - pt
> 
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 8, 2018 at 3:10:15 AM UTC-6, Bruno Marchal wrote:
>
>
> On 5 Nov 2018, at 18:05, Philip Thrift > 
> wrote:
>
>
>
> On Friday, November 2, 2018 at 3:47:58 AM UTC-5, Bruno Marchal wrote:
>>
>>
>> On 1 Nov 2018, at 19:59, Philip Thrift  wrote:
>>
>>
>>
>> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:
>>>
>>>
>>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  wrote:
>>>
>>> *> infinite time Turing machines are more powerful than ordinary Turing 
 machines*
>>>
>>>
>>> That is true, it is also true that if dragons existed they would be 
>>> dangerous and if I had some cream I could have strawberries and cream, if I 
>>> had some strawberries.   
>>>
>>> *> How  "real" you think this is depends on whether you are a Platonist 
 or a fictionalist.*

>>>
>>> No, it depends on if you think logical contradictions can exist, if they 
>>> can then there is no point in reading any mathematical proof and logic is 
>>> no longer a useful tool for anything.
>>>
>>> John K Clark
>>>
>>>

>> Of course logics are fiction too. (They're just languages after all.)
>>
>>
>>
>> There is a logical language, but that is different from a logical theory. 
>> It is important to distinguish the languages from the theories, and the 
>> theories from the models/interpretations.
>>
>> Bruno
>>
>>
>>
>  
> Logics correspond to type-theoretic programming languages.
>
>
> ?
>
> That would restrict the meaning of logic to the logic obtained by the 
> Curry-Howard morphism. There is no compelling reason to do that.
>
> Bruno
>
>
>
I don't know. Even Hegel's logic is not immune:

https://ncatlab.org/nlab/show/Hegel%27s+%22Logic%22+as+Modal+Type+Theory

*Hegel's "Logic" as Modal Type Theory*

Abstract *While analytic philosophy famously rejected the speculative 
metaphysics of Hegel in favor of the analysis of concepts by means of 
mathematical logic, in particular predicate logic, recent developments in 
the foundations of mathematics via homotopy type theory offer a way to 
re-read Hegel as having useful formal meaning not in predicate logic, but 
in ‘modal type theory’. The essence of this suggestion has been made by 
Lawvere in 1991, which however remains largely unnoticed. Here we aim to 
give a transparent account of this perspective both philosophically as well 
as category-theoretically. We then further expand on Lawvere’s 
formalization of Hegel’s “Science of Logic” in terms of the categorical 
semantics given by cohesive higher toposes. We discuss how there is a 
useful formalization of a fair bit of modern fundamental physics, in fact 
of local gauge quantum field theory, to be found here.*

 - pt

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 8, 2018 at 3:14:36 AM UTC-6, Bruno Marchal wrote:
>
>
> On 5 Nov 2018, at 19:26, Philip Thrift > 
> wrote:
>
>
>
> On Monday, November 5, 2018 at 11:14:00 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 5 Nov 2018, at 11:41, Philip Thrift  wrote:
>>
>>
>>
>> But I claim an experience-processing computer (like our brain) is not 
>> super-Turing, but is non-Turing: All *information* it can process is 
>> Turing-computable, but it also processes *experience*.
>>
>>
>>
>> I think we agree on this. Experience is NOT information processing. That 
>> is provable using very standard definition (the greek one) and using 
>> mechanism.
>>
>> But you go out of mechanism by your use of matter in the process of those 
>> experiences. Which seems to me very weird, as it is like invoking a 
>> supernatural being (some primitive matter) which is actually part of the 
>> difficulty when solving the mind-body problem, with or even without 
>> mechanism.
>>
>> It would be nice if you study the first steps of the Universal Dovetailer 
>> Argument so that we might perhaps be able to isolate where we might really 
>> differ or not, beyond your apparent belief in “matter”.
>>
>> Cf  
>> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
>>   
>>
>> Bruno
>>
>>
>>
>
> The way I see it is from what I've called the (pragmatic)  *PLTOS *framework. 
> At the end of the workday, one needs something that is running *inside of*
>  or *as* a computer. (in the world we are living in.)
>
>https://codicalist.wordpress.com/2018/09/30/real-computationalism/
>
> Here the idea is the robot scientist has a conscious agent program (CAP) 
> codebase, but needs to compile it into a working object. The CAP codebase 
> is the "theory" (which could include UD code as you have defined it). 
>
> So the scientist could compile CAP to run inside existing of hardware, or 
> use a synthetic compiler (matter compiler, molecular assembler, ...) to 
> make "new" hardware (which could be "squishy") with the programming 
> embedded. 
>
> *What is the nature of the hardware that allows this task to be achieved? *is 
> a question the robot scientist faces. That gets into what kinds of 
> compilers/transformers are needed (the T in PLTOS).
>
>
>
> That might help with pragmatic issue, but make the metaphysics rather 
> obscure, at least to me. The notion of primitive matter just does not make 
> any sense with computationalism. You cannot invoque an ontological 
> commitment when searching an explanation in metaphysics. That is not valid.
>
> Bruno
>
>
>
The CAP programmer/scientist/engineer is not bothered with metaphysics. *Is 
the output or object of my study made of matter, or number?* doesn't come 
up.

- pt


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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 5 Nov 2018, at 20:13, Quentin Anciaux  wrote:
> 
> https://en.m.wikipedia.org/wiki/Oracle_machine 
> 
> Le lun. 5 nov. 2018 19:28, Quentin Anciaux  > a écrit :
> 
> 
> Le lun. 5 nov. 2018 19:17, John Clark  > a écrit :
> On Mon, Nov 5, 2018 at 8:51 AM Quentin Anciaux  > wrote:
> 
> >>There is no evidence fire breathing dragons exist in nature but if one did 
> >>it would not produce a logical contradiction, however Turing proved over 80 
> >>years ago that a oracle that could solve the Halting Problem would. 
> 
> > It does not, it "solves" it for turing machines... it does not for turing 
> > machine + oracle...  there is no contradiction.
> 
> In a way that's true but the price paid is one of ambiguity. You say the 
> oracle can predict if any Turing Machine will halt, OK but the oracle is not 
> a Turing Machine so can the oracle predict if it itself will halt? Nobody 
> known how the oracle works so nobody can say but if it can then it can't and 
> I can prove it.
> 
> 
> It can't... Again, the oracle solves it for TM... Not for TMO.. But another 
> oracle... Call it O2... Can solve it for TMO... But not for TMO2... Etc
> 
> Let's give the turing machine + oracle you mentioned a name, I'll call it a 
> TMO. If the TMO can solve the Halting problem then if I feed in any Turing 
> Machine it can tell me if it halts or not. Any computer that is not a oracle 
> can be reduced to a Turing Machine regardless of it circuit design, so let's 
> say the TMO has 2 slots for input and one slot for output, if I feed in the 
> circuit logic design blueprints of any computer into one slot the TMO can 
> simulate that computer, and if I feed in  program data into the other slot 
> that TMO will output either "Halt" meaning the simulated machine operating on 
> that data will eventually stop or the TMO will output "not halt" meaning  the 
> simulated machine operating on that data will never stop.
> 
> I will now make a new machine called X, it has 3 parts to it. The first part 
> of X  is just a Xerox copy machine, feed in one program and it outputs 2 
> identical programs. The second part of X is the TMO and it receives the 2 
> programs as input from the Xerox machine's outputs, and the TMO then outputs 
> either "halt" or "not halt". The third and last part of X is a very simple 
> machine called the negator, it receives as input the output of the TMO and if 
> the input to the negator is "Halt" the negator will go into a infinite loop 
> and if the input is "not halt" the negator will print "halt" and then stop.
> 
> Now let's draw the blueprint circuit design of the entire X machine that 
> fully defines it, then make 2 copies of it and feed it into the TMO; so the 
> TMO is now trying to figure out if the X machine will halt if it is fed its 
> own blueprint as data. If the TMO says "halt" the X machine will not halt and 
> the TMO was wrong.  If the TMO says "not halt" the X machine will halt and 
> the TMO was wrong again. Therefore the TMO that can tell if any Turing 
> Machine will halt or not can not logically exist.  
> 
> I suppose you could argue that the oracle operates according to some sort of 
> magic so you couldn't have the blueprints of it and therefore you couldn't 
> have the blueprints of the entire X machine, but then the very question of 
> whether the X machine halts is not a well defined question because the X 
> machine itself is not well defined and the properties of the oracle are 
> ambiguous. So oracle or no oracle, anything that can always tell if any well 
> defined program will halt or not halt when run on a well defined computer 
> will  lead to a logical contradiction.
> 
>  John K Clark



Quentin is right. In fact oracle have been introduced by Turing to study if 
adding non computable information could overcome incompleteness, and what 
Turing did was that it does not. Machines with oracle, being for the PI_1 
halting problem, or the PI_2 totality problem, or for qG (which is also 
PI_2-complete) remains arithmetically incomplete. qG* can be shown 
PI_1-complete with the oracle of the whole arithmetical truth. Even god 
(arithmetical truth) has to be invoked an infinity of times to solve an 
arbitrary self-reference problem. 

But this is of no use for us, as there are no more evidence for an oracle in 
nature, and worst, if we are machine, we cannot distinguish in a finite time if 
something is an oracle, or just a machine more complex than ourselves. The 
interest in Oracle is purely negative: they do not overcome the incompleteness 
phenomenon. In fact the theology of the machine (the G* theory) is valid for 
basically all reasonable non-machine-extensions.

Bruno




> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 5 Nov 2018, at 19:26, Philip Thrift  wrote:
> 
> 
> 
> On Monday, November 5, 2018 at 11:14:00 AM UTC-6, Bruno Marchal wrote:
> 
>> On 5 Nov 2018, at 11:41, Philip Thrift > wrote:
>> 
>> 
>> But I claim an experience-processing computer (like our brain) is not 
>> super-Turing, but is non-Turing: All information it can process is 
>> Turing-computable, but it also processes experience.
> 
> 
> I think we agree on this. Experience is NOT information processing. That is 
> provable using very standard definition (the greek one) and using mechanism.
> 
> But you go out of mechanism by your use of matter in the process of those 
> experiences. Which seems to me very weird, as it is like invoking a 
> supernatural being (some primitive matter) which is actually part of the 
> difficulty when solving the mind-body problem, with or even without mechanism.
> 
> It would be nice if you study the first steps of the Universal Dovetailer 
> Argument so that we might perhaps be able to isolate where we might really 
> differ or not, beyond your apparent belief in “matter”.
> 
> Cf  
> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html 
>   
> 
> Bruno
> 
> 
> 
> 
> The way I see it is from what I've called the (pragmatic)  PLTOS framework. 
> At the end of the workday, one needs something that is running inside of or 
> as a computer. (in the world we are living in.)
> 
>https://codicalist.wordpress.com/2018/09/30/real-computationalism/
> 
> Here the idea is the robot scientist has a conscious agent program (CAP) 
> codebase, but needs to compile it into a working object. The CAP codebase is 
> the "theory" (which could include UD code as you have defined it). 
> 
> So the scientist could compile CAP to run inside existing of hardware, or use 
> a synthetic compiler (matter compiler, molecular assembler, ...) to make 
> "new" hardware (which could be "squishy") with the programming embedded. 
> 
> What is the nature of the hardware that allows this task to be achieved? is a 
> question the robot scientist faces. That gets into what kinds of 
> compilers/transformers are needed (the T in PLTOS).


That might help with pragmatic issue, but make the metaphysics rather obscure, 
at least to me. The notion of primitive matter just does not make any sense 
with computationalism. You cannot invoque an ontological commitment when 
searching an explanation in metaphysics. That is not valid.

Bruno



> 
> - pt
>  
> 
> 
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 5 Nov 2018, at 18:05, Philip Thrift  wrote:
> 
> 
> 
> On Friday, November 2, 2018 at 3:47:58 AM UTC-5, Bruno Marchal wrote:
> 
>> On 1 Nov 2018, at 19:59, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:
>> 
>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift > wrote:
>> 
>> > infinite time Turing machines are more powerful than ordinary Turing 
>> > machines
>> 
>> That is true, it is also true that if dragons existed they would be 
>> dangerous and if I had some cream I could have strawberries and cream, if I 
>> had some strawberries.   
>> 
>> > How  "real" you think this is depends on whether you are a Platonist or a 
>> > fictionalist.
>> 
>> No, it depends on if you think logical contradictions can exist, if they can 
>> then there is no point in reading any mathematical proof and logic is no 
>> longer a useful tool for anything.
>> 
>> John K Clark
>> 
>> 
>> 
>> Of course logics are fiction too. (They're just languages after all.)
> 
> 
> There is a logical language, but that is different from a logical theory. It 
> is important to distinguish the languages from the theories, and the theories 
> from the models/interpretations.
> 
> Bruno
> 
> 
> 
>  
> Logics correspond to type-theoretic programming languages.

?

That would restrict the meaning of logic to the logic obtained by the 
Curry-Howard morphism. There is no compelling reason to do that.

Bruno




> 
> - pt
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 5 Nov 2018, at 14:48, John Clark  wrote:
> 
> On Mon, Nov 5, 2018 at 4:39 AM Bruno Marchal  > wrote:
> 
> >>> No Turing machine can solve the halting problem. You are right on this. 
> >>> But an oracle can, or a machine with infinite speed can.
>  
> >>If such a oracle could exist
>  
> > In what sense? 
> 
> Whoever said there is no such thing as a stupid question was wrong.
> 
> >>then logical contradictions could too
> 
> > That does not follow. I don’t think that there are any evidence for such 
> > oracle in nature, but such existence would not introduce any contradiction.
> 
> For god's sake! There is no evidence fire breathing dragons exist in nature 
> but if one did it would not produce a logical contradiction, however Turing 
> proved over 80 years ago that a oracle that could solve the Halting Problem 
> would. 

No. He didn’t. You make that up.

Bruno




> 
>  John K Clark
> 
> 
> 
> 
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Re: Mathematical Universe Hypothesis

[Quentin Anciaux]

https://en.m.wikipedia.org/wiki/Oracle_machine

Le lun. 5 nov. 2018 19:28, Quentin Anciaux  a écrit :

>
>
> Le lun. 5 nov. 2018 19:17, John Clark  a écrit :
>
>> On Mon, Nov 5, 2018 at 8:51 AM Quentin Anciaux 
>> wrote:
>>
>> >>There is no evidence fire breathing dragons exist in nature but if one
 did it would not produce a logical contradiction, however Turing proved
 over 80 years ago that a oracle that could solve the Halting Problem would.

>>>
>>> *> It does not, it "solves" it for turing machines... it does not for
>>> turing machine + oracle...  there is no contradiction.*
>>>
>>
>> In a way that's true but the price paid is one of ambiguity. You say the
>> oracle can predict if any Turing Machine will halt, OK but the oracle is
>> not a Turing Machine so can the oracle predict if it itself will halt?
>> Nobody known how the oracle works so nobody can say but if it can then it
>> can't and I can prove it.
>>
>
>
> It can't... Again, the oracle solves it for TM... Not for TMO.. But
> another oracle... Call it O2... Can solve it for TMO... But not for TMO2...
> Etc
>
>>
>> Let's give the turing machine + oracle you mentioned a name, I'll call
>> it a TMO. If the TMO can solve the Halting problem then if I feed in any
>> Turing Machine it can tell me if it halts or not. Any computer that is not
>> a oracle can be reduced to a Turing Machine regardless of it circuit
>> design, so let's say the TMO has 2 slots for input and one slot for
>> output, if I feed in the circuit logic design blueprints of any computer
>> into one slot the TMO can simulate that computer, and if I feed in  program
>> data into the other slot that TMO will output either "Halt" meaning the
>> simulated machine operating on that data will eventually stop or the TMO
>> will output "not halt" meaning  the simulated machine operating on that
>> data will never stop.
>>
>> I will now make a new machine called X, it has 3 parts to it. The first
>> part of X  is just a Xerox copy machine, feed in one program and it outputs
>> 2 identical programs. The second part of X is the TMO and it receives the 2
>> programs as input from the Xerox machine's outputs, and the TMO then
>> outputs either "halt" or "not halt". The third and last part of X is a very
>> simple machine called the negator, it receives as input the output of
>> the TMO and if the input to the negator is "Halt" the negator will go
>> into a infinite loop and if the input is "not halt" the negator will
>> print "halt" and then stop.
>>
>> Now let's draw the blueprint circuit design of the entire X machine that
>> fully defines it, then make 2 copies of it and feed it into the TMO; so
>> the TMO is now trying to figure out if the X machine will halt if it is
>> fed its own blueprint as data. If the TMO says "halt" the X machine will
>> not halt and the TMO was wrong.  If the TMO says "not halt" the X
>> machine will halt and the TMO was wrong again. Therefore the TMO that
>> can tell if any Turing Machine will halt or not can not logically exist.
>>
>> I suppose you could argue that the oracle operates according to some sort
>> of magic so you couldn't have the blueprints of it and therefore you
>> couldn't have the blueprints of the entire X machine, but then the very
>> question of whether the X machine halts is not a well defined question
>> because the X machine itself is not well defined and the properties of the
>> oracle are ambiguous. So oracle or no oracle, anything that can always tell
>> if any well defined program will halt or not halt when run on a well
>> defined computer will  lead to a logical contradiction.
>>
>>  John K Clark
>>
>> --
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>>
>

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Re: Mathematical Universe Hypothesis

[Quentin Anciaux]

Le lun. 5 nov. 2018 19:17, John Clark  a écrit :

> On Mon, Nov 5, 2018 at 8:51 AM Quentin Anciaux  wrote:
>
> >>There is no evidence fire breathing dragons exist in nature but if one
>>> did it would not produce a logical contradiction, however Turing proved
>>> over 80 years ago that a oracle that could solve the Halting Problem would.
>>>
>>
>> *> It does not, it "solves" it for turing machines... it does not for
>> turing machine + oracle...  there is no contradiction.*
>>
>
> In a way that's true but the price paid is one of ambiguity. You say the
> oracle can predict if any Turing Machine will halt, OK but the oracle is
> not a Turing Machine so can the oracle predict if it itself will halt?
> Nobody known how the oracle works so nobody can say but if it can then it
> can't and I can prove it.
>


It can't... Again, the oracle solves it for TM... Not for TMO.. But another
oracle... Call it O2... Can solve it for TMO... But not for TMO2... Etc

>
> Let's give the turing machine + oracle you mentioned a name, I'll call it
> a TMO. If the TMO can solve the Halting problem then if I feed in any
> Turing Machine it can tell me if it halts or not. Any computer that is not
> a oracle can be reduced to a Turing Machine regardless of it circuit
> design, so let's say the TMO has 2 slots for input and one slot for
> output, if I feed in the circuit logic design blueprints of any computer
> into one slot the TMO can simulate that computer, and if I feed in  program
> data into the other slot that TMO will output either "Halt" meaning the
> simulated machine operating on that data will eventually stop or the TMO
> will output "not halt" meaning  the simulated machine operating on that
> data will never stop.
>
> I will now make a new machine called X, it has 3 parts to it. The first
> part of X  is just a Xerox copy machine, feed in one program and it outputs
> 2 identical programs. The second part of X is the TMO and it receives the 2
> programs as input from the Xerox machine's outputs, and the TMO then
> outputs either "halt" or "not halt". The third and last part of X is a very
> simple machine called the negator, it receives as input the output of the
> TMO and if the input to the negator is "Halt" the negator will go into a
> infinite loop and if the input is "not halt" the negator will print
> "halt" and then stop.
>
> Now let's draw the blueprint circuit design of the entire X machine that
> fully defines it, then make 2 copies of it and feed it into the TMO; so
> the TMO is now trying to figure out if the X machine will halt if it is
> fed its own blueprint as data. If the TMO says "halt" the X machine will
> not halt and the TMO was wrong.  If the TMO says "not halt" the X machine
> will halt and the TMO was wrong again. Therefore the TMO that can tell if
> any Turing Machine will halt or not can not logically exist.
>
> I suppose you could argue that the oracle operates according to some sort
> of magic so you couldn't have the blueprints of it and therefore you
> couldn't have the blueprints of the entire X machine, but then the very
> question of whether the X machine halts is not a well defined question
> because the X machine itself is not well defined and the properties of the
> oracle are ambiguous. So oracle or no oracle, anything that can always tell
> if any well defined program will halt or not halt when run on a well
> defined computer will  lead to a logical contradiction.
>
>  John K Clark
>
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Monday, November 5, 2018 at 11:14:00 AM UTC-6, Bruno Marchal wrote:
>
>
> On 5 Nov 2018, at 11:41, Philip Thrift  wrote:
>
>
>
> But I claim an experience-processing computer (like our brain) is not 
> super-Turing, but is non-Turing: All *information* it can process is 
> Turing-computable, but it also processes *experience*.
>
>
>
> I think we agree on this. Experience is NOT information processing. That 
> is provable using very standard definition (the greek one) and using 
> mechanism.
>
> But you go out of mechanism by your use of matter in the process of those 
> experiences. Which seems to me very weird, as it is like invoking a 
> supernatural being (some primitive matter) which is actually part of the 
> difficulty when solving the mind-body problem, with or even without 
> mechanism.
>
> It would be nice if you study the first steps of the Universal Dovetailer 
> Argument so that we might perhaps be able to isolate where we might really 
> differ or not, beyond your apparent belief in “matter”.
>
> Cf  
> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
>   
>
> Bruno
>
>
>

The way I see it is from what I've called the (pragmatic)  *PLTOS *framework. 
At the end of the workday, one needs something that is running *inside of*
 or *as* a computer. (in the world we are living in.)

   https://codicalist.wordpress.com/2018/09/30/real-computationalism/

Here the idea is the robot scientist has a conscious agent program (CAP) 
codebase, but needs to compile it into a working object. The CAP codebase 
is the "theory" (which could include UD code as you have defined it). 

So the scientist could compile CAP to run inside existing of hardware, or 
use a synthetic compiler (matter compiler, molecular assembler, ...) to 
make "new" hardware (which could be "squishy") with the programming 
embedded. 

*What is the nature of the hardware that allows this task to be achieved? *is 
a question the robot scientist faces. That gets into what kinds of 
compilers/transformers are needed (the T in PLTOS).

- pt
 


>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Mon, Nov 5, 2018 at 8:51 AM Quentin Anciaux  wrote:

>>There is no evidence fire breathing dragons exist in nature but if one
>> did it would not produce a logical contradiction, however Turing proved
>> over 80 years ago that a oracle that could solve the Halting Problem would.
>>
>
> *> It does not, it "solves" it for turing machines... it does not for
> turing machine + oracle...  there is no contradiction.*
>

In a way that's true but the price paid is one of ambiguity. You say the
oracle can predict if any Turing Machine will halt, OK but the oracle is
not a Turing Machine so can the oracle predict if it itself will halt?
Nobody known how the oracle works so nobody can say but if it can then it
can't and I can prove it.

Let's give the turing machine + oracle you mentioned a name, I'll call it a
TMO. If the TMO can solve the Halting problem then if I feed in any Turing
Machine it can tell me if it halts or not. Any computer that is not a
oracle can be reduced to a Turing Machine regardless of it circuit design,
so let's say the TMO has 2 slots for input and one slot for output, if I
feed in the circuit logic design blueprints of any computer into one slot
the TMO can simulate that computer, and if I feed in  program data into the
other slot that TMO will output either "Halt" meaning the simulated machine
operating on that data will eventually stop or the TMO will output "not
halt" meaning  the simulated machine operating on that data will never stop.

I will now make a new machine called X, it has 3 parts to it. The first
part of X  is just a Xerox copy machine, feed in one program and it outputs
2 identical programs. The second part of X is the TMO and it receives the 2
programs as input from the Xerox machine's outputs, and the TMO then
outputs either "halt" or "not halt". The third and last part of X is a very
simple machine called the negator, it receives as input the output of the
TMO and if the input to the negator is "Halt" the negator will go into a
infinite loop and if the input is "not halt" the negator will print "halt"
and then stop.

Now let's draw the blueprint circuit design of the entire X machine that
fully defines it, then make 2 copies of it and feed it into the TMO; so the
TMO is now trying to figure out if the X machine will halt if it is fed its
own blueprint as data. If the TMO says "halt" the X machine will not halt
and the TMO was wrong.  If the TMO says "not halt" the X machine will halt
and the TMO was wrong again. Therefore the TMO that can tell if any Turing
Machine will halt or not can not logically exist.

I suppose you could argue that the oracle operates according to some sort
of magic so you couldn't have the blueprints of it and therefore you
couldn't have the blueprints of the entire X machine, but then the very
question of whether the X machine halts is not a well defined question
because the X machine itself is not well defined and the properties of the
oracle are ambiguous. So oracle or no oracle, anything that can always tell
if any well defined program will halt or not halt when run on a well
defined computer will  lead to a logical contradiction.

 John K Clark

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 5 Nov 2018, at 11:41, Philip Thrift  wrote:
> 
> 
> 
> On Monday, November 5, 2018 at 3:36:59 AM UTC-6, Bruno Marchal wrote:
> 
>> On 2 Nov 2018, at 15:02, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Friday, November 2, 2018 at 3:45:53 AM UTC-5, Bruno Marchal wrote:
>> 
>>> On 1 Nov 2018, at 19:43, John Clark > wrote:
>>> 
>>> 
>>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift > wrote:
>>> 
>>> > infinite time Turing machines are more powerful than ordinary Turing 
>>> > machines
>>> 
>>> That is true, it is also true that if dragons existed they would be 
>>> dangerous and if I had some cream I could have strawberries and cream, if I 
>>> had some strawberries.   
>>> 
>>> > How  "real" you think this is depends on whether you are a Platonist or a 
>>> > fictionalist.
>>> 
>>> No, it depends on if you think logical contradictions can exist, if they 
>>> can then there is no point in reading any mathematical proof and logic is 
>>> no longer a useful tool for anything.
>>> 
>> 
>> 
>> No Turing machine can solve the halting problem. You are right on this. But 
>> an oracle can, or a machine with infinite speed can.
>> 
>> Now, such machine have only be introduced (by Turing) to show that even such 
>> “Turing machine with magical power making them able to solve the halting 
>> problem” are still limited and cannot solve, for example the totality 
>> problem (also an arithmetical). 
>> 
>> Turing showed that there is a hierarchy of problem in arithmetic, where 
>> adding magic (his “oracle”) never make any machine complete. It is a way to 
>> show how complex the arithmetical reality is. Adding more and more magical 
>> power does not lead to completeness. 
>> 
>> Post and Kleene have related such hierarchies with the number of alternating 
>> quantifiers used in the arithmetical expression. P is a sigma_0 = pi_0 
>> formula, without quantifier.
>> 
>> ExP(x, y). Sigma_1 (negation = AxP(x,y) = Pi_1, more complex than sigma_1, 
>> already not computable).
>> ExAyP(x, y, z)  = Sigma_2 (beyond today’s math!) (negation = Pi_2).
>> Etc. 
>> 
>> More and more “infinite task” are needed.
>> 
>> Note that such magic does not change the “theology”. It remains the same 
>> variants of the Gödel-Löb-Solovay self-reference logics (G and G*).
>> 
>> Bruno
>> 
>> 
>> 
>> 
>> There are other "Turing machine" models other than infinite-time ones people 
>> have "invented", e.g. inductive Turing machines:
>> 
>> Algorithmic complexity as a criterion of unsolvability
>> https://pdfs.semanticscholar.org/cd8f/442a9f7667891fff6f276a1bc638dd59b937.pdf
>>  
>> 
>>  :
>> 
>> Let us take an inductive Turing machine M that given a description of the 
>> Turing machine T and first n + 1 words x0, x1, . . . , xn from the list x0, 
>> x1, . . . , xn, . . ., produces the (n + 1)th partial output. This output is 
>> equal to 1 when the machine T halts for all words x0, x1, . . . , xn given 
>> as its input, and is equal to 0 when the machine T does not halt for, at 
>> least, one of these words. In such a way, the machine M solves the totality 
>> problem for Turing machines.
>> 
>> ?
>> 
>> 
>> cf.
>> https://en.wikipedia.org/wiki/Super-recursive_algorithm#Inductive_Turing_machines
>>  
>> 
>> https://bitrumagora.wordpress.com/about/marl-burgin/ 
>> 
>> 
>> 
>> Nothing is settled in computing.
> 
> 
> But this does not clearly violate Church-Thesis. Inference inductive is not 
> the same as computing. We know that there are many different Turing machine, 
> which are not equivalent for proving or inducting, etc. All humans are like 
> that. We are still the same *as* Turing machine (combinators, etc.). 
> Universality is with respect to computing, and is false with everything else. 
> Now, if you add magical, or actual infinities, or oracles, or infinite speed, 
> then you get machine which are no more digital finite machine, and so cannot 
> violate the Church-Turing thesis either. 
> 
> Bruno
> 
> 
> 
> 
> 
> From all the super-Turing math and CS news (I've followed over the years), 
> there seems to be a consensus forming:
> 
> 
>  There are no super-Turing computers! (that can be found in nature or 
> manufactured by us)
> 
> 
> cf. 
> https://phys.org/news/2015-09-limit-church-turing-thesis-accounts-noisy.html 
> 
> The only ones are fictional ones (the infinite-time and  super-recursive ones 
> above).
> 
> So that seems to be the consensus.

Thank you for the good news, although I do not care on consensus too much, 
except to despair of humanity ...



> 
> 
> But I claim an experience-processing computer (like our brain) is not 
> super-Turing, but is non-Turing: All information it can process is 
> Turing-computable, but it also processes experience.


I think we agree on this. Experience is NOT 

Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Friday, November 2, 2018 at 3:47:58 AM UTC-5, Bruno Marchal wrote:
>
>
> On 1 Nov 2018, at 19:59, Philip Thrift > 
> wrote:
>
>
>
> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:
>>
>>
>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  wrote:
>>
>> *> infinite time Turing machines are more powerful than ordinary Turing 
>>> machines*
>>
>>
>> That is true, it is also true that if dragons existed they would be 
>> dangerous and if I had some cream I could have strawberries and cream, if I 
>> had some strawberries.   
>>
>> *> How  "real" you think this is depends on whether you are a Platonist 
>>> or a fictionalist.*
>>>
>>
>> No, it depends on if you think logical contradictions can exist, if they 
>> can then there is no point in reading any mathematical proof and logic is 
>> no longer a useful tool for anything.
>>
>> John K Clark
>>
>>
>>>
> Of course logics are fiction too. (They're just languages after all.)
>
>
>
> There is a logical language, but that is different from a logical theory. 
> It is important to distinguish the languages from the theories, and the 
> theories from the models/interpretations.
>
> Bruno
>
>
>
 
Logics correspond to type-theoretic programming languages.

- pt

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Re: Mathematical Universe Hypothesis

[Quentin Anciaux]

Le lun. 5 nov. 2018 à 14:48, John Clark  a écrit :

> On Mon, Nov 5, 2018 at 4:39 AM Bruno Marchal  wrote:
>
> *>>> No Turing machine can solve the halting problem. You are right on
 this. But an oracle can, or a machine with infinite speed can.*
>>>
>>>
>
> >>If such a oracle could exist
>>
>>
>
> > *In what sense?*
>>
>
> Whoever said there is no such thing as a stupid question was wrong.
>
> >>then logical contradictions could too
>>
>>
>> > *That does not follow. I don’t think that there are any evidence for
>> such oracle in nature, but such existence would not introduce any
>> contradiction.*
>>
>
> For god's sake! There is no evidence fire breathing dragons exist in
> nature but if one did it would not produce a logical contradiction, however
> Turing proved over 80 years ago that a oracle that could solve the Halting
> Problem would.
>

It does not, it "solves" it for turing machines... it does not for turing
machine + oracle...  there is no contradiction.


>  John K Clark
>
>
>
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Re: Mathematical Universe Hypothesis

[John Clark]

On Mon, Nov 5, 2018 at 4:39 AM Bruno Marchal  wrote:

*>>> No Turing machine can solve the halting problem. You are right on
>>> this. But an oracle can, or a machine with infinite speed can.*
>>
>>

>>If such a oracle could exist
>
>

> *In what sense?*
>

Whoever said there is no such thing as a stupid question was wrong.

>>then logical contradictions could too
>
>
> > *That does not follow. I don’t think that there are any evidence for
> such oracle in nature, but such existence would not introduce any
> contradiction.*
>

For god's sake! There is no evidence fire breathing dragons exist in nature
but if one did it would not produce a logical contradiction, however Turing
proved over 80 years ago that a oracle that could solve the Halting Problem
would.

 John K Clark

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Monday, November 5, 2018 at 3:36:59 AM UTC-6, Bruno Marchal wrote:
>
>
> On 2 Nov 2018, at 15:02, Philip Thrift > 
> wrote:
>
>
>
> On Friday, November 2, 2018 at 3:45:53 AM UTC-5, Bruno Marchal wrote:
>>
>>
>> On 1 Nov 2018, at 19:43, John Clark  wrote:
>>
>>
>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  wrote:
>>
>> *> infinite time Turing machines are more powerful than ordinary Turing 
>>> machines*
>>
>>
>> That is true, it is also true that if dragons existed they would be 
>> dangerous and if I had some cream I could have strawberries and cream, if I 
>> had some strawberries.   
>>
>> *> How  "real" you think this is depends on whether you are a Platonist 
>>> or a fictionalist.*
>>>
>>
>> No, it depends on if you think logical contradictions can exist, if they 
>> can then there is no point in reading any mathematical proof and logic is 
>> no longer a useful tool for anything.
>>
>>
>>
>> No Turing machine can solve the halting problem. You are right on this. 
>> But an oracle can, or a machine with infinite speed can.
>>
>> Now, such machine have only be introduced (by Turing) to show that even 
>> such “Turing machine with magical power making them able to solve the 
>> halting problem” are still limited and cannot solve, for example the 
>> totality problem (also an arithmetical). 
>>
>> Turing showed that there is a hierarchy of problem in arithmetic, where 
>> adding magic (his “oracle”) never make any machine complete. It is a way to 
>> show how complex the arithmetical reality is. Adding more and more magical 
>> power does not lead to completeness. 
>>
>> Post and Kleene have related such hierarchies with the number of 
>> alternating quantifiers used in the arithmetical expression. P is a sigma_0 
>> = pi_0 formula, without quantifier.
>>
>> ExP(x, y). Sigma_1 (negation = AxP(x,y) = Pi_1, more complex than 
>> sigma_1, already not computable).
>> ExAyP(x, y, z)  = Sigma_2 (beyond today’s math!) (negation = Pi_2).
>> Etc. 
>>
>> More and more “infinite task” are needed.
>>
>> Note that such magic does not change the “theology”. It remains the same 
>> variants of the Gödel-Löb-Solovay self-reference logics (G and G*).
>>
>> Bruno
>>
>>
>>
>>
> There are other "Turing machine" models other than infinite-time ones 
> people have "invented", e.g.* inductive* Turing machines:
>
> *Algorithmic complexity as a criterion of unsolvability*
>
> https://pdfs.semanticscholar.org/cd8f/442a9f7667891fff6f276a1bc638dd59b937.pdf
>  
> :
>
> Let us take an *inductive Turing machine M *that given a description of 
> the Turing machine T and first n + 1 words x0, x1, . . . , xn from the list 
> x0, x1, . . . , xn, . . ., produces the (n + 1)th partial output. This 
> output is equal to 1 when the machine T halts for all words x0, x1, . . . , 
> xn given as its input, and is equal to 0 when the machine T does not halt 
> for, at least, one of these words. In such a way, *the machine M solves 
> the totality problem for Turing machines*.
>
> ?
>
>
> cf.
>
> https://en.wikipedia.org/wiki/Super-recursive_algorithm#Inductive_Turing_machines
> https://bitrumagora.wordpress.com/about/marl-burgin/
>
>
> *Nothing is settled in computing.*
>
>
>
> But this does not clearly violate Church-Thesis. Inference inductive is 
> not the same as computing. We know that there are many different Turing 
> machine, which are not equivalent for proving or inducting, etc. All humans 
> are like that. We are still the same *as* Turing machine (combinators, 
> etc.). Universality is with respect to computing, and is false with 
> everything else. Now, if you add magical, or actual infinities, or oracles, 
> or infinite speed, then you get machine which are no more digital finite 
> machine, and so cannot violate the Church-Turing thesis either. 
>
> Bruno
>
>
>


>From all the super-Turing math and CS news (I've followed over the years), 
there seems to be a consensus forming:


 *There are no super-Turing computers!* (that can be found in nature or 
manufactured by us)


cf. 
https://phys.org/news/2015-09-limit-church-turing-thesis-accounts-noisy.html 

The only ones are *fictional* ones (the infinite-time and  super-recursive 
ones above).

So that seems to be the consensus.


But I claim an experience-processing computer (like our brain) is not 
super-Turing, but is non-Turing: All *information* it can process is 
Turing-computable, but it also processes *experience*.


- pt



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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 2 Nov 2018, at 17:47, John Clark  wrote:
> 
> On Fri, Nov 2, 2018 at 12:16 AM  > wrote:
> 
> > You sound like a young fool who has no respect for his elders. 
> 
> And you sound like a old fool who has placed so much respect for his elders 
> it approaches the level of ancestor worship. But It's not just you, this 
> entire list's reverence for the ancient Greeks has reached comic proportions.


But you are the one still unable to criticise Aristotle metaphysics. 

There two huge different way to consider Reality: Plato’s conception, and 
Aristotle’s one.

To make thing short, Aristotle’s believe only in what he can see touch, etc. 
And Plato suggests that what we see is only the shadow, or a symptom of some 
deeper, non physical, reality.

To abstract from Plato, consists in (unconscious?) reverence to Aristotle. 

Bruno




> 
>  > Zeno pointed out something significant
> 
> When Zeno  pointed it out it was a significant puzzle with no obvious answer, 
> but in the last 2500 years we've learned a thing or two and an answer has 
> been found so it is no longer a paradox.
> 
> John K Clark
> 
> 
> 
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 2 Nov 2018, at 18:06, John Clark  wrote:
> 
> On Fri, Nov 2, 2018 at 4:45 AM Bruno Marchal  > wrote:
> 
> > No Turing machine can solve the halting problem. You are right on this. But 
> > an oracle can, or a machine with infinite speed can.
> 
> If such a oracle could exist

In what sense? I guess you mean in the physical sense. 



> then logical contradictions could too


That does not follow. I don’t think that there are any evidence for such oracle 
in nature, but such existence would not introduce any contradiction.

Bruno




> and then there would be no point in listening to your arguments or anybody's 
> logical argument about anything because mathematics and even logic itself 
> would be purest form of nonsense. 
> 
> > Note that such magic does not change the “theology” [...]
> 
> Sorry, I don't know what you said after that, I fell asleep.
> 
>  John K Clark
> 
> 
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 2 Nov 2018, at 15:02, Philip Thrift  wrote:
> 
> 
> 
> On Friday, November 2, 2018 at 3:45:53 AM UTC-5, Bruno Marchal wrote:
> 
>> On 1 Nov 2018, at 19:43, John Clark > wrote:
>> 
>> 
>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift > > wrote:
>> 
>> > infinite time Turing machines are more powerful than ordinary Turing 
>> > machines
>> 
>> That is true, it is also true that if dragons existed they would be 
>> dangerous and if I had some cream I could have strawberries and cream, if I 
>> had some strawberries.   
>> 
>> > How  "real" you think this is depends on whether you are a Platonist or a 
>> > fictionalist.
>> 
>> No, it depends on if you think logical contradictions can exist, if they can 
>> then there is no point in reading any mathematical proof and logic is no 
>> longer a useful tool for anything.
>> 
> 
> 
> No Turing machine can solve the halting problem. You are right on this. But 
> an oracle can, or a machine with infinite speed can.
> 
> Now, such machine have only be introduced (by Turing) to show that even such 
> “Turing machine with magical power making them able to solve the halting 
> problem” are still limited and cannot solve, for example the totality problem 
> (also an arithmetical). 
> 
> Turing showed that there is a hierarchy of problem in arithmetic, where 
> adding magic (his “oracle”) never make any machine complete. It is a way to 
> show how complex the arithmetical reality is. Adding more and more magical 
> power does not lead to completeness. 
> 
> Post and Kleene have related such hierarchies with the number of alternating 
> quantifiers used in the arithmetical expression. P is a sigma_0 = pi_0 
> formula, without quantifier.
> 
> ExP(x, y). Sigma_1 (negation = AxP(x,y) = Pi_1, more complex than sigma_1, 
> already not computable).
> ExAyP(x, y, z)  = Sigma_2 (beyond today’s math!) (negation = Pi_2).
> Etc. 
> 
> More and more “infinite task” are needed.
> 
> Note that such magic does not change the “theology”. It remains the same 
> variants of the Gödel-Löb-Solovay self-reference logics (G and G*).
> 
> Bruno
> 
> 
> 
> 
> There are other "Turing machine" models other than infinite-time ones people 
> have "invented", e.g. inductive Turing machines:
> 
> Algorithmic complexity as a criterion of unsolvability
> https://pdfs.semanticscholar.org/cd8f/442a9f7667891fff6f276a1bc638dd59b937.pdf
>  :
> 
> Let us take an inductive Turing machine M that given a description of the 
> Turing machine T and first n + 1 words x0, x1, . . . , xn from the list x0, 
> x1, . . . , xn, . . ., produces the (n + 1)th partial output. This output is 
> equal to 1 when the machine T halts for all words x0, x1, . . . , xn given as 
> its input, and is equal to 0 when the machine T does not halt for, at least, 
> one of these words. In such a way, the machine M solves the totality problem 
> for Turing machines.
> 
> ?
> 
> 
> cf.
> https://en.wikipedia.org/wiki/Super-recursive_algorithm#Inductive_Turing_machines
> https://bitrumagora.wordpress.com/about/marl-burgin/
> 
> 
> Nothing is settled in computing.


But this does not clearly violate Church-Thesis. Inference inductive is not the 
same as computing. We know that there are many different Turing machine, which 
are not equivalent for proving or inducting, etc. All humans are like that. We 
are still the same *as* Turing machine (combinators, etc.). Universality is 
with respect to computing, and is false with everything else. Now, if you add 
magical, or actual infinities, or oracles, or infinite speed, then you get 
machine which are no more digital finite machine, and so cannot violate the 
Church-Turing thesis either. 

Bruno





> 
> - pt
> 
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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Friday, November 2, 2018 at 4:48:05 PM UTC, John Clark wrote:
>
> On Fri, Nov 2, 2018 at 12:16 AM > wrote:
>
> *> You sound like a young fool who has no respect for his elders*. 
>
>
> And you sound like a old fool who has placed so much respect for his 
> elders it approaches the level of ancestor worship. But It's not just you, 
> this entire list's reverence for the ancient Greeks has reached comic 
> proportions.
>


*Hard to see what's in front of your nose, or just to understand the logic 
involved. AG *

>
>  > *Zeno pointed out something significant*
>
>
> When Zeno  pointed it out it was a significant puzzle with no obvious 
> answer, but in the last 2500 years we've learned a thing or two and an 
> answer has been found so it is no longer a paradox. 
>

*For you, presumably, the answer is that moving test particles know 
Calculus. AG *

>
> John K Clark
>
>
>
>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Fri, Nov 2, 2018 at 4:45 AM Bruno Marchal  wrote:

*> No Turing machine can solve the halting problem. You are right on this.
> But an oracle can, or a machine with infinite speed can.*
>

If such a oracle could exist then logical contradictions could too and then
there would be no point in listening to your arguments or anybody's logical
argument about anything because mathematics and even logic itself would be
purest form of nonsense.

> *Note that such magic does not change the “theology”* [...]
>

Sorry, I don't know what you said after that, I fell asleep.

 John K Clark


>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Fri, Nov 2, 2018 at 12:16 AM  wrote:

*> You sound like a young fool who has no respect for his elders*.


And you sound like a old fool who has placed so much respect for his elders
it approaches the level of ancestor worship. But It's not just you, this
entire list's reverence for the ancient Greeks has reached comic
proportions.

 > *Zeno pointed out something significant*


When Zeno  pointed it out it was a significant puzzle with no obvious
answer, but in the last 2500 years we've learned a thing or two and an
answer has been found so it is no longer a paradox.

John K Clark

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Friday, November 2, 2018 at 3:45:53 AM UTC-5, Bruno Marchal wrote:
>
>
> On 1 Nov 2018, at 19:43, John Clark > 
> wrote:
>
>
> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  > wrote:
>
> *> infinite time Turing machines are more powerful than ordinary Turing 
>> machines*
>
>
> That is true, it is also true that if dragons existed they would be 
> dangerous and if I had some cream I could have strawberries and cream, if I 
> had some strawberries.   
>
> *> How  "real" you think this is depends on whether you are a Platonist or 
>> a fictionalist.*
>>
>
> No, it depends on if you think logical contradictions can exist, if they 
> can then there is no point in reading any mathematical proof and logic is 
> no longer a useful tool for anything.
>
>
>
> No Turing machine can solve the halting problem. You are right on this. 
> But an oracle can, or a machine with infinite speed can.
>
> Now, such machine have only be introduced (by Turing) to show that even 
> such “Turing machine with magical power making them able to solve the 
> halting problem” are still limited and cannot solve, for example the 
> totality problem (also an arithmetical). 
>
> Turing showed that there is a hierarchy of problem in arithmetic, where 
> adding magic (his “oracle”) never make any machine complete. It is a way to 
> show how complex the arithmetical reality is. Adding more and more magical 
> power does not lead to completeness. 
>
> Post and Kleene have related such hierarchies with the number of 
> alternating quantifiers used in the arithmetical expression. P is a sigma_0 
> = pi_0 formula, without quantifier.
>
> ExP(x, y). Sigma_1 (negation = AxP(x,y) = Pi_1, more complex than sigma_1, 
> already not computable).
> ExAyP(x, y, z)  = Sigma_2 (beyond today’s math!) (negation = Pi_2).
> Etc. 
>
> More and more “infinite task” are needed.
>
> Note that such magic does not change the “theology”. It remains the same 
> variants of the Gödel-Löb-Solovay self-reference logics (G and G*).
>
> Bruno
>
>
>
>
There are other "Turing machine" models other than infinite-time ones 
people have "invented", e.g.* inductive* Turing machines:

*Algorithmic complexity as a criterion of unsolvability*
https://pdfs.semanticscholar.org/cd8f/442a9f7667891fff6f276a1bc638dd59b937.pdf 
:

Let us take an *inductive Turing machine M *that given a description of the 
Turing machine T and first n + 1 words x0, x1, . . . , xn from the list x0, 
x1, . . . , xn, . . ., produces the (n + 1)th partial output. This output 
is equal to 1 when the machine T halts for all words x0, x1, . . . , xn 
given as its input, and is equal to 0 when the machine T does not halt for, 
at least, one of these words. In such a way, *the machine M solves the 
totality problem for Turing machines*.

?


cf.
https://en.wikipedia.org/wiki/Super-recursive_algorithm#Inductive_Turing_machines
https://bitrumagora.wordpress.com/about/marl-burgin/


*Nothing is settled in computing.*

- pt

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 1 Nov 2018, at 19:59, Philip Thrift  wrote:
> 
> 
> 
> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:
> 
> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  > wrote:
> 
> > infinite time Turing machines are more powerful than ordinary Turing 
> > machines
> 
> That is true, it is also true that if dragons existed they would be dangerous 
> and if I had some cream I could have strawberries and cream, if I had some 
> strawberries.   
> 
> > How  "real" you think this is depends on whether you are a Platonist or a 
> > fictionalist.
> 
> No, it depends on if you think logical contradictions can exist, if they can 
> then there is no point in reading any mathematical proof and logic is no 
> longer a useful tool for anything.
> 
> John K Clark
> 
> 
> 
> Of course logics are fiction too. (They're just languages after all.)


There is a logical language, but that is different from a logical theory. It is 
important to distinguish the languages from the theories, and the theories from 
the models/interpretations.

Bruno



> 
> - pt
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 1 Nov 2018, at 19:43, John Clark  wrote:
> 
> 
> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  > wrote:
> 
> > infinite time Turing machines are more powerful than ordinary Turing 
> > machines
> 
> That is true, it is also true that if dragons existed they would be dangerous 
> and if I had some cream I could have strawberries and cream, if I had some 
> strawberries.   
> 
> > How  "real" you think this is depends on whether you are a Platonist or a 
> > fictionalist.
> 
> No, it depends on if you think logical contradictions can exist, if they can 
> then there is no point in reading any mathematical proof and logic is no 
> longer a useful tool for anything.
> 


No Turing machine can solve the halting problem. You are right on this. But an 
oracle can, or a machine with infinite speed can.

Now, such machine have only be introduced (by Turing) to show that even such 
“Turing machine with magical power making them able to solve the halting 
problem” are still limited and cannot solve, for example the totality problem 
(also an arithmetical). 

Turing showed that there is a hierarchy of problem in arithmetic, where adding 
magic (his “oracle”) never make any machine complete. It is a way to show how 
complex the arithmetical reality is. Adding more and more magical power does 
not lead to completeness. 

Post and Kleene have related such hierarchies with the number of alternating 
quantifiers used in the arithmetical expression. P is a sigma_0 = pi_0 formula, 
without quantifier.

ExP(x, y). Sigma_1 (negation = AxP(x,y) = Pi_1, more complex than sigma_1, 
already not computable).
ExAyP(x, y, z)  = Sigma_2 (beyond today’s math!) (negation = Pi_2).
Etc. 

More and more “infinite task” are needed.

Note that such magic does not change the “theology”. It remains the same 
variants of the Gödel-Löb-Solovay self-reference logics (G and G*).

Bruno








> John K Clark
> 
> 
> 
>  
> 
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 1, 2018 at 6:33:31 PM UTC-5, Philip Thrift wrote:
>
>
>
> On Thursday, November 1, 2018 at 6:15:50 PM UTC-5, Brent wrote:
>>
>>
>>
>> On 11/1/2018 4:02 PM, Philip Thrift wrote:
>>
>>
>>
>> On Thursday, November 1, 2018 at 4:02:56 PM UTC-5, Brent wrote: 
>>>
>>>
>>>
>>> On 11/1/2018 11:59 AM, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote: 


 On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  
 wrote:

 *> infinite time Turing machines are more powerful than ordinary Turing 
> machines*


 That is true, it is also true that if dragons existed they would be 
 dangerous and if I had some cream I could have strawberries and cream, if 
 I 
 had some strawberries.   

 *> How  "real" you think this is depends on whether you are a Platonist 
> or a fictionalist.*
>

 No, it depends on if you think logical contradictions can exist, if 
 they can then there is no point in reading any mathematical proof and 
 logic 
 is no longer a useful tool for anything.

 John K Clark


>
>>> Of course logics are fiction too. (They're just languages after all.)
>>>
>>>
>>> OK.  Sentences written down are physical and not fictions.  But can they 
>>> be contradictory?  How does "This page is red." contradict "This page is 
>>> blue." unless they have some meaning as propositions.  But this must be a 
>>> relation between a proposition (an abstract thing) and a fact (the color of 
>>> this page).
>>>
>>> Brent
>>>
>>
>>
>>
>>
>> Sentences, like this one, are physical *only* in the sense that they are 
>> (in this case) made up of electronic bits displayed on a screen (as you are 
>> looking at right now, maybe on a laptop or smartphone) - or they could be 
>> made up of ink strokes on paper, etc.
>>
>>
>> One can't read anything more into them physically that that. What one 
>> reads out of them (a person looking at this sentence, or a computer 
>> scanning one) is a difference matter.
>>
>> There are no abstractions in an immaterial sense.
>>
>>
>> But there are abstractions in the sense that the same proposition is 
>> instantiated in different substrates.   So the contradiction can be between 
>> different instances, e.g. a spoken sentence can contradict a written one.
>>
>> Brent
>>
>
>
> "the same proposition is instantiated in different substrates"
>
>
> Those are in reality different propositions (sentences) materially because 
> they are made up of different particles in difference locations.
>
> There is no "proposition" existing in a Platonic realm that appears here 
> on Earth in different "fleshes".
>
> We group all these material proposition particulars together, but only 
> pragmatically, and call this grouping "a proposition".
>
> - pt
>

I remembered the case of the

*Intentionally blank page *[Wikipedia]

"Sometimes, these pages carry a notice such as "This page [is] 
intentionally left blank." Such notices typically appear in printed works, 
such as legal documents, manuals, and exam papers, in which the reader 
might otherwise suspect that the blank pages are due to a printing error 
and where missing pages might have serious consequences."

So if one sees a page in a book or document with only *This page 
intentionally left blank* printed in the middle of it, one might say "But 
it's not blank! I see *This page intentionally left blank *printed on it! 
My eyes don't lie!"

- pt



 

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Thursday, November 1, 2018 at 5:47:09 PM UTC, John Clark wrote:
>
> On Thu, Nov 1, 2018 at 8:18 AM > wrote:
>
> *> motion can't be done in finite steps*
>
>
> It can if Spacetime is granular, 
>



*It is unethical to truncate my comment in an attempt to win an argument. 
Of course motion can occur if spacetime is granular. That was the point of 
my argument. The assumption of infinite divisibility is the fallacy, which 
Zeno alerted us to. AG*
 

> and even if it's not and Spacetime is continuous motion is still possible 
> and Calculus tells us how.
>

*How does an object in motion know about Calculus? As Phil points out, it 
doesn't. AG*

But Zeno can not tell us which of these explanations is correct and so 
> joins the ranks of all the other ancient Greeks who are of absolutely no 
> help in solving modern cutting edge scientific, mathematical or 
> philosophical problems. 
>

*You sound like a young fool who has no respect for his elders. Zeno 
pointed out something significant IMO. The fact that you fail to recognize 
it is your problem, not his. AG *

>
> John K Clark
>  
>

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 1, 2018 at 6:15:50 PM UTC-5, Brent wrote:
>
>
>
> On 11/1/2018 4:02 PM, Philip Thrift wrote:
>
>
>
> On Thursday, November 1, 2018 at 4:02:56 PM UTC-5, Brent wrote: 
>>
>>
>>
>> On 11/1/2018 11:59 AM, Philip Thrift wrote:
>>
>>
>>
>> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote: 
>>>
>>>
>>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  wrote:
>>>
>>> *> infinite time Turing machines are more powerful than ordinary Turing 
 machines*
>>>
>>>
>>> That is true, it is also true that if dragons existed they would be 
>>> dangerous and if I had some cream I could have strawberries and cream, if I 
>>> had some strawberries.   
>>>
>>> *> How  "real" you think this is depends on whether you are a Platonist 
 or a fictionalist.*

>>>
>>> No, it depends on if you think logical contradictions can exist, if they 
>>> can then there is no point in reading any mathematical proof and logic is 
>>> no longer a useful tool for anything.
>>>
>>> John K Clark
>>>
>>>

>> Of course logics are fiction too. (They're just languages after all.)
>>
>>
>> OK.  Sentences written down are physical and not fictions.  But can they 
>> be contradictory?  How does "This page is red." contradict "This page is 
>> blue." unless they have some meaning as propositions.  But this must be a 
>> relation between a proposition (an abstract thing) and a fact (the color of 
>> this page).
>>
>> Brent
>>
>
>
>
>
> Sentences, like this one, are physical *only* in the sense that they are 
> (in this case) made up of electronic bits displayed on a screen (as you are 
> looking at right now, maybe on a laptop or smartphone) - or they could be 
> made up of ink strokes on paper, etc.
>
>
> One can't read anything more into them physically that that. What one 
> reads out of them (a person looking at this sentence, or a computer 
> scanning one) is a difference matter.
>
> There are no abstractions in an immaterial sense.
>
>
> But there are abstractions in the sense that the same proposition is 
> instantiated in different substrates.   So the contradiction can be between 
> different instances, e.g. a spoken sentence can contradict a written one.
>
> Brent
>


"the same proposition is instantiated in different substrates"


Those are in reality different propositions (sentences) materially because 
they are made up of different particles in difference locations.

There is no "proposition" existing in a Platonic realm that appears here on 
Earth in different "fleshes".

We group all these material proposition particulars together, but only 
pragmatically, and call this grouping "a proposition".

- pt

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 11/1/2018 4:02 PM, Philip Thrift wrote:



On Thursday, November 1, 2018 at 4:02:56 PM UTC-5, Brent wrote:



On 11/1/2018 11:59 AM, Philip Thrift wrote:



On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:


On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift
 wrote:

/> infinite time Turing machines are more powerful than
ordinary Turing machines/


That is true, it is also true that if dragons existed they
would be dangerous and if I had some cream I could have
strawberries and cream, if I had some strawberries.

/> How  "real" you think this is depends on whether you
are a *Platonist *or a*fictionalist*./


No, it depends on if you think logical contradictions can
exist, if they can then there is no point in reading any
mathematical proof and logic is no longer a useful tool for
anything.

John K Clark



Of course logics are fiction too. (They're just languages after all.)


OK.  Sentences written down are physical and not fictions. But can
they be contradictory?  How does "This page is red." contradict
"This page is blue." unless they have some meaning as
propositions.  But this must be a relation between a proposition
(an abstract thing) and a fact (the color of this page).

Brent





Sentences, like this one, are physical *only* in the sense that they 
are (in this case) made up of electronic bits displayed on a screen 
(as you are looking at right now, maybe on a laptop or smartphone) - 
or they could be made up of ink strokes on paper, etc.



One can't read anything more into them physically that that. What one 
reads out of them (a person looking at this sentence, or a computer 
scanning one) is a difference matter.


There are no abstractions in an immaterial sense.


But there are abstractions in the sense that the same proposition is 
instantiated in different substrates.   So the contradiction can be 
between different instances, e.g. a spoken sentence can contradict a 
written one.


Brent

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 1, 2018 at 4:02:56 PM UTC-5, Brent wrote:
>
>
>
> On 11/1/2018 11:59 AM, Philip Thrift wrote:
>
>
>
> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote: 
>>
>>
>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  wrote:
>>
>> *> infinite time Turing machines are more powerful than ordinary Turing 
>>> machines*
>>
>>
>> That is true, it is also true that if dragons existed they would be 
>> dangerous and if I had some cream I could have strawberries and cream, if I 
>> had some strawberries.   
>>
>> *> How  "real" you think this is depends on whether you are a Platonist 
>>> or a fictionalist.*
>>>
>>
>> No, it depends on if you think logical contradictions can exist, if they 
>> can then there is no point in reading any mathematical proof and logic is 
>> no longer a useful tool for anything.
>>
>> John K Clark
>>
>>
>>>
> Of course logics are fiction too. (They're just languages after all.)
>
>
> OK.  Sentences written down are physical and not fictions.  But can they 
> be contradictory?  How does "This page is red." contradict "This page is 
> blue." unless they have some meaning as propositions.  But this must be a 
> relation between a proposition (an abstract thing) and a fact (the color of 
> this page).
>
> Brent
>




Sentences, like this one, are physical *only* in the sense that they are 
(in this case) made up of electronic bits displayed on a screen (as you are 
looking at right now, maybe on a laptop or smartphone) - or they could be 
made up of ink strokes on paper, etc.


One can't read anything more into them physically that that. What one reads 
out of them (a person looking at this sentence, or a computer scanning one) 
is a difference matter.

There are no abstractions in an immaterial sense.

- pt

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 11/1/2018 11:59 AM, Philip Thrift wrote:



On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:


On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift > wrote:

/> infinite time Turing machines are more powerful than
ordinary Turing machines/


That is true, it is also true that if dragons existed they would
be dangerous and if I had some cream I could have strawberries and
cream, if I had some strawberries.

/> How  "real" you think this is depends on whether you are a
*Platonist *or a*fictionalist*./


No, it depends on if you think logical contradictions can exist,
if they can then there is no point in reading any mathematical
proof and logic is no longer a useful tool for anything.

John K Clark



Of course logics are fiction too. (They're just languages after all.)


OK.  Sentences written down are physical and not fictions.  But can they 
be contradictory?  How does "This page is red." contradict "This page is 
blue." unless they have some meaning as propositions. But this must be a 
relation between a proposition (an abstract thing) and a fact (the color 
of this page).


Brent

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 1, 2018 at 2:33:31 PM UTC-5, John Clark wrote:
>
> On Thu, Nov 1, 2018 at 3:11 PM Philip Thrift  > wrote:
>
> > How does *the arrow shot at a target *(in Zeno's Paradox) *compute* the 
>> truth of the forall-exists quantifier construct in the Caucy definition?
>>
>
> I know how calculus computes it, I don't know for a fact the arrow 
> computes it the same way but whatever the method the arrow uses it comes up 
> with the same answer that calculus does, and calculus proves there is no 
> logical contradiction and hence no paradox in what the arrow is doing.
>
> > *When one simulates the arrow shot at a target on a computer using a 
>> numerical calculus software package, there are only floating-point numbers,*
>>
>
> If you don't like approximations and floating-point numbers and want an 
> exact answer then run Mathematica on your computer and solve it 
> symbolically, it can solve calculus problems much better than you can.  
>
> John K Clark
>
>
>
That nature itself is performing symbolic computing is even more 
interesting. 

What about the big thing now,* automatic differentiation*?
- https://en.wikipedia.org/wiki/Automatic_differentiation

see differentiable programming space.

One can various formalisms that "work" (give the "right answers") but that 
doesn't tell you which specific one of those formalisms is "true" or what 
the arrow is in-itself.

- pt


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Re: Mathematical Universe Hypothesis

[John Clark]

On Thu, Nov 1, 2018 at 3:11 PM Philip Thrift  wrote:

> How does *the arrow shot at a target *(in Zeno's Paradox) *compute* the
> truth of the forall-exists quantifier construct in the Caucy definition?
>

I know how calculus computes it, I don't know for a fact the arrow computes
it the same way but whatever the method the arrow uses it comes up with the
same answer that calculus does, and calculus proves there is no logical
contradiction and hence no paradox in what the arrow is doing.

> *When one simulates the arrow shot at a target on a computer using a
> numerical calculus software package, there are only floating-point numbers,*
>

If you don't like approximations and floating-point numbers and want an
exact answer then run Mathematica on your computer and solve it
symbolically, it can solve calculus problems much better than you can.

John K Clark

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 1, 2018 at 1:48:16 PM UTC-5, John Clark wrote:
>
> On Thu, Nov 1, 2018 at 2:43 PM Philip Thrift  > wrote:
>
> *> Even if spacetime is "continuous", what motion is in reality is not 
>> resolved by a Cauchy-type of (ε, δ)-definition of limit*
>>
>
> Why not?
>
> John K Clark
>
>  
>

How does *the arrow shot at a target *(in Zeno's Paradox) *compute* the 
truth of the forall-exists quantifier construct in the Caucy definition? Or 
what is computing the truth of that for the arrow?

When one simulates the arrow shot at a target on a computer using a 
numerical calculus software package, there are only floating-point numbers, 
and the arrow "gets to the target"  because the finite floating-point 
number resolution makes it so.

- pt


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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:
>
>
> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  > wrote:
>
> *> infinite time Turing machines are more powerful than ordinary Turing 
>> machines*
>
>
> That is true, it is also true that if dragons existed they would be 
> dangerous and if I had some cream I could have strawberries and cream, if I 
> had some strawberries.   
>
> *> How  "real" you think this is depends on whether you are a Platonist or 
>> a fictionalist.*
>>
>
> No, it depends on if you think logical contradictions can exist, if they 
> can then there is no point in reading any mathematical proof and logic is 
> no longer a useful tool for anything.
>
> John K Clark
>
>
>>
Of course logics are fiction too. (They're just languages after all.)

- pt

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Re: Mathematical Universe Hypothesis

[John Clark]

On Thu, Nov 1, 2018 at 2:43 PM Philip Thrift  wrote:

*> Even if spacetime is "continuous", what motion is in reality is not
> resolved by a Cauchy-type of (ε, δ)-definition of limit*
>

Why not?

John K Clark

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Re: Mathematical Universe Hypothesis

[John Clark]

On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  wrote:

*> infinite time Turing machines are more powerful than ordinary Turing
> machines*


That is true, it is also true that if dragons existed they would be
dangerous and if I had some cream I could have strawberries and cream, if I
had some strawberries.

*> How  "real" you think this is depends on whether you are a Platonist or
> a fictionalist.*
>

No, it depends on if you think logical contradictions can exist, if they
can then there is no point in reading any mathematical proof and logic is
no longer a useful tool for anything.

John K Clark





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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 1, 2018 at 12:47:09 PM UTC-5, John Clark wrote:
>
> On Thu, Nov 1, 2018 at 8:18 AM > wrote:
>
> *> motion can't be done in finite steps*
>
>
> It can if Spacetime is granular, and even if it's not and Spacetime is 
> continuous motion is still possible and Calculus tells us how. But Zeno can 
> not tell us which of these explanations is correct and so joins the ranks 
> of all the other ancient Greeks who are of absolutely no help in solving 
> modern cutting edge scientific, mathematical or philosophical problems. 
>
> John K Clark
>
 


Even if spacetime is "continuous", what motion is *in reality* is not 
resolved by a Cauchy-type of (ε, δ)-definition of limit 
[ https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit ]. 
Zeno's paradox is still fundamentally problematic in the real world. The 
foundations of mathematics itself with respect to physics is in question, 
hence cohesive homotopy type theory. The fact that calculus works where it 
is applied successfully is a pragmatic outcome, not a proof that Platonic 
mathematics is actual reality itself.

- pt


 
>

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 1, 2018 at 12:31:13 PM UTC-5, John Clark wrote:
>
> On Wed, Oct 31, 2018 at 3:14 PM Philip Thrift  > wrote:
>
> From  https://www.cs.auckland.ac.nz/~cristian/talks/selected/BeamerATM.pdf
>>
>> *> An accelerated Turing machine (sometimes called Zeno machine) is a 
>> Turing machine that takes 2^−n units of time (say seconds) to perform its 
>> nth step; we assume that steps are in some sense identical except for the 
>> time taken for their execution.*
>>
>
> You can assume anything you like and you can define a dragon as a fire 
> breathing flying reptile if you like, but definitions don't cause something 
> to suddenly come into existence.
>
> > *The following ATM can solve the halting problem of an arbitrarily 
>> given TM T and input w in finite time: *
>>
>
> The creator of this ATM made a crucial assumption namely "we assume that 
> steps are in some sense identical except for the time taken for their 
> execution". To me that is equivalent to saying at the end of step 3 in a 
> mathematical proof just before going to step 4 "at this point we assume a 
> miracle occurs". But there is a even more fundamental problem,  solving the 
> Halting Problem is logically contradictory. 
>
> If the ATM can solve the Halting problem then if I feed in any problem it 
> can tell me if it halts or not. Let's say the ATM has 2 slots for input and 
> one slot for output, if I feed in the circuit logic design blueprints of 
> any computer into one slot the ATM can simulate that computer, and if I 
> feed in  program data into the other slot that ATM  will output either 
> "Halt" meaning the simulated machine operating on that data will stop or 
> the ATM will output "not halt" meaning  the simulated machine operating 
> on that data will not stop.
>
> I will now make a new machine called X, it has 3 parts to it. The first 
> part of X  is just a Xerox copy machine, feed in one program and it outputs 
> 2 identical programs. The second part of X is the ATM and it receives the 2 
> programs as input from the Xerox machine's outputs, and the ATM then 
> outputs either "halt" or "not halt". The third and last part of X is a very 
> simple machine called the negator, it receives as input the output of the 
> ATM and if the input to the negator is "Halt" the negator will go into a 
> infinite loop and if the input is "not halt" the negator will print "halt" 
> and then stop.
>
> Now lets draw the blueprint circuit design of the entire X machine that 
> fully defines it, then make 2 copies of it and feed it into the ATM; so the 
> ATM is now trying to figure out if the X machine will halt if it is fed its 
> own blueprint as data. If the ATM says "halt" the X machine will not halt 
> and the ATM was wrong.  If the ATM says "not halt" the X machine will 
> halt and the ATM was wrong again. 
>
> Therefore the ATM can not logically exist.
>
> John K Clark 
>




Zeno machines are just infinite-time Turing machines whose theory has been 
developed by @JDHamkins  and others.

http://jdh.hamkins.org/ittms/

*The Power of Infinite Time Machines How powerful are these machines? *

*Perhaps the first thing to notice is that the halting problem for Turing 
machines is infinite time decidable. This is true because with an infinite 
time Turing machine one can simulate an ordinary Turing machine 
computation. Either the simulation halts in finitely many steps, or else 
after ω many steps the machine reaches the limit state, and so by giving 
the output Yes or No, respectively, in these two situations, the halting 
problem is solved. Thus infinite time Turing machines are more powerful 
than ordinary Turing machines: they can decide sets which are undecidable 
by Turing machines. The next theorem greatly improves on this.*

Theorem 2.1 The truth of any arithmetic statement is infinite time 
decidable.




All of this is standard in computability theory: There are levels of Turing 
machines starting at level 0 where a TM at level n+1 solves the haling 
problem of level n.

How  "real" you think this is depends on whether you are a *Platonist *or a* 
fictionalist*. For it to be "real" in the natural world would require a 
physical hypercomputaional substrate, like a hypothetical black hole 
(relativistic) computer.

- pt


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Re: Mathematical Universe Hypothesis

[John Clark]

On Thu, Nov 1, 2018 at 8:18 AM  wrote:

*> motion can't be done in finite steps*


It can if Spacetime is granular, and even if it's not and Spacetime is
continuous motion is still possible and Calculus tells us how. But Zeno can
not tell us which of these explanations is correct and so joins the ranks
of all the other ancient Greeks who are of absolutely no help in solving
modern cutting edge scientific, mathematical or philosophical problems.

John K Clark

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Re: Mathematical Universe Hypothesis

[John Clark]

On Wed, Oct 31, 2018 at 3:14 PM Philip Thrift  wrote:

>From  https://www.cs.auckland.ac.nz/~cristian/talks/selected/BeamerATM.pdf
>
> *> An accelerated Turing machine (sometimes called Zeno machine) is a
> Turing machine that takes 2^−n units of time (say seconds) to perform its
> nth step; we assume that steps are in some sense identical except for the
> time taken for their execution.*
>

You can assume anything you like and you can define a dragon as a fire
breathing flying reptile if you like, but definitions don't cause something
to suddenly come into existence.

> *The following ATM can solve the halting problem of an arbitrarily given
> TM T and input w in finite time: *
>

The creator of this ATM made a crucial assumption namely "we assume that
steps are in some sense identical except for the time taken for their
execution". To me that is equivalent to saying at the end of step 3 in a
mathematical proof just before going to step 4 "at this point we assume a
miracle occurs". But there is a even more fundamental problem,  solving the
Halting Problem is logically contradictory.

If the ATM can solve the Halting problem then if I feed in any problem it
can tell me if it halts or not. Let's say the ATM has 2 slots for input and
one slot for output, if I feed in the circuit logic design blueprints of
any computer into one slot the ATM can simulate that computer, and if I
feed in  program data into the other slot that ATM  will output either
"Halt" meaning the simulated machine operating on that data will stop or
the ATM will output "not halt" meaning  the simulated machine operating on
that data will not stop.

I will now make a new machine called X, it has 3 parts to it. The first
part of X  is just a Xerox copy machine, feed in one program and it outputs
2 identical programs. The second part of X is the ATM and it receives the 2
programs as input from the Xerox machine's outputs, and the ATM then
outputs either "halt" or "not halt". The third and last part of X is a very
simple machine called the negator, it receives as input the output of the
ATM and if the input to the negator is "Halt" the negator will go into a
infinite loop and if the input is "not halt" the negator will print "halt"
and then stop.

Now lets draw the blueprint circuit design of the entire X machine that
fully defines it, then make 2 copies of it and feed it into the ATM; so the
ATM is now trying to figure out if the X machine will halt if it is fed its
own blueprint as data. If the ATM says "halt" the X machine will not halt
and the ATM was wrong.  If the ATM says "not halt" the X machine will halt
and the ATM was wrong again.

Therefore the ATM can not logically exist.

John K Clark

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Thursday, November 1, 2018 at 2:09:41 PM UTC+1, agrays...@gmail.com 
wrote:
>
>
>
> On Wednesday, October 31, 2018 at 3:38:55 PM UTC, John Clark wrote:
>>
>> On Tue, Oct 30, 2018 at 10:16 PM  wrote:
>>
>> >>What you described is a infinite number  of FIXED length discrete 
 steps, and if that is what motion is motion would indeed be impossible, 
 but 
 its not the infinity that makes it impossible its the fixed length.

>>>
>>> *>Of course it's the infinity under THIS scenario. The point is this is 
>>> one way to do the task, but fails precisely because of the infinity. AG *
>>>
>>
>> That is incorrect. 
>>
>
> When I wrote "THIS scenario", I meant the one with fixed length discrete 
> steps which cannot be completed in finite time. It's explained by the 
> fallacy of assuming space is infinitely divisible. AG
>

Why would you assume that each step in Zeno's presentation would take a 
fixed length of time? If you are moving at a constant speed, you traverse 
half the distance at half the time.

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Wednesday, October 31, 2018 at 3:38:55 PM UTC, John Clark wrote:
>
> On Tue, Oct 30, 2018 at 10:16 PM > 
> wrote:
>
> >>What you described is a infinite number  of FIXED length discrete 
>>> steps, and if that is what motion is motion would indeed be impossible, but 
>>> its not the infinity that makes it impossible its the fixed length.
>>>
>>
>> *>Of course it's the infinity under THIS scenario. The point is this is 
>> one way to do the task, but fails precisely because of the infinity. AG *
>>
>
> That is incorrect. 
>

When I wrote "THIS scenario", I meant the one with fixed length discrete 
steps which cannot be completed in finite time. It's explained by the 
fallacy of assuming space is infinitely divisible. AG 

> A infinite number of tasks CAN be completed in a finite time if the 
> duration of the first task is half a second and the second is a quarter of 
> a second and the third a eighth of a second etc.  In this case even though 
> there are a infinite number of tasks they are all completed in exactly one 
> second. 
>
> But obviously if there are a infinite number of tasks with a *fixed 
> length* they can't all be completed in a finite time. That was your 
> original scenario so obviously that's not the way motion works.
>
> John K Clark
>
>  
>
>>
>>
>>>  
>>>
 > *So, since motion surely seems demonstrable, why can't the task be 
 done as I described? Answer; because space isn't infinitely divisible.*
>>>
>>>
>>> That is one possible answer, the other is that the infinite number of 
>>> tasks are NOT of fixed length but decrease in a geometric progression that 
>>> converges. As I said , Zeno is of no help in deciding which of these 2 
>>> answers is correct.
>>>
>>> John K Clark  
>>>
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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Wednesday, October 31, 2018 at 3:38:55 PM UTC, John Clark wrote:
>
> On Tue, Oct 30, 2018 at 10:16 PM > 
> wrote:
>
> >>What you described is a infinite number  of FIXED length discrete 
>>> steps, and if that is what motion is motion would indeed be impossible, but 
>>> its not the infinity that makes it impossible its the fixed length.
>>>
>>
>> *>Of course it's the infinity under THIS scenario. The point is this is 
>> one way to do the task, but fails precisely because of the infinity. AG *
>>
>
> That is incorrect. A infinite number of tasks CAN be completed in a finite 
> time if the duration of the first task is half a second and the second is a 
> quarter of a second and the third a eighth of a second etc.  In this case 
> even though there are a infinite number of tasks they are all completed in 
> exactly one second. 
>
> But obviously if there are a infinite number of tasks with a *fixed 
> length* they can't all be completed in a finite time. That was your 
> original scenario so obviously that's not the way motion works.
>

*Of course. You're proving that motion is possible, which we already know, 
or very strongly believe. It's like you've proven that a circle is round. I 
think there's a subtle point here you miss; namely, that since motion can't 
be done in finite steps due to the divergence in my model (and I think 
Zeno's as well), the question is why? I think it's because space is not 
infinitely divisible, established logically by this model. AG *

>
> John K Clark
>
>  
>
>>
>>
>>>  
>>>
 > *So, since motion surely seems demonstrable, why can't the task be 
 done as I described? Answer; because space isn't infinitely divisible.*
>>>
>>>
>>> That is one possible answer, the other is that the infinite number of 
>>> tasks are NOT of fixed length but decrease in a geometric progression that 
>>> converges. As I said , Zeno is of no help in deciding which of these 2 
>>> answers is correct.
>>>
>>> John K Clark  
>>>
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Wednesday, October 31, 2018 at 11:13:17 AM UTC-5, John Clark wrote:
>
>
>
> On Tue, Oct 30, 2018 at 1:30 PM Philip Thrift  > wrote:
>
> > *More formally, a **Zeno machine is a Turing machine that*
>
>
> The rules of Zeno's machine never change so if its a Turing Machine it's 
> must be a one state Turing Machine, the very simplest type. But there are 
> only 64 different one state Turing Machines and none of them are Zeno's 
> machine. So it's not a Turing Machine, Zeno's machine is just not powerful 
> enough to be even the simplest type of Turing Machine. 
>
> John K Clark
>



A Zeno Machine (ZM) - or Accelerated Turing Machine (ATM) - can solve the 
Turing Machine (TM)* halting problem*:

>From  https://www.cs.auckland.ac.nz/~cristian/talks/selected/BeamerATM.pdf

An accelerated Turing machine (sometimes called *Zeno machine*) is a Turing 
machine that takes 2^−n units of time (say seconds) to perform its nth 
step; we assume that steps are in some sense identical except for the time 
taken for their execution.


The following ATM can solve the halting problem of an arbitrarily given TM 
T and input w in finite time: 

begin program
write 0 on the first position of the output tape;
set i = 1;
begin loop
simulate the first i steps of T on w;
if T(w) has halted, then write 1 on the
first position of the output tape;
i = i + 1;
end loop
end program

- pt


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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Oct 2018, at 12:33, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Tuesday, October 30, 2018 at 9:45:09 AM UTC, Bruno Marchal wrote:
> 
>> On 29 Oct 2018, at 17:54, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Monday, October 29, 2018 at 4:07:41 PM UTC, John Clark wrote:
>> On Sun, Oct 28, 2018 at 2:56 PM > wrote:
>> 
>>  > What's your view of Zeno's paradox which implies motion is impossible.
>> 
>> Zeno thought it was obvious if you added an infinite number of nonzero 
>> lengths or nonzero times together you would always get something that was  
>> nfinite, and that is the foundation of his paradox; but with modern calculus 
>> we know that sometimes that isn't true, and when it isn't true calculus can 
>> tell you exactly what the FINITE length or finite time interval turns out to 
>> be. For example, the sum, of the infinite series: 
>> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>> 
>> John K Clark
>> 
>> This doesn't resolve Zeno's paradox. AG 
> 
> 
> It does.
> 
> I don't think you understand Zeno's paradox. Why don't you state it in your 
> own words to test your knowledge?. AG

Your own presentation seems to me more like the paradox of the light bulb, 
which we light on for 1 second, then off for 1/2 second, on for 1/4s, etc. Is 
it light on or of after two seconds?

I use the standard formulation, and I agree with John Clark's invocation of 
elementary series theory, as solving the paradox. 

If you insist that Zeno want a still at each step, then it is like light bulb 
paradox, where I have not yet any definite opinion, or it is like the paradox 
of the guy who want both an infinitely precise picture of the arrow, and an 
idea of its velocity, but when he get that infinitely precise picture, he can 
only conclude that the arrow is immobile.

Bruno




> 
> The greeks understood that an infinite sum can converge. The math was not 
> rigoroius, and they wrongly believed that it is enough that the general term 
> tend to zero for the series to converge, which will be refuted many centuries 
> later by Oresme (a French bishop and mathematician) with the harmonic series:
> 1 + 1/2 + 1/3 + 1/4 + 1/5 + …. which diverges (like ln(n)).
> Cauchy made the math rigorous here, and mathematical logic even rehabilitates 
> the infinitesimals of Newton and Leibniz, but, Imo, Cauchy works is better.
> 
> Bruno
> 
> 
> 
> 
> 
> 
>> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Oct 2018, at 12:01, Tomas Pales  wrote:
> 
> 
> 
> On Tuesday, October 30, 2018 at 10:36:59 AM UTC+1, Bruno Marchal wrote:
> 
> Any object can be inconsistently defined. I can define the moon by the set of 
> squared circles.
> 
> The set of squared circles is the empty set. The moon is not an empty set, it 
> has a complex internal structure.
> 
> Anyway, the word "define" has two meanings which need to be distinguished. 
> "An object is defined" may mean:
> 
> 1) "An object is described" (this usually means that there must be someone 
> who defines/describes the object)
> 
> 2) "An object is constituted/formed" (this doesn't require anyone to define 
> the object, just as the fact that an object is composed of parts doesn't 
> require a composer)
> 
> When I say that an object is consistently or inconsistently defined, I mean 
> defined in the second sense. That's the existential/ontological sense. An 
> inconsistently defined object is not identical to itself, it is not what it 
> is, it does not have the properties it has. Such an object is nonsense, it 
> cannot exist, it is not really an object, it is nothing. The definition of an 
> object in the first sense is true/accurate iff it corresponds to the 
> definition of the object in the second sense. 
>  
>> - and this I mean in the absolute sense, regardless of theory: an object 
>> that is not identical to itself is inconsistent in any theory. Such an 
>> object cannot exist. All other objects can exist somewhere.
> 
> You are not using the (logical) terms in their standard meaning. It is hard 
> to follow. I don’t undersetand what you mean by object.
> 
> Sorry, by "object" I mean anything that exists. Not nothing.
>  
> 
> With mechanism, the axiom of infinity leads to an inflation of predictions, 
> which is not what we are experiencing
> 
> That may mean that we live in a finite mathematical structure. Still, that 
> doesn't rule out the existence of infinite mathematical structures. If they 
> are consistent, why wouldn't they exist?


The elegance of mechanism is that it explains, by assuming only very simple 
rule, why the numbers eventually discover the infinities in their own mind, and 
correctly so. 

We get an explanation why the finite number can dispense themselves of using 
infinities to throw some light on themselves. With a simple ontology (any 
universal system will do) we get the phenomenological reality of matter and 
analysis, and beyond.

And it can be tested, and perhaps completed in case we are not machine, but 
actual gods, which I doubt. That would not change much in the approach, only 
make it technical more demanding. But let us not put the complexity in the 
start. We can add it if it is needed.

Bruno




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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Oct 2018, at 10:50, Philip Thrift  wrote:
> 
> 
> 
> On Tuesday, October 30, 2018 at 4:29:01 AM UTC-5, Bruno Marchal wrote:
> 
>> On 29 Oct 2018, at 11:24, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Monday, October 29, 2018 at 4:35:39 AM UTC-5, Bruno Marchal wrote:
>> 
>> 
>> Because finite numbers can be shown to have infinite hallucinations, 
>> especially when they mess with other finite numbers. And that leads to a 
>> testable theology, which includes an explanation of where both quanta and 
>> qualia comes from. Then assuming more than that in the ontology, introduces 
>> unnecessary difficulties, probably inconsistency or deflation of 
>> predictions. (Usually called white rabbit in this list (and in my long 
>> version thesis).
>> 
>> Bruno
>> 
>> 
>> 
>> 
>> Hallucinations and qualia can be derived from numbers (numerical reality) is 
>> one thesis. But what is the test?
>> 
>> In material reality, numbers do not exist (aka mathematical fictionalism). 
>> So positing numbers would add more to the ontology (a Platonic realm in 
>> addition to the material realm).
> 
> I do not assume a primary material reality. Eventually, I assume only 
> elementary arithmetic, or elementary combinator theory, and anything Turing 
> equivalent. 
> 
> 
> 
>> 
>> Material reality supports both information (numberical) processing and 
>> experience (qualia) processing. The alternative thesis.
> 
> Primary matter is what make the mind-body problem unsolvable. Given the mack 
> of evidence of it, why assume it?
> 
> 
>> 
>> That I am conscious is the test that there is a material reality.
> 
> 
> Consciousness does not seem material to me. Consciousness is the test of the 
> existence of consciousness. To infer a material reality from a conscious 
> experience is an extrapolation, and once you bet on mechanism, it does not 
> make much sense. No problem, as you seem both materialist and non mechanist. 
> We are working in different theory.
> 
> Bruno
> 
> 
> 
> I think I've always followed the direction of pragmatism, or more precisely 
> Rortian neopragmatism since Philosophy and the Mirror of Nature.
> 
> I see the (modal logical) language as explored in "The universal numbers: 
> From Biology to Physics" is of interest to agent programming language 
> theorists (and they indeed utilize those logics in their research).
> 
> But when the "code meets the road" so to speak, and conscious robots need to 
> be compiled, matter will be needed to actually make them, there there is 
> where the matter matters!


But how would a universal number feel a difference of consciousness between 
being in an emulation of the quantum wave of our cluster of galaxies with 
10^100 decimals correct, and being in in such a cluster? 

What role matter plays? If it is only for saying “real”, it is an error in 
metaphysics. You could as well add that we need matter so that God can bless it.

In arithmetic, we don’t have *that* problem, we just listen to the 
machine/numbers, and decide to not treat them as zombie when they complain on 
this or that (the universal number are never 100% satisfied!).

We do have another problem: which is that matter has to emerge from an infinite 
competition in between all universal numbers below our substitution level. But 
that is quite close to Feynman formulation of QM, in a many 
computations/world/mind setting. Where the physicists are confused, the 
mechanist can say we told you. And, oh, yes, the hyper-mechanist can say that 
too, and that is a weakness of my approach, in a sense, which is that we can 
distinguish experimentally between mechanism, hypermechanism, or a number of 
version of mechanism + oracle. But again, that is a reason more to chose the 
simplest option. If we find a reason to believe in miracle, oracle and 
contextual divine entity on the terrestrial plane, it can still be time to 
weaken and generalise the mechanist hypothesis. Note that only the arithmetical 
gods *quite* close to arithmetical truth (which is above all arithmetical gods) 
get supplementary axioms to their self-reference logic G and G*. I have studied 
some of those “gods”, notably those whose “believability” predicate is defined 
by “true in all V_kappa models of ZF”. You need to add []([]A->B) v [](([]B & 
B) -> []A) to G.
With the way I proceed, in is not impossible to test this in some future, in 
the corresponding “material” variant of G, but that is not for tomorrow.

Bruno






> 
> - pt
> 
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Re: Mathematical Universe Hypothesis

[John Clark]

On Tue, Oct 30, 2018 at 1:30 PM Philip Thrift  wrote:

> *More formally, a **Zeno machine is a Turing machine that*


The rules of Zeno's machine never change so if its a Turing Machine it's
must be a one state Turing Machine, the very simplest type. But there are
only 64 different one state Turing Machines and none of them are Zeno's
machine. So it's not a Turing Machine, Zeno's machine is just not powerful
enough to be even the simplest type of Turing Machine.

John K Clark



>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Tue, Oct 30, 2018 at 10:16 PM  wrote:

>>What you described is a infinite number  of FIXED length discrete steps,
>> and if that is what motion is motion would indeed be impossible, but its
>> not the infinity that makes it impossible its the fixed length.
>>
>
> *>Of course it's the infinity under THIS scenario. The point is this is
> one way to do the task, but fails precisely because of the infinity. AG *
>

That is incorrect. A infinite number of tasks CAN be completed in a finite
time if the duration of the first task is half a second and the second is a
quarter of a second and the third a eighth of a second etc.  In this case
even though there are a infinite number of tasks they are all completed in
exactly one second.

But obviously if there are a infinite number of tasks with a *fixed length*
they can't all be completed in a finite time. That was your original
scenario so obviously that's not the way motion works.

John K Clark



>
>
>>
>>
>>> > *So, since motion surely seems demonstrable, why can't the task be
>>> done as I described? Answer; because space isn't infinitely divisible.*
>>
>>
>> That is one possible answer, the other is that the infinite number of
>> tasks are NOT of fixed length but decrease in a geometric progression that
>> converges. As I said , Zeno is of no help in deciding which of these 2
>> answers is correct.
>>
>> John K Clark
>>
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

What I see in the tech news is about things like *Quantum Monte Carlo* for 
chemistry on high-performance computing platforms like ones from @
OpenPOWERorg .

That's a lot of bits-flipping-per-second.

Also, see *Differentiable Functional Programming* (e.g. DiffSharp) vs. 
Mathematica, etc.
- 
http://www.robots.ox.ac.uk/~gunes/assets/pdf/baydin-2016-slides-functionallondoners.pdf

- pt

On Tuesday, October 30, 2018 at 2:38:31 PM UTC-5, Brent wrote:
>
> The calculus problems that computers can solve exactly don't have complex 
> boundary conditions, including arbitrary dynamic terms, that are only 
> defined numerically.
>
> Brent
>
> On 10/30/2018 8:43 AM, John Clark wrote:
>
>
>
> On Tue, Oct 30, 2018 at 2:22 AM Philip Thrift  > wrote:
>
> *> Engineers today are ultrafintiitists in practice: They design airplanes 
>> and bridges with computer software that runs on computers with a fixed, 
>> finite number of bits that are ever used. *
>
>
> For over 40 years computers have been able to solve calculus problems 
> symbolically and get EXACT answers and do it better than any human can, 
> just look at  Mathematica. Sometimes engineers use numerical approximations 
> not because they think calculus is wrong, no engineer is that dumb, but 
> because sometimes the equations are so complex even Mathematica can't find 
> a solution and because an approximation is good enough to make sure the 
> bridge won't fall down
>
> John K Clark 
>
>
>

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Tuesday, October 30, 2018 at 11:04:31 PM UTC, John Clark wrote:
>
> On Tue, Oct 30, 2018 at 3:44 PM > wrote:
>
> *> You miss the point. If the task is done in discrete steps as I 
>> described, which is apriori conceivable, motion is impossible.*
>
>
> What you described is a infinite number  of FIXED length discrete steps, 
> and if that is what motion is motion would indeed be impossible, but its 
> not the infinity that makes it impossible its the fixed length.
>

*Of course it's the infinity under THIS scenario. The point is this is one 
way to do the task, but fails precisely because of the infinity. AG *

>
>  
>
>> > *So, since motion surely seems demonstrable, why can't the task be 
>> done as I described? Answer; because space isn't infinitely divisible.*
>
>
> That is one possible answer, the other is that the infinite number of 
> tasks are NOT of fixed length but decrease in a geometric progression that 
> converges. As I said , Zeno is of no help in deciding which of these 2 
> answers is correct.
>
> John K Clark  
>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Tue, Oct 30, 2018 at 3:44 PM  wrote:

*> You miss the point. If the task is done in discrete steps as I
> described, which is apriori conceivable, motion is impossible.*


What you described is a infinite number  of FIXED length discrete steps,
and if that is what motion is motion would indeed be impossible, but its
not the infinity that makes it impossible its the fixed length.



> > *So, since motion surely seems demonstrable, why can't the task be done
> as I described? Answer; because space isn't infinitely divisible.*


That is one possible answer, the other is that the infinite number of tasks
are NOT of fixed length but decrease in a geometric progression that
converges. As I said , Zeno is of no help in deciding which of these 2
answers is correct.

John K Clark

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Tuesday, October 30, 2018 at 11:46:53 PM UTC+1, Brent wrote:
>
>
>
> On 10/30/2018 2:49 PM, Tomas Pales wrote:
>
>
>
> On Tuesday, October 30, 2018 at 8:14:31 PM UTC+1, Brent wrote: 
>>
>>
>>
>> On 10/30/2018 4:01 AM, Tomas Pales wrote:
>>
>>
>>
>> On Tuesday, October 30, 2018 at 10:36:59 AM UTC+1, Bruno Marchal wrote:
>>
>>>
>>> Any object can be inconsistently defined. I can define the moon by the 
>>> set of squared circles.
>>>
>>
>> The set of squared circles is the empty set. The moon is not an empty 
>> set, it has a complex internal structure.
>>
>> Anyway, the word "define" has two meanings which need to be 
>> distinguished. "An object is *defined*" may mean:
>>
>> 1) "An object is *described*" (this usually means that there must be 
>> someone who defines/describes the object)
>>
>> 2) "An object is *constituted/formed*" (this doesn't require anyone to 
>> define the object, just as the fact that an object is composed of parts 
>> doesn't require a composer)
>>
>>
>> Where did you come up with these?  To define an object means to cite 
>> sufficient characteristics of the object so that it is distinguished from 
>> all other objects.  It is described in the sense of 1) supra, but the 
>> description need not be extensive; simple ostensive definition by pointing 
>> suffices, which is probably how you learned the definition of "Moon".
>>
>> Your "definition" 2) makes no sense.  Listing all the constituents of an 
>> object to what level?  atoms?  quantum fields?  And how does that even 
>> suffice to distinguish an object from other objects with the same 
>> constituents?  When you've tried to use your idea of "consistently defined" 
>> you've resorted to including all relations to other objects in the 
>> "consistent definition" which makes the object distinct from other objects 
>> but which makes the definition of an object unknowable.
>>
>
> In the first sense, an object is defined by someone. In the second sense, 
> an object is defined by its properties, parts and relations.   
>
>
> But those are to numerous and uncertain to ever be known.  And why would 
> you use the word "defined" instead of "constituted" when "defined" clearly 
> refers to making definite which can be done by much less than listing all 
> the constituents?
>

I just wanted to point out two different meanings of "define" because Bruno 
said he could define the moon inconsistently. He could do so, by mistake or 
whatever he meant, but the moon cannot be defined inconsistently in the 
second sense (because it wouldn't exist). 

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/30/2018 2:49 PM, Tomas Pales wrote:



On Tuesday, October 30, 2018 at 8:14:31 PM UTC+1, Brent wrote:



On 10/30/2018 4:01 AM, Tomas Pales wrote:



On Tuesday, October 30, 2018 at 10:36:59 AM UTC+1, Bruno Marchal
wrote:


Any object can be inconsistently defined. I can define the
moon by the set of squared circles.


The set of squared circles is the empty set. The moon is not an
empty set, it has a complex internal structure.

Anyway, the word "define" has two meanings which need to be
distinguished. "An object is /defined/" may mean:

1) "An object is /described/" (this usually means that there must
be someone who defines/describes the object)

2) "An object is /constituted/formed/" (this doesn't require
anyone to define the object, just as the fact that an object is
composed of parts doesn't require a composer)


Where did you come up with these?  To define an object means to
cite sufficient characteristics of the object so that it is
distinguished from all other objects.  It is described in the
sense of 1) supra, but the description need not be extensive;
simple ostensive definition by pointing suffices, which is
probably how you learned the definition of "Moon".

Your "definition" 2) makes no sense.  Listing all the constituents
of an object to what level?  atoms?  quantum fields?  And how does
that even suffice to distinguish an object from other objects with
the same constituents?  When you've tried to use your idea of
"consistently defined" you've resorted to including all relations
to other objects in the "consistent definition" which makes the
object distinct from other objects but which makes the definition
of an object unknowable.


In the first sense, an object is defined by someone. In the second 
sense, an object is defined by its properties, parts and relations.


But those are to numerous and uncertain to ever be known.  And why would 
you use the word "defined" instead of "constituted" when "defined" 
clearly refers to making definite which can be done by much less than 
listing all the constituents?


Brent

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Tuesday, October 30, 2018 at 5:30:51 PM UTC, John Clark wrote:
>
>
>
> On Tue, Oct 30, 2018 at 12:29 PM Philip Thrift  > wrote:
>
>
> *> By the word "approximation" above in reference to what is being 
>> approximating seems to assume that the natural world itself  - the 
>> materials out of which the bridge or airplane is made, the air, the 
>> bedrock, the whole constructions and environment -  are continuous and 
>> differentiable in the mathematical sense of standard calculus. But why 
>> would one assume that the world is in reality that?*
>
>
> I don't assume that. What I'm saying is that if things are continuous then 
> Zeno's paradox is not a paradox and if things are discrete and not 
> continuous then Zeno's paradox is still not a paradox.  In other words Zeno 
> is of no help whatsoever.
>
> John K Clark
>

*You miss the point. If the task is done in discrete steps as I described, 
which is apriori conceivable, motion is impossible. So, since motion surely 
seems demonstrable, why can't the task be done as I described? Answer; 
because space isn't infinitely divisible. If you check Wiki on Zeno Paradox 
and review the solutions offered through history, Henri Bergson came to the 
same conclusion I have offered, but he didn't extend it far enough. AG*

>
>> That would assume a mathematical reality a la Tegmark (which he himself 
>> doesn't believe).
>>
>> - pt
>>
>>
>>
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Re: Mathematical Universe Hypothesis

[Brent Meeker]

The calculus problems that computers can solve exactly don't have 
complex boundary conditions, including arbitrary dynamic terms, that are 
only defined numerically.


Brent

On 10/30/2018 8:43 AM, John Clark wrote:



On Tue, Oct 30, 2018 at 2:22 AM Philip Thrift > wrote:


/> Engineers today are ultrafintiitists in practice: They design
airplanes and bridges with computer software that runs on
computers with a fixed, finite number of bits that are ever used. /


For over 40 years computers have been able to solve calculus problems 
symbolically and get EXACT answers and do it better than any human 
can, just look at  Mathematica. Sometimes engineers use numerical 
approximations not because they think calculus is wrong, no engineer 
is that dumb, but because sometimes the equations are so complex even 
Mathematica can't find a solution and because an approximation is good 
enough to make sure the bridge won't fall down


John K Clark





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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/30/2018 4:01 AM, Tomas Pales wrote:



On Tuesday, October 30, 2018 at 10:36:59 AM UTC+1, Bruno Marchal wrote:


Any object can be inconsistently defined. I can define the moon by
the set of squared circles.


The set of squared circles is the empty set. The moon is not an empty 
set, it has a complex internal structure.


Anyway, the word "define" has two meanings which need to be 
distinguished. "An object is /defined/" may mean:


1) "An object is /described/" (this usually means that there must be 
someone who defines/describes the object)


2) "An object is /constituted/formed/" (this doesn't require anyone to 
define the object, just as the fact that an object is composed of 
parts doesn't require a composer)


Where did you come up with these?  To define an object means to cite 
sufficient characteristics of the object so that it is distinguished 
from all other objects.  It is described in the sense of 1) supra, but 
the description need not be extensive; simple ostensive definition by 
pointing suffices, which is probably how you learned the definition of 
"Moon".


Your "definition" 2) makes no sense.  Listing all the constituents of an 
object to what level?  atoms?  quantum fields?  And how does that even 
suffice to distinguish an object from other objects with the same 
constituents?  When you've tried to use your idea of "consistently 
defined" you've resorted to including all relations to other objects in 
the "consistent definition" which makes the object distinct from other 
objects but which makes the definition of an object unknowable.


Brent



When I say that an object is consistently or inconsistently defined, I 
mean defined in the second sense. That's the existential/ontological 
sense. An inconsistently defined object is not identical to itself, it 
is not what it is, it does not have the properties it has. Such an 
object is nonsense, it cannot exist, it is not really an object, it is 
nothing. The definition of an object in the first sense is 
true/accurate iff it corresponds to the definition of the object in 
the second sense.



- and this I mean in the absolute sense, regardless of theory: an
object that is not identical to itself is inconsistent in any
theory. Such an object cannot exist. All other objects can exist
somewhere.


You are not using the (logical) terms in their standard meaning.
It is hard to follow. I don’t undersetand what you mean by object.


Sorry, by "object" I mean anything that exists. Not nothing.


With mechanism, the axiom of infinity leads to an inflation of
predictions, which is not what we are experiencing


That may mean that we live in a finite mathematical structure. Still, 
that doesn't rule out the existence of infinite mathematical 
structures. If they are consistent, why wouldn't they exist?

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Tuesday, October 30, 2018 at 12:30:51 PM UTC-5, John Clark wrote:
>
>
>
> On Tue, Oct 30, 2018 at 12:29 PM Philip Thrift  > wrote:
>
>
> *> By the word "approximation" above in reference to what is being 
>> approximating seems to assume that the natural world itself  - the 
>> materials out of which the bridge or airplane is made, the air, the 
>> bedrock, the whole constructions and environment -  are continuous and 
>> differentiable in the mathematical sense of standard calculus. But why 
>> would one assume that the world is in reality that?*
>
>
> I don't assume that. What I'm saying is that if things are continuous then 
> Zeno's paradox is not a paradox and if things are discrete and not 
> continuous then Zeno's paradox is still not a paradox.  In other words Zeno 
> is of no help whatsoever.
>
> John K Clark
>
>>
>>
In the case of continuous-differentiable spacetime (in actual reality) 
there is still the problem of there being a supertask (Zeno machine), 
unless one goes to cohesive homotopy type theory.

- pt

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Re: Mathematical Universe Hypothesis

[John Clark]

On Tue, Oct 30, 2018 at 12:29 PM Philip Thrift 
wrote:


*> By the word "approximation" above in reference to what is being
> approximating seems to assume that the natural world itself  - the
> materials out of which the bridge or airplane is made, the air, the
> bedrock, the whole constructions and environment -  are continuous and
> differentiable in the mathematical sense of standard calculus. But why
> would one assume that the world is in reality that?*


I don't assume that. What I'm saying is that if things are continuous then
Zeno's paradox is not a paradox and if things are discrete and not
continuous then Zeno's paradox is still not a paradox.  In other words Zeno
is of no help whatsoever.

John K Clark






>
> That would assume a mathematical reality a la Tegmark (which he himself
> doesn't believe).
>
> - pt
>
>
>
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Tuesday, October 30, 2018 at 12:24:04 PM UTC-5, John Clark wrote:
>
>
>
"there CAN be a infinite number of variable pauses in which each pause is 
half the length of the previous pause" 

You realize that is what a Zeno machine is based on:

More formally, a *Zeno machine* is a Turing machine that takes 2−*n* units 
of time to perform its *n*-th step; thus, the first step takes 0.5 units of 
time, the second takes 0.25, the third 0.125 and so on, so that after one 
unit of time, a countably infinite 
 (i.e. ℵ0 
) number of steps will 
have been performed.

- pt

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Re: Mathematical Universe Hypothesis

[John Clark]

> On Tuesday, October 30, 2018 at 7:44:35 AM UTC-5, agrays...@gmail.com
wrote:

you can think of Zeno's paradox as an infinite sequence of tasks, each one
> separated by a finite fixed pause. The complete task cannot be completed in
> finite time


Then all Zeno did was show you shouldn't think of motion like that. There
can NOT be a infinite number of fixed pauses after each micro-task, but
there CAN be a infinite number of variable pauses in which each pause is
half the length of the previous pause.


> *> Minor correction; the solution is that space (not space and time) is
> not infinitely divisible. AG*


You can't treat time and space as unrelated things like that. If the Planck
Length is the smallest possible length (a big if) then the Planck Time of
5.4*10^-43 seconds is the smallest possible amount of time, it is the
amount of time it takes light to travel the Planck length.

  John K Clark







>
>>
>
>
>
>
> As has been stated many times in philosophy of science writing, the
> quantum solution is indeed the best resolution of Zen'o's Paradox (ZP) so
> far.
>
>
> The other approach, where in reality there are smooth continua, requires
> cohesive entities:
>
> https://ncatlab.org/nlab/show/cohesive+topos
>
> That is a bigger pill to swallow.
>
>
> - pt
>
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Tuesday, October 30, 2018 at 7:44:35 AM UTC-5, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, October 30, 2018 at 12:38:16 PM UTC, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Monday, October 29, 2018 at 10:15:28 PM UTC, John Clark wrote:
>>>
>>>
>>> On Mon, Oct 29, 2018 at 5:21 PM  wrote:
>>>
>>> >*If you try to traverse a unit distance in infinite steps such as 1/2, 
 1/4, 1/8, 1/16 and so forth, the sum converges to 1, but you will never 
 traverse the distance even though the sum converges.*
>>>
>>>
>>> Never? If what you say is true then calculus is wrong. I don't think 
>>> calculus is wrong.
>>>
>>> John K Clark 
>>>
>>
>> *Nothing wrong with calculus. Rather, you can think of Zeno's paradox as 
>> an infinite sequence of tasks, each one separated by a finite fixed pause. 
>> The complete task cannot be completed in finite time even though the 
>> spatial sum converges, allegedly showing that motion is impossible. The 
>> solution is the recognition that space and time are not infinitely 
>> divisible. AG*
>>
>
> *Minor correction; the solution is that space (not space and time) is not 
> infinitely divisible. AG *
>
>>




As has been stated many times in philosophy of science writing, the quantum 
solution is indeed the best resolution of Zen'o's Paradox (ZP) so far.


The other approach, where in reality there are smooth continua, requires 
cohesive entities:

https://ncatlab.org/nlab/show/cohesive+topos

That is a bigger pill to swallow.


- pt

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Tuesday, October 30, 2018 at 10:44:00 AM UTC-5, John Clark wrote:
>
>
>
> On Tue, Oct 30, 2018 at 2:22 AM Philip Thrift  > wrote:
>
> *> Engineers today are ultrafintiitists in practice: They design airplanes 
>> and bridges with computer software that runs on computers with a fixed, 
>> finite number of bits that are ever used. *
>
>
> For over 40 years computers have been able to solve calculus problems 
> symbolically and get EXACT answers and do it better than any human can, 
> just look at  Mathematica. Sometimes engineers use numerical approximations 
> not because they think calculus is wrong, no engineer is that dumb, but 
> because sometimes the equations are so complex even Mathematica can't find 
> a solution and because an approximation is good enough to make sure the 
> bridge won't fall down
>
> John K Clark 
>
>
>
>
By the word "approximation" above in reference to what is being 
approximating seems to assume that the natural world itself  - the 
materials out of which the bridge or airplane is made, the air, the 
bedrock, the whole constructions and environment -  are continuous and 
differentiable in the mathematical sense of standard calculus. But why 
would one assume that the world is *in reality **that*?

That would assume a mathematical reality a la Tegmark (which he himself 
doesn't believe).

- pt



>>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Tue, Oct 30, 2018 at 2:22 AM Philip Thrift  wrote:

*> Engineers today are ultrafintiitists in practice: They design airplanes
> and bridges with computer software that runs on computers with a fixed,
> finite number of bits that are ever used. *


For over 40 years computers have been able to solve calculus problems
symbolically and get EXACT answers and do it better than any human can,
just look at  Mathematica. Sometimes engineers use numerical approximations
not because they think calculus is wrong, no engineer is that dumb, but
because sometimes the equations are so complex even Mathematica can't find
a solution and because an approximation is good enough to make sure the
bridge won't fall down

John K Clark






>
>

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Oct 2018, at 23:46, Brent Meeker  wrote:
> 
> 
> 
> On 10/29/2018 1:06 AM, Philip Thrift wrote:
>> 
>> 
>> On Sunday, October 28, 2018 at 7:48:57 PM UTC-5, Brent wrote:
>> 
>> 
>> On 10/28/2018 9:17 AM, Philip Thrift wrote:
>>> 
>>> Instead of relativism, philosophers talk of perspectivism.
>>> 
>>> (Nietzsche is said to be the father of perspectivism. I say, actually, 
>>> Kant. ...)
>>> 
>>> A Scientist sees a bunch of phenomena (recorded as data) and says, I have 
>>> written a theory θ in a language λ that models the data!. Other Scientists 
>>> say, I have done the same, but mine's "better"! So then there are a bunch 
>>> of θ_λs (perspectives). The odd thing is that each Scientist talks about 
>>> their pet θ_λ as being the world-as-it-is.  
>> 
>> You must be thinking of philosophers.  Scientists propose an experiment to 
>> see which theory is better.
>> 
>> Brent
>> 
>> 
>> 
>> I don't see much evidence for that. Look at the 100s of papers on arXiv on 
>> all the competing models for quantum gravity, dark matter, dark energy, 
>> modified gravity, cosmic inflation, ...
>> 
>> 
>> And these papers are written mostly by Ph.D. physicists, not Ph.D. 
>> philosophers.
> 
> 
> And some propose empirical tests. Have you seen even one philosopher propose 
> an empirical test?


Newton, Huygens, etc. Of course that “natural philosophy” is now called 
“physical science". 

For metaphysics/theology, you need to wait … for my work :) It is hard to 
imagine something more easily refutable (in principle): compare the physical 
reality (inferred by observation) and the physical reality (deduced by 
mechanism + the math of machine’s introspection).



> 
> Phyicist:  I need $200,000 for a new vacuum chamber to test my theory.
> Dean: You physicists, always asking for money.  Why can't you be like the 
> mathematicians?  All they need are pencil, paper, and erasers.  Or like the 
> philosophers.  All they need is pencil and paper.

Lol

Note that a mathematician, and even a physicist, does not necessarily need an 
eraser, only a big trash. Well, if mechanism and/or quantum mechanics is right.
 In fact erasers (absolute erasers) probably do not exist.

Bruno




> 
>> 
>> - pt
>> 
>> 
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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Monday, October 29, 2018 at 4:07:41 PM UTC, John Clark wrote:
>
> On Sun, Oct 28, 2018 at 2:56 PM > wrote:
>
>  > *What's your view of Zeno's paradox which implies motion is 
>> impossible.*
>
>
> Zeno thought it was obvious if you added an infinite number of nonzero 
> lengths or nonzero times together you would always get something that was  
> nfinite, and that is the foundation of his paradox; 
>

*I think you meant to write "infinite". In any event, Bruno claims in a 
subsequent post that the Greeks knew that an infinite series CAN 
converge.What is your evidence that Zeno didn't believe this? I stated my 
view of Zeno's paradox and its solution. AG*
 

> but with modern calculus we know that sometimes that isn't true, and when 
> it isn't true calculus can tell you exactly what the FINITE length or 
> finite time interval turns out to be. For example, the sum, of the infinite 
> series: 
> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>
> John K Clark
>
>
>
>
>
>

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Tuesday, October 30, 2018 at 12:38:16 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Monday, October 29, 2018 at 10:15:28 PM UTC, John Clark wrote:
>>
>>
>> On Mon, Oct 29, 2018 at 5:21 PM  wrote:
>>
>> >*If you try to traverse a unit distance in infinite steps such as 1/2, 
>>> 1/4, 1/8, 1/16 and so forth, the sum converges to 1, but you will never 
>>> traverse the distance even though the sum converges.*
>>
>>
>> Never? If what you say is true then calculus is wrong. I don't think 
>> calculus is wrong.
>>
>> John K Clark 
>>
>
> *Nothing wrong with calculus. Rather, you can think of Zeno's paradox as 
> an infinite sequence of tasks, each one separated by a finite fixed pause. 
> The complete task cannot be completed in finite time even though the 
> spatial sum converges, allegedly showing that motion is impossible. The 
> solution is the recognition that space and time are not infinitely 
> divisible. AG*
>

*Minor correction; the solution is that space (not space and time) is not 
infinitely divisible. AG *

>
>
>>
>>
>>  
>>
>>>
>>>

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Monday, October 29, 2018 at 10:15:28 PM UTC, John Clark wrote:
>
>
> On Mon, Oct 29, 2018 at 5:21 PM > wrote:
>
> >*If you try to traverse a unit distance in infinite steps such as 1/2, 
>> 1/4, 1/8, 1/16 and so forth, the sum converges to 1, but you will never 
>> traverse the distance even though the sum converges.*
>
>
> Never? If what you say is true then calculus is wrong. I don't think 
> calculus is wrong.
>
> John K Clark 
>

*Nothing wrong with calculus. Rather, you can think of Zeno's paradox as an 
infinite sequence of tasks, each one separated by a finite fixed pause. The 
complete task cannot be completed in finite time even though the spatial 
sum converges, allegedly showing that motion is impossible. The solution is 
the recognition that space and time are not infinitely divisible. AG*

>
>
>
>  
>
>>
>>

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Tuesday, October 30, 2018 at 9:45:09 AM UTC, Bruno Marchal wrote:
>
>
> On 29 Oct 2018, at 17:54, agrays...@gmail.com  wrote:
>
>
>
> On Monday, October 29, 2018 at 4:07:41 PM UTC, John Clark wrote:
>>
>> On Sun, Oct 28, 2018 at 2:56 PM  wrote:
>>
>>  > *What's your view of Zeno's paradox which implies motion is 
>>> impossible.*
>>
>>
>> Zeno thought it was obvious if you added an infinite number of nonzero 
>> lengths or nonzero times together you would always get something that was  
>> nfinite, and that is the foundation of his paradox; but with modern 
>> calculus we know that sometimes that isn't true, and when it isn't true 
>> calculus can tell you exactly what the FINITE length or finite time 
>> interval turns out to be. For example, the sum, of the infinite series: 
>> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>>
>> John K Clark
>>
>
> This doesn't resolve Zeno's paradox. AG 
>
>
>
> It does. 
>

*I don't think you understand Zeno's paradox. Why don't you state it in 
your own words to test your knowledge?. AG*

The greeks understood that an infinite sum can converge. The math was not 
> rigoroius, and they wrongly believed that it is enough that the general 
> term tend to zero for the series to converge, which will be refuted many 
> centuries later by Oresme (a French bishop and mathematician) with the 
> harmonic series:
> 1 + 1/2 + 1/3 + 1/4 + 1/5 + …. which diverges (like ln(n)).
> Cauchy made the math rigorous here, and mathematical logic even 
> rehabilitates the infinitesimals of Newton and Leibniz, but, Imo, Cauchy 
> works is better.
>
> Bruno
>
>
>
>
>
>
>
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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Tuesday, October 30, 2018 at 10:36:59 AM UTC+1, Bruno Marchal wrote:

>
> Any object can be inconsistently defined. I can define the moon by the set 
> of squared circles.
>

The set of squared circles is the empty set. The moon is not an empty set, 
it has a complex internal structure.

Anyway, the word "define" has two meanings which need to be distinguished. 
"An object is *defined*" may mean:

1) "An object is *described*" (this usually means that there must be 
someone who defines/describes the object)

2) "An object is *constituted/formed*" (this doesn't require anyone to 
define the object, just as the fact that an object is composed of parts 
doesn't require a composer)

When I say that an object is consistently or inconsistently defined, I mean 
defined in the second sense. That's the existential/ontological sense. An 
inconsistently defined object is not identical to itself, it is not what it 
is, it does not have the properties it has. Such an object is nonsense, it 
cannot exist, it is not really an object, it is nothing. The definition of 
an object in the first sense is true/accurate iff it corresponds to the 
definition of the object in the second sense. 
 

> - and this I mean in the absolute sense, regardless of theory: an object 
> that is not identical to itself is inconsistent in any theory. Such an 
> object cannot exist. All other objects can exist somewhere.
>
>
> You are not using the (logical) terms in their standard meaning. It is 
> hard to follow. I don’t undersetand what you mean by object.
>

Sorry, by "object" I mean anything that exists. Not nothing.
 

>
> With mechanism, the axiom of infinity leads to an inflation of 
> predictions, which is not what we are experiencing
>

That may mean that we live in a finite mathematical structure. Still, that 
doesn't rule out the existence of infinite mathematical structures. If they 
are consistent, why wouldn't they exist?

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Tuesday, October 30, 2018 at 4:55:13 AM UTC-5, Bruno Marchal wrote:
>
>
> On 29 Oct 2018, at 23:48, Philip Thrift > 
> wrote:
>
>
>
> On Monday, October 29, 2018 at 5:15:28 PM UTC-5, John Clark wrote:
>>
>>
>> On Mon, Oct 29, 2018 at 5:21 PM  wrote:
>>
>> >*If you try to traverse a unit distance in infinite steps such as 1/2, 
>>> 1/4, 1/8, 1/16 and so forth, the sum converges to 1, but you will never 
>>> traverse the distance even though the sum converges.*
>>
>>
>> Never? If what you say is true then calculus is wrong. I don't think 
>> calculus is wrong.
>>
>> John K Clark 
>>
>>
>>
>>
>
>  
> To a mathematical *ultrafinitist* [ 
> https://en.wikipedia.org/wiki/Ultrafinitism ], the standard calculus is 
> wrong.
>
> One can salvage some version of standard calculus, but a lot of care is 
> needed to never define any process that assumes a completed infinite number 
> of steps.
>
>
> That is finitism. Ultrafinitisme asks for a bigger natural numbers. It is 
> close to nonsense for me, but finitism accept the potential infinite and 
> reject actual infinite. Ultra-finitism rejets both potential and actual 
> infinite.
>
> With mechanism, the ontology is finitists (not ultra-finitist), and the 
> many phenomenologies is unbodundably big, beyond the infinite, somehow.
>
> Bruno
>
>
>
>
In any case, doing all of math on computers *here on Earth* makes 
one explicitly an ultrafinitist  because there are only a limited, finite 
number of bits one can ever have available!

- pt

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Oct 2018, at 23:48, Philip Thrift  wrote:
> 
> 
> 
> On Monday, October 29, 2018 at 5:15:28 PM UTC-5, John Clark wrote:
> 
> On Mon, Oct 29, 2018 at 5:21 PM > wrote:
> 
> >If you try to traverse a unit distance in infinite steps such as 1/2, 1/4, 
> >1/8, 1/16 and so forth, the sum converges to 1, but you will never traverse 
> >the distance even though the sum converges.
> 
> Never? If what you say is true then calculus is wrong. I don't think calculus 
> is wrong.
> 
> John K Clark 
> 
> 
> 
> 
> 
>  
> To a mathematical ultrafinitist [ https://en.wikipedia.org/wiki/Ultrafinitism 
> ], the standard calculus is wrong.
> 
> One can salvage some version of standard calculus, but a lot of care is 
> needed to never define any process that assumes a completed infinite number 
> of steps.

That is finitism. Ultrafinitisme asks for a bigger natural numbers. It is close 
to nonsense for me, but finitism accept the potential infinite and reject 
actual infinite. Ultra-finitism rejets both potential and actual infinite.

With mechanism, the ontology is finitists (not ultra-finitist), and the many 
phenomenologies is unbodundably big, beyond the infinite, somehow.

Bruno



> 
> - pt
> 
> 
> 
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Tuesday, October 30, 2018 at 4:29:01 AM UTC-5, Bruno Marchal wrote:
>
>
> On 29 Oct 2018, at 11:24, Philip Thrift > 
> wrote:
>
>
>
> On Monday, October 29, 2018 at 4:35:39 AM UTC-5, Bruno Marchal wrote:
>>
>>
>>
>> Because finite numbers can be shown to have infinite hallucinations, 
>> especially when they mess with other finite numbers. And that leads to a 
>> testable theology, which includes an explanation of where both quanta and 
>> qualia comes from. Then assuming more than that in the ontology, introduces 
>> unnecessary difficulties, probably inconsistency or deflation of 
>> predictions. (Usually called white rabbit in this list (and in my long 
>> version thesis).
>>
>> Bruno
>>
>>
>>
>
> *Hallucinations and qualia can be derived from numbers* *(numerical 
> reality) *is one thesis. But what is the test?
>
> In material reality, numbers do not exist (aka mathematical fictionalism). 
> So positing numbers would add more to the ontology (a Platonic realm in 
> addition to the material realm).
>
>
> I do not assume a primary material reality. Eventually, I assume only 
> elementary arithmetic, or elementary combinator theory, and anything Turing 
> equivalent. 
>
>
>
>
> *Material reality supports both information (numberical) processing and 
> experience (qualia) processing.* The alternative thesis.
>
>
> Primary matter is what make the mind-body problem unsolvable. Given the 
> mack of evidence of it, why assume it?
>
>
>
> That I am conscious is the test that there is a material reality.
>
>
>
> Consciousness does not seem material to me. Consciousness is the test of 
> the existence of consciousness. To infer a material reality from a 
> conscious experience is an extrapolation, and once you bet on mechanism, it 
> does not make much sense. No problem, as you seem both materialist and non 
> mechanist. We are working in different theory.
>
> Bruno
>
>
>
I think I've always followed the direction of pragmatism, or more precisely 
Rortian neopragmatism since* Philosophy and the Mirror of Nature*.

I see the (modal logical) language as explored in "The universal numbers: 
>From Biology to Physics" is of interest to *agent programming language 
theorists* (and they indeed utilize those logics in their research).

But when the "code meets the road" so to speak, and conscious robots need 
to be compiled, matter will be needed* to actually make them,* there there 
is where the matter matters!

- pt

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Oct 2018, at 19:55, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Monday, October 29, 2018 at 6:36:47 PM UTC, Philip Thrift wrote:
> 
> 
> On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote:
> On Sun, Oct 28, 2018 at 2:56 PM > wrote:
> 
>  > What's your view of Zeno's paradox which implies motion is impossible.
> 
> Zeno thought it was obvious if you added an infinite number of nonzero 
> lengths or nonzero times together you would always get something that was  
> nfinite, and that is the foundation of his paradox; but with modern calculus 
> we know that sometimes that isn't true, and when it isn't true calculus can 
> tell you exactly what the FINITE length or finite time interval turns out to 
> be. For example, the sum, of the infinite series: 
> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
> 
> John K Clark
> 
> 
> 
> 
> It is still a paradox as discussed in foundational physics and mathematical 
> writing, when one leaves the naive calculus as taught in high school or 
> college.
> 
> What if Tegmark is right, and one should banish the word "infinite" once and 
> for all, so "sum of the infinite series" could not even be mentioned!


Banishing the infinite from the ontology is a good idea, but it will kept 
playing an important role in the phenomenology, and in the meta-theories. 



> 
> The problem is we do not know what spacetime is, really.
> 
> https://blogs.unimelb.edu.au/sciencecommunication/2017/10/22/zenos-paradox-the-puzzle-that-keeps-on-giving/
>  
> 
>  :
> ...
> 
> So, has this puzzle been solved once and for all?

The original mathematical paradox has been solved. But physical version of it, 
in some theories,  can be problematical.

Bruno



> 
> Quantum physics has probably given us our most convincing answer to the 
> paradox so far, but it is not a certainty. The question of whether space is 
> continuous or made up of discrete units is still debated among physicists 
> (there are experiments currently trying to test this), and quantum mechanics 
> itself is known not to be a complete theory of the universe. If history is 
> any indication, this isn’t the last we’ll hear of Zeno’s paradox.
> 
> 
> - pt
> 
> Clark misstated the paradox, but it seems clear it depends on assuming space 
> is infinitely divisible. So the resolution MUST be that space is discrete 
> even though our most sensitive measurements to date have not detected it.  LC 
> can speak to this. And the problem has nothing to do with whether the word 
> 'infinite" enters the analysis. One can do calculus without ever using that 
> word to describe limits, etc. Great! So now I know the resolution of Zeno's 
> paradox, and the physical fact that space must be discrete! Gotta love it. AG
>  
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Oct 2018, at 17:54, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Monday, October 29, 2018 at 4:07:41 PM UTC, John Clark wrote:
> On Sun, Oct 28, 2018 at 2:56 PM > wrote:
> 
>  > What's your view of Zeno's paradox which implies motion is impossible.
> 
> Zeno thought it was obvious if you added an infinite number of nonzero 
> lengths or nonzero times together you would always get something that was  
> nfinite, and that is the foundation of his paradox; but with modern calculus 
> we know that sometimes that isn't true, and when it isn't true calculus can 
> tell you exactly what the FINITE length or finite time interval turns out to 
> be. For example, the sum, of the infinite series: 
> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
> 
> John K Clark
> 
> This doesn't resolve Zeno's paradox. AG 


It does. The greeks understood that an infinite sum can converge. The math was 
not rigoroius, and they wrongly believed that it is enough that the general 
term tend to zero for the series to converge, which will be refuted many 
centuries later by Oresme (a French bishop and mathematician) with the harmonic 
series:
1 + 1/2 + 1/3 + 1/4 + 1/5 + …. which diverges (like ln(n)).
Cauchy made the math rigorous here, and mathematical logic even rehabilitates 
the infinitesimals of Newton and Leibniz, but, Imo, Cauchy works is better.

Bruno






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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Oct 2018, at 11:38, Tomas Pales  wrote:
> 
> 
> 
> On Monday, October 29, 2018 at 10:35:39 AM UTC+1, Bruno Marchal wrote:
> 
>> On 28 Oct 2018, at 16:16, Tomas Pales > 
>> wrote:
>> 
>> 
>> 
>> On Sunday, October 28, 2018 at 3:37:16 PM UTC+1, Bruno Marchal wrote:
>> 
>>> On 26 Oct 2018, at 21:33, Tomas Pales > wrote:
>>> 
>>> 
>>> 
>>> On Friday, October 26, 2018 at 8:06:03 PM UTC+2, Bruno Marchal wrote:
>>> 
>>> OK. But it seemed to me you said that is better not to make unnecessary 
>>> assumption.
>>> 
>>> My only ontological assumption is that existence is logical consistency.
>> 
>> Logical consistency is an attribute of theories, or some class of chatty 
>> machines. I do not understand what you mean.
>> 
>> I mean that an object exists iff it is consistently defined. In other words, 
>> it is identical to itself. It is what it is and is not what it is not.
> 
> 
> An objet cannot be inconsistent. Its existence can be inconsistent in this or 
> that theory.
> 
> An object can be inconsistent in the sense that it can be inconsistently 
> defined

Any object can be inconsistently defined. I can define the moon by the set of 
squared circles.




> - and this I mean in the absolute sense, regardless of theory: an object that 
> is not identical to itself is inconsistent in any theory. Such an object 
> cannot exist. All other objects can exist somewhere.

You are not using the (logical) terms in their standard meaning. It is hard to 
follow. I don’t undersetand what you mean by object.





> 
>> But by assuming fewer objects (only finite natural numbers) you assume more 
>> principles: in addition to the principle of consistency you assume the 
>> axioms of finite arithmetic, to restrict the number of consistent objects to 
>> finite natural numbers. This restriction seems arbitrary; why would only 
>> finite natural numbers exist when it is possible that also other objects 
>> exist?
> 
> 
> Because finite numbers can be shown to have infinite hallucinations, 
> especially when they mess with other finite numbers. And that leads to a 
> testable theology, which includes an explanation of where both quanta and 
> qualia comes from. Then assuming more than that in the ontology, introduces 
> unnecessary difficulties, probably inconsistency or deflation of predictions. 
> (Usually called white rabbit in this list (and in my long version thesis).
> 
> I understand that not restricting ontology to finite arithmetic can be 
> impractical or can contain objects whose consistency we cannot confirm. But 
> reality doesn't seem to care whether we find it practical or whether we can 
> confirm its consistency.

We need to bet on some reality. A (reasonable) theory is consistent if and only 
if it admits a model/reality.

The problem of the ontology is not a practical problem. With mechanism, the 
axiom of infinity leads to an inflation of predictions, which is not what we 
are experiencing.

Bruno




> 
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Oct 2018, at 11:24, Philip Thrift  wrote:
> 
> 
> 
> On Monday, October 29, 2018 at 4:35:39 AM UTC-5, Bruno Marchal wrote:
> 
> 
> Because finite numbers can be shown to have infinite hallucinations, 
> especially when they mess with other finite numbers. And that leads to a 
> testable theology, which includes an explanation of where both quanta and 
> qualia comes from. Then assuming more than that in the ontology, introduces 
> unnecessary difficulties, probably inconsistency or deflation of predictions. 
> (Usually called white rabbit in this list (and in my long version thesis).
> 
> Bruno
> 
> 
> 
> 
> Hallucinations and qualia can be derived from numbers (numerical reality) is 
> one thesis. But what is the test?
> 
> In material reality, numbers do not exist (aka mathematical fictionalism). So 
> positing numbers would add more to the ontology (a Platonic realm in addition 
> to the material realm).

I do not assume a primary material reality. Eventually, I assume only 
elementary arithmetic, or elementary combinator theory, and anything Turing 
equivalent. 



> 
> Material reality supports both information (numberical) processing and 
> experience (qualia) processing. The alternative thesis.

Primary matter is what make the mind-body problem unsolvable. Given the mack of 
evidence of it, why assume it?


> 
> That I am conscious is the test that there is a material reality.


Consciousness does not seem material to me. Consciousness is the test of the 
existence of consciousness. To infer a material reality from a conscious 
experience is an extrapolation, and once you bet on mechanism, it does not make 
much sense. No problem, as you seem both materialist and non mechanist. We are 
working in different theory.

Bruno




> 
> - pt
> 
> 
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Oct 2018, at 10:55, Philip Thrift  wrote:
> 
> 
> 
> On Monday, October 29, 2018 at 4:44:49 AM UTC-5, Bruno Marchal wrote:
> 
>> On 28 Oct 2018, at 17:17, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Sunday, October 28, 2018 at 10:27:56 AM UTC-5, Bruno Marchal wrote:
>> 
>>> On 27 Oct 2018, at 22:59, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Saturday, October 27, 2018 at 3:21:33 PM UTC-5, Philip Thrift wrote:
>>> 
>>> 
>>> On Saturday, October 27, 2018 at 2:52:51 PM UTC-5, Brent wrote:
>>> 
>>> 
>>> On 10/26/2018 11:50 PM, Philip Thrift wrote:
 Logical consistency is a relation between sentences.  It's not about 
 existence.  The sentences might be about the existence of something, but 
 that's different.  Or the sentences may have variables quantified by 
 existential quantifiers, but that's different too.  To say logical 
 consistency is needed for existence would be a category error.
 
 Brent
 
 In other words:
 
 https://www.lrb.co.uk/v08/n07/richard-rorty/the-contingency-of-language 
  :
 
 
 As long as we think that there is some relation called ‘fitting the world’ 
 or ‘expressing the real nature of the human self’ which can be possessed 
 or lacked by vocabularies-as-wholes, we shall continue the traditional 
 philosophical search for a criterion which will tell us which vocabularies 
 have this desirable feature. But if we could ever become reconciled to the 
 idea that reality is indifferent to our descriptions of it, and that the 
 human self is created by the use of a vocabulary rather than being 
 adequately or inadequately expressed in a vocabulary, then we should at 
 last have assimilated what was true in the romantic idea that truth is 
 made rather than found. What is true about this claim is just that 
 languages are made rather than found, and that truth is a property of 
 linguistic entities, of sentences.
 
  - pt
>>> 
>>> But what is true about the sentence, "What is true about this claim is just 
>>> that languages are made rather than found, and that truth is a property of 
>>> linguistic entities, of sentences."?  Is it not correspondence with some 
>>> physical events, i.e. facts?
>>> 
>>> Brent
>>> 
>>> 
>>> In the Rortian philosophical world of neopragmatism [ 
>>> https://en.wikipedia.org/wiki/Neopragmatism 
>>>  ], the correspondence concept 
>>> of truth is wrong:
>>> 
>>> "The thought was that in order for a statement or proposition to be true it 
>>> must give facts which correspond to what is actually present in reality. 
>>> This is called the correspondence theory of truth and is to be 
>>> distinguished from a neopragmatic conception of truth."
>>> 
>>> A "neopragmatic conception of truth"has Rorty, Quine, Wittgenstein, ... 
>>> spins, but it's basically that language is in a pragmatic relationship with 
>>> reality.
>>> 
>>> - pt
>>> 
>>> Or a Rortian way to put it: Truth claims are just sentences in reference to 
>>> other sentences. 
>> 
>> Truth claims, yes, and gossip. But we can also bet on a reality making sense 
>> of the sentences, and if we want to progress build from what we can agree 
>> on, (even if we interpret it differently). If not, we will fall in 
>> relativism, which is inconsistent at the start, as it asks us to relativise 
>> relativism, which needs some absolute.
>> 
>> Bruno
>> 
>> 
>> 
>> Instead of relativism, philosophers talk of perspectivism.
> 
> 
> Perpectivisme still assume some reality, be it numbers or matter. What you 
> said above looks more relativism than perspectivism. 
> 
> Mechanism is perspectivist, given that the ontology is any Turing complete 
> theory, and physics, mathematics, psychology theology are explained from 
> perspective (self-rerefntial different modes imposed by incompleteness).
> 
> 
> 
>> 
>> (Nietzsche is said to be the father of perspectivism. I say, actually, Kant. 
>> ...)
>> 
>> A Scientist sees a bunch of phenomena (recorded as data) and says, I have 
>> written a theory θ in a language λ that models the data!. Other Scientists 
>> say, I have done the same, but mine's "better"! So then there are a bunch of 
>> θ_λs (perspectives). The odd thing is that each Scientist talks about their 
>> pet θ_λ as being the world-as-it-is.  
> 
> That are not scientist. A genuine scientist will only ask why this or that 
> theory, and ask for experimental testing and decision about it.
> 
> Bruno
> 
> 
> 
> 
> 
> Like I've shown, there seems to be little evidence of that. There must be a 
> lot of un-"genuine" scientists writing articles today. See also Sabine 
> Hossenfelder's book Lost in Math.


Most scientists are genuine in their own fields, but can lost the scientific 
attitude in the fields of their colleagues, or in the fundamental science, 
which has stop 529 years ago.

Re: Mathematical Universe Hypothesis

[Philip Thrift]

All

On Monday, October 29, 2018 at 8:27:49 PM UTC-5, John Clark wrote:
>
> On Mon, Oct 29, 2018 at 6:48 PM Philip Thrift  > wrote:
>
> > To a mathematical ultrafinitist [ 
>> https://en.wikipedia.org/wiki/Ultrafinitism ], the standard calculus is 
>> wrong.
>
>
> Then I don't want to ever cross a bridge or fly in a airplane that was 
> designed by a engineer that is a ultrafinitist. 
>
> John k Clark 
>
>
>
>>
Engineers today are ultrafintiitists in practice: They design airplanes and 
bridges with computer software that runs on computers with a fixed, finite 
number of bits that are ever used. 

- pt

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Re: Mathematical Universe Hypothesis

[John Clark]

On Mon, Oct 29, 2018 at 6:48 PM Philip Thrift  wrote:

> To a mathematical ultrafinitist [
> https://en.wikipedia.org/wiki/Ultrafinitism ], the standard calculus is
> wrong.


Then I don't want to ever cross a bridge or fly in a airplane that was
designed by a engineer that is a ultrafinitist.

John k Clark



>

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Tuesday, October 30, 2018 at 12:00:10 AM UTC+1, Brent wrote:
>
>
>
> Imagine a universe that is the set of all triangles. That means that a law 
> of this universe determines that only triangles can be members of this 
> universe. Surely it would be a logical inconsistency if a circle was a 
> member of this universe. 
>
>
> No.  It would mean you were mistaken that this universe had only triangles.
>>
>
> No, there can be no non-triangles in the set of all triangles. 
>
> Then you were mistaken to hypothesize a circle in that universe.
>

Just to show you that you were mistaken to hypothesize a pink elephant in a 
universe in which it doesn't exist. To hypothesize a pink elephant in a 
universe in which it doesn't exist is like to hypothesize a non-triangle in 
the set of all triangles. Your hypothesis was contradictory and so it 
doesn't correspond to reality.

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/29/2018 3:38 AM, Tomas Pales wrote:
An object can be inconsistent in the sense that it can be 
inconsistently defined - and this I mean in the absolute sense, 
regardless of theory: an object that is not identical to itself is 
inconsistent in any theory. Such an object cannot exist. All other 
objects can exist somewhere.


You keep giving this convoluted formula or your theory in terms of 
"consistently defined".   But you apparently want to include physical 
laws in the measure of consistency AND the mere empirical fact (like the 
elephant in my den) that violates no law of physics and certainly not 
logic.  So your theory that every consistently defined object exists has 
no standard except that the object either is observed to exist or can be 
the subject of a sentence asserting its existence "in another 
universe".  So baldly stated it is clear that it has no content whatsoever.


Brent

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Monday, October 29, 2018 at 5:46:13 PM UTC-5, Brent wrote:
>
>
>
> On 10/29/2018 1:06 AM, Philip Thrift wrote:
>
>
>
> On Sunday, October 28, 2018 at 7:48:57 PM UTC-5, Brent wrote: 
>>
>>
>>
>> On 10/28/2018 9:17 AM, Philip Thrift wrote:
>>
>>
>> Instead of relativism, philosophers talk of *perspectivism*.
>>
>> (Nietzsche is said to be the father of perspectivism. I say, actually, 
>> Kant. ...)
>>
>> A Scientist sees a bunch of phenomena (recorded as data) and says, I have 
>> written a theory θ in a language λ that models the data!. Other Scientists 
>> say, I have done the same, but mine's "better"! So then there are a bunch 
>> of θ_λs (perspectives). The odd thing is that each Scientist talks about 
>> their pet θ_λ as being the world-as-it-is.  
>>
>>
>> You must be thinking of philosophers.  Scientists propose an experiment 
>> to see which theory is better.
>>
>> Brent
>>
>
>
>
> I don't see much evidence for that. Look at the 100s of papers on arXiv on 
> all the competing models for quantum gravity, dark matter, dark energy, 
> modified gravity, cosmic inflation, ...
>
>
> And these papers are written mostly by *Ph.D. physicists, n*ot Ph.D. 
> philosophers.
>
>
>
> And some propose empirical tests. Have you seen even one philosopher 
> propose an empirical test?
>
> Brent
> Phyicist:  I need $200,000 for a new vacuum chamber to test my theory.
> Dean: You physicists, always asking for money.  Why can't you be like the 
> mathematicians?  All they need are pencil, paper, and erasers.  Or like the 
> philosophers.  All they need is pencil and paper.
>
>
I don't know if a philosopher has proposed a physics experiment, but I was 
talking about physicists who say that theories can be chosen based on 
factors decoupled from experiments.


*Beyond Falsifiability: Normal Science in a Multiverse*
Sean M. Carroll
(Submitted on 15 Jan 2018)
https://arxiv.org/abs/1801.05016


*Cosmological models that invoke a multiverse - a collection of 
unobservable regions of space where conditions are very different from the 
region around us - are controversial, on the grounds that unobservable 
phenomena shouldn't play a crucial role in legitimate scientific theories. 
I argue that the way we evaluate multiverse models is precisely the same as 
the way we evaluate any other models, on the basis of abduction, Bayesian 
inference, and empirical success. There is no scientifically respectable 
way to do cosmology without taking into account different possibilities for 
what the universe might be like outside our horizon. Multiverse theories 
are utterly conventionally scientific, even if evaluating them can be 
difficult in practice.*



- pt

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/29/2018 3:09 AM, Tomas Pales wrote:



On Monday, October 29, 2018 at 5:54:10 AM UTC+1, Brent wrote:



On 10/28/2018 7:54 PM, Tomas Pales wrote:



On Monday, October 29, 2018 at 3:17:58 AM UTC+1, Brent wrote:



On 10/28/2018 5:18 PM, Tomas Pales wrote:



On Monday, October 29, 2018 at 12:33:23 AM UTC+1, Brent wrote:


  There is no logical inconsistency in a flying pink
elephant existing right now in my den beside me. But
don't see one.


First, it is not clear whether the existence of a flying
pink elephant in your den is consistent with the rest of
this universe. Many things may seem consistent while they
are actually inconsistent. Before the 20th century it seemed
consistent with the laws of our universe that there was no
speed limit or that the energy of a particle could vary
continuously. Now we know that these phenomena are
inconsistent in our universe and that's why they don't exist
here.


You don't seem to know the difference between /logically
consistent/="not entailing a contradiction by the rules of
inference"  and /nomologically consistent/ = "not contrary to
the laws of nature".  It is still /logically/ consistent for
a particle to be faster than light.


Not in a universe where faster than light speed is prohibited.


What does it mean to say FTL is logically prohibited?


If our universe is defined in such a way that objects contained in it 
cannot exceed a certain speed limit, then it would be logically 
inconsistent with this definition of the universe if it contained 
objects that can exceed such a speed limit.


Which just an instance of the general, vacuous proposition that whatever 
exists has a consistent description.  Which is not the same as it's 
converse.






The problem with trying to use nomological consistency to
imply existence is that we don't know the possible laws of
nature and that observation trumps theory as to what is
nomologically possible.  So no matter what you think are the
laws of nature, if you see something contrary to them it just
means they are wrong.


It doesn't matter whether we know what the laws of the universe
are. Whatever the laws are, if they prohibit something then it
cannot happen, otherwise there would be a logical inconsistency.


But that's why your "theory" is completely vacuous.


The theory explains why there is something instead of nothing. If it's 
vacuous, so much the better; it means it's necessarily true.


It doesn't "explain" it; it merely asserts it.  And what ever empirical 
evidence seems to contradict it is countered as being otherwise in other 
universes.  So it is completely empty.



Whatever is observed is, by definition, logically consistent.


And it's an obvious fact that whatever is observed is what it is and 
is not what it is not.


  Remember when it was "logically inconsistent" for a particle to
be two places at the same time...then, OOPS!...quantum mechanics
came along.


/You/ should remember that next time you claim with confidence that 
something is or is not logically consistent (like that pink elephant).


You accepted that it was contradicted by the evidence - so you 
hypothesized another universe to save your "theory".  They people who 
discovered quantum mechanics did it in this world.







Imagine a universe that is the set of all triangles. That means that 
a law of this universe determines that only triangles can be members 
of this universe. Surely it would be a logical inconsistency if a 
circle was a member of this universe.


No.  It would mean you were mistaken that this universe had only
triangles.


No, there can be no non-triangles in the set of all triangles.

Then you were mistaken to hypothesize a circle in that universe.  I was 
accepting your premise "If a circle was a member of this universe." and 
drawing the empirical conclusion.   You're trying to posit two 
hypotheses that are in contradiction and say that it makes the second 
one false.  From a contradiction alone there is no way to say which 
clause is false.


Brent

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Monday, October 29, 2018 at 5:15:28 PM UTC-5, John Clark wrote:
>
>
> On Mon, Oct 29, 2018 at 5:21 PM > wrote:
>
> >*If you try to traverse a unit distance in infinite steps such as 1/2, 
>> 1/4, 1/8, 1/16 and so forth, the sum converges to 1, but you will never 
>> traverse the distance even though the sum converges.*
>
>
> Never? If what you say is true then calculus is wrong. I don't think 
> calculus is wrong.
>
> John K Clark 
>
>
>
>

 
To a mathematical *ultrafinitist* 
[ https://en.wikipedia.org/wiki/Ultrafinitism ], the standard calculus is 
wrong.

One can salvage some version of standard calculus, but a lot of care is 
needed to never define any process that assumes a completed infinite number 
of steps.

- pt


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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/29/2018 1:06 AM, Philip Thrift wrote:



On Sunday, October 28, 2018 at 7:48:57 PM UTC-5, Brent wrote:



On 10/28/2018 9:17 AM, Philip Thrift wrote:


Instead of relativism, philosophers talk of *perspectivism*.

(Nietzsche is said to be the father of perspectivism. I say,
actually, Kant. ...)

A Scientist sees a bunch of phenomena (recorded as data) and
says, I have written a theory θ in a language λ that models the
data!. Other Scientists say, I have done the same, but mine's
"better"! So then there are a bunch of θ_λs (perspectives). The
odd thing is that each Scientist talks about their pet θ_λ as
being the world-as-it-is.


You must be thinking of philosophers.  Scientists propose an
experiment to see which theory is better.

Brent




I don't see much evidence for that. Look at the 100s of papers on 
arXiv on all the competing models for quantum gravity, dark matter, 
dark energy, modified gravity, cosmic inflation, ...



And these papers are written mostly by *Ph.D. physicists, n*ot Ph.D. 
philosophers.



And some propose empirical tests. Have you seen even one philosopher 
propose an empirical test?


Brent
Phyicist:  I need $200,000 for a new vacuum chamber to test my theory.
Dean: You physicists, always asking for money.  Why can't you be like 
the mathematicians?  All they need are pencil, paper, and erasers.  Or 
like the philosophers.  All they need is pencil and paper.




- pt


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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Monday, October 29, 2018 at 10:21:52 PM UTC+1, agrays...@gmail.com wrote:
>
>
>
> On Monday, October 29, 2018 at 8:33:32 PM UTC, Tomas Pales wrote:
>>
>>
>>
>> On Monday, October 29, 2018 at 7:36:47 PM UTC+1, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote:

 On Sun, Oct 28, 2018 at 2:56 PM  wrote:

  > *What's your view of Zeno's paradox which implies motion is 
> impossible.*


 Zeno thought it was obvious if you added an infinite number of nonzero 
 lengths or nonzero times together you would always get something that was  
 nfinite, and that is the foundation of his paradox; but with modern 
 calculus we know that sometimes that isn't true, and when it isn't 
 true calculus can tell you exactly what the FINITE length or finite 
 time interval turns out to be. For example, the sum, of the infinite series
 : 
 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.

 John K Clark




>>> It is still a paradox as discussed in foundational physics and 
>>> mathematical writing, when one leaves the naive calculus as taught in high 
>>> school or college.
>>>
>>
>> The calculus solution seems fine to me, what's the problem with it?
>>
>
> *If you try to traverse a unit distance in infinite steps such as 1/2, 
> 1/4, 1/8, 1/16 and so forth, the sum converges to 1, but you will never 
> traverse the distance even though the sum converges.*
>

Why not? Say you move at a constant speed v and you want to traverse 
distance d. To traverse half the distance takes time d/2v; to traverse a 
quarter of the distance takes time d/4v; to traverse an eighth of the 
distance takes time d/8v, etc. When you add up the times d/2v + d/4v + d/8v 
+ ... with calculus you get total time d/v, a finite number. You traverse 
the distance in a finite time.

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Re: Mathematical Universe Hypothesis

[John Clark]

On Mon, Oct 29, 2018 at 5:21 PM  wrote:

>*If you try to traverse a unit distance in infinite steps such as 1/2,
> 1/4, 1/8, 1/16 and so forth, the sum converges to 1, but you will never
> traverse the distance even though the sum converges.*


Never? If what you say is true then calculus is wrong. I don't think
calculus is wrong.

John K Clark





>
>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Mon, Oct 29, 2018 at 2:36 PM Philip Thrift  wrote:

>>Zeno thought it was obvious if you added an infinite number of nonzero
>> lengths or nonzero times together you would always get something that was
>> nfinite, and that is the foundation of his paradox; but with modern
>> calculus we know that sometimes that isn't true, and when it isn't true
>> calculus can tell you exactly what the FINITE length or finite time
>> interval turns out to be. For example, the sum, of the infinite series:
>> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>>
>
> *> It is still a paradox*
>

It sure doesn't seem like a very good paradox to me. With calculus you can
prove that 1/2 +1/4 + 1/8 + 1/16 + 1/25 + (1/2)^N is EXACTLY equal to
1,  so Achilles may need to take a infinite number of steps to catch the
tortoise but each step takes half the time to make as the previous step, so
Achilles catches up in a finite amount of time.

John K Clark

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Monday, October 29, 2018 at 8:33:32 PM UTC, Tomas Pales wrote:
>
>
>
> On Monday, October 29, 2018 at 7:36:47 PM UTC+1, Philip Thrift wrote:
>>
>>
>>
>> On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote:
>>>
>>> On Sun, Oct 28, 2018 at 2:56 PM  wrote:
>>>
>>>  > *What's your view of Zeno's paradox which implies motion is 
 impossible.*
>>>
>>>
>>> Zeno thought it was obvious if you added an infinite number of nonzero 
>>> lengths or nonzero times together you would always get something that was  
>>> nfinite, and that is the foundation of his paradox; but with modern 
>>> calculus we know that sometimes that isn't true, and when it isn't true 
>>> calculus can tell you exactly what the FINITE length or finite time 
>>> interval turns out to be. For example, the sum, of the infinite series: 
>>> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>>>
>>> John K Clark
>>>
>>>
>>>
>>>
>> It is still a paradox as discussed in foundational physics and 
>> mathematical writing, when one leaves the naive calculus as taught in high 
>> school or college.
>>
>
> The calculus solution seems fine to me, what's the problem with it?
>

*If you try to traverse a unit distance in infinite steps such as 1/2, 1/4, 
1/8, 1/16 and so forth, the sum converges to 1, but you will never traverse 
the distance even though the sum converges. This is Zeno's paradox. Clearly 
it depends on space being infinitely divisible. But since motion IS 
possible, the solution of Zeno's paradox must be that space is discrete 
(not "discreet"). AG*

Of course if space is discreet then you can solve the Zeno paradox without 
> calculus.
>
>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Sun, Oct 28, 2018 at 8:46 PM Brent Meeker  wrote:

 >>gravity is 10^36 times weaker than electromagnetism
>
>
> >*This is because the comparison is to the gravitational attraction of
> elementary particles, such as two protons.  But the masses of elementary
> particles like protons are not fundamental. *
>

The standard model says electrons ARE fundamental and the difference
between the two forces between the 2 electrons is even greater than it is
between 2 protons because the electromagnetic force is just as strong but,
because they are less massive, the gravitational force between 2 electrons
is 1835 weaker than the gravitational force between 2 protons.


> *> They are massless except for internal energy or for the small coupling
> to the Higgs field. *
>

According to the standard model the Higgs field gives mass to fundamental
particles that have no internal structure like electrons and quarks, but as
you pointed out protons and neutrons are not fundamental particles. If you
added up the mass of all the electrons and quarks in your body it would
only amount to about 1% of your mass, 99% comes not from the Higgs field
but from the binding energy that keeps the quarks inside the protons and
neutrons because, due to E=Mc^2,  we can equate energy and mass.

Neutrinos also have mass, its much less even than the electron's but its
not zero, and nobody knows why, the standard model can't explain it and
neither can anything else that we know about.


> > The* fundamental* unit of mass is the Planck mass
>

Maybe, maybe not, some theories say so but there is not a scrap of
experimental evidence in support of the idea. If we had a good quantum
theory of gravity we could test it but we don't.


> >
> *and when it is used the force between two fundamental masses is 137 times
> greater than the EM force between two unit charges.*
>

1/137 is very close to the fine structure constant and it relates the
strength of the electromagnetic interaction between 2 electrons,
specifically it is the ratio between  the energy needed to overcome the
electrostatic repulsion between two electrons a distance d apart and the
energy in one photon with a wavelength (2PI)*d.  The only thing it has to
do with gravity I know about is if d is the Planck length then the energy
in the photon is so large and is concentrated into such a small space that
it becomes a Black Hole.  Quantum mechanics can't tell us what happens if d
is smaller than that and neither can General Relativity, that's why we need
a quantum theory of gravity.

 John K Clark

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Monday, October 29, 2018 at 7:36:47 PM UTC+1, Philip Thrift wrote:
>
>
>
> On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote:
>>
>> On Sun, Oct 28, 2018 at 2:56 PM  wrote:
>>
>>  > *What's your view of Zeno's paradox which implies motion is 
>>> impossible.*
>>
>>
>> Zeno thought it was obvious if you added an infinite number of nonzero 
>> lengths or nonzero times together you would always get something that was  
>> nfinite, and that is the foundation of his paradox; but with modern 
>> calculus we know that sometimes that isn't true, and when it isn't true 
>> calculus can tell you exactly what the FINITE length or finite time 
>> interval turns out to be. For example, the sum, of the infinite series: 
>> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>>
>> John K Clark
>>
>>
>>
>>
> It is still a paradox as discussed in foundational physics and 
> mathematical writing, when one leaves the naive calculus as taught in high 
> school or college.
>

The calculus solution seems fine to me, what's the problem with it?

Of course if space is discreet then you can solve the Zeno paradox without 
calculus.

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Monday, October 29, 2018 at 7:06:47 PM UTC, Philip Thrift wrote:
>
>
>
> On Monday, October 29, 2018 at 1:55:27 PM UTC-5, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Monday, October 29, 2018 at 6:36:47 PM UTC, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote:

 On Sun, Oct 28, 2018 at 2:56 PM  wrote:

  > *What's your view of Zeno's paradox which implies motion is 
> impossible.*


 Zeno thought it was obvious if you added an infinite number of nonzero 
 lengths or nonzero times together you would always get something that was  
 nfinite, and that is the foundation of his paradox; but with modern 
 calculus we know that sometimes that isn't true, and when it isn't 
 true calculus can tell you exactly what the FINITE length or finite 
 time interval turns out to be. For example, the sum, of the infinite series
 : 
 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.

 John K Clark




>>> It is still a paradox as discussed in foundational physics and 
>>> mathematical writing, when one leaves the naive calculus as taught in high 
>>> school or college.
>>>
>>> *What if Tegmark is right, and one should banish the word "infinite" 
>>> once and for all, so "sum of the infinite series" could not even be 
>>> mentioned!*
>>>
>>> The problem is we do not know what spacetime is, really.
>>>
>>>
>>> https://blogs.unimelb.edu.au/sciencecommunication/2017/10/22/zenos-paradox-the-puzzle-that-keeps-on-giving/
>>>  
>>> :
>>> ...
>>>
>>> *So, has this puzzle been solved once and for all?*
>>>
>>> *Quantum physics has probably given us our most convincing answer to the 
>>> paradox so far, but it is not a certainty. The question of whether space is 
>>> continuous or made up of discrete units is still debated among physicists 
>>> (there are experiments currently trying to test this), and quantum 
>>> mechanics itself is known not to be a complete theory of the universe. If 
>>> history is any indication, this isn’t the last we’ll hear of Zeno’s 
>>> paradox.*
>>>
>>>
>>> - pt
>>>
>>
>> *Clark misstated the paradox, but it seems clear it depends on assuming 
>> space is infinitely divisible. So the resolution MUST be that space is 
>> discrete even though our most sensitive measurements to date have not 
>> detected it.  LC can speak to this. And the problem has nothing to do with 
>> whether the word 'infinite" enters the analysis. One can do calculus 
>> without ever using that word to describe limits, etc. Great! So now I know 
>> the resolution of Zeno's paradox, and the physical fact that space must be 
>> discrete! Gotta love it. AG*
>>
>>>  
>>>
>>
> Spacetime is a mystery, and it's discrete vs. continuous is perhaps an 
> oversimplification.
>
> There are other mathematical models theorists pursue (check arXiv), e.g. 
> fractal.
>

*Whatever it is, it's not continuous. I think my analysis of Zeno's paradox 
is conclusive. Call the Nobel committee. AG *

>
> Scale relativity and fractal spacetime: theory and applications
> Laurent Nottale 
> 
> https://arxiv.org/abs/0812.3857
>
> - pt
>

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Monday, October 29, 2018 at 1:55:27 PM UTC-5, agrays...@gmail.com wrote:
>
>
>
> On Monday, October 29, 2018 at 6:36:47 PM UTC, Philip Thrift wrote:
>>
>>
>>
>> On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote:
>>>
>>> On Sun, Oct 28, 2018 at 2:56 PM  wrote:
>>>
>>>  > *What's your view of Zeno's paradox which implies motion is 
 impossible.*
>>>
>>>
>>> Zeno thought it was obvious if you added an infinite number of nonzero 
>>> lengths or nonzero times together you would always get something that was  
>>> nfinite, and that is the foundation of his paradox; but with modern 
>>> calculus we know that sometimes that isn't true, and when it isn't true 
>>> calculus can tell you exactly what the FINITE length or finite time 
>>> interval turns out to be. For example, the sum, of the infinite series: 
>>> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>>>
>>> John K Clark
>>>
>>>
>>>
>>>
>> It is still a paradox as discussed in foundational physics and 
>> mathematical writing, when one leaves the naive calculus as taught in high 
>> school or college.
>>
>> *What if Tegmark is right, and one should banish the word "infinite" once 
>> and for all, so "sum of the infinite series" could not even be mentioned!*
>>
>> The problem is we do not know what spacetime is, really.
>>
>>
>> https://blogs.unimelb.edu.au/sciencecommunication/2017/10/22/zenos-paradox-the-puzzle-that-keeps-on-giving/
>>  
>> :
>> ...
>>
>> *So, has this puzzle been solved once and for all?*
>>
>> *Quantum physics has probably given us our most convincing answer to the 
>> paradox so far, but it is not a certainty. The question of whether space is 
>> continuous or made up of discrete units is still debated among physicists 
>> (there are experiments currently trying to test this), and quantum 
>> mechanics itself is known not to be a complete theory of the universe. If 
>> history is any indication, this isn’t the last we’ll hear of Zeno’s 
>> paradox.*
>>
>>
>> - pt
>>
>
> *Clark misstated the paradox, but it seems clear it depends on assuming 
> space is infinitely divisible. So the resolution MUST be that space is 
> discrete even though our most sensitive measurements to date have not 
> detected it.  LC can speak to this. And the problem has nothing to do with 
> whether the word 'infinite" enters the analysis. One can do calculus 
> without ever using that word to describe limits, etc. Great! So now I know 
> the resolution of Zeno's paradox, and the physical fact that space must be 
> discrete! Gotta love it. AG*
>
>>  
>>
>
Spacetime is a mystery, and it's discrete vs. continuous is perhaps an 
oversimplification.

There are other mathematical models theorists pursue (check arXiv), e.g. 
fractal.

Scale relativity and fractal spacetime: theory and applications
Laurent Nottale 

https://arxiv.org/abs/0812.3857

- pt

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Monday, October 29, 2018 at 6:36:47 PM UTC, Philip Thrift wrote:
>
>
>
> On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote:
>>
>> On Sun, Oct 28, 2018 at 2:56 PM  wrote:
>>
>>  > *What's your view of Zeno's paradox which implies motion is 
>>> impossible.*
>>
>>
>> Zeno thought it was obvious if you added an infinite number of nonzero 
>> lengths or nonzero times together you would always get something that was  
>> nfinite, and that is the foundation of his paradox; but with modern 
>> calculus we know that sometimes that isn't true, and when it isn't true 
>> calculus can tell you exactly what the FINITE length or finite time 
>> interval turns out to be. For example, the sum, of the infinite series: 
>> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>>
>> John K Clark
>>
>>
>>
>>
> It is still a paradox as discussed in foundational physics and 
> mathematical writing, when one leaves the naive calculus as taught in high 
> school or college.
>
> *What if Tegmark is right, and one should banish the word "infinite" once 
> and for all, so "sum of the infinite series" could not even be mentioned!*
>
> The problem is we do not know what spacetime is, really.
>
>
> https://blogs.unimelb.edu.au/sciencecommunication/2017/10/22/zenos-paradox-the-puzzle-that-keeps-on-giving/
>  
> :
> ...
>
> *So, has this puzzle been solved once and for all?*
>
> *Quantum physics has probably given us our most convincing answer to the 
> paradox so far, but it is not a certainty. The question of whether space is 
> continuous or made up of discrete units is still debated among physicists 
> (there are experiments currently trying to test this), and quantum 
> mechanics itself is known not to be a complete theory of the universe. If 
> history is any indication, this isn’t the last we’ll hear of Zeno’s 
> paradox.*
>
>
> - pt
>

*Clark misstated the paradox, but it seems clear it depends on assuming 
space is infinitely divisible. So the resolution MUST be that space is 
discrete even though our most sensitive measurements to date have not 
detected it.  LC can speak to this. And the problem has nothing to do with 
whether the word 'infinite" enters the analysis. One can do calculus 
without ever using that word to describe limits, etc. Great! So now I know 
the resolution of Zeno's paradox, and the physical fact that space must be 
discrete! Gotta love it. AG*

>  
>

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote:
>
> On Sun, Oct 28, 2018 at 2:56 PM > wrote:
>
>  > *What's your view of Zeno's paradox which implies motion is 
>> impossible.*
>
>
> Zeno thought it was obvious if you added an infinite number of nonzero 
> lengths or nonzero times together you would always get something that was  
> nfinite, and that is the foundation of his paradox; but with modern 
> calculus we know that sometimes that isn't true, and when it isn't true 
> calculus can tell you exactly what the FINITE length or finite time 
> interval turns out to be. For example, the sum, of the infinite series: 
> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>
> John K Clark
>
>
>
>
It is still a paradox as discussed in foundational physics and mathematical 
writing, when one leaves the naive calculus as taught in high school or 
college.

*What if Tegmark is right, and one should banish the word "infinite" once 
and for all, so "sum of the infinite series" could not even be mentioned!*

The problem is we do not know what spacetime is, really.

https://blogs.unimelb.edu.au/sciencecommunication/2017/10/22/zenos-paradox-the-puzzle-that-keeps-on-giving/
 
:
...

*So, has this puzzle been solved once and for all?*

*Quantum physics has probably given us our most convincing answer to the 
paradox so far, but it is not a certainty. The question of whether space is 
continuous or made up of discrete units is still debated among physicists 
(there are experiments currently trying to test this), and quantum 
mechanics itself is known not to be a complete theory of the universe. If 
history is any indication, this isn’t the last we’ll hear of Zeno’s 
paradox.*


- pt
 

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Monday, October 29, 2018 at 4:07:41 PM UTC, John Clark wrote:
>
> On Sun, Oct 28, 2018 at 2:56 PM > wrote:
>
>  > *What's your view of Zeno's paradox which implies motion is 
>> impossible.*
>
>
> Zeno thought it was obvious if you added an infinite number of nonzero 
> lengths or nonzero times together you would always get something that was  
> nfinite, and that is the foundation of his paradox; but with modern 
> calculus we know that sometimes that isn't true, and when it isn't true 
> calculus can tell you exactly what the FINITE length or finite time 
> interval turns out to be. For example, the sum, of the infinite series: 
> 1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.
>
> John K Clark
>

This doesn't resolve Zeno's paradox. AG 

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Re: Mathematical Universe Hypothesis

[John Clark]

On Sun, Oct 28, 2018 at 2:56 PM  wrote:

 > *What's your view of Zeno's paradox which implies motion is impossible.*


Zeno thought it was obvious if you added an infinite number of nonzero
lengths or nonzero times together you would always get something that was
nfinite, and that is the foundation of his paradox; but with modern
calculus we know that sometimes that isn't true, and when it isn't true
calculus can tell you exactly what the FINITE length or finite time
interval turns out to be. For example, the sum, of the infinite series:
1+1/4+1/9+1/16+1/25 + 1/36 +  1/N^2 is EXACTLY equal to (PI^2)/6.

John K Clark

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Monday, October 29, 2018 at 4:54:10 AM UTC, Brent wrote:
>
>
>
> On 10/28/2018 7:54 PM, Tomas Pales wrote:
>
>
>
> On Monday, October 29, 2018 at 3:17:58 AM UTC+1, Brent wrote: 
>>
>>
>>
>> On 10/28/2018 5:18 PM, Tomas Pales wrote:
>>
>>
>>
>> On Monday, October 29, 2018 at 12:33:23 AM UTC+1, Brent wrote: 
>>>
>>>
>>>   There is no logical inconsistency in a flying pink elephant existing 
>>> right now in my den beside me. But don't see one.
>>>
>>
>> First, it is not clear whether the existence of a flying pink elephant in 
>> your den is consistent with the rest of this universe. Many things may seem 
>> consistent while they are actually inconsistent. Before the 20th century it 
>> seemed consistent with the laws of our universe that there was no speed 
>> limit or that the energy of a particle could vary continuously. Now we know 
>> that these phenomena are inconsistent in our universe and that's why they 
>> don't exist here.
>>
>>
>> You don't seem to know the difference between *logically consistent*="not 
>> entailing a contradiction by the rules of inference"  and *nomologically 
>> consistent* = "not contrary to the laws of nature".  It is still 
>> *logically* consistent for a particle to be faster than light.
>>
>
> Not in a universe where faster than light speed is prohibited.
>
>
> What does it mean to say FTL is logically prohibited?
>
>
>  
>
>> The problem with trying to use nomological consistency to imply existence 
>> is that we don't know the possible laws of nature and that observation 
>> trumps theory as to what is nomologically possible.  So no matter what you 
>> think are the laws of nature, if you see something contrary to them it just 
>> means they are wrong.
>>
>
> It doesn't matter whether we know what the laws of the universe are. 
> Whatever the laws are, if they prohibit something then it cannot happen, 
> otherwise there would be a logical inconsistency. 
>
>
> But that's why your "theory" is completely vacuous. Whatever is observed 
> is, by definition, logically consistent.  Remember when it was "logically 
> inconsistent" for a particle to be two places at the same time...then, 
> OOPS!...quantum mechanics came along.
>


*Haven't you read Bruce's recent analysis and mine independently last 
summer, that what you claim is based on a fallacious interpretation of a 
superposition? Since one can decompose and represent a wf in many different 
bases, the assertion that the system the wf represents as its state is 
physically one or another basis makes no sense. Nor, of course, that it is 
simultaneously in the component states when the components depend on the 
basis chosen. AG*

>
>
> Imagine a universe that is the set of all triangles. That means that a law 
> of this universe determines that only triangles can be members of this 
> universe. Surely it would be a logical inconsistency if a circle was a 
> member of this universe. 
>
>
> No.  It would mean you were mistaken that this universe had only triangles.
>
> Brent
>

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