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: Interpretation of Superposition

[Pierz]

On Monday, October 15, 2018 at 9:40:39 PM UTC+11, agrays...@gmail.com wrote:
>
>
>
> On Sunday, October 14, 2018 at 5:08:42 PM UTC, smitra wrote:
>>
>> On 14-10-2018 15:24, agrays...@gmail.com wrote: 
>> > In a two state system, such as a qubit, what forces the interpretation 
>> > that the system is in both states simultaneously before measurement, 
>> > versus the interpretation that we just don't what state it's in before 
>> > measurement? Is the latter interpretation equivalent to Einstein 
>> > Realism? And if so, is this the interpretation allegedly falsified by 
>> > Bell experiments? AG 
>>
>> It is indeed inconsistent with QM itself as Bell has shown. Experiments 
>> have later demonstrated that the Bell inequalities are violated in 
>> precisely the way predicted by QM.  This then rules out local hidden 
>> variables, therefore the information about the outcome of a measurement 
>> is not already present locally in the environment. 
>>
>> Saibal 
>>
>
> What puzzles me is this; why would the Founders assume that a system in a 
> superposition is in all component states simultaneously -- contradicting 
> the intuitive appeal of Einstein realism -- when that assumption is not 
> used in calculating probabilities (since the component states are 
> orthogonal)? AG 
>

I think because of interference. Consider the paradigmatic double slit, 
with the single electron going through it. It sure looks like the electron 
was in two place at once, doesn't it? I'm not sure what you mean by "that 
assumption is not used in calculating probabilities". If you take a 
sum-over-histories approach it's explicitly assumed the electron went via 
all possible paths. I don't see what the orthogonality of the basis vectors 
(and hence component states) has to do with the question of interpretation 
of superposition. Clearly the system will be measured in only one state, 
and this is what the orthogonal vectors represent. However the quantum 
state itself typically spans more than one dimension of the vector space - 
that's what a superposition is. However I think when physicists say that 
the superposition is in all states simultaneously, it's only in a manner of 
speaking - a way of conveying the mathematical situation in natural 
language that is inherently classical. Reading Born's exchange of letters 
with Einstein (I'm proud to say Born was my great grandfather), it's clear 
that Born had a conception of QM that was still very realistic in the 
Einstein sense. Though they disagreed significantly and somewhat heatedly, 
Born still seems to have regarded QM probabilities as classical 
probabilities in disguise. I don't think he would ever have endorsed the 
notion that a particle is truly in all of the states of the superposition 
simultaneously. 
 

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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: Combinator 6 (Turing Universality, the Mu operator)

[Bruno Marchal]

> On 31 Oct 2018, at 13:47, Philip Thrift  wrote:
> 
> 
> Bruno,
> 
> Have you looked at various SKI interpreters around that could be used? 
> Several now (on GitHub) in JavaScript. Also in Haskell. And there's the 
> Unlambda system by David Madore.


A long time ago, I have programmed in LISP and PROLOG, even been paid for 
that!, but since some time, … I procrastine c++ and/or Python, there is too 
much things to do and explore …

But I might take a look. My last attempt to search for some good “little” LISP 
has failed. It would be cool to run the Universal Dovetailer one more time :)

The mathematical problem: to find the measure on the sigma_-sentences. The 
method: use the “classical definition” on Gödel’s beweisbar provability.

The bad news: physics appears (seemingly) in the intuitionist quantum logic. 
Quanta are already qualia. They are only locally sharable, physics is first 
person plural.

I am not sure I like that, but then, in science, we are not paid for 
confortable “truth”. “Truth” is in quote as this what follows from the 
mechanist hypothesis (or the sigma_1 restriction) and no one claim that 
Mechanism is true.

Bruno



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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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>

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