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

['Brent Meeker' via Everything List]

On 3/7/2019 2:15 PM, Lawrence Crowell wrote:
This makes a lot of sense, for in the biological world certain 
problems that are NP are figured out. This runs from ants finding the 
minimal distance for their trails or even protistans negotiating some 
space. Ants are good at approximately solving the traveling salesman 
problem, the classic NP algorithm.


Not really.  The 'ants' are just part of an algorithm that solves the 
traveling salesman program, and they aren't accurate simulations of 
ants.  Real ants don't make tours of vertices and they don't go back and 
update their pheromone trail.


Brent

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

[Lawrence Crowell]

On Wednesday, March 6, 2019 at 12:20:13 PM UTC-6, Bruno Marchal wrote:
>
>
> On 6 Mar 2019, at 11:47, Lawrence Crowell  > wrote:
>
> On Monday, March 4, 2019 at 6:24:35 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 3 Mar 2019, at 20:49, Lawrence Crowell  
>> wrote:
>>
>> On Sunday, March 3, 2019 at 7:58:01 AM UTC-6, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Sunday, March 3, 2019 at 7:32:00 AM UTC-6, Lawrence Crowell wrote:
>>>
>>> Bringing Gödel into physics is treading on a mine field as it is. 
 Believe me, most physicists react in horror at the mere suggestion of 
 this. 
 I have this suspicion however that quantum measurement is a a sort of 
 Gödel 
 self-reference with quantum information or qubits. This may, at least 
 within how we describe quantum mechanics if it should turn out to be not 
 how the quantum world actually is, be one reason why we have this growing 
 pantheon of quantum interpretations and no apparent way to decide which is 
 definitively correct. 
  

>>>
>>>  
>>> I still think it's Darwin, not Gödel,  that has anything to do with  
>>> "quantum measurement".
>>>
>>> But physicists recoil in horror from that.
>>>
>>> - pt
>>>
>>
>> Darwinian logic did put down the Aristotelian-Cartesian hierarchical 
>> structure with respect to biology. 
>>
>>
>> OK. Darwin use both mechanism (quasi-explicitly), and is understood 
>> usually in the materialist frame, but Darwin just do not address that 
>> question.
>>
>>
>>
>> Aristotle and Plato are the two most known Hellenic philosophers because 
>> their systems of thought were wrapped into the New Testament Bible. Plato 
>> had this idea of there being a hierarchy of being, which was taken up by St 
>> Paul, carried further by Augustine, Aquinas and eventually encoded by 
>> Descartes. Descartes had this hierarchy of structure over function, design 
>> over material form etc, which was carried into science during the 17th and 
>> 18th century. In some ways Newtonian mechanics was seen as a confirmation 
>> of Descartes' metaphysics.
>>
>>
>> That is true. Today we know that Newtonian Mechanics is highly not 
>> computable. But Newton saw that, and indeed, distrusted his Mechanics, and 
>> saw it as an approximation. 
>>
>>
>>
> I would say classical mechanics is NP computable.
>
>
>
> In classical mechanics, the three body problem is Turing universal, I 
> think. No doubt for for the many body problem as the billiard board 
> computer illustrates.
>
> Any theorem complete for arbitrary finite Newtonian mechanical system will 
> be Turing complete, and thus essentially undecidable (in the sense of 
> Tarski: it means that all its effective consistent extensions are 
> undecidable as well). Turing universal = partial computable (not total 
> computable).
>
>
>
I think chaotic dynamics is a case of NP. The sensitive dependence on 
initial conditions means the Turing machine will take exponential 
space/time 2^N to compute the system N iterations into the future. This can 
then only in general be computed on a nondeterministic TM, or the algorithm 
is NP. There are a whole host of processes that are algorithmically NP, 
such as the fermionic sign problem. That is a big bugger of a problem.

As I have maybe indicated the de Sitter spacetime is in effect the single 
hyperboloid that covers the cones. The anti-de Sitter spacetimes are the 
two hyperboloids inside the cones. For this reason the dS is timelike or 
with topology RxS^n for R = reals for time and S^n space. The AdS contained 
in the cones as a signature flip with topology S^1xR^n, so time globally is 
in loops. The two meet at "infinity" on the cones, which in relativity we 
call scri^{±∞}. So in some sense we can think of the AdS and dS as 
transformable into each other. They are connected at the conformal boundary 
of the AdS, so the physical content of the two are identical. They are to 
get further into this related by a system similar to the momentum cone 
condition for the Haldane chain in solid state physics. They are connected 
at a holographic screen. So for AdS_5 a junction condition on a holographic 
screen inside AdS_5 will be AdS_4 if the ΔG_{ab} < 0 and dS_4 
if ΔG_{ab} ≥ 0. We are in this scheme in a dS_4.

Now here is where algorithms get into the picture. The AdS_5 has closed 
timelike curves, and so algorithms that are NP can be run in P. Aaronson 
has a paper in this. So the computations that occur in our cosmology are P 
or timelike without time loops, but they are coupled to quantum processes 
that are time loops. In this way the sign problem is not something that 
consumes a vast amount of qubits in the observable universe. 

This makes a lot of sense, for in the biological world certain problems 
that are NP are figured out. This runs from ants finding the minimal 
distance for their trails or even protistans negotiating some space. Ants 
are good at approximately solving the traveling salesman problem, the 
classic NP 

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

[Philip Thrift]

On Thursday, March 7, 2019 at 11:47:41 AM UTC-6, Bruno Marchal wrote:
>
>
> On 6 Mar 2019, at 22:10, Philip Thrift > 
> wrote:
>
>
>
> On Wednesday, March 6, 2019 at 12:20:13 PM UTC-6, Bruno Marchal wrote:
>>
>>
>>
>> We cannot predict in advance if a machine will stop. The extensional 
>> equality of machines, or combinators, is unsolvable. 
>>
>>
>
> There is some conceptual and practical division between mathematics and 
> applied mathematics
>
>
> Yes. But note that the division we can made there are dependent of the 
> metaphysics.
>
> Then Gödel has shown that we can apply mathematics to metamathematics, and 
> that a large part of metamathematics is in mathematics, so mathematics have 
> application in mathematics. But that is obvious through the representation 
> theorems, and my factors. We can say that the theory of complex analysis 
> has found extraordinary application in the pure number theory, like Riemann 
> discovered. 
>
> Category theory is born from the discovery of abstract pattern relying 
> many application of some branch of math to another branch of math. It helps 
> mathematician to not reinvent the wheel all the time.
>
>
>
> (and there are institutionally separate Mathematics (PM, P for "Pure") and 
> Applied Mathematics (AM) Departments or Divisions at *some* universities.
>
>
> Yes. That has been the root of my problem with some local academician. I 
> naively stated that I decide to study mathematics because I saw application 
> of mathematical logic (the second recursion theorem) to biology (like I 
> have shown in my paper “Amoeba, Planaria and Dreaming machine”. But I was 
> told that mathematical logic was taught in the section of Pure Mathematics, 
> where it was very badly seen to apply mathematics to anything but 
> mathematics. This illustrates it makes no sense to decide that some part of 
> math are pure or not.
>
> And this is even more true with mechanism.  There is no more an 
> ontological physical reality, or any gods of that sort (which have never 
> been tested, actually, except with my work, of course, where the test was 
> negative for “Matter”). So the fundamental reality becomes mathematical. 
> And we are pure mathematical object living in a mathematical reality. That 
> is not entirely correct, because the internal phenomenology, for technical 
> reason, escapes even the whole of mathematics. So, eventually, the reality 
> is theological, to be correct. But the theology of the machines is a 
> theory, which today, is classified in pure mathematics (the logic of 
> provability). 
>
>
>
>
>
>
> There is a PM and an AM way of approaching what "computing" is.
>
>
>
> Yes, even in arithmetic. The universal machine discover that there is a 
> big difference between being implemented by a nameable “in principle” 
> universal number, and being implemented by something emerging from an 
> infinity of computations from the first person points of view. The first 
> leads to the theory G* (the “scientific theology of the ideally sound 
> machine”), and the others leads to quantum logic and physics, and the right 
> one, if mechanism is correct.
>
>
>
>
>
>
> In an AM way of thinking, no computer can run forever, assuming what 
> scientists theorize about the future of the universe (big freeze, crunch, 
> etc.).
>
>
> And assuming some physical reality. If you do serious metaphysics, it is 
> better to invoke an ontological commitment only in last ressort. Invoking 
> an ontological or primary physical universe is like saying “and god made 
> it”. That does not work. It is wishful thinking, provably if Mechanism is 
> assumed.
>
>
>
>
>
> AM would see computing as being nothing more than what can be done on 
> material computers, natural or manmade. 
>
>
> Computation have been discovered in arithmetic, before physics.
>
> Of course, the fact that we have cells and brains suggest, once we 
> understand that a computation is an arithmetical notion,  that the physical 
> reality too is Turing complete. But with mechanism, to solve the mind-body 
> problem, you have to derive the physical reality (and its Turing 
> completeness) from arithmetic. It is nota question of choice.
>
> Of course you can say that in your religion, machine cannot have souls, 
> that you are not a machine, and so you can believe in the fantasy you want. 
> That is what we do since we have put theology out of science (just to make 
> it possible for some tyran to exploit people).
>
> Or you can try to build a precise non computationalist theory of mind, and 
> how to test it, in which case the computationalist theory will gives many 
> hint. Indeed, if some logics the universal machine gives for matter is 
> contradicted by nature, we do have a precise hint how to transform the 
> machine theory to get a correct non mechanist theory.
> Today, such theory does not exist, Nature follows perfectly well 
> Mechanism,and the theory of apparent matter given by all classical 
> universal machine,  

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

['Brent Meeker' via Everything List]

On 3/7/2019 9:11 AM, Bruno Marchal wrote:

On 7 Mar 2019, at 05:48, 'Brent Meeker' via Everything List 
 wrote:



On 3/6/2019 10:20 AM, Bruno Marchal wrote:

I use mechanism in the sense that if little daemon substitute each piece of my 
brain, at some resolution level,  by functional digital equivalent, then my 
consciousness would not notice the difference.

According to your theory, your consciousness is instantiated by the 
computational threads of the universal dovetailer, which exists within 
arithmetic.  So whether a piece of your brain is present, replaced, or removed 
should make no difference to you consciousness.


Proof?

Yes, at first sight, naively, the universal dovetailing predicts white rabbits, 
or even white noise. But this is like forgetting the definition of the subject 
given (the Gödel-Löbian machines), and the fact that the thread in the 
Universal dovetailing is entirely structured by the nuance of provability 
imposed by incompleteness.

Then the math shows that we get a quantum logic for the 3p physics, another 
quantum logics for the 1p physics, and even (I was wrong in my original thesis) 
a quantum logic for the 1p-soul. Plotinus was right on this, the soul has 
already a foot in matter, even if that quantum logic is an intuitionist quantum 
logic.

If I belong to a normal history, for those arithmetical quantum logic,  where 
some people decide to remove a piece of my brain, the probability will be high 
that I will survive that lobotomic experience in the “continuum” of 
continuations which are executed in the sigma_1 arithmetic (equivalent to a 
universal dovetailing).


Why is the probability not 1.0.  Why is there any effect at all in any 
continuation?  Why is experience dependent on physics, if it is just a 
matter of timeless arithmetical relations.


Brent



And mechanism is not my theory. Nor is the G* theology, which is just the truth 
theory of all classical Löbian machine, as demonstrate by the work of Gödel, Löb 
and Solovay. I have not invented the intensional variants. ([]p & p) has been 
discovered by Goldblatt and Boolos, well studied by Artemov. And yes, I point on 
the existence of infinitely many others, some crucial to derive “Matter” from 
arithmetic in the manner prescribed by Mechanism (or, actually Neoplatonism).

Bruno




Brent

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Re: When Did Consciousness Begin?

['Brent Meeker' via Everything List]

On 3/7/2019 8:57 AM, Bruno Marchal wrote:


On 6 Mar 2019, at 20:57, 'Brent Meeker' via Everything List 
> wrote:




On 3/6/2019 5:48 AM, Bruno Marchal wrote:

Every time I mention this you strike back at the straw man of primitive 
matter...which I never refer to.

But then, why do you criticise the theorem? Maybe you don’t? Bt then why are 
you saying that elementary arithmetic is not a TOE? It explain the coupling 
consciousness/matter using only elementary arithmetic.


My criticism of the theory is different from my criticism of your 
repeated claim that you have eliminated and matter and attributing 
anything to it is "Aristotles error".   My criticism of the theory 
that arithmetic is a TOE is that arithmetic proves too much.



That looks like Deutsch criticism on Schmidhuber type of 
computationalist explanation.


But, this omit completely the first person indeterminacy, which not 
only explains (in a testable way) the origin of the physical laws, but 
above all makes the physics unique, and invariant for all machines.


The postulation of a primary universe, on the contrary, explains only 
the current first person prediction by using an identity thesis which 
is inconsistent with mechanism.


You're back to criticizing a strawman "primary" universe which I didn't 
mention.


Physics fails both for the prediction of “seeing an eclipse”, and miss 
the mind-body problem.


Let's see arithmetic predict an eclipse.  ISTM that you the ONLY thing 
your theory predicts is the ineffability of consciousness.


Compared to the explanation in arithmetic, there is just no 
explanation given for the physical experiment and experience. It works 
very well locally, but only by using an inconsistent metaphysics. In 
fact, it does not tackle the fundamental question, and gives recipe to 
make prediction, without attempting to explains why we can be 
conscious of the prediction.


But your "mechanism" doesn't explain it either.  It simply identifies it 
with logical inferences.


Brent



With mechanism we get the whole fundamental science, already 
axiomatised completely (thanks to Solovay- at the propositional level. 
I don’t see it explains too much. You might confuse Mechanism and 
digital physics. Digital physics just assume that there is some u such 
that phi_u is the physical universe. That reduce physics to 
arithmetic, but that explains too much, or nothing. And is wrong. With 
mechanism, even if some u plays some more special role, that choice of 
u and that role have to be explained, given the differentiation of 
conscious on all relative computational computations.


Bruno






Brent

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

[Bruno Marchal]

> On 6 Mar 2019, at 22:10, Philip Thrift  wrote:
> 
> 
> 
> On Wednesday, March 6, 2019 at 12:20:13 PM UTC-6, Bruno Marchal wrote:
> 
> 
> We cannot predict in advance if a machine will stop. The extensional equality 
> of machines, or combinators, is unsolvable. 
> 
> 
> 
> There is some conceptual and practical division between mathematics and 
> applied mathematics

Yes. But note that the division we can made there are dependent of the 
metaphysics.

Then Gödel has shown that we can apply mathematics to metamathematics, and that 
a large part of metamathematics is in mathematics, so mathematics have 
application in mathematics. But that is obvious through the representation 
theorems, and my factors. We can say that the theory of complex analysis has 
found extraordinary application in the pure number theory, like Riemann 
discovered. 

Category theory is born from the discovery of abstract pattern relying many 
application of some branch of math to another branch of math. It helps 
mathematician to not reinvent the wheel all the time.



> (and there are institutionally separate Mathematics (PM, P for "Pure") and 
> Applied Mathematics (AM) Departments or Divisions at some universities.

Yes. That has been the root of my problem with some local academician. I 
naively stated that I decide to study mathematics because I saw application of 
mathematical logic (the second recursion theorem) to biology (like I have shown 
in my paper “Amoeba, Planaria and Dreaming machine”. But I was told that 
mathematical logic was taught in the section of Pure Mathematics, where it was 
very badly seen to apply mathematics to anything but mathematics. This 
illustrates it makes no sense to decide that some part of math are pure or not.

And this is even more true with mechanism.  There is no more an ontological 
physical reality, or any gods of that sort (which have never been tested, 
actually, except with my work, of course, where the test was negative for 
“Matter”). So the fundamental reality becomes mathematical. And we are pure 
mathematical object living in a mathematical reality. That is not entirely 
correct, because the internal phenomenology, for technical reason, escapes even 
the whole of mathematics. So, eventually, the reality is theological, to be 
correct. But the theology of the machines is a theory, which today, is 
classified in pure mathematics (the logic of provability). 






> There is a PM and an AM way of approaching what "computing" is.


Yes, even in arithmetic. The universal machine discover that there is a big 
difference between being implemented by a nameable “in principle” universal 
number, and being implemented by something emerging from an infinity of 
computations from the first person points of view. The first leads to the 
theory G* (the “scientific theology of the ideally sound machine”), and the 
others leads to quantum logic and physics, and the right one, if mechanism is 
correct.





> 
> In an AM way of thinking, no computer can run forever, assuming what 
> scientists theorize about the future of the universe (big freeze, crunch, 
> etc.).

And assuming some physical reality. If you do serious metaphysics, it is better 
to invoke an ontological commitment only in last ressort. Invoking an 
ontological or primary physical universe is like saying “and god made it”. That 
does not work. It is wishful thinking, provably if Mechanism is assumed.




> 
> AM would see computing as being nothing more than what can be done on 
> material computers, natural or manmade. 

Computation have been discovered in arithmetic, before physics.

Of course, the fact that we have cells and brains suggest, once we understand 
that a computation is an arithmetical notion,  that the physical reality too is 
Turing complete. But with mechanism, to solve the mind-body problem, you have 
to derive the physical reality (and its Turing completeness) from arithmetic. 
It is nota question of choice.

Of course you can say that in your religion, machine cannot have souls, that 
you are not a machine, and so you can believe in the fantasy you want. That is 
what we do since we have put theology out of science (just to make it possible 
for some tyran to exploit people).

Or you can try to build a precise non computationalist theory of mind, and how 
to test it, in which case the computationalist theory will gives many hint. 
Indeed, if some logics the universal machine gives for matter is contradicted 
by nature, we do have a precise hint how to transform the machine theory to get 
a correct non mechanist theory.
Today, such theory does not exist, Nature follows perfectly well Mechanism,and 
the theory of apparent matter given by all classical universal machine,  thanks 
to QM.  

There is no evidence for your metaphysical ontological commitment. Given that 
it makes the mind-body problem unsolvable since a long time, and that mechanism 
explains consciousness and matter already, up to the infinite 

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

[Bruno Marchal]

> On 7 Mar 2019, at 05:48, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 3/6/2019 10:20 AM, Bruno Marchal wrote:
>> I use mechanism in the sense that if little daemon substitute each piece of 
>> my brain, at some resolution level,  by functional digital equivalent, then 
>> my consciousness would not notice the difference.
> 
> According to your theory, your consciousness is instantiated by the 
> computational threads of the universal dovetailer, which exists within 
> arithmetic.  So whether a piece of your brain is present, replaced, or 
> removed should make no difference to you consciousness.


Proof?

Yes, at first sight, naively, the universal dovetailing predicts white rabbits, 
or even white noise. But this is like forgetting the definition of the subject 
given (the Gödel-Löbian machines), and the fact that the thread in the 
Universal dovetailing is entirely structured by the nuance of provability 
imposed by incompleteness.

Then the math shows that we get a quantum logic for the 3p physics, another 
quantum logics for the 1p physics, and even (I was wrong in my original thesis) 
a quantum logic for the 1p-soul. Plotinus was right on this, the soul has 
already a foot in matter, even if that quantum logic is an intuitionist quantum 
logic.

If I belong to a normal history, for those arithmetical quantum logic,  where 
some people decide to remove a piece of my brain, the probability will be high 
that I will survive that lobotomic experience in the “continuum” of 
continuations which are executed in the sigma_1 arithmetic (equivalent to a 
universal dovetailing). 

And mechanism is not my theory. Nor is the G* theology, which is just the truth 
theory of all classical Löbian machine, as demonstrate by the work of Gödel, 
Löb and Solovay. I have not invented the intensional variants. ([]p & p) has 
been discovered by Goldblatt and Boolos, well studied by Artemov. And yes, I 
point on the existence of infinitely many others, some crucial to derive 
“Matter” from arithmetic in the manner prescribed by Mechanism (or, actually 
Neoplatonism).

Bruno



> 
> Brent
> 
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Re: When Did Consciousness Begin?

[Bruno Marchal]

> On 6 Mar 2019, at 20:57, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 3/6/2019 5:48 AM, Bruno Marchal wrote:
>>> Every time I mention this you strike back at the straw man of primitive 
>>> matter...which I never refer to.
>> But then, why do you criticise the theorem? Maybe you don’t? Bt then why are 
>> you saying that elementary arithmetic is not a TOE? It explain the coupling 
>> consciousness/matter using only elementary arithmetic.
> 
> My criticism of the theory is different from my criticism of your repeated 
> claim that you have eliminated and matter and attributing anything to it is 
> "Aristotles error".   My criticism of the theory that arithmetic is a TOE is 
> that arithmetic proves too much.  


That looks like Deutsch criticism on Schmidhuber type of computationalist 
explanation.

But, this omit completely the first person indeterminacy, which not only 
explains (in a testable way) the origin of the physical laws, but above all 
makes the physics unique, and invariant for all machines.

The postulation of a primary universe, on the contrary, explains only the 
current first person prediction by using an identity thesis which is 
inconsistent with mechanism. Physics fails both for the prediction of “seeing 
an eclipse”, and miss the mind-body problem. Compared to the explanation in 
arithmetic, there is just no explanation given for the physical experiment and 
experience. It works very well locally, but only by using an inconsistent 
metaphysics. In fact, it does not tackle the fundamental question, and gives 
recipe to make prediction, without attempting to explains why we can be 
conscious of the prediction.

With mechanism we get the whole fundamental science, already axiomatised 
completely (thanks to Solovay- at the propositional level. I don’t see it 
explains too much. You might confuse Mechanism and digital physics. Digital 
physics just assume that there is some u such that phi_u is the physical 
universe. That reduce physics to arithmetic, but that explains too much, or 
nothing. And is wrong. With mechanism, even if some u plays some more special 
role, that choice of u and that role have to be explained, given the 
differentiation of conscious on all relative computational computations.

Bruno




> 
> Brent
> 
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Re: What is the largest integer you can write in 5 seconds?

[John Clark]

On Thu, Mar 7, 2019 at 8:18 AM Bruno Marchal  wrote:

*> Usually, when asked to name a big number, we mean to provide a number
> that e can compute in a finite time (no matter how long). BB(8000) will be
> rejected, because it is not a definite description, or name, because BB is
> not computable.*
>

Assuming you're just using 2 symbols (like 0 and 1) there are (16001)^8000
different 8000 state Turing Machines. And that is a very large number but a
finite one. And one of those machines makes the largest number of FINITE
operations before halting. And that number of operations is BB(8000).  Even
theoretically, much less practically,  you can never compute that number
but I have given a unique description of it, no other 8000 state Turing
Machine has that propertie.

 John K Clark

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Re: What is the largest integer you can write in 5 seconds?

[Bruno Marchal]

> On 5 Mar 2019, at 19:05, John Clark  wrote:
> 
> It's easy to prove that the Busy Beaver Function grows faster than ANY 
> computable function because if there were such a faster growing function you 
> could use it to solve the Halting Problem. So if you're ever in a contest to 
> see who can name the largest integer in less than 5 seconds just write 
> BB(9000) and you'll probably win.





Usually, when asked to name a big number, we mean to provide a number that e 
can compute in a finite time (no matter how long). BB(8000) will be rejected, 
because it is not a definite description, or name, because BB is not computable.

How to name a big number? You can start with a sequence of growing function, 
like addition, multiplication, expoenntation, iteration, quintation, hexaxion, 
etc. (each one is just the iteration of the preceding one).

Then, calling those functions F_0, F_1, F_2, … F_i, … you can get a “limit” by 
diagonalising them, which gives a growing total function, as all F_i are total, 
and it grow more quickly:

G_0(n) = F_n(n) + 1,

And then a full new sequence G_0, G_1, G_2, …

And you can diagonalise on that sequence too, and again and again. This will 
work on the whole range of the constructive (aka recursive) ordinals.

So, if you need to write the description of a big number, the usual method will 
be to name a big constructive infinite ordinal, like epsilon_zer, for example, 
although there are much bigger one … and write:

F_epsilon-0 (999).

See my old post on this published here a (long) time ago, for a more detailed 
account, going far above epsilon_zero.

It is a cute problem we can ask six years old children. Usually some write 
9+9+9+9+… +9, on the whole paper. Some write 9*9*9*9*9¨… *9. Later they get 
better ideas, and can discuss this all along their secondary school. To get the 
transfinite constructive original, you need the second recursion theorem of 
Kleene, which is con course much more advanced.

O course, if a non computable number number is asked, and still want to win, 
you can do the same statring from BB(8000), like 

F_epsilon-0(BB(8000)). But again, that is usually not accepted, because the 
“name” is not constructive, and usually a name must be a constructive definite 
description.

Bruno





> 
> John K Clark
> 
> 
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Re: Are there real numbers that cannot be defined?

[Bruno Marchal]

> On 6 Mar 2019, at 14:43, John Clark  wrote:
> 
> On Wed, Mar 6, 2019 at 8:30 AM Bruno Marchal  > wrote:
> 
> > You confirm my theory that strong (non agnostic) atheism is radical 
> > religious fundamentalism
> 
> I've never heard you or anybody else criticize me that brilliantly before, 
> you sure put me in my place. I am devastated!


Lol. 

The fact remains. Anyone mocking the science theology, helps the radicals, who 
have separated theology from science to mix it with (fake) politics (and real 
tyranny). You are under the influence of the post 529 pseudo-christian 
propaganda. You defend, not intentionally I suppose, those who want us 
remaining non educated. 
The greek theology (not the greek mythology!) is at the origin of mathematics, 
physics, and even mathematical logic more recently.

Note that the USSR, which have banned both religion and theology, did the same 
thing with biology. By mixing it with the state, it becomes obscurantist and 
non sensical (which led to a big famine).



> 
> > By theology, you know that  [...]  Plato define God by [...]
> 
> I'm sorry did you say something? I think I fell asleep 

Since long …
Since 529, somehow, I guess. 

Bruno



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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 6, 2019 at 11:42:33 AM UTC-7, Brent wrote:
>
>
>
> On 3/6/2019 1:27 AM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, March 6, 2019 at 1:03:16 AM UTC-7, Brent wrote: 
>>
>>
>>
>> On 3/5/2019 10:02 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agray...@gmail.com 
>>> wrote: 



 On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote: 
>
>
>
> On 2/28/2019 4:07 AM, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 2/27/2019 4:58 PM, agrays...@gmail.com wrote:
>>
>> *Are you assuming uniqueness to tensors; that only tensors can 
>> produce covariance in 4-space? Is that established or a mathematical 
>> speculation? TIA, AG *
>>
>>
>> That's looking at it the wrong way around.  Anything that transforms 
>> as an object in space, must be representable by tensors. The informal 
>> definition of a tensor is something that transforms like an object, i.e. 
>> in 
>> three space it's something that has a location and an orientation and 
>> three 
>> extensions.  Something that doesn't transform as a tensor under 
>> coordinate 
>> system changes is something that depends on the arbitrary choice of 
>> coordinate system and so cannot be a fundamental physical object.
>>
>> Brent
>>
>
> 1) Is it correct to say that tensors in E's field equations can be 
> represented as 4x4 matrices which have different representations 
> depending 
> on the coordinate system being used, but represent the same object? 
>
>
> That's right as far as it goes.   Tensors can be of any order.  The 
> curvature tensor is 4x4x4x4.
>
> 2) In SR we use the LT to transform from one* non-accelerating* frame 
> to another. In GR, what is the transformation for going from one 
> *accelerating* frame to another? 
>
>
> The Lorentz transform, but only in a local patch.
>

 *That's what I thought you would say. But how does this advance 
 Einstein's presumed project of finding how the laws of physics are 
 invariant for accelerating frames? How did it morph into a theory of 
 gravity? TIA, AG *

>>>
>>> *Or suppose, using GR, that two frames are NOT within the same local 
>>> patch.  If we can't use the LT, how can we transform from one frame to the 
>>> other? TIA, AG *
>>>
>>> *Or suppose we have two arbitrary accelerating frames, again NOT within 
>>> the same local patch, is it true that Maxwell's Equations are covariant 
>>> under some transformation, and what is that transformation? TIA, AG*
>>>
>>
>>
>> *I think I can simplify my issue here, if indeed there is an issue: did 
>> Einstein, or anyone, ever prove what I will call the General Principle of 
>> Relativity, namely that the laws of physics are invariant for accelerating 
>> frames? If the answer is affirmative, is there a transformation equation 
>> for Maxwell's Equations which leaves them unchanged for arbitrary 
>> accelerating frames? TIA, AG *
>>
>>
>> Your question isn't clear.  If you're simply asking about the equations 
>> describing physics* as expressed* in an accelerating (e.g. rotating) 
>> reference frame, that's pretty trivial.  You write the equations in 
>> whatever reference frame is convenient (usually an inertial one) and then 
>> transform the coordinates to the accelerated frame coordinates.   But if 
>> you're asking about what equations describe some physical system while it 
>> is being accelerated as compared to it not being accelerated, that's more 
>> complicated. 
>>
>
> *Thanks, but I wasn't referring to either of those cases; rather, the case 
> of transforming from one accelerating frame to another accelerating frame, 
> and whether the laws of physics are invariant. *
>
>
> For simplicity consider just flat Minkowski space time.  If you know the 
> motion of a particle in reference frame, whether the reference frame is 
> accelerated or not, you can determine its motion in any other reference 
> frame.  As for the particle path through spacetime, that's just some 
> geometric path and you're changing from describing it in one coordinate 
> system to describing it in another system...no physics is changing, just 
> the description.  If the reference frames are accelerated you get extra 
> terms in this description, like "centrifugal acceleration" which are just 
> artifacts of the frame choice. This is the same as in Newtonian mechanics.  
>
> But if the particle is actually accelerated, then there may be more to the 
> problem than just it's world line through spacetime.  For example, if the 
> particle has an electric charge, then it will radiate when accelerated and 
> there will be a