Re: Two Mathematicians in a Bunker and Existence of Pi

[socra...@bezeqint.net]

Where does the information come from?
 / Quantum Theory as Quantum Information /
===…
#
Does information begin on the quarks level?
No. Quark cannot leave an atom.
Maybe does proton have quant of information?
No. Single proton has no quant of information.
Why?
Because information can be transfered only by
electromagnetic fields. And we don’t have a theory
about protono-magnetic fields.
#
In our earthly world there is only one fundamental
 particle -  electron who can transfer information.
Can an electron be quant of information?
Maybe at first glance this seems to be a rather senseless questions.
 But  . . . . .
Energy is electromagnetic waves (em).
In 1904 Lorentz proved: there isn’t em waves without Electron
It means the source of these em waves must be an Electron
The electron and the em waves they are physical reality
 ==
#
1900, 1905
Planck and Einstein found the energy of electron: E=h*f.
1916
Sommerfeld found the formula of electron : e^2=ah*c,
 it means: e = +ah*c  and  e = -ah*c.
1928
Dirac found two more formulas of electron’s energy:
  +E=Mc^2  and  -E=Mc^2.
According to QED in interaction with vacuum electron’s
energy is infinite: E= ∞
Questions.
Why does the simplest particle - electron have six ( 6 ) formulas ?
Why does electron obey five ( 5) Laws ?
a) Law of conservation and transformation energy/ mass
b) Maxwell’s equations
c) Heisenberg Uncertainty Principle / Law
d) Pauli Exclusion Principle/ Law
e) Fermi-Dirac statistics
 #.
What is an electron ?
Now nobody knows
 In the internet we can read hundreds theories about electron
All of them are problematical
We can read hundreds books about philosophy of physics.
But how can we trust them if we don’t know what is electron ?
.
Quote by Heinrich Hertz on Maxwell's equations:

"One cannot escape the feeling that these mathematical formulae
have an independent existence and an intelligence of their own,
that they are wiser than we are, wiser even than their discoverers,
that we get more out of them than was originally put into them."
.
Ladies and Gentlemen !
Friends !
Electron is not as simple as we think and, maybe, he is wiser than we
are.
==.
#
We know, there is no information transfer
without energy transfer. More correct: there is no quant
information transfer without quant energy transfer.
And the electron has the least  electric charge.
It means it has some quant of the least information.
What can electron do with this information?
Let us look the Mendeleev / Moseley periodic table.
We can see  that electron interacts with proton
and creates atom of hydrogen.
 This is simplest design, which  was created by electron.
And we can see how this information grows and reaches
high informational level. And the most complex design,
 which was created by electron is the Man.
The Man is alive essence. Animals, birds, fish are alive essences.
And an atom? And atom is also alive design.
The free atom of hydrogen can live about 1000 seconds.
And someone a long time ago has already said, that if to give
suffices time to atom of hydrogen, he would turn into Man.
Maybe it is better not to search about "dark, virtual particles "
but to understand what the electron is,
because even now nobody knows what electron is.
===
In my opinion the Electron is quant of information.
 Was I mistaken?No !
 Because according to Pauli Exclusion Principle
only one single electron can be in the atom.
This electron reanimates the atom.
This electron manages  the atom.
If the atom contains more than one electron
(for example - two), this atom represents " Siamese twins".
Save us, the Great God, of having such atoms, such children!
Each of us has an Electron, but we do not know it.
#
Many years ago man has accustomed some wild
animals (wolf, horse, cat, bull , etc.)
and has made them domestic ones.
But the man understands badly the four-footed friends.
In 1897 J. J. Thomson discovered new particle - electron.
Gradually man has accustomed electron to work for him.
But the man does not understand what an electron is.
By my peasant logic at first it is better to understand
the closest and simplest particle photon /electron and
then to study the  far away space and another particles.
==.
Best wishes.
Israel Sadovnik.  Socratus.
=…
P.S.
 Robert Milliken, who measured a charge of electron,
in his  Nobel speech ( 1923  ) told,  that he knew nothing
about the “last essence of electron”.
#
The verse: The world of electron.

But maybe these electrons are World,
where there are five continents:
the art,
 knowledge,
wars,
thrones
and the memory of forty centuries.
/ Valery Brusov./
===…


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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 09 Mar 2012, at 01:47, Stephen P. King wrote:


On 3/8/2012 1:43 PM, Bruno Marchal wrote:


On 07 Mar 2012, at 18:36, Pzomby wrote:

Yes, but even the symbols =, +, x, *, are notations that are
substitutes for words. Eg. Equals, addition or union,  
multiplication.

The operational notations are words used to describe the formulation
of the model.


Hmm... OK.
In logic they are symbol associated with axioms and rules, and they  
have (standard) semantics, for exemple the mathematical "meaning"  
of + is given by the set {(0,0,0) (0, 1, 1), (1,0, 1) (1,1,2)   
(6,7, 13), ..., (1, 23, 24), }.


I could not resist! So they are infinite after all!



Who ever doubt this? Comp is based on N, the phi_i and the W_i (most  
of which are infinite). Church thesis needs infinities, and the first  
person view on the (infinite) arithmetical reality is beyond the  
nameable infinities.


The confusion might come from the fact that those infinities are  
epistemological, but the epistemology does exist. Yet the ontology,  
although finitistic, is not ultrafinitistic and so needs too a  
potential omega.





Yes. Then it is Ok to use it for that.  eg. 1stness, 2ndness,  
3rdness

in sport races gives a quality of feeling to the participants,
observers/bettors.


OK. But I would say the "quality" of being the first is more in the  
mind of the machine winning the competition, or in the mind of the  
machines members of the jury, than in the ordering relation itself.


Are these not equivalent in the Platonic sense?


?



After all, we are considering universal machinery that ignores any  
kind of local gauge symmetry.


?













Are numbers (ordinal) necessarily qualitative descriptions?


Perhaps. In the comp frame, I prefer to ascribe the qualities of
numbers, by the possible computational relation that they have with
respect to their most probable universal environment. This is more
akin with the human conception of quality as being a lived  
experience.

But what you say might make sense in some other contexts.



It is the “lived experience” that is reality as I understand.


OK. That is the reality of subjective experience, but we can bet  
there is something independent of that reality, and which might be  
responsible for that reality.


It seems to me that any one that would bet against that "there  
is something independent of that reality" would be a sucker or a  
solipsist


OK.



or some superposition thereof! How does this tie into 1p  
indeterminancy?


What is the problem?











The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process.  eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001.  In nature: January in central Europe exudes certain
environmental qualitative conditions.


Once universal numbers are in relation with other one, many  
qualitative conditions can happen, assuming digital mechanism.


Wait a second, does not digital mechanism assume a fixed  
substitution level?


OK. What is the problem?











Numerals symbolize number position (as in particular instants in  
the

sequence of the continuum of time).


OK. But that's quantitative for me, or at least a "3p" type of  
notion.

Quality is more 1p, and can be handled at the meta-level by modal
logic, or by (often non standard) logics.

Bruno



Duration of time is quantitative.  Existing conditions in the  
duration

are qualitative.


I doubt this. I would bet that if time can be quantitative, and  
objectively measured by different observers, the duration notion is  
more qualitative, and subjective.


How can a "measure of change" be anything but quantitative?


What about change of mood, or change of taste?



Given that we are seriously considering that all of our 1p and 3p  
tropes are, literally, nothing more than numbers and relations  
between them, what else is there?


The machine 1p are (provably) not "number relations". They are  
qualitative modalities of relative number self-reference, related to  
non sharable truth that machines can be aware of. The physical reality  
has to be among them by the UD-Argument, except for a part of them  
being first person plural sharable.


The 1p are what the machine talk about when looking inward. That sorts  
of things have just no 3p description at all, neither number or  
anything 3-mathematical. They do have only 3p meta-logical accounts,  
like this very paragraph, but this should not be confused with what  
they are.













You state: “Quality is more 1p” but it is not exclusive to 1p.   
Humans

observe and have  empathy for others qualitative conditions and
states.


I agree.

It could be that "qualities" are just spectral ranging over  
local gauges... THink of how we can associate even an infinite field  
of continuous transformations with a single point using fiber  
bundles. I strongly suspect that this is exactly equivalent to

Re: Two Mathematicians in a Bunker and Existence of Pi

[Stephen P. King]

On 3/8/2012 1:43 PM, Bruno Marchal wrote:

On 07 Mar 2012, at 18:36, Pzomby wrote:




On Mar 7, 5:29 am, Bruno Marchal  wrote:





OK.
But it is not valid to infer from this, that mathematics is *about*
description.
On the contrary, mathematicians reason on "models" (realities,
structures), and they use description like all scientists.
mathematical logic is the science which study precisely the difference
between description (theories) and their interpretations (in from of
mathematical structure).
As you mention the notion of cardinal, a discovery here made by
logicians is that the notion of cardinal is relative. A set can have a
high cardinality in one model, and yet admit a bijection with N in
another model.



Yes, but even the symbols =, +, x, *, are notations that are
substitutes for words. Eg. Equals, addition or union, multiplication.
The operational notations are words used to describe the formulation
of the model.


Hmm... OK.
In logic they are symbol associated with axioms and rules, and they 
have (standard) semantics, for exemple the mathematical "meaning" of + 
is given by the set {(0,0,0) (0, 1, 1), (1,0, 1) (1,1,2)  (6,7, 
13), ..., (1, 23, 24), }.





Dear Bruno,

I could not resist! So they are infinite after all! Umm, where did 
I see the idea of representing things as equivalence classes... LOL! I 
wrote of that a while back... Whatever... My apologies, I am in a good 
mood and being my normal sarcastic self.










“In common usage, an ordinal number is an adjective which describes
the numerical position of an object, e.g., first, second, third,
etc.” http://mathworld.wolfram.com/OrdinalNumber.html



Are the “ordinal” numbers actually adjectives describing the
relational position in a sequence (first, second,…one-ness, two-ness
etc.)?


They can be used for that. But they can be much more than that.



Yes. Then it is Ok to use it for that.  eg. 1stness, 2ndness, 3rdness
in sport races gives a quality of feeling to the participants,
observers/bettors.


OK. But I would say the "quality" of being the first is more in the 
mind of the machine winning the competition, or in the mind of the 
machines members of the jury, than in the ordering relation itself.


Are these not equivalent in the Platonic sense? After all, we are 
considering universal machinery that ignores any kind of local gauge 
symmetry.











Are numbers (ordinal) necessarily qualitative descriptions?


Perhaps. In the comp frame, I prefer to ascribe the qualities of
numbers, by the possible computational relation that they have with
respect to their most probable universal environment. This is more
akin with the human conception of quality as being a lived experience.
But what you say might make sense in some other contexts.



It is the “lived experience” that is reality as I understand.


OK. That is the reality of subjective experience, but we can bet there 
is something independent of that reality, and which might be 
responsible for that reality.


It seems to me that any one that would bet against that "there is 
something independent of that reality" would be a sucker or a solipsist 
or some superposition thereof! How does this tie into 1p indeterminancy?







The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process.  eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001.  In nature: January in central Europe exudes certain
environmental qualitative conditions.


Once universal numbers are in relation with other one, many 
qualitative conditions can happen, assuming digital mechanism.


Wait a second, does not digital mechanism assume a fixed 
substitution level?











Numerals symbolize number position (as in particular instants in the
sequence of the continuum of time).


OK. But that's quantitative for me, or at least a "3p" type of notion.
Quality is more 1p, and can be handled at the meta-level by modal
logic, or by (often non standard) logics.

Bruno



Duration of time is quantitative.  Existing conditions in the duration
are qualitative.


I doubt this. I would bet that if time can be quantitative, and 
objectively measured by different observers, the duration notion is 
more qualitative, and subjective.


How can a "measure of change" be anything but quantitative? Given 
that we are seriously considering that all of our 1p and 3p tropes are, 
literally, nothing more than numbers and relations between them, what 
else is there?







You state: “Quality is more 1p” but it is not exclusive to 1p.  Humans
observe and have  empathy for others qualitative conditions and
states.


I agree.

It could be that "qualities" are just spectral ranging over local 
gauges... THink of how we can associate even an infinite field of 
continuous transformations with a single point using fiber bundles. I 
strongly suspect that this is exactly equivalent to "infinite 
computations runnin

Re: Two Mathematicians in a Bunker and Existence of Pi

[Craig Weinberg]

On Mar 8, 1:43 pm, Bruno Marchal  wrote:
> On 07 Mar 2012, at 18:36, Pzomby wrote:
> > You state: “Quality is more 1p” but it is not exclusive to 1p.  Humans
> > observe and have  empathy for others qualitative conditions and
> > states.

>I agree.

That's still only 1p shared. An inanimate object has no empathy for
others qualitative conditions, but it does respect their mass,
density, velocity, etc...quantitative (or anti-qualitative) qualities.

Craig

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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 07 Mar 2012, at 18:36, Pzomby wrote:




On Mar 7, 5:29 am, Bruno Marchal  wrote:





OK.
But it is not valid to infer from this, that mathematics is *about*
description.
On the contrary, mathematicians reason on "models" (realities,
structures), and they use description like all scientists.
mathematical logic is the science which study precisely the  
difference

between description (theories) and their interpretations (in from of
mathematical structure).
As you mention the notion of cardinal, a discovery here made by
logicians is that the notion of cardinal is relative. A set can  
have a

high cardinality in one model, and yet admit a bijection with N in
another model.



Yes, but even the symbols =, +, x, *, are notations that are
substitutes for words. Eg. Equals, addition or union, multiplication.
The operational notations are words used to describe the formulation
of the model.


Hmm... OK.
In logic they are symbol associated with axioms and rules, and they  
have (standard) semantics, for exemple the mathematical "meaning" of +  
is given by the set {(0,0,0) (0, 1, 1), (1,0, 1) (1,1,2)  (6,7,  
13), ..., (1, 23, 24), }.










“In common usage, an ordinal number is an adjective which describes
the numerical position of an object, e.g., first, second, third,
etc.”  http://mathworld.wolfram.com/OrdinalNumber.html



Are the “ordinal” numbers actually adjectives describing the
relational position in a sequence (first, second,…one-ness, two-ness
etc.)?


They can be used for that. But they can be much more than that.



Yes. Then it is Ok to use it for that.  eg. 1stness, 2ndness, 3rdness
in sport races gives a quality of feeling to the participants,
observers/bettors.


OK. But I would say the "quality" of being the first is more in the  
mind of the machine winning the competition, or in the mind of the  
machines members of the jury, than in the ordering relation itself.









Are numbers (ordinal) necessarily qualitative descriptions?


Perhaps. In the comp frame, I prefer to ascribe the qualities of
numbers, by the possible computational relation that they have with
respect to their most probable universal environment. This is more
akin with the human conception of quality as being a lived  
experience.

But what you say might make sense in some other contexts.



It is the “lived experience” that is reality as I understand.


OK. That is the reality of subjective experience, but we can bet there  
is something independent of that reality, and which might be  
responsible for that reality.





The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process.  eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001.  In nature: January in central Europe exudes certain
environmental qualitative conditions.


Once universal numbers are in relation with other one, many  
qualitative conditions can happen, assuming digital mechanism.









Numerals symbolize number position (as in particular instants in the
sequence of the continuum of time).


OK. But that's quantitative for me, or at least a "3p" type of  
notion.

Quality is more 1p, and can be handled at the meta-level by modal
logic, or by (often non standard) logics.

Bruno



Duration of time is quantitative.  Existing conditions in the duration
are qualitative.


I doubt this. I would bet that if time can be quantitative, and  
objectively measured by different observers, the duration notion is  
more qualitative, and subjective.





You state: “Quality is more 1p” but it is not exclusive to 1p.  Humans
observe and have  empathy for others qualitative conditions and
states.


I agree.

Bruno


http://iridia.ulb.ac.be/~marchal/


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Re: Two Mathematicians in a Bunker and Existence of Pi

[Pzomby]

On Mar 7, 5:29 am, Bruno Marchal  wrote:
> On 06 Mar 2012, at 20:44, Pzomby wrote:
>

>
> > On Mar 6, 10:14 am, Bruno Marchal  wrote:
> >> On 06 Mar 2012, at 17:32, meekerdb wrote:
>
> >>> On 3/6/2012 4:26 AM, Bruno Marchal wrote:
>
> > It's a language game.
>
>  The word "game" is so fuzzy that this says nothing at all. Game
>  theory is a branch of mathematics.
>
> >>> But "language" says something.  It says mathematics is about
> >>> description.
>
> >> Mathematicians search what is language independent, and description
> >> independent. They don't like when a result depends on the choice of a
> >> base. Mathematics is more about structures and laws.
>
> >> Math uses languages, but is not a language, even if it can be used as
> >> such in physics. But there is more to that.
>
> > Bruno:
>
> > “Cardinal” numbers with values appear to necessarily use language to
> > describe the unit being measured or quantified (tons, kilos, etc.)?
> > Quantitative description.
>
> OK.
> But it is not valid to infer from this, that mathematics is *about*
> description.
> On the contrary, mathematicians reason on "models" (realities,
> structures), and they use description like all scientists.
> mathematical logic is the science which study precisely the difference
> between description (theories) and their interpretations (in from of
> mathematical structure).
> As you mention the notion of cardinal, a discovery here made by
> logicians is that the notion of cardinal is relative. A set can have a
> high cardinality in one model, and yet admit a bijection with N in
> another model.
>
>
Yes, but even the symbols =, +, x, *, are notations that are
substitutes for words. Eg. Equals, addition or union, multiplication.
The operational notations are words used to describe the formulation
of the model.


>
> > “In common usage, an ordinal number is an adjective which describes
> > the numerical position of an object, e.g., first, second, third,
> > etc.”  http://mathworld.wolfram.com/OrdinalNumber.html
>
> > Are the “ordinal” numbers actually adjectives describing the
> > relational position in a sequence (first, second,…one-ness, two-ness
> > etc.)?
>
> They can be used for that. But they can be much more than that.


Yes. Then it is Ok to use it for that.  eg. 1stness, 2ndness, 3rdness
in sport races gives a quality of feeling to the participants,
observers/bettors.


>
> > Are numbers (ordinal) necessarily qualitative descriptions?
>
> Perhaps. In the comp frame, I prefer to ascribe the qualities of
> numbers, by the possible computational relation that they have with
> respect to their most probable universal environment. This is more
> akin with the human conception of quality as being a lived experience.
> But what you say might make sense in some other contexts.


It is the “lived experience” that is reality as I understand.

The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process.  eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001.  In nature: January in central Europe exudes certain
environmental qualitative conditions.

>
> > Numerals symbolize number position (as in particular instants in the
> > sequence of the continuum of time).
>
> OK. But that's quantitative for me, or at least a "3p" type of notion.
> Quality is more 1p, and can be handled at the meta-level by modal
> logic, or by (often non standard) logics.
>
> Bruno


Duration of time is quantitative.  Existing conditions in the duration
are qualitative.

You state: “Quality is more 1p” but it is not exclusive to 1p.  Humans
observe and have  empathy for others qualitative conditions and
states.

Pz

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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 07 Mar 2012, at 16:34, Stephen P. King wrote:




I am trying to be consistent and agree with your explanations  
but it is difficult. It is not your fault, our natural languages are  
biased inherently toward certain modalities of thinking to the  
exclusion of others. I was commenting on your wording, semantics.


OK.






If matter is an appearance (and not a substance), does this not  
allow a form of "mind acting on matter"?

[BM]
In a large sense of that expression.


[SPK]
OK, then does this not contradict what you wrote: " Indeed  
Matter, but matter only, is what the mind cannot act on." I am  
trying to understand what you where thinking... I think of matter in  
terms of its best representation "that whose behavior is best  
computationally emulated only by itself" - following S. Wolfram's  
reasoning - it has a fixed point property in this way, but it is not  
the same fixed point as that of Kleene, it is the fixed point of  
Brouwer. It is "topological", not "logical". The relation between  
them is the main feature or 'kernel" of the process dual aspect  
monism that I advocate.


I still don't know what is your theory. Also the set theoretic  
semantic of the S4 modal logic is toplogical, so it is not necessary  
to oppose logic and topology, especially in context having non  
classical meta logics, like with the intensional variant of self- 
reference.








One only need to consider that the selection process whereby the  
"next" state in time of a configuration of matter is done by a  
computation.

[BM]
This does not really work. matter is a question of observable, by  
machine, and the way you talk leads to the digital physics  
confusion, with the idea that matter is generated by programs, when  
matter is seen by programs, due to the first person indeterminacy,  
which bears on infinities of computations, not just one. They might  
be a winner program, but that's an open problem in the comp theory.


[SPK]
I am accepting as true the conjecture that there is no "winner  
program" in any kind of global sense, there are only local optimal  
winners.


It is an open problem in comp. Empirically, we might say that there  
are evidence for universal quantum dovetailing, perhaps even made by  
the "music of he primes", given the bizarre behavior of the zeta  
functions, whose non trivial zero seems to emulate a form of quantum  
chaotic repulsion, which to my knowledge might be a candidate for  
quantum dovetailing. I don't know.





In this way I do not suffer from the measure problem.


But comp reduce the "belief in matter" to the measure problem. By not  
having the "problem of matter", you miss the needed solution of it  
which would justify the quanta and the qualia when we assume  
computationalism.




The local optimal winner idea is the same as a "Strategy" that tends  
to an equilibrium. My reasoning follows the same reasoning of what  
occurs in the question of whether hypergames are finite or not.





A real example of this idea is implemented in the generation  
of  MMORPG games that are very popular. Consider the Bostrom-like  
question: Since we cannot prove that our physical reality is not a  
MMORPG virtual world, should we not bet that it actually is?

[BM]
?


[SPK]
Have you seen any virtual reality generating programs and  
studied how they deal with concurrency problems? Do you understand  
the concurrency problem?



Sure. I told you that the best work on that, imo, are the work of  
Abramski, and Girard, Duncan, etc.
I already explained that we might use that some day. Sure. It is very  
interesting. But to get both the qualia and the quanta, such logics  
need to be extracted from self-reference.




It is basically that computations cannot effectively solve resource  
allocation problems. You might be blind to this because of your  
Platonist interpretation of computation and mathematics in  
general... :-(


You could as well say that comp is blind on black holes, because we  
have not yet derived their existence from comp. It makes no sense.






Comp precisely entails that we are in infinities of "video games".  
So we can test if we are at the level zero, or if we  are  
simulated, just by comparing the physics then being infinity of  
games, which is unique and well  defined (the Z and X logics, and  
their higher order extension) with what we observe.


[SPK]
This is inherently difficult because we can only access finite  
computational resources to do that test in the physical world and  
the test requires infinite repetition to yield non-trivial results.  
This is the measure problem all over again!


It can't be the same measure problem, given that "physics" has to be  
the solution of the measure problem.



Do you see how the test by falsification is almost impossible and  
thus your thesis that COMP is falsifiable is very easy to argue  
against with weak arguments?


Then such arguments should be used as a clue

Re: Two Mathematicians in a Bunker and Existence of Pi

[Stephen P. King]

On 3/7/2012 8:18 AM, Bruno Marchal wrote:


On 06 Mar 2012, at 19:43, Stephen P. King wrote:


On 3/6/2012 12:52 PM, Bruno Marchal wrote:


On 06 Mar 2012, at 17:53, meekerdb wrote:


On 3/6/2012 5:54 AM, Bruno Marchal wrote:
That specific retrodiction came from Bruno's hypothesis which is 
that universes are generated by computation.  What is computable 
is much less than all mathematics.


This is not my hypothesis. It might be Fredkin or Schmidhuber 
hypothesis, but not mine. My hypothesis is the hypothesis that "I 
am a machine", which is ambiguous, so I put it in the form of "yes 
doctor", which means that there exist a level such that my 
consciousness remains unchanged for a digital functional 
substitution done at that level.


And then the reasoning shows that the physical universe(s), are 
not generated by any computation. Computations generated my 
consciousness, and the physical universe is what my consciousness 
can predict from the mixing of determinacy and 1-indterminacy in 
the UD* (or sigma_1 part of arithmetic).


If I had written universes are indirectly generated by computation, 
would that have reflected your view?


Better.
But the presence of the word "generated" might still lead to 
confusion in this setting. Universe(s) are only observed, It is, or 
they are the 'natural solution' of the comp diophantine measure 
problem, which bear on the first person.




The only catch I see is that you wrote "can predict" instead of 
"must predict".  Are you allowing for some agency here?  m
I allow for agency, but not at that level. Indeed Matter, but matter 
only, is what the mind cannot act on. But the mind can act on the 
mind, and agency emerges at higher levels.


Dear Bruno,

Why does it seem that you are tacitly accepting the definition of 
matter as a "substance" as Descartes did in his substance dualism?

[BM]
I precisely don't do that. That's when I use the word "primitive 
matter" for the aristotelian conception of matter, which is more 
primary than substantial, but is still primary.


Dear Bruno,

I am trying to be consistent and agree with your explanations but 
it is difficult. It is not your fault, our natural languages are biased 
inherently toward certain modalities of thinking to the exclusion of 
others. I was commenting on your wording, semantics.





If matter is an appearance (and not a substance), does this not allow 
a form of "mind acting on matter"?

[BM]
In a large sense of that expression.


[SPK]
OK, then does this not contradict what you wrote: " Indeed Matter, 
but matter only, is what the mind cannot act on." I am trying to 
understand what you where thinking... I think of matter in terms of its 
best representation "that whose behavior is best computationally 
emulated only by itself" - following S. Wolfram's reasoning - it has a 
fixed point property in this way, but it is not the same fixed point as 
that of Kleene, it is the fixed point of Brouwer. It is "topological", 
not "logical". The relation between them is the main feature or 'kernel" 
of the process dual aspect monism that I advocate.




One only need to consider that the selection process whereby the 
"next" state in time of a configuration of matter is done by a 
computation.

[BM]
This does not really work. matter is a question of observable, by 
machine, and the way you talk leads to the digital physics confusion, 
with the idea that matter is generated by programs, when matter is 
seen by programs, due to the first person indeterminacy, which bears 
on infinities of computations, not just one. They might be a winner 
program, but that's an open problem in the comp theory.


[SPK]
I am accepting as true the conjecture that there is no "winner 
program" in any kind of global sense, there are only local optimal 
winners. In this way I do not suffer from the measure problem. The local 
optimal winner idea is the same as a "Strategy 
" that tends to 
an equilibrium . My 
reasoning follows the same reasoning of what occurs in the question of 
whether hypergames are finite or not.





A real example of this idea is implemented in the generation of 
MMORPG games 
 
that are very popular. Consider the Bostrom-like 
 question: Since 
we cannot prove that our physical reality is not a MMORPG virtual 
world, should we not bet that it actually is?

[BM]
?


[SPK]
Have you seen any virtual reality generating programs and studied 
how they deal with concurrency problems? Do you understand the 
concurrency problem? It is basically that computations cannot 
effectively solve resource allocation problems. You might be blind to 
this because of your Platonist interpretation of computation and 
mathematics in general... :-(


Comp precise

Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 06 Mar 2012, at 20:44, Pzomby wrote:




On Mar 6, 10:14 am, Bruno Marchal  wrote:

On 06 Mar 2012, at 17:32, meekerdb wrote:


On 3/6/2012 4:26 AM, Bruno Marchal wrote:



It's a language game.



The word "game" is so fuzzy that this says nothing at all. Game
theory is a branch of mathematics.



But "language" says something.  It says mathematics is about
description.


Mathematicians search what is language independent, and description
independent. They don't like when a result depends on the choice of a
base. Mathematics is more about structures and laws.

Math uses languages, but is not a language, even if it can be used as
such in physics. But there is more to that.


Bruno:

“Cardinal” numbers with values appear to necessarily use language to
describe the unit being measured or quantified (tons, kilos, etc.)?
Quantitative description.


OK.
But it is not valid to infer from this, that mathematics is *about*  
description.
On the contrary, mathematicians reason on "models" (realities,  
structures), and they use description like all scientists.
mathematical logic is the science which study precisely the difference  
between description (theories) and their interpretations (in from of  
mathematical structure).
As you mention the notion of cardinal, a discovery here made by  
logicians is that the notion of cardinal is relative. A set can have a  
high cardinality in one model, and yet admit a bijection with N in  
another model.






“In common usage, an ordinal number is an adjective which describes
the numerical position of an object, e.g., first, second, third,
etc.”  http://mathworld.wolfram.com/OrdinalNumber.html

Are the “ordinal” numbers actually adjectives describing the
relational position in a sequence (first, second,…one-ness, two-ness
etc.)?


They can be used for that. But they can be much more than that.




Are numbers (ordinal) necessarily qualitative descriptions?


Perhaps. In the comp frame, I prefer to ascribe the qualities of  
numbers, by the possible computational relation that they have with  
respect to their most probable universal environment. This is more  
akin with the human conception of quality as being a lived experience.  
But what you say might make sense in some other contexts.





Numerals symbolize number position (as in particular instants in the
sequence of the continuum of time).


OK. But that's quantitative for me, or at least a "3p" type of notion.  
Quality is more 1p, and can be handled at the meta-level by modal  
logic, or by (often non standard) logics.


Bruno


http://iridia.ulb.ac.be/~marchal/



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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 06 Mar 2012, at 19:43, Stephen P. King wrote:


On 3/6/2012 12:52 PM, Bruno Marchal wrote:



On 06 Mar 2012, at 17:53, meekerdb wrote:


On 3/6/2012 5:54 AM, Bruno Marchal wrote:


That specific retrodiction came from Bruno's hypothesis which is  
that universes are generated by computation.  What is computable  
is much less than all mathematics.


This is not my hypothesis. It might be Fredkin or Schmidhuber  
hypothesis, but not mine. My hypothesis is the hypothesis that "I  
am a machine", which is ambiguous, so I put it in the form of  
"yes doctor", which means that there exist a level such that my  
consciousness remains unchanged for a digital functional  
substitution done at that level.


And then the reasoning shows that the physical universe(s), are  
not generated by any computation. Computations generated my  
consciousness, and the physical universe is what my consciousness  
can predictfrom the mixing of determinacy and 1- 
indterminacy in the UD* (or sigma_1 part of arithmetic).


If I had written universes are indirectly generated by  
computation, would that have reflected your view?


Better.
But the presence of the word "generated" might still lead to  
confusion in this setting. Universe(s) are only observed, It is, or  
they are the 'natural solution' of the comp diophantine measure  
problem, which bear on the first person.




The only catch I see is that you wrote "can predict" instead of  
"must predict".  Are you allowing for some agency here?  m
I allow for agency, but not at that level. Indeed Matter, but  
matter only, is what the mind cannot act on. But the mind can act  
on the mind, and agency emerges at higher levels.


Dear Bruno,

Why does it seem that you are tacitly accepting the definition  
of matter as a "substance" as Descartes did in his substance dualism?


I precisely don't do that. That's when I use the word "primitive  
matter" for the aristotelian conception of matter, which is more  
primary than substantial, but is still primary.



If matter is an appearance (and not a substance), does this not  
allow a form of "mind acting on matter"?


In a large sense of that expression.



One only need to consider that the selection process whereby the  
"next" state in time of a configuration of matter is done by a  
computation.


This does not really work. matter is a question of observable, by  
machine, and the way you talk leads to the digital physics confusion,  
with the idea that matter is generated by programs, when matter is  
seen by programs, due to the first person indeterminacy, which bears  
on infinities of computations, not just one. They might be a winner  
program, but that's an open problem in the comp theory.




A real example of this idea is implemented in the generation of   
MMORPG games that are very popular. Consider the Bostrom-like  
question: Since we cannot prove that our physical reality is not a  
MMORPG virtual world, should we not bet that it actually is?


?

Comp precisely entails that we are in infinities of "video games". So  
we can test if we are at the level zero, or if we are simulated, just  
by comparing the physics hen being infinity of games, which is unique  
and well  defined (the Z and X logics, and their higher order  
extension) with what we observe.




One test for this question is to consider the upper bounds on the  
ability to detect differences in features at smaller and smaller  
scales. If, for example, space-time is "granular" then this would  
almost certainly prove that our physical world is isomorphic to a  
MMORPG.


The contrary. Comp a priori makes matter into a continuum. You  
confuse, like many, comp and digital physics.




This idea would be compatible with COMP if we can identify the  
"players of the MMORPG"  with the individual Löbian machines.
Given that some very resent observations of ultra-high energy  
gamma photons indicate that space-time is not granular, we need a  
more sophisticated theory to get the idea to work.


Not at all. Comp implies high plausibility of the existence of a  
physical continuum, given that physics becomes an infinite sum of  
infinite computations, including infinite dovetailing on infinities of  
fields, including the reals. You are not yet taking into account the  
role of the first person indeterminacy in the translation of the comp  
body problem into a measure problem on the whole UD*, I think.






No. The reason why "my consciousness" can predict, as opposed to  
"must predict", is the first person indeterminacy. It is the fact  
that I cannot know which machine I am, nor which computations  
executes the relevant states.


We can have partial information set, like, assuming bla-bla-bla, if  
I am duplicate in {W, M}, I will feel to be in M or in W. That is  
disjuncts. But by UDA-(step 8 included), I have to say at each  
instant I will be in u1, u2, u3, u4, ... that is the infinite  
sequence of programs generating 

Re: Two Mathematicians in a Bunker and Existence of Pi

[Pzomby]

On Mar 6, 10:14 am, Bruno Marchal  wrote:
> On 06 Mar 2012, at 17:32, meekerdb wrote:
>
> > On 3/6/2012 4:26 AM, Bruno Marchal wrote:
>
> >>> It's a language game.
>
> >> The word "game" is so fuzzy that this says nothing at all. Game
> >> theory is a branch of mathematics.
>
> > But "language" says something.  It says mathematics is about
> > description.
>
> Mathematicians search what is language independent, and description
> independent. They don't like when a result depends on the choice of a
> base. Mathematics is more about structures and laws.
>
> Math uses languages, but is not a language, even if it can be used as
> such in physics. But there is more to that.

Bruno:

“Cardinal” numbers with values appear to necessarily use language to
describe the unit being measured or quantified (tons, kilos, etc.)?
Quantitative description.

“In common usage, an ordinal number is an adjective which describes
the numerical position of an object, e.g., first, second, third,
etc.”  http://mathworld.wolfram.com/OrdinalNumber.html

Are the “ordinal” numbers actually adjectives describing the
relational position in a sequence (first, second,…one-ness, two-ness
etc.)?  Are numbers (ordinal) necessarily qualitative descriptions?
Numerals symbolize number position (as in particular instants in the
sequence of the continuum of time).

Thanks

>
> Are you agnostic about the question if reality is physical, or
> mathematical, or theological or ?. To say that math is on description
> seem a bit physicalist.
>
> Comp makes the tiny sigma_1 segment of arithmetic rather fundamental.
> We don't (nor can need) more "reality" than that, for this is from
> inside (epistemologically, ...)  *very* big, and structured. It is far
> bigger from inside than from outside.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/

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Re: Two Mathematicians in a Bunker and Existence of Pi

[Stephen P. King]

On 3/6/2012 12:52 PM, Bruno Marchal wrote:


On 06 Mar 2012, at 17:53, meekerdb wrote:


On 3/6/2012 5:54 AM, Bruno Marchal wrote:
That specific retrodiction came from Bruno's hypothesis which is 
that universes are generated by computation.  What is computable is 
much less than all mathematics.


This is not my hypothesis. It might be Fredkin or Schmidhuber 
hypothesis, but not mine. My hypothesis is the hypothesis that "I am 
a machine", which is ambiguous, so I put it in the form of "yes 
doctor", which means that there exist a level such that my 
consciousness remains unchanged for a digital functional 
substitution done at that level.


And then the reasoning shows that the physical universe(s), are not 
generated by any computation. Computations generated my 
consciousness, and the physical universe is what my consciousness 
can predict from the mixing of determinacy and 1-indterminacy in the 
UD* (or sigma_1 part of arithmetic).


If I had written universes are indirectly generated by computation, 
would that have reflected your view?


Better.
But the presence of the word "generated" might still lead to confusion 
in this setting. Universe(s) are only observed, It is, or they are the 
'natural solution' of the comp diophantine measure problem, which bear 
on the first person.




The only catch I see is that you wrote "can predict" instead of "must 
predict".  Are you allowing for some agency here?  m
I allow for agency, but not at that level. Indeed Matter, but matter 
only, is what the mind cannot act on. But the mind can act on the 
mind, and agency emerges at higher levels.


Dear Bruno,

Why does it seem that you are tacitly accepting the definition of 
matter as a "substance" as Descartes did in his substance dualism? If 
matter is an appearance (and not a substance), does this not allow a 
form of "mind acting on matter"? One only need to consider that the 
selection process whereby the "next" state in time of a configuration of 
matter is done by a computation.
A real example of this idea is implemented in the generation of 
MMORPG games 
 
that are very popular. Consider the Bostrom-like 
 question: Since we 
cannot prove that our physical reality is not a MMORPG virtual world, 
should we not bet that it actually is? One test for this question is to 
consider the upper bounds on the ability to detect differences in 
features at smaller and smaller scales. If, for example, space-time is 
"granular" then this would almost certainly prove that our physical 
world is isomorphic to a MMORPG. This idea would be compatible with COMP 
if we can identify the "players of the MMORPG"  with the individual 
Löbian machines.
Given that some very resent observations of ultra-high energy gamma 
photons indicate that space-time is not granular, we need a more 
sophisticated theory to get the idea to work.


No. The reason why "my consciousness" can predict, as opposed to "must 
predict", is the first person indeterminacy. It is the fact that I 
cannot know which machine I am, nor which computations executes the 
relevant states.


We can have partial information set, like, assuming bla-bla-bla, if I 
am duplicate in {W, M}, I will feel to be in M or in W. That is 
disjuncts. But by UDA-(step 8 included), I have to say at each instant 
I will be in u1, u2, u3, u4, ... that is the infinite sequence of 
programs generating my current state. They all compete in the measure, 
and "we" can only see the result of that from inside. Here the 1p and 
its invariance for the delays explains that such "results" never 
appear in the UD, but is on the border of UD*.


Does not first person indeterminacy also occur in any kind of 
displacement of relative position, no matter how small that displacement 
might be? But we have to consider more than one kind of change. We have 
to consider relative changes for all possible observables such that 
thecanonical conjugate rule 
 is preserved.


Onward!

Stephen

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Re: Two Mathematicians in a Bunker and Existence of Pi

[Craig Weinberg]

On Mar 6, 7:07 am, Evgenii Rudnyi  wrote:
> Craig,
>
> The danger to society comes not from mathematicians, rather it could
> come from technologists.

Yes. I don't think the problem is with mathematicians, it's with
hospital administrators, insurance companies, investment banks,
attorneys, judges, governments, etc who feel compelled to apply
mathematical-seeming solutions to all human problems.

> Recently I have read
>
> Jaron Lanier, You Are Not a Gadget: A Manifesto

I saw that too. It's good to see him back around.

>
> and the author shows that the society should pay more attention to what
> Silicon Valley geeks are silently doing. Just one quote
>
> "Ideals are important in the world of technology, but the mechanism by
> which ideals influence events is different than in other spheres of
> life. Technologists don't use persuasion to influence you - or, at
> least, we don't do it very well. There are a few master communicators
> among us (like Steve Jobs), but for the most part we aren't particularly
> seductive."
>
> "We make up extensions to your being, like remote eyes and ears
> (web-cams and mobile phones) and expanded memory (the world of details
> you can search for online). These become the structures by which you
> connect to the world and other people. These structures in turn can
> change how you conceive of yourself and the world. We tinker with your
> philosophy by direct manipulation of your cognitive experience, not
> indirectly, through argument. It takes only a tiny group of engineers to
> create technology that can shape the entire future of human experience
> with incredible speed. Therefore, crucial arguments about the human
> relationship with technology should take place between developers and
> users before such direct manipulations are designed. This book is about
> those arguments."
>
> As for sensations, I do not know. Yesterday after I have read your
> email, I went to an Italian restaurant. A small dinner, actually I
> wanted just a glass of good red Italian wine, but then I took also a
> small plate of cheese assorti with a couple of salad leaves, pepperoni
> and bread. I have enjoyed my dinner. Whether wine, bread, cheese, salad
> and pepperoni have enjoyed it too, I do not know. I would not mind, if
> they did.

Hehe. It is hard to imagine that there are experiences going on in the
wine and cheese, but really, not much more than it is hard to imagine
billions of organisms and molecules being there instead of what we
think we see and taste. Not sure whether the bread knows the
difference between being on a plate or in a stomach, but I have less
of a problem imagining that the cells of our tongue and stomach are
sharing a bit of celebratory feelings with our brain at having eaten
them

Craig.

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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 06 Mar 2012, at 17:32, meekerdb wrote:


On 3/6/2012 4:26 AM, Bruno Marchal wrote:



It's a language game.


The word "game" is so fuzzy that this says nothing at all. Game  
theory is a branch of mathematics.


But "language" says something.  It says mathematics is about  
description.


Mathematicians search what is language independent, and description  
independent. They don't like when a result depends on the choice of a  
base. Mathematics is more about structures and laws.


Math uses languages, but is not a language, even if it can be used as  
such in physics. But there is more to that.


Are you agnostic about the question if reality is physical, or  
mathematical, or theological or ?. To say that math is on description  
seem a bit physicalist.


Comp makes the tiny sigma_1 segment of arithmetic rather fundamental.  
We don't (nor can need) more "reality" than that, for this is from  
inside (epistemologically, ...)  *very* big, and structured. It is far  
bigger from inside than from outside.


Bruno



http://iridia.ulb.ac.be/~marchal/



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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 06 Mar 2012, at 17:53, meekerdb wrote:


On 3/6/2012 5:54 AM, Bruno Marchal wrote:


That specific retrodiction came from Bruno's hypothesis which is  
that universes are generated by computation.  What is computable  
is much less than all mathematics.


This is not my hypothesis. It might be Fredkin or Schmidhuber  
hypothesis, but not mine. My hypothesis is the hypothesis that "I  
am a machine", which is ambiguous, so I put it in the form of "yes  
doctor", which means that there exist a level such that my  
consciousness remains unchanged for a digital functional  
substitution done at that level.


And then the reasoning shows that the physical universe(s), are not  
generated by any computation. Computations generated my  
consciousness, and the physical universe is what my consciousness  
can predict from the mixing of determinacy and 1-indterminacy in  
the UD* (or sigma_1 part of arithmetic).


If I had written universes are indirectly generated by computation,  
would that have reflected your view?


Better.
But the presence of the word "generated" might still lead to confusion  
in this setting. Universe(s) are only observed, It is, or they are the  
'natural solution' of the comp diophantine measure problem, which bear  
on the first person.




The only catch I see is that you wrote "can predict" instead of  
"must predict".  Are you allowing for some agency here?  m
I allow for agency, but not at that level. Indeed Matter, but matter  
only, is what the mind cannot act on. But the mind can act on the  
mind, and agency emerges at higher levels.
No. The reason why "my consciousness" can predict, as opposed to "must  
predict", is the first person indeterminacy. It is the fact that I  
cannot know which machine I am, nor which computations executes the  
relevant states.


We can have partial information set, like, assuming bla-bla-bla, if I  
am duplicate in {W, M}, I will feel to be in M or in W. That is  
disjuncts. But by UDA-(step 8 included), I have to say at each instant  
I will be in u1, u2, u3, u4, ... that is the infinite sequence of  
programs generating my current state. They all compete in the measure,  
and "we" can only see the result of that from inside. Here the 1p and  
its invariance for the delays explains that such "results" never  
appear in the UD, but is on the border of UD*.


Bruno


http://iridia.ulb.ac.be/~marchal/



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Re: Two Mathematicians in a Bunker and Existence of Pi

[meekerdb]

On 3/6/2012 5:54 AM, Bruno Marchal wrote:
That specific retrodiction came from Bruno's hypothesis which is that universes are 
generated by computation.  What is computable is much less than all mathematics.


This is not my hypothesis. It might be Fredkin or Schmidhuber hypothesis, but not mine. 
My hypothesis is the hypothesis that "I am a machine", which is ambiguous, so I put it 
in the form of "yes doctor", which means that there exist a level such that my 
consciousness remains unchanged for a digital functional substitution done at that level.


And then the reasoning shows that the physical universe(s), are not generated by any 
computation. Computations generated my consciousness, and the physical universe is what 
my consciousness can predict from the mixing of determinacy and 1-indterminacy in the 
UD* (or sigma_1 part of arithmetic).


If I had written universes are indirectly generated by computation, would that have 
reflected your view?  The only catch I see is that you wrote "can predict" instead of 
"must predict".  Are you allowing for some agency here?


Brent

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Re: Two Mathematicians in a Bunker and Existence of Pi

[meekerdb]

On 3/6/2012 4:26 AM, Bruno Marchal wrote:

It's a language game.


The word "game" is so fuzzy that this says nothing at all. Game theory is a branch of 
mathematics.


But "language" says something.  It says mathematics is about description.

Brent

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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 06 Mar 2012, at 16:40, Evgenii Rudnyi wrote:


On 06.03.2012 14:21 Bruno Marchal said the following:


On 06 Mar 2012, at 12:22, Evgenii Rudnyi wrote:


Stephen,

The life is full of paradoxes. My point was that while philosophers
cannot solve apparently simple problems (well, these problems happen
not to be simple), engineers continue doing their business
successfully. How they do it? I believe, exactly this way, they  
try to

understand what they do not know. Then they make trials, run tests,
etc. and finally with some luck we get a new technology. Whether the
theory of everything exists or not, happens not be essential for the
success in engineering. I do not know why.

Right now I am at the end of Beweistheorien (Proof Theories) by Prof
Hoenen

http://www.podcasts.uni-freiburg.de/podcast_content?id_content=24

At the end of his course, he considers the ontological arguments  
where

the goal was to proof existence from pure logic.


This is weird. Since the failure of Whitehead and Russell, it is
admitted that we cannot prove existence, even of the number zero,  
from

logic alone.



I have meant the history of such an attempt. It is interesting to  
learn how people have tried it and in what context. It was new for me.


OK.






A pretty interesting attempt. Still there is a huge gap between  
logic

and existence and it seems that engineers successfully fills it. Ask
them, how they do it.


This is weirder. Engineers prove that things exist, in theory which
assume that some things exist. That is not different than proving the
existence of prime or universal number or relation, from the  
assumption
of the existence of the numbers. It is always relative proof of  
existence.


Strictly speaking you are right. What I wanted to say is that  
engineers do not care about this but this does not prevent them from  
doing useful things. So in a way it is working.



OK, but be careful not to become an instrumentalist, which, to be  
short, defines roughly truth by useful.


The problem is that the notion of useful is subject dependent. In that  
sense, a proposition like "cannabis is dangerous" might be decided to  
be true, because it will work very well for a (large) category of  
persons (like pharmaceutical lobbies, jail lobbies, textile lobbies,  
steel lobbies, wood based paper lobbies, the underground untaxed  
economy, the children (who will find it everywhere and will not need  
to show the ID).


Lies work very well, for some term, for some people, but it can deform  
truth, if that exists, and led science and eventually everyone go  
astray. Instrumentalism leads to manipulism, or gangsterism. It leads  
to the confusion between truth and power.


Bruno


http://iridia.ulb.ac.be/~marchal/



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Re: Two Mathematicians in a Bunker and Existence of Pi

[Evgenii Rudnyi]

On 06.03.2012 14:21 Bruno Marchal said the following:


On 06 Mar 2012, at 12:22, Evgenii Rudnyi wrote:


Stephen,

The life is full of paradoxes. My point was that while philosophers
cannot solve apparently simple problems (well, these problems happen
not to be simple), engineers continue doing their business
successfully. How they do it? I believe, exactly this way, they try to
understand what they do not know. Then they make trials, run tests,
etc. and finally with some luck we get a new technology. Whether the
theory of everything exists or not, happens not be essential for the
success in engineering. I do not know why.

Right now I am at the end of Beweistheorien (Proof Theories) by Prof
Hoenen

http://www.podcasts.uni-freiburg.de/podcast_content?id_content=24

At the end of his course, he considers the ontological arguments where
the goal was to proof existence from pure logic.


This is weird. Since the failure of Whitehead and Russell, it is
admitted that we cannot prove existence, even of the number zero, from
logic alone.



I have meant the history of such an attempt. It is interesting to learn 
how people have tried it and in what context. It was new for me.





A pretty interesting attempt. Still there is a huge gap between logic
and existence and it seems that engineers successfully fills it. Ask
them, how they do it.


This is weirder. Engineers prove that things exist, in theory which
assume that some things exist. That is not different than proving the
existence of prime or universal number or relation, from the assumption
of the existence of the numbers. It is always relative proof of existence.


Strictly speaking you are right. What I wanted to say is that engineers 
do not care about this but this does not prevent them from doing useful 
things. So in a way it is working.


Evgenii


Bruno




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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 06 Mar 2012, at 05:42, meekerdb wrote:


On 3/5/2012 8:28 PM, Jason Resch wrote:




On Mon, Mar 5, 2012 at 7:24 PM, meekerdb   
wrote:

On 3/5/2012 4:57 PM, Jason Resch wrote:




On Mon, Mar 5, 2012 at 12:26 PM, meekerdb   
wrote:

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.

When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to  
the

diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will  
think it over.


However, I do not completely understand you. How the geometry of  
physical space in which mathematicians reside influences the  
definition of Pi? Mathematicians will consider just Euclidean  
geometry, that's it. In my view, whether the physical space  
Euclidean or not, does not influence the work of mathematicians.


Exactly. Hence mathematics =/= reality.

This is like comparing the kidney of a whale to a liver of a  
whale, and deciding whale=/=whale.  You can't compare one limited  
subset of the whole (such as the local part of this universe) with  
another subset of the whole (euclidean geometry), and decide that  
the whole (of mathematics) is different from the whole (of reality).


The same mathematicians in the same place could 'prove the  
existence' of the meeting point of parallel lines or that through a  
point there is more than one line parallel to a given line.  So no  
matter what they measure in their bunker it will be consistent with  
one or the other.  So you can only hold that mathematics=reality if  
you assume everything not self-contradictory exists in reality;


Okay.

but that was what the bunker thought experiment was intended to test.

I fail to see how the bunker experiment tests this.  The bunker  
experiment seems to assume that mathematical reality is or depends  
upon a physical representation.


You've essentially made it untestable by saying, well it may fail  
HERE but somewhere (Platonia?) it's really true.


People used to say Darwin's theory was untestable, because  
evolution was such a slow process they thought it could never be  
observed.  Some on this list have argued that the hypothesis has  
already survived one test: the unpredictability in quantum mechanics.


That specific retrodiction came from Bruno's hypothesis which is  
that universes are generated by computation.  What is computable is  
much less than all mathematics.


This is not my hypothesis. It might be Fredkin or Schmidhuber  
hypothesis, but not mine. My hypothesis is the hypothesis that "I am a  
machine", which is ambiguous, so I put it in the form of "yes doctor",  
which means that there exist a level such that my consciousness  
remains unchanged for a digital functional substitution done at that  
level.


And then the reasoning shows that the physical universe(s), are not  
generated by any computation. Computations generated my consciousness,  
and the physical universe is what my consciousness can predict from  
the mixing of determinacy and 1-indterminacy in the UD* (or sigma_1  
part of arithmetic).







If instead we found our environment and observations of it to be  
perfectly deterministic, this would have ruled out   
mechanism+a single or finite universe.  Further, there is a growing  
collection of evidence that in most universes, conscious life is  
impossible.


There's a popular idea that most possible universes are inhospitable  
to conscious life: a theory that might well be false under Bruno's  
hypothesis in which consciousness and universes are both realized by  
computation.


Not really. Only consciousness (although there are instant  
consciousness: each conscious interval might interfere with the result  
of the indeterminacy, and in case the level is very low, that might  
play a role in the qualia).




In any case it doesn't warrant the conclusion that all possible  
universes exist.


Well, it might be simpler to say that comp entails the non existence,  
and even the non sense of any ontologically primary physical universe.
For a comp believer, physical universe is a failed hypothesis. It does  
not explain the appearance of physical universes, as UDA shows (or  
should show).






  This can also be considered as confirmation of the theory that  
there exists a huge diversity in structures tha

Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 06 Mar 2012, at 12:22, Evgenii Rudnyi wrote:


Stephen,

The life is full of paradoxes. My point was that while philosophers  
cannot solve apparently simple problems (well, these problems happen  
not to be simple), engineers continue doing their business  
successfully. How they do it? I believe, exactly this way, they try  
to understand what they do not know. Then they make trials, run  
tests, etc. and finally with some luck we get a new technology.  
Whether the theory of everything exists or not, happens not be  
essential for the success in engineering. I do not know why.


Right now I am at the end of Beweistheorien (Proof Theories) by Prof  
Hoenen


http://www.podcasts.uni-freiburg.de/podcast_content?id_content=24

At the end of his course, he considers the ontological arguments  
where the goal was to proof existence from pure logic.


This is weird. Since the failure of Whitehead and Russell, it is  
admitted that we cannot prove existence, even of the number zero, from  
logic alone.





A pretty interesting attempt. Still there is a huge gap between  
logic and existence and it seems that engineers successfully fills  
it. Ask them, how they do it.


This is weirder. Engineers prove that things exist, in theory which  
assume that some things exist. That is not different than proving the  
existence of prime or universal number or relation, from the  
assumption of the existence of the numbers. It is always relative  
proof of existence.


Bruno




On 05.03.2012 14:34 Stephen P. King said the following:

On 3/5/2012 7:01 AM, Evgenii Rudnyi wrote:

John,

It is not that bad to say that we do not know something. Yet, it  
might
be even better to specify more accurately what exactly we do not  
know.


Think of your younger colleagues that do chemistry research right  
now.

Chemists have been quite successful and the story continues. The
concepts of atom, molecule, macromolecule, electron density, etc.  
have

helped a lot along this way. We may take this concepts ontologically
or just pragmatically, this is after all not that important.  
Materials

science seems not to be affected.

Evgenii


...


Hi Evgenii,

This is a very fascinating statement to me and I find John's  
comments to

be very wise! "...it might be even better to specify more accurately
what exactly we do not know. " Does it not lead to a paradox? For  
if we
could state exactly what we do not know then it would be the case  
that

we do in fact know it and thus "we would known what we do not know",
which appears to be a contradiction.
Is this a sample of a more general kind of situation that is  
inevitable

given the idea of self-reference? It seems to me that we need to
consider that Bivalency
 can be a  
source of

error sometimes, or claim that knowledge is impossible. (note the
bivalence here! LOL!) I am focusing on this because it it part of my
overall critique of the idea of a Theory of Everything. For example,
what exactly does it mean for a sentence to have a definite truth  
value
absent the ability to evaluate that truth value? This is what I see  
your

hypothetical situation as discussing

Onward!

Stephen



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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 05 Mar 2012, at 19:26, meekerdb wrote:


On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.


When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to  
the

diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent




I agree that this assumption might not be the best one. I will  
think it over.


However, I do not completely understand you. How the geometry of  
physical space in which mathematicians reside influences the  
definition of Pi? Mathematicians will consider just Euclidean  
geometry, that's it. In my view, whether the physical space  
Euclidean or not, does not influence the work of mathematicians.


Exactly. Hence mathematics =/= reality.


Right. But this does not prove that reality is not mathematical.





In any case, the problem remains. What is mathematics under the  
assumption of physicalism? Do you have any idea?


It's a language game.


The word "game" is so fuzzy that this says nothing at all. Game theory  
is a branch of mathematics.




A physicist goes off to a conference. After a week his suit’s gotten  
soiled and crumpled, so he goes out to look for a dry cleaner.  
Walking down the main street of town, he comes upon a store with a  
lot of signs out front. One of them says “Dry Cleaning.” So he goes  
in with his dirty suit and asks when he can come back to pick it up.  
The mathematician who owns the shop replies, “I’m terribly sorry,  
but we don’t do dry cleaning.” “What?” exclaims the puzzled  
physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do  
anything here,” replies the mathematician. “We only sell signs!”

--- Alain Connes, in Changeux


Connes is a mathematical realist. Are you sure the joke is not from  
Changeux who is strongly physicalist?


Bruno

http://iridia.ulb.ac.be/~marchal/



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Re: Two Mathematicians in a Bunker and Existence of Pi

[Evgenii Rudnyi]

Craig,

The danger to society comes not from mathematicians, rather it could 
come from technologists. Recently I have read


Jaron Lanier, You Are Not a Gadget: A Manifesto

and the author shows that the society should pay more attention to what 
Silicon Valley geeks are silently doing. Just one quote


"Ideals are important in the world of technology, but the mechanism by 
which ideals influence events is different than in other spheres of 
life. Technologists don't use persuasion to influence you - or, at 
least, we don't do it very well. There are a few master communicators 
among us (like Steve Jobs), but for the most part we aren't particularly 
seductive."


"We make up extensions to your being, like remote eyes and ears 
(web-cams and mobile phones) and expanded memory (the world of details 
you can search for online). These become the structures by which you 
connect to the world and other people. These structures in turn can 
change how you conceive of yourself and the world. We tinker with your 
philosophy by direct manipulation of your cognitive experience, not 
indirectly, through argument. It takes only a tiny group of engineers to 
create technology that can shape the entire future of human experience 
with incredible speed. Therefore, crucial arguments about the human 
relationship with technology should take place between developers and 
users before such direct manipulations are designed. This book is about 
those arguments."


As for sensations, I do not know. Yesterday after I have read your 
email, I went to an Italian restaurant. A small dinner, actually I 
wanted just a glass of good red Italian wine, but then I took also a 
small plate of cheese assorti with a couple of salad leaves, pepperoni 
and bread. I have enjoyed my dinner. Whether wine, bread, cheese, salad 
and pepperoni have enjoyed it too, I do not know. I would not mind, if 
they did.


Evgenii


On 05.03.2012 06:33 Craig Weinberg said the following:

On Mar 4, 3:07 pm, Evgenii Rudnyi  wrote:



I personally still at the position that there are some material objects,
atoms, molecules, crystals, etc., that are independent from the mind.


If you assume that the human mind is the only sense in the entire
cosmos then there are going to be a lot of strange conclusions that
come up. Think about the hundreds of billions of galaxies...the
billions of organisms on this planet alone.. were all of them utterly
blind and deaf to their own existence for their entire history until
the moment that Homo sapiens began to take an interest in them from
their home on this remote speck of dust?

"Thereafter I have got suddenly a question, why mathematical models
(physical laws) are working at all to describe the Universe when there
was no mind. "

It has to do with levels of perception, or what I call perceptual
inertia. Worlds. The more intelligent you are, the more worlds you can
make sense of. The more you can make sense of the motivations and
processes of lesser worlds. As the collective intelligence of our
species has concentrated the knowledge available to each of us, we
gathered meta-perceptual commonalities. Mathematical models are
actually common perception/participation strategies as characterized
by ourselves as outside observers. We are made of matter, so we see
ourselves reflected in a particular way in matter. A way which is both
intimately familiar and alien to us.

The problem is that matter is only half of the story. We are also made
of ourselves. We need mathematical models to plumb the depths of
mysteries which are beyond our own frame of reference. Mysteries that
cut across distant levels like physics and chemistry. The closer we
get to our own level of perception however, the less mathematical
models tell the whole story. Biology, zoology, anthropology,
psychology, all benefit from mathematical models to some extent, but
they fall short of modeling what it is to be alive, to be a person,
etc. Mathematics is by definition an exterior facing manipulation. It
begins by counting on our fingers - an exterior computation which
transforms part of our body to a true set of objects - generic,
recursive, controllable. Our fingers are not a mind. They are the
beginnings of the mind offloading its grunt work onto objects. It is a
way of generalizing part of ourselves to make it seem like it is not
part of ourselves.'

Right now, in the post-Enlightenment era, our success with mathematics
has been so impressive that we have begun to imagine that we ourselves
have a mathematical basis. It is a little like following the counting
of the fingers back into the brain to find where smaller and smaller
fingers are counting. If we try a sense-based model instead, there is
no problem with mathematics being both a high level symbolic
experience within a human cortex as well as indirect experiences of
low level microcosmic events or other events which can be detected and
controlled externally with physical instruments. This is what sense
does.

Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 05 Mar 2012, at 19:03, Evgenii Rudnyi wrote:


On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.


When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent




I agree that this assumption might not be the best one. I will think  
it over.


However, I do not completely understand you. How the geometry of  
physical space in which mathematicians reside influences the  
definition of Pi? Mathematicians will consider just Euclidean  
geometry, that's it. In my view, whether the physical space  
Euclidean or not, does not influence the work of mathematicians.


In any case, the problem remains. What is mathematics under the  
assumption of physicalism? Do you have any idea?



What most mathematicians believe is that mathematics are the laws true  
in all physical universes. And physics is true in one physical universe.
But with the mechanist hypothesis, we know better:  the physical laws  
are invariant in all numbers' dreams, and physical universe are shared  
computations. This explains also (not directly) the non sharable  
truth, the contingent one, etc.
The advantage is that we can explain both quanta and qualia, without  
postulating a physical, nor a mental realm, just by listening to the  
machine, and not taking them for zombie.
It hurts our intuition, today, but science always do that, since its  
claim that the earth is not the center of reality. With comp we can  
even understand why science has to hurt machine's intuition.


So a physicalist has just to find non mechanist theory of mind, if we  
want the physical universe to be ontological (existing in some primary  
sense).


Bruno



http://iridia.ulb.ac.be/~marchal/



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Re: Two Mathematicians in a Bunker and Existence of Pi

[Evgenii Rudnyi]

Stephen,

The life is full of paradoxes. My point was that while philosophers 
cannot solve apparently simple problems (well, these problems happen not 
to be simple), engineers continue doing their business successfully. How 
they do it? I believe, exactly this way, they try to understand what 
they do not know. Then they make trials, run tests, etc. and finally 
with some luck we get a new technology. Whether the theory of everything 
exists or not, happens not be essential for the success in engineering. 
I do not know why.


Right now I am at the end of Beweistheorien (Proof Theories) by Prof Hoenen

http://www.podcasts.uni-freiburg.de/podcast_content?id_content=24

At the end of his course, he considers the ontological arguments where 
the goal was to proof existence from pure logic. A pretty interesting 
attempt. Still there is a huge gap between logic and existence and it 
seems that engineers successfully fills it. Ask them, how they do it.


Evgenii

On 05.03.2012 14:34 Stephen P. King said the following:

On 3/5/2012 7:01 AM, Evgenii Rudnyi wrote:

John,

It is not that bad to say that we do not know something. Yet, it might
be even better to specify more accurately what exactly we do not know.

Think of your younger colleagues that do chemistry research right now.
Chemists have been quite successful and the story continues. The
concepts of atom, molecule, macromolecule, electron density, etc. have
helped a lot along this way. We may take this concepts ontologically
or just pragmatically, this is after all not that important. Materials
science seems not to be affected.

Evgenii


...


Hi Evgenii,

This is a very fascinating statement to me and I find John's comments to
be very wise! "...it might be even better to specify more accurately
what exactly we do not know. " Does it not lead to a paradox? For if we
could state exactly what we do not know then it would be the case that
we do in fact know it and thus "we would known what we do not know",
which appears to be a contradiction.
Is this a sample of a more general kind of situation that is inevitable
given the idea of self-reference? It seems to me that we need to
consider that Bivalency
 can be a source of
error sometimes, or claim that knowledge is impossible. (note the
bivalence here! LOL!) I am focusing on this because it it part of my
overall critique of the idea of a Theory of Everything. For example,
what exactly does it mean for a sentence to have a definite truth value
absent the ability to evaluate that truth value? This is what I see your
hypothetical situation as discussing

Onward!

Stephen



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Re: Two Mathematicians in a Bunker and Existence of Pi

[acw]

On 3/6/2012 06:59, meekerdb wrote:

On 3/5/2012 9:34 PM, Jason Resch wrote:



On Mon, Mar 5, 2012 at 10:42 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 3/5/2012 8:28 PM, Jason Resch wrote:



On Mon, Mar 5, 2012 at 7:24 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 3/5/2012 4:57 PM, Jason Resch wrote:



On Mon, Mar 5, 2012 at 12:26 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians
prove the
existence of Pi.


When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will think
it over.

However, I do not completely understand you. How the geometry of
physical space in which mathematicians reside influences the
definition of Pi? Mathematicians will consider just Euclidean
geometry, that's it. In my view, whether the physical space Euclidean
or not, does not influence the work of mathematicians.


Exactly. Hence mathematics =/= reality.


This is like comparing the kidney of a whale to a liver of a whale, and
deciding whale=/=whale. You can't compare one limited subset of the
whole
(such as the local part of this universe) with another subset of the
whole
(euclidean geometry), and decide that the whole (of mathematics) is
different
from the whole (of reality).


The same mathematicians in the same place could 'prove the existence'
of the
meeting point of parallel lines or that through a point there is more
than one
line parallel to a given line. So no matter what they measure in
their bunker
it will be consistent with one or the other. So you can only hold that
mathematics=reality if you assume everything not self-contradictory
exists in
reality;


Okay.

but that was what the bunker thought experiment was intended to test.


I fail to see how the bunker experiment tests this. The bunker
experiment seems to
assume that mathematical reality is or depends upon a physical
representation.

You've essentially made it untestable by saying, well it may fail
HERE but
somewhere (Platonia?) it's really true.


People used to say Darwin's theory was untestable, because evolution
was such a
slow process they thought it could never be observed. Some on this
list have
argued that the hypothesis has already survived one test: the
unpredictability in
quantum mechanics.


That specific retrodiction came from Bruno's hypothesis which is that
universes are
generated by computation. What is computable is much less than all
mathematics.


The existence of all mathematical structures implies the existence of
all programs, which is observationally indistinguishable from Bruno's
result taking only the integers to exist.


That they are observationally indistinguishable is vacuously satisfied
by them both being unobservable.


I find the existence of all consistent structures to be a simpler
theory. If the integers can exist, why cant the Mandlebrot set, or the
Calabi–Yau manifolds?


I didn't say that things descriable by those mathematics *can't* exist.
I just said I don't believe they do. Yaweh *could* exist (and according
to you does) but I don't believe he does.

Comparing everything-type theories with a random personal deity with 
contradictory properties is a strawman.




If instead we found our environment and observations of it to be
perfectly
deterministic, this would have ruled out mechanism+a single or finite
universe. Further, there is a growing collection of evidence that in
most universes,
conscious life is impossible.


There's a popular idea that most possible universes are inhospitable
to conscious
life: a theory that might well be false under Bruno's hypothesis in which
consciousness and universes are both realized by computation.


In Bruno's theory, "physical universes" are considered observations of
minds.


Hmm? Is that right? The UD* certainly must generate lots of programs
without human-like consciousness, e.g. this universe in which dinosaurs
weren't killed off. So I'm not clear on why there wouldn't be infinitely
many universes without conscious beings.


Dinosaurs could very well be conscious, but not self-conscious, sort of 
like in-a-moment experience with very few memories or continuity. 
Consciousness should not be confused with 
self-awareness/self-consciousness. A mathe

Re: Two Mathematicians in a Bunker and Existence of Pi

[meekerdb]

On 3/5/2012 9:34 PM, Jason Resch wrote:



On Mon, Mar 5, 2012 at 10:42 PM, meekerdb > wrote:


On 3/5/2012 8:28 PM, Jason Resch wrote:



On Mon, Mar 5, 2012 at 7:24 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 3/5/2012 4:57 PM, Jason Resch wrote:



On Mon, Mar 5, 2012 at 12:26 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi 
means.
During the initial stage of the experiment 
mathematicians
prove the
existence of Pi.


When mathematicians 'prove the existence' of something they 
are just
showing that something which satisfies a certain definition 
can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the 
circumference to the
diameter of a circle in Euclidean geometry. But what does 
that mean
if geometry is not Euclidean; and we know it's not since 
these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they 
apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will 
think
it over.

However, I do not completely understand you. How the geometry of
physical space in which mathematicians reside influences the
definition of Pi? Mathematicians will consider just Euclidean
geometry, that's it. In my view, whether the physical space 
Euclidean
or not, does not influence the work of mathematicians.


Exactly. Hence mathematics =/= reality.


This is like comparing the kidney of a whale to a liver of a whale, and
deciding whale=/=whale.  You can't compare one limited subset of the 
whole
(such as the local part of this universe) with another subset of the 
whole
(euclidean geometry), and decide that the whole (of mathematics) is 
different
from the whole (of reality).


The same mathematicians in the same place could 'prove the existence' 
of the
meeting point of parallel lines or that through a point there is more 
than one
line parallel to a given line.  So no matter what they measure in their 
bunker
it will be consistent with one or the other.  So you can only hold that
mathematics=reality if you assume everything not self-contradictory 
exists in
reality;


Okay.

but that was what the bunker thought experiment was intended to test.


I fail to see how the bunker experiment tests this.  The bunker experiment 
seems to
assume that mathematical reality is or depends upon a physical 
representation.

You've essentially made it untestable by saying, well it may fail HERE 
but
somewhere (Platonia?) it's really true.


People used to say Darwin's theory was untestable, because evolution was 
such a
slow process they thought it could never be observed.  Some on this list 
have
argued that the hypothesis has already survived one test: the 
unpredictability in
quantum mechanics.


That specific retrodiction came from Bruno's hypothesis which is that 
universes are
generated by computation.  What is computable is much less than all 
mathematics.


The existence of all mathematical structures implies the existence of all programs, 
which is observationally indistinguishable from Bruno's result taking only the integers 
to exist.


That they are observationally indistinguishable is vacuously satisfied by them both being 
unobservable.


I find the existence of all consistent structures to be a simpler theory.  If the 
integers can exist, why cant the Mandlebrot set, or the Calabi–Yau manifolds?


I didn't say that things descriable by those mathematics *can't* exist.  I just said I 
don't believe they do.  Yaweh *could* exist (and according to you does) but I don't 
believe he does.






If instead we found our environment and observations of it to be perfectly
deterministic, this would have ruled out mechanism+a single or finite universe. 
Further, there is a growing collection of evidence that in most universes,

conscious life is impossible.


There's a popular idea that most possible universes are inhospitable to 
conscious
life: a theory that might well be false under Bruno's hypothesis in which
consciousness and universes are both realized by computati

Re: Two Mathematicians in a Bunker and Existence of Pi

[Jason Resch]

On Mon, Mar 5, 2012 at 10:42 PM, meekerdb  wrote:

>  On 3/5/2012 8:28 PM, Jason Resch wrote:
>
>
>
> On Mon, Mar 5, 2012 at 7:24 PM, meekerdb  wrote:
>
>>  On 3/5/2012 4:57 PM, Jason Resch wrote:
>>
>>
>>
>> On Mon, Mar 5, 2012 at 12:26 PM, meekerdb  wrote:
>>
>>> On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
>>>
 On 05.03.2012 18:29 meekerdb said the following:

> On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
>
>> The experiment takes an operational approach to what Pi means.
>> During the initial stage of the experiment mathematicians prove the
>> existence of Pi.
>>
>
> When mathematicians 'prove the existence' of something they are just
> showing that something which satisfies a certain definition can be
> inferred from a certain set of axioms. In your example the
> mathematicians may define Pi as the ratio of the circumference to the
> diameter of a circle in Euclidean geometry. But what does that mean
> if geometry is not Euclidean; and we know it's not since these
> mathematicians are in the gravitational field of the Earth.
> Mathematics is about abstract propositions. Whether they apply to
> reality is a separate question.
>
> Brent
>
>
>
 I agree that this assumption might not be the best one. I will think it
 over.

 However, I do not completely understand you. How the geometry of
 physical space in which mathematicians reside influences the definition of
 Pi? Mathematicians will consider just Euclidean geometry, that's it. In my
 view, whether the physical space Euclidean or not, does not influence the
 work of mathematicians.

>>>
>>>  Exactly. Hence mathematics =/= reality.
>>
>>
>>  This is like comparing the kidney of a whale to a liver of a whale, and
>> deciding whale=/=whale.  You can't compare one limited subset of the whole
>> (such as the local part of this universe) with another subset of the whole
>> (euclidean geometry), and decide that the whole (of mathematics) is
>> different from the whole (of reality).
>>
>>
>>  The same mathematicians in the same place could 'prove the existence' of
>> the meeting point of parallel lines or that through a point there is more
>> than one line parallel to a given line.  So no matter what they measure in
>> their bunker it will be consistent with one or the other.  So you can only
>> hold that mathematics=reality if you assume everything not
>> self-contradictory exists in reality;
>>
>
> Okay.
>
>
>>  but that was what the bunker thought experiment was intended to test.
>>
>
> I fail to see how the bunker experiment tests this.  The bunker experiment
> seems to assume that mathematical reality is or depends upon a physical
> representation.
>
>
>> You've essentially made it untestable by saying, well it may fail HERE
>> but somewhere (Platonia?) it's really true.
>>
>
> People used to say Darwin's theory was untestable, because evolution was
> such a slow process they thought it could never be observed.  Some on this
> list have argued that the hypothesis has already survived one test: the
> unpredictability in quantum mechanics.
>
>
> That specific retrodiction came from Bruno's hypothesis which is that
> universes are generated by computation.  What is computable is much less
> than all mathematics.
>

The existence of all mathematical structures implies the existence of all
programs, which is observationally indistinguishable from Bruno's result
taking only the integers to exist.  I find the existence of all consistent
structures to be a simpler theory.  If the integers can exist, why cant the
Mandlebrot set, or the Calabi–Yau manifolds?


>
>
>  If instead we found our environment and observations of it to be
> perfectly deterministic, this would have ruled out mechanism+a single or
> finite universe.  Further, there is a growing collection of evidence that
> in most universes, conscious life is impossible.
>
>
> There's a popular idea that most possible universes are inhospitable to
> conscious life: a theory that might well be false under Bruno's hypothesis
> in which consciousness and universes are both realized by computation.
>

In Bruno's theory, "physical universes" are considered observations of
minds.  Where I use the term, I refer to independent structures (both seen
and unseen).


> In any case it doesn't warrant the conclusion that all possible universes
> exist.
>
>
No, it doesn't prove they all exist, just that there are perhaps infinitely
many universes almost exactly like this one.  Which, while not proving
everything exists, is certainly something we would expect to find if indeed
everything exists.

There are all these reasons and arguments that are compatible with and
suggestive of the idea that all is out there.  I haven't seen one offered
piece of evidence from you that would suggest the idea of mathematical
reality is false.  So tell me: for what reason(s) do you reject the
hypothesis?


>
>Th

Re: Two Mathematicians in a Bunker and Existence of Pi

[meekerdb]

On 3/5/2012 8:28 PM, Jason Resch wrote:



On Mon, Mar 5, 2012 at 7:24 PM, meekerdb > wrote:


On 3/5/2012 4:57 PM, Jason Resch wrote:



On Mon, Mar 5, 2012 at 12:26 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi 
means.
During the initial stage of the experiment mathematicians 
prove the
existence of Pi.


When mathematicians 'prove the existence' of something they are 
just
showing that something which satisfies a certain definition can 
be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference 
to the
diameter of a circle in Euclidean geometry. But what does that 
mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply 
to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will 
think it over.

However, I do not completely understand you. How the geometry of 
physical
space in which mathematicians reside influences the definition of 
Pi?
Mathematicians will consider just Euclidean geometry, that's it. In 
my
view, whether the physical space Euclidean or not, does not 
influence the
work of mathematicians.


Exactly. Hence mathematics =/= reality.


This is like comparing the kidney of a whale to a liver of a whale, and 
deciding
whale=/=whale.  You can't compare one limited subset of the whole (such as 
the
local part of this universe) with another subset of the whole (euclidean 
geometry),
and decide that the whole (of mathematics) is different from the whole (of 
reality).


The same mathematicians in the same place could 'prove the existence' of 
the meeting
point of parallel lines or that through a point there is more than one line 
parallel
to a given line.  So no matter what they measure in their bunker it will be
consistent with one or the other.  So you can only hold that 
mathematics=reality if
you assume everything not self-contradictory exists in reality;


Okay.

but that was what the bunker thought experiment was intended to test.


I fail to see how the bunker experiment tests this.  The bunker experiment seems to 
assume that mathematical reality is or depends upon a physical representation.


You've essentially made it untestable by saying, well it may fail HERE but 
somewhere
(Platonia?) it's really true.


People used to say Darwin's theory was untestable, because evolution was such a slow 
process they thought it could never be observed.  Some on this list have argued that the 
hypothesis has already survived one test: the unpredictability in quantum mechanics.


That specific retrodiction came from Bruno's hypothesis which is that universes are 
generated by computation.  What is computable is much less than all mathematics.


If instead we found our environment and observations of it to be perfectly 
deterministic, this would have ruled out mechanism+a single or finite universe.  
Further, there is a growing collection of evidence that in most universes, conscious 
life is impossible.


There's a popular idea that most possible universes are inhospitable to conscious life: a 
theory that might well be false under Bruno's hypothesis in which consciousness and 
universes are both realized by computation.  In any case it doesn't warrant the conclusion 
that all possible universes exist.


  This can also be considered as confirmation of the theory that there exists a huge 
diversity in structures that have existence.  Just because one proposed test will not 
work should not imply a theory is untestable.


A final thought: Consider what our universe would look like if you were a being outside 
it.  You would not be affected by the gravity of objects in our universe, for gravity 
only affects physical objects in this universe.  You could not see the stars or galaxies 
of our universe, for photons never leave it.  There would be no relativity of size, or 
time, or distance between your perspective and that within our universe.  You could not 
say what time it happened to be in our universe, or whether the world had even formed 
yet or long ago ended.  You could in no way make your presence known to us in this 
universe, for our universe is bound to follow certain fixed laws.  In summary, outside 
our universe there is no evidence we

Re: Two Mathematicians in a Bunker and Existence of Pi

[Jason Resch]

On Mon, Mar 5, 2012 at 7:24 PM, meekerdb  wrote:

>  On 3/5/2012 4:57 PM, Jason Resch wrote:
>
>
>
> On Mon, Mar 5, 2012 at 12:26 PM, meekerdb  wrote:
>
>> On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
>>
>>> On 05.03.2012 18:29 meekerdb said the following:
>>>
 On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

> The experiment takes an operational approach to what Pi means.
> During the initial stage of the experiment mathematicians prove the
> existence of Pi.
>

 When mathematicians 'prove the existence' of something they are just
 showing that something which satisfies a certain definition can be
 inferred from a certain set of axioms. In your example the
 mathematicians may define Pi as the ratio of the circumference to the
 diameter of a circle in Euclidean geometry. But what does that mean
 if geometry is not Euclidean; and we know it's not since these
 mathematicians are in the gravitational field of the Earth.
 Mathematics is about abstract propositions. Whether they apply to
 reality is a separate question.

 Brent



>>> I agree that this assumption might not be the best one. I will think it
>>> over.
>>>
>>> However, I do not completely understand you. How the geometry of
>>> physical space in which mathematicians reside influences the definition of
>>> Pi? Mathematicians will consider just Euclidean geometry, that's it. In my
>>> view, whether the physical space Euclidean or not, does not influence the
>>> work of mathematicians.
>>>
>>
>>  Exactly. Hence mathematics =/= reality.
>
>
>  This is like comparing the kidney of a whale to a liver of a whale, and
> deciding whale=/=whale.  You can't compare one limited subset of the whole
> (such as the local part of this universe) with another subset of the whole
> (euclidean geometry), and decide that the whole (of mathematics) is
> different from the whole (of reality).
>
>
> The same mathematicians in the same place could 'prove the existence' of
> the meeting point of parallel lines or that through a point there is more
> than one line parallel to a given line.  So no matter what they measure in
> their bunker it will be consistent with one or the other.  So you can only
> hold that mathematics=reality if you assume everything not
> self-contradictory exists in reality;
>

Okay.


> but that was what the bunker thought experiment was intended to test.
>

I fail to see how the bunker experiment tests this.  The bunker experiment
seems to assume that mathematical reality is or depends upon a physical
representation.


> You've essentially made it untestable by saying, well it may fail HERE but
> somewhere (Platonia?) it's really true.
>

People used to say Darwin's theory was untestable, because evolution was
such a slow process they thought it could never be observed.  Some on this
list have argued that the hypothesis has already survived one test: the
unpredictability in quantum mechanics.  If instead we found our environment
and observations of it to be perfectly deterministic, this would have ruled
out mechanism+a single or finite universe.  Further, there is a growing
collection of evidence that in most universes, conscious life is
impossible.  This can also be considered as confirmation of the theory that
there exists a huge diversity in structures that have existence.  Just
because one proposed test will not work should not imply a theory is
untestable.

A final thought: Consider what our universe would look like if you were a
being outside it.  You would not be affected by the gravity of objects in
our universe, for gravity only affects physical objects in this universe.
You could not see the stars or galaxies of our universe, for photons never
leave it.  There would be no relativity of size, or time, or distance
between your perspective and that within our universe.  You could not say
what time it happened to be in our universe, or whether the world had even
formed yet or long ago ended.  You could in no way make your presence known
to us in this universe, for our universe is bound to follow certain fixed
laws.  In summary, outside our universe there is no evidence we even exist;
our entire universe is merely an abstract, immutable and timeless
mathematical object.  From the outside, one could study our universe
through the window of math and computer simulation, but observation through
your senses or any measurement apparatus would never reveal its existence.

Jason


>
> Brent
>
>
>
>>
>>
>>
>>> In any case, the problem remains. What is mathematics under the
>>> assumption of physicalism? Do you have any idea?
>>>
>>
>>  It's a language game.
>>
>>
>  This is what Hilbert proposed and what others such as Bertrand Russel
> tried to prove, but instead the opposite was proved in 1931.  Mathematical
> truth transcends the symbol manipulation game defined by any set of axioms.
>
>  Jason
>
>
>> Brent
>> A physicist goes off to a conference. After a week his suit’s g

Re: Two Mathematicians in a Bunker and Existence of Pi

[meekerdb]

On 3/5/2012 4:57 PM, Jason Resch wrote:



On Mon, Mar 5, 2012 at 12:26 PM, meekerdb > wrote:


On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove 
the
existence of Pi.


When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to 
the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will think it 
over.

However, I do not completely understand you. How the geometry of 
physical space
in which mathematicians reside influences the definition of Pi? 
Mathematicians
will consider just Euclidean geometry, that's it. In my view, whether 
the
physical space Euclidean or not, does not influence the work of 
mathematicians.


Exactly. Hence mathematics =/= reality.


This is like comparing the kidney of a whale to a liver of a whale, and deciding 
whale=/=whale.  You can't compare one limited subset of the whole (such as the local 
part of this universe) with another subset of the whole (euclidean geometry), and decide 
that the whole (of mathematics) is different from the whole (of reality).


The same mathematicians in the same place could 'prove the existence' of the meeting point 
of parallel lines or that through a point there is more than one line parallel to a given 
line.  So no matter what they measure in their bunker it will be consistent with one or 
the other.  So you can only hold that mathematics=reality if you assume everything not 
self-contradictory exists in reality; but that was what the bunker thought experiment was 
intended to test.  You've essentially made it untestable by saying, well it may fail HERE 
but somewhere (Platonia?) it's really true.


Brent





In any case, the problem remains. What is mathematics under the 
assumption of
physicalism? Do you have any idea?


It's a language game.


This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, 
but instead the opposite was proved in 1931.  Mathematical truth transcends the symbol 
manipulation game defined by any set of axioms.


Jason

Brent
A physicist goes off to a conference. After a week his suit’s gotten soiled 
and
crumpled, so he goes out to look for a dry cleaner. Walking down the main 
street of
town, he comes upon a store with a lot of signs out front. One of them says 
“Dry
Cleaning.” So he goes in with his dirty suit and asks when he can come back 
to pick
it up. The mathematician who owns the shop replies, “I’m terribly sorry, 
but we
don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign 
outside
says ‘Dry Cleaning’!” “We do not do anything here,” replies the 
mathematician. “We
only sell signs!”
--- Alain Connes, in Changeux



Evgenii


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Re: Two Mathematicians in a Bunker and Existence of Pi

[Jason Resch]

On Mon, Mar 5, 2012 at 12:26 PM, meekerdb  wrote:

> On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
>
>> On 05.03.2012 18:29 meekerdb said the following:
>>
>>> On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
>>>
 The experiment takes an operational approach to what Pi means.
 During the initial stage of the experiment mathematicians prove the
 existence of Pi.

>>>
>>> When mathematicians 'prove the existence' of something they are just
>>> showing that something which satisfies a certain definition can be
>>> inferred from a certain set of axioms. In your example the
>>> mathematicians may define Pi as the ratio of the circumference to the
>>> diameter of a circle in Euclidean geometry. But what does that mean
>>> if geometry is not Euclidean; and we know it's not since these
>>> mathematicians are in the gravitational field of the Earth.
>>> Mathematics is about abstract propositions. Whether they apply to
>>> reality is a separate question.
>>>
>>> Brent
>>>
>>>
>>>
>> I agree that this assumption might not be the best one. I will think it
>> over.
>>
>> However, I do not completely understand you. How the geometry of physical
>> space in which mathematicians reside influences the definition of Pi?
>> Mathematicians will consider just Euclidean geometry, that's it. In my
>> view, whether the physical space Euclidean or not, does not influence the
>> work of mathematicians.
>>
>
> Exactly. Hence mathematics =/= reality.


This is like comparing the kidney of a whale to a liver of a whale, and
deciding whale=/=whale.  You can't compare one limited subset of the whole
(such as the local part of this universe) with another subset of the whole
(euclidean geometry), and decide that the whole (of mathematics) is
different from the whole (of reality).


>
>
>
>> In any case, the problem remains. What is mathematics under the
>> assumption of physicalism? Do you have any idea?
>>
>
> It's a language game.
>
>
This is what Hilbert proposed and what others such as Bertrand Russel tried
to prove, but instead the opposite was proved in 1931.  Mathematical
truth transcends the symbol manipulation game defined by any set of axioms.

Jason


> Brent
> A physicist goes off to a conference. After a week his suit’s gotten
> soiled and crumpled, so he goes out to look for a dry cleaner. Walking down
> the main street of town, he comes upon a store with a lot of signs out
> front. One of them says “Dry Cleaning.” So he goes in with his dirty suit
> and asks when he can come back to pick it up. The mathematician who owns
> the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.”
> “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry
> Cleaning’!” “We do not do anything here,” replies the mathematician. “We
> only sell signs!”
> --- Alain Connes, in Changeux
>
>
>
>> Evgenii
>>
>>
> --
> You received this message because you are subscribed to the Google Groups
> "Everything List" group.
> To post to this group, send email to 
> everything-list@googlegroups.**com
> .
> To unsubscribe from this group, send email to everything-list+unsubscribe@
> **googlegroups.com .
> For more options, visit this group at http://groups.google.com/**
> group/everything-list?hl=en
> .
>
>

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Re: Two Mathematicians in a Bunker and Existence of Pi

[meekerdb]

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.


When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent




I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which 
mathematicians reside influences the definition of Pi? Mathematicians will consider just 
Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, 
does not influence the work of mathematicians.


Exactly. Hence mathematics =/= reality.



In any case, the problem remains. What is mathematics under the assumption of 
physicalism? Do you have any idea?


It's a language game.

Brent
A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, 
so he goes out to look for a dry cleaner. Walking down the main street of town, he comes 
upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in 
with his dirty suit and asks when he can come back to pick it up. The mathematician who 
owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” 
exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do 
anything here,” replies the mathematician. “We only sell signs!”

--- Alain Connes, in Changeux



Evgenii



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Re: Two Mathematicians in a Bunker and Existence of Pi

[Evgenii Rudnyi]

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.


When mathematicians 'prove the existence' of something they are just
 showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
 diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent




I agree that this assumption might not be the best one. I will think it 
over.


However, I do not completely understand you. How the geometry of 
physical space in which mathematicians reside influences the definition 
of Pi? Mathematicians will consider just Euclidean geometry, that's it. 
In my view, whether the physical space Euclidean or not, does not 
influence the work of mathematicians.


In any case, the problem remains. What is mathematics under the 
assumption of physicalism? Do you have any idea?


Evgenii

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Re: Two Mathematicians in a Bunker and Existence of Pi

[meekerdb]

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means. During the initial stage 
of the experiment mathematicians prove the existence of Pi.


When mathematicians 'prove the existence' of something they are just showing that 
something which satisfies a certain definition can be inferred from a certain set of 
axioms.  In your example the mathematicians may define Pi as the ratio of the 
circumference to the diameter of a circle in Euclidean geometry. But what does that mean 
if geometry is not Euclidean; and we know it's not since these mathematicians are in the 
gravitational field of the Earth.  Mathematics is about abstract propositions.  Whether 
they apply to reality is a separate question.


Brent


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Re: Two Mathematicians in a Bunker and Existence of Pi

[Stephen P. King]

On 3/5/2012 7:01 AM, Evgenii Rudnyi wrote:

John,

It is not that bad to say that we do not know something. Yet, it might 
be even better to specify more accurately what exactly we do not know.


Think of your younger colleagues that do chemistry research right now. 
Chemists have been quite successful and the story continues. The 
concepts of atom, molecule, macromolecule, electron density, etc. have 
helped a lot along this way. We may take this concepts ontologically 
or just pragmatically, this is after all not that important. Materials 
science seems not to be affected.


Evgenii



On 05.03.2012 00:17 John Mikes said the following:

Hello, Evgenii, my fellow (former) chemist: I ended up after my 38
patents in (environmental-polymer) chemistry with an agnosticism, not
'believeing' in the atom (don't even mention 'molecules' or the
macromolecules I created). It is all the figment of the human mind to
EXPLAIN whatever transpired into our 'model' of presently knowables
from (some?) infinite complexity - way beyond our imaginative power.
Maxim: EVERYTHING *does* exist that pops up in the mind, if not
otherwise: as an idea - in the mind. That is not too much help for
your condition of "independently from the mind", but nothing we can
'think of' is independent from the mind. Pi is a formulatin of some
effect humans found in the figment of their physical world
explanations. The fact that we cannot express it in real numbers has
nothing to do with its 'existence'. The 'effect did not evolve, it
came with the "big Bang" (if you are a believer of it). Not with that
'retrograde history' of course, lineraly as it is drawn, reversing a
postulated developmental course that is by far not 'linear'. Also: we
have no proof that everything that ever showed up for us NOW is still
available for us to know of. Also it is childish to apply the
mathematics of our expanded universe to the un-really concentrated
energy-knot of the alleged beginning. (Physics as well). (Just think
about the fairytale of the Inflation).

Please do not position your executable 2 scientists in the bunker
before the human mind invented (discovered, as some would say) the
zero. Or: writing. Or: before the Great Greeks (Euclide, Plato,
Archimedes, Aristotle etc.) The 'setup' is by all means within my
dismissal of 'thought experiments'. IMO PI is a human formulation of
something that is more than just human.

Regards

John



Hi Evgenii,

This is a very fascinating statement to me and I find John's 
comments to be very wise! "...it might be even better to specify more 
accurately what exactly we do not know. " Does it not lead to a paradox? 
For if we could state exactly what we do not know then it would be the 
case that we do in fact know it and thus "we would known what we do not 
know", which appears to be a contradiction.
Is this a sample of a more general kind of situation that is 
inevitable given the idea of self-reference? It seems to me that we need 
to consider that Bivalency 
 can be a source of 
error sometimes, or claim that knowledge is impossible. (note the 
bivalence here! LOL!) I am focusing on this because it it part of my 
overall critique of the idea of a Theory of Everything. For example, 
what exactly does it mean for a sentence to have a definite truth value 
absent the ability to evaluate that truth value? This is what I see your 
hypothetical situation as discussing


Onward!

Stephen

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Re: Two Mathematicians in a Bunker and Existence of Pi

[Evgenii Rudnyi]

John,

It is not that bad to say that we do not know something. Yet, it might 
be even better to specify more accurately what exactly we do not know.


Think of your younger colleagues that do chemistry research right now. 
Chemists have been quite successful and the story continues. The 
concepts of atom, molecule, macromolecule, electron density, etc. have 
helped a lot along this way. We may take this concepts ontologically or 
just pragmatically, this is after all not that important. Materials 
science seems not to be affected.


Evgenii



On 05.03.2012 00:17 John Mikes said the following:

Hello, Evgenii, my fellow (former) chemist: I ended up after my 38
patents in (environmental-polymer) chemistry with an agnosticism, not
'believeing' in the atom (don't even mention 'molecules' or the
macromolecules I created). It is all the figment of the human mind to
EXPLAIN whatever transpired into our 'model' of presently knowables
from (some?) infinite complexity - way beyond our imaginative power.
Maxim: EVERYTHING *does* exist that pops up in the mind, if not
otherwise: as an idea - in the mind. That is not too much help for
your condition of "independently from the mind", but nothing we can
'think of' is independent from the mind. Pi is a formulatin of some
effect humans found in the figment of their physical world
explanations. The fact that we cannot express it in real numbers has
nothing to do with its 'existence'. The 'effect did not evolve, it
came with the "big Bang" (if you are a believer of it). Not with that
'retrograde history' of course, lineraly as it is drawn, reversing a
postulated developmental course that is by far not 'linear'. Also: we
have no proof that everything that ever showed up for us NOW is still
available for us to know of. Also it is childish to apply the
mathematics of our expanded universe to the un-really concentrated
energy-knot of the alleged beginning. (Physics as well). (Just think
about the fairytale of the Inflation).

Please do not position your executable 2 scientists in the bunker
before the human mind invented (discovered, as some would say) the
zero. Or: writing. Or: before the Great Greeks (Euclide, Plato,
Archimedes, Aristotle etc.) The 'setup' is by all means within my
dismissal of 'thought experiments'. IMO PI is a human formulation of
something that is more than just human.

Regards

John


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Re: Two Mathematicians in a Bunker and Existence of Pi

[Evgenii Rudnyi]

Bruno,

Thanks for your comments. You are right. It is necessary to be more 
accurate with terms. I have read about physicalism on SEP and I see that 
I do not need mechanism right now. By the way, where I can read about 
mechanism? I see nothing on SEP.


Below is a new version of the problem. I have left Pi though.

Evgenii

P.S. I like a lot this quote about physicalism from SEP

"The first thing to say when considering the truth of physicalism is 
that we live in an overwhelmingly physicalist or materialist 
intellectual culture. The result is that, as things currently stand, the 
standards of argumentation required to persuade someone of the truth of 
physicalism are much lower than the standards required to persuade 
someone of its negation. (The point here is a perfectly general one: if 
you already believe or want something to be true, you are likely to 
accept fairly low standards of argumentation for its truth.)"


I should confess that it describes my personal feeling very well. Cheers 
to philosophers.



An experiment to perform in order to find experimentally what is the 
meaning of Pi under the physicalism hypothesis


Version 2.0

*Assumptions*
-
I assume physicalism. From SEP

http://plato.stanford.edu/entries/physicalism/

"Physicalism is the thesis that everything is physical, or as 
contemporary philosophers sometimes put it, that everything supervenes 
on, or is necessitated by, the physical."


"The general idea is that the nature of the actual world (i.e. the 
universe and everything in it) conforms to a certain condition, the 
condition of being physical. Of course, physicalists don't deny that the 
world might contain many items that at first glance don't seem physical 
— items of a biological, or psychological, or moral, or social nature. 
But they insist nevertheless that at the end of the day such items are 
either physical or supervene on the physical."


"Physicalism is sometimes known as ‘materialism’; indeed, on one strand 
to contemporary usage, the terms ‘physicalism’ and ‘materialism’ are 
interchangeable."


*Problem*
-
The Pi number enjoys extensive use in physics. This raises the question 
what Pi means under the physicalism hypothesis.


*Experiment*


Below there is a description of the experiment that one could think of 
to check the relationships between Pi and physicalism.


Let us take a completely isolated bunker where the experiment begins. 
There are two mathematicians in the bunker and the initial conditions 
are enough so that mathematicians can comfortably work for awhile and 
prove the existence of Pi on a paper. Eventually the oxygen in the 
bunker will run over and both mathematicians die.


From a physicalism viewpoint, we have a dynamical system that 
eventually comes to the equilibrium state. Because of experimental 
settings, we can neglect the interaction with environment and I hope 
that this could be done even for the quantum mechanics treatment.


The experiment takes an operational approach to what Pi means. During 
the initial stage of the experiment mathematicians prove the existence 
of Pi. This should be enough to claim that Pi is present in the bunker 
at least for some moments.


*Questions to discuss*
--

How Pi supervenes to the physical states of the bunker with mathematicians?

Is Pi invariant in respect to states of the dynamical system in question 
or not?




On 04.03.2012 18:48 Bruno Marchal said the following:


On 04 Mar 2012, at 17:12, Evgenii Rudnyi wrote:


Bruno,

Actually it is not a joke. I guess it is my first step toward
Platonia. As I am a chemist by background, the problem might be not
 mathematically correct indeed. Yet, if you could help, we could
improve it in this respect.

The background is as follows. I am a chemist and I am still at the
 level of what you refer to as physicalism or mechanism.


Hmm... You should read more carefully the post. On the contrary I
claim, and explain, that mechanism and physicalism are incompatible.

I am aware that physicalist, naturalist and materialist tend to use
mechanism as a sort of modern way to put the mind under the rug.

You can see all what I am talking about as an explanation that not
only mechanism does not solve the mind-body problem, but on the
contrary, it leads to the falsity of physicalism and the necessity to
explain where the physical (and physicalist) *belief* come from.

Mechanism entails the negation of physicalism. That's what the UDA is
 all about.

The physical reality is not the fundamental reality. The physical
reality will reappear as the way the border of the mathematical
reality looks when seen form inside, from some points of view
(actually the points of view of predicting measurement values).

I can argue that with comp, concerning the basic ontological level,
it is absolutely undecidable if there is anything more than the
numbers, that 

Re: Two Mathematicians in a Bunker and Existence of Pi

[Craig Weinberg]

On Mar 4, 3:07 pm, Evgenii Rudnyi  wrote:

>
> I personally still at the position that there are some material objects,
> atoms, molecules, crystals, etc., that are independent from the mind.

If you assume that the human mind is the only sense in the entire
cosmos then there are going to be a lot of strange conclusions that
come up. Think about the hundreds of billions of galaxies...the
billions of organisms on this planet alone.. were all of them utterly
blind and deaf to their own existence for their entire history until
the moment that Homo sapiens began to take an interest in them from
their home on this remote speck of dust?

"Thereafter I have got suddenly a question, why mathematical models
(physical laws) are working at all to describe the Universe when there
was no mind. "

It has to do with levels of perception, or what I call perceptual
inertia. Worlds. The more intelligent you are, the more worlds you can
make sense of. The more you can make sense of the motivations and
processes of lesser worlds. As the collective intelligence of our
species has concentrated the knowledge available to each of us, we
gathered meta-perceptual commonalities. Mathematical models are
actually common perception/participation strategies as characterized
by ourselves as outside observers. We are made of matter, so we see
ourselves reflected in a particular way in matter. A way which is both
intimately familiar and alien to us.

The problem is that matter is only half of the story. We are also made
of ourselves. We need mathematical models to plumb the depths of
mysteries which are beyond our own frame of reference. Mysteries that
cut across distant levels like physics and chemistry. The closer we
get to our own level of perception however, the less mathematical
models tell the whole story. Biology, zoology, anthropology,
psychology, all benefit from mathematical models to some extent, but
they fall short of modeling what it is to be alive, to be a person,
etc. Mathematics is by definition an exterior facing manipulation. It
begins by counting on our fingers - an exterior computation which
transforms part of our body to a true set of objects - generic,
recursive, controllable. Our fingers are not a mind. They are the
beginnings of the mind offloading its grunt work onto objects. It is a
way of generalizing part of ourselves to make it seem like it is not
part of ourselves.'

Right now, in the post-Enlightenment era, our success with mathematics
has been so impressive that we have begun to imagine that we ourselves
have a mathematical basis. It is a little like following the counting
of the fingers back into the brain to find where smaller and smaller
fingers are counting. If we try a sense-based model instead, there is
no problem with mathematics being both a high level symbolic
experience within a human cortex as well as indirect experiences of
low level microcosmic events or other events which can be detected and
controlled externally with physical instruments. This is what sense
does. It jumps to conclusions. It ties levels together figuratively.
We want to move our hand, and we just do it. We don't have to
consciously transduce a signal through neural and muscular fibers. We
couldn't find a muscle fiber even if we wanted to.

This is what mathematics does for us, it extends our minds
figuratively outside of our native scale of perception, so that we
can, in a way, make more of the universe part of our figurative body.
Of course, just as we control our limbs without knowing what is really
going on under the skin, we should not mistake our success with
controlling through mathematical models for understanding the truth -
particularly the truth of our own native perceptual frame, which as
much more subtle and non-mathematical potentials. It could well be the
case that introducing our external control schemas into our own world
is having increasingly toxic consequences, draining the significance
out of culture and promoting an unstoppable drone of financial
computation which consumes the whole of civilization. We may find out
that our mastery over our universe has a Sorcerer's Apprentice side
which reduces itself to an automaton even as it automates everything
around it.

Craig

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Re: Two Mathematicians in a Bunker and Existence of Pi

[Evgenii Rudnyi]

I understand your logic but then immediately comes a question where 
mathematics objects exist. In this case Bruno is consistent when he says 
that everything is formed from the mathematical objects in Platonia. Do 
you mean the same?


I personally still at the position that there are some material objects, 
atoms, molecules, crystals, etc., that are independent from the mind. I 
believe that this is quite a typical position for natural sciences. Then 
it is hard to imagine how mathematical objects coexist with physical 
objects. Some sort of dualism?


Evgenii

On 04.03.2012 17:28 Brian Tenneson said the following:

There is an important distinction between the names and notations of
mathematics and the objects of study of mathematics.  I believe the
former are inventions of humans while the latter exist independently
of mankind. For example, I am saying that the symbol 0 is an
invention of mankind but what is pointed to by the symbol 0 is not an
invention of mankind.

I can't give you absolute proof especially when we're going to
assume different things (i.e., we live in different paradigms).  One
thing that gives me a clue about my conclusion is that mathematical
objects will not exist any less if humanity were to go extinct.
However, arguing that is like arguing for a particular answer to a
koan.



On Sun, Mar 4, 2012 at 8:12 AM, Evgenii Rudnyi
wrote:



Yet, according to my current view, mathematics has been created by
the mankind.





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Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 04 Mar 2012, at 17:12, Evgenii Rudnyi wrote:


Bruno,

Actually it is not a joke. I guess it is my first step toward  
Platonia. As I am a chemist by background, the problem might be not  
mathematically correct indeed. Yet, if you could help, we could  
improve it in this respect.


The background is as follows. I am a chemist and I am still at the  
level of what you refer to as physicalism or mechanism.


Hmm... You should read more carefully the post. On the contrary I  
claim, and explain, that mechanism and physicalism are incompatible.


I am aware that physicalist, naturalist and materialist tend to use  
mechanism as a sort of modern way to put the mind under the rug.


You can see all what I am talking about as an explanation that not  
only mechanism does not solve the mind-body problem, but on the  
contrary, it leads to the falsity of physicalism and the necessity to  
explain where the physical (and physicalist) *belief* come from.


Mechanism entails the negation of physicalism. That's what the UDA is  
all about.


The physical reality is not the fundamental reality. The physical  
reality will reappear as the way the border of the mathematical  
reality looks when seen form inside, from some points of view  
(actually the points of view of predicting measurement values).


I can argue that with comp, concerning the basic ontological level, it  
is absolutely undecidable if there is anything more than the numbers,  
that is 0, the successor of zero, the successor of the successor of  
zero, ...


And every lawful thing is deducible from the laws of addition and  
multiplication (that you have learn is school, and certainly apply in  
chemistry).


So, with mechanism, physics is not the fundamental science. Physics  
has to be reduced to digital machine (number) biology, psychology,  
theology (given that non provable truth have a big role in the origin  
of matter).





Before I consider your theorem, first I would like to understand  
better in my own terms what physicalsim and mechanism mean and what  
are the limits. When you talk about this, it is too fast for me.


You have to do the thought experiment. You have to admit the  
hypothesis, if only for the sake of the argument.





According to a common view in natural sciences, a human being (and  
hence mind) has been created during evolution.


Something like that might be locally correct, but appears to be wrong  
in the comp (digital mechanist) theory.




Right now however, after following discussion here, I have a problem  
with mathematics along this way. Science has been pretty successful  
with mathematical models in physics, chemistry and even in biology.  
Yet, according to my current view, mathematics has been created by  
the mankind. Thereafter I have got suddenly a question, why  
mathematical models (physical laws) are working at all to describe  
the Universe when there was no mind. The mathematics, it seems, was  
not there at the times of Big Bang.


You might confuse mathematics, branch of human science, and the  
possible mathematical reality.


The mathematical reality does not depend on the physical reality, and  
a large part of it might no depend on the human mind.


For example the fact that 17 is prime, is a mathematical fact which  
does not depend on the presence of human. It is just the fact that a  
line of 17 distinguishable objects cannot be cut in a finite of part  
to be reassembled into a rectangle different from the line itself. For  
example 8 is not prime because the line


. . . . . . . .

can be cut and become

. . . .
. . . .

You might convince you experimentally that 17 is prime in this way,  
but you can also prove it entirely as a consequence of the laws of  
addition and multiplication. No concept of physics enter in this at  
all. You might *apparently* need a physical reality to convince a  
human being that 17 is prime, but you don't need to refer to it to  
transmit the concept of prime number, despite it can helps for the  
intuition, like above.








We cannot repeat Big Bang to understand this.


Remember that we (try) to be scientist, meaning that we cannot commit  
ourself ontologically, except by making clear our postulate. The big- 
bang theory is a theory, an hypothesis, which usually assume an  
ontological (primitively existing) universe.


With mechanism, that theory is already refuted by UDA+MGA.

What is the big bang, then. Open problem. Most plausibly a first  
person plural sharable computational state of some universal number.






According to the current economic situation, it is highly unlikely  
that taxpayers are ready to spend money on bigger and bigger  
particle accelerators. Hence my proposal. If we cannot repeat Big  
Bang, then for a relatively small budget we could make easily a  
local heat death of a small Universe with two mathematicians and see  
what happens with mathematics there. In a way, we repeat evolution  
in the reverse direction.


I 

Re: Two Mathematicians in a Bunker and Existence of Pi

[Brian Tenneson]

There is an important distinction between the names and notations of
mathematics and the objects of study of mathematics.  I believe the former
are inventions of humans while the latter exist independently of mankind.
For example, I am saying that the symbol 0 is an invention of mankind but
what is pointed to by the symbol 0 is not an invention of mankind.

I can't give you absolute proof especially when we're going to assume
different things (i.e., we live in different paradigms).  One thing that
gives me a clue about my conclusion is that mathematical objects will not
exist any less if humanity were to go extinct.  However, arguing that is
like arguing for a particular answer to a koan.



On Sun, Mar 4, 2012 at 8:12 AM, Evgenii Rudnyi  wrote:

>
> Yet, according to my current view, mathematics has been created by the
> mankind.
>

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Re: Two Mathematicians in a Bunker and Existence of Pi

[Evgenii Rudnyi]

Bruno,

Actually it is not a joke. I guess it is my first step toward Platonia. 
As I am a chemist by background, the problem might be not mathematically 
correct indeed. Yet, if you could help, we could improve it in this respect.


The background is as follows. I am a chemist and I am still at the level 
of what you refer to as physicalism or mechanism. Before I consider your 
theorem, first I would like to understand better in my own terms what 
physicalsim and mechanism mean and what are the limits. When you talk 
about this, it is too fast for me.


According to a common view in natural sciences, a human being (and hence 
mind) has been created during evolution. Right now however, after 
following discussion here, I have a problem with mathematics along this 
way. Science has been pretty successful with mathematical models in 
physics, chemistry and even in biology. Yet, according to my current 
view, mathematics has been created by the mankind. Thereafter I have got 
suddenly a question, why mathematical models (physical laws) are working 
at all to describe the Universe when there was no mind. The mathematics, 
it seems, was not there at the times of Big Bang.


We cannot repeat Big Bang to understand this. According to the current 
economic situation, it is highly unlikely that taxpayers are ready to 
spend money on bigger and bigger particle accelerators. Hence my 
proposal. If we cannot repeat Big Bang, then for a relatively small 
budget we could make easily a local heat death of a small Universe with 
two mathematicians and see what happens with mathematics there. In a 
way, we repeat evolution in the reverse direction.


It would be nice to exclude mind out of consideration at all but as this 
is impossible my goal was to reduce its role as possible. We know that 
mathematics is what mathematicians do. Pi is a nice number and most of 
taxpayers have heard about it. In the experiment we could allow 
mathematicians to write the prove that Pi exists on a paper, it would be 
even simpler. If you think that some other mathematical object would be 
nicer, please make your suggestion.


So, at the beginning of the experiment we have mind (two working brains 
of mathematicians) and they prove on the paper that a given mathematical 
object exists. An open question to discuss is what happens with this 
mathematical object at the end of the experiment.


Evgenii


On 04.03.2012 14:39 Bruno Marchal said the following:


On 04 Mar 2012, at 13:27, Evgenii Rudnyi wrote:


An experiment to perform in order to prove experimentally whether
Pi exists independently from the mind

The idea came during discussion on embryophysics list

http://groups.google.com/group/embryophysics/t/419d3c1fec30e3b5

Below there is a description of the experiment that one could think
of to check the relationships between Mathematics, Mind and Nature
(the MMN experiment). In my view this could be done as a real
experiment (so this is actually not a thought experiment) provided
we find two mathematicians who agree to sacrifice their life for
science. I believe that this should be not that difficult provided
the importance of the experiment for the modern science.

Let us take a completely isolated bunker where the experiment
begins. The initial conditions are enough so that mathematicians
can comfortably chat for awhile with each other about Pi and prove
that it exists. Eventually the oxygen in the bunker will run over
and both mathematicians die. From a viewpoint of a natural science,
we have a dynamical system that eventually comes to the equilibrium
state. I assume that at the beginning when mathematicians prove
that Pi exists we have a consequence of physical states where Pi
exists indeed. If you are in doubt, please suggest any other
physical states where you say that Pi exists. The goal of the
experiment is to establish what happens with Pi at the end when the
system reaches the stationary state.

Because of experimental settings, we can neglect the interaction
with environment and I hope that this could be done even for the
quantum mechanics treatment.

Before the experiment will be perform in real, you can take your
bet on whether Pi is retained after the death of mathematicians or
not.


I confess I cannot make any sense of what you say here. What do you
mean by "Pi is retained", how do you verify this (after the death of
the mathematicians)?

Also, what is the initial theory that you have to use to interpret
the experience?

I have no clue of the meaning of "I assume that at the beginning when
 mathematicians prove that Pi exists we have a consequence of
physical states where Pi exists indeed". "consequence of physical
states where Pi exists" contains too many vague abuse of languages.

When mathematicians proves that Pi exists, they assume a lot (real
numbers, circles, length of enough smooth curves, set theory, etc.).

Usually, they don't prove that Pi exist, they assume that all Cauchy
 sequences define some number, call

Re: Two Mathematicians in a Bunker and Existence of Pi

[Bruno Marchal]

On 04 Mar 2012, at 13:27, Evgenii Rudnyi wrote:

An experiment to perform in order to prove experimentally whether Pi  
exists independently from the mind


The idea came during discussion on embryophysics list

http://groups.google.com/group/embryophysics/t/419d3c1fec30e3b5

Below there is a description of the experiment that one could think  
of to check the relationships between Mathematics, Mind and Nature  
(the MMN experiment). In my view this could be done as a real  
experiment (so this is actually not a thought experiment) provided  
we find two mathematicians who agree to sacrifice their life for  
science. I believe that this should be not that difficult provided  
the importance of the experiment for the modern science.


Let us take a completely isolated bunker where the experiment  
begins. The initial conditions are enough so that mathematicians can  
comfortably chat for awhile with each other about Pi and prove that  
it exists. Eventually the oxygen in the bunker will run over and  
both mathematicians die. From a viewpoint of a natural science, we  
have a dynamical system that eventually comes to the equilibrium  
state. I assume that at the beginning when mathematicians prove that  
Pi exists we have a consequence of physical states where Pi exists  
indeed. If you are in doubt, please suggest any other physical  
states where you say that Pi exists. The goal of the experiment is  
to establish what happens with Pi at the end when the system reaches  
the stationary state.


Because of experimental settings, we can neglect the interaction  
with environment and I hope that this could be done even for the  
quantum mechanics treatment.


Before the experiment will be perform in real, you can take your bet  
on whether Pi is retained after the death of mathematicians or not.


I confess I cannot make any sense of what you say here. What do you  
mean by "Pi is retained", how do you verify this (after the death of  
the mathematicians)?


Also, what is the initial theory that you have to use to interpret the  
experience?


I have no clue of the meaning of "I assume that at the beginning when  
mathematicians prove that Pi exists we have a consequence of physical  
states where Pi exists indeed".  "consequence of physical states where  
Pi exists" contains too many vague abuse of languages.


When mathematicians proves that Pi exists, they assume a lot (real  
numbers, circles, length of enough smooth curves, set theory, etc.).


Usually, they don't prove that Pi exist, they assume that all Cauchy  
sequences define some number, called "real number", and they show that  
curves sufficiently smooth have a length definable by such a sequence.  
Then they define Pi, by the ratio of the length of a circle with its  
diameter, and build the Cauchy sequence defining it.


And also, why those two poor mathematicians have to die? Is not Earth  
close enough, and the death of Archimedes enough? (assuming the rest  
makes sense).


You might just be joking, perhaps.

Bruno

http://iridia.ulb.ac.be/~marchal/



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