Weyl on mathematics vs. reality

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Evgenii Rudnyi

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Nov 3, 2012, 3:01:41 PM11/3/12
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Some more quotes from Bas C Van Fraassen Scientific Representation:
Paradoxes of Perspective. This time on what Weyl has said on isomorphism
between mathematics and reality.

p. 208 "Herman Weyl expressed the fundamental insight as follows in 1934:

'A science can never determine its subject-matter expect up to
isomorphic representation. The idea of isomorphism indicates the
self-understood, insurmountable barrier of knowledge. [...T]oward the
"nature" of its objects science maintains complete indifference.' (Weyl
1934:19)

The initial assertion is clearly based on two basic convictions:

o that scientific representation is mathematical, and
o that in mathematics no distinction cuts across structural sameness."

p. 209 "Weyl illustrates this with the example of a color space and an
isomorphic geometric object. ... The color space is a region on the
projective plane. If we can nevertheless distinguish the one from the
other, or from other attribute spaces with that structure, doesn't that
mean that we can know more that what science, so conceived, can deliver?
Weyl accompanies his point about this limitation with an immediate
characterization of the 'something else' which is then left un-represented.

'This - for example what distinguish the colors from the point of the
projective plane - one can only know in immediate alive intuition.' (Ibid.)"

p. 210 "We seem to be left with four equally unpalatable alternatives:

o that either the point about isomorphism and mathematics is mistaken, or

o that scientific representation is not at bottom mathematical
representation alone, or

o that science is necessarily incomplete in a way we can know it to be
incomplete, or

o that those apparent differences to us, cutting across isomorphism,
are illusory.

In his comment about immediate alive intuition, Weyl appears to opt for
the second, or perhaps the third, alternative. But on the either of
this, we face a perplexing epistemological question: Is there something
that I could know to be the case, and which is not expressed by a
proposition that could be part of some scientific theory?"

Evgenii
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http://blog.rudnyi.ru/tag/bas-c-van-fraassen

Craig Weinberg

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Nov 3, 2012, 7:44:34 PM11/3/12
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Nice. I was just writing about mathematics and use of symbols: http://s33light.org/post/34935613677

Craig

Alberto G. Corona

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Nov 3, 2012, 7:47:00 PM11/3/12
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: Is there something that I could know to be the case, and which is not expressed by a proposition that could be part of some scientific theory?"

Yes . "I love my mother" is some knowledge that I know , and is not part of a scientific theory. 
We know reality because we live in the reality, We do not approximate reality by theories. We directly know reality because we live within it.  Our  primary knowledge is intuitive, historic, direct.. It is _the_ reality.  

A theory is a second class of knowledge about a model that approximate reality, maybe upto a point of an isomorphism with some-part-of reality, but certainly, not an isomorphism that embraces the whole reality, because we could never know if we have modelized the entire reality, nether if this modelization is accurate.

The legitimate usage of the models is  to refine this intuitive knowledge. But at the worst, a model can  negate our direct knowledge and try to create an alternative reality. In this case the theorist reclaim the model as the reality. Thus the theorist .reclaim a complete knowledge of reality. In this case the theorist is outside of science, even if it is  within the science industry, and becomes a sort of gnostic preacher



--
Alberto.

meekerdb

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Nov 3, 2012, 9:58:19 PM11/3/12
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It seems to me he left out the most likely case: that our science is incomplete in a way
we know.

Brent

meekerdb

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Nov 3, 2012, 10:28:12 PM11/3/12
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On 11/3/2012 6:47 PM, Alberto G. Corona wrote:


: Is there something that I could know to be the case, and which is not expressed by a proposition that could be part of some scientific theory?"

Yes . "I love my mother" is some knowledge that I know , and is not part of a scientific theory.

But could it be is the question.  There could be a scientific theory that Alberto Corona loves his mother and you could know the theory.



We know reality because we live in the reality, We do not approximate reality by theories. We directly know reality because we live within it.  Our  primary knowledge is intuitive, historic, direct.. It is _the_ reality.  

A theory is a second class of knowledge about a model that approximate reality, maybe upto a point of an isomorphism with some-part-of reality, but certainly, not an isomorphism that embraces the whole reality, because we could never know if we have modelized the entire reality, nether if this modelization is accurate.

The legitimate usage of the models is  to refine this intuitive knowledge. But at the worst, a model can  negate our direct knowledge and try to create an alternative reality. In this case the theorist reclaim the model as the reality. Thus the theorist .reclaim a complete knowledge of reality. In this case the theorist is outside of science, even if it is  within the science industry, and becomes a sort of gnostic preacher

Yes, a model that includes everything is impossible (and not even useful), but it might still be that each thing you know is part of some model.


Evgenii Rudnyi

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Nov 4, 2012, 2:12:06 AM11/4/12
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On 04.11.2012 02:58 meekerdb said the following:
> On 11/3/2012 2:01 PM, Evgenii Rudnyi wrote:

...

>> p. 210 "We seem to be left with four equally unpalatable
>> alternatives:
>>
>> o that either the point about isomorphism and mathematics is
>> mistaken, or
>>
>> o that scientific representation is not at bottom mathematical
>> representation alone, or
>>
>> o that science is necessarily incomplete in a way we can know it
>> to be incomplete, or
>>
>> o that those apparent differences to us, cutting across
>> isomorphism, are illusory.
>>
>> In his comment about immediate alive intuition, Weyl appears to opt
>> for the second, or perhaps the third, alternative. But on the
>> either of this, we face a perplexing epistemological question: Is
>> there something that I could know to be the case, and which is not
>> expressed by a proposition that could be part of some scientific
>> theory?"
>
> It seems to me he left out the most likely case: that our science is
> incomplete in a way we know.
>
> Brent
>

Could you please express this knowledge explicitly?

Evgenii

Evgenii Rudnyi

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Nov 4, 2012, 2:18:31 AM11/4/12
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On 04.11.2012 00:47 Alberto G. Corona said the following:
>>
>> : Is there something that I could know to be the case, and which is
>> not expressed by a proposition that could be part of some
>> scientific theory?"
>>
>> Yes . "I love my mother" is some knowledge that I know , and is not
>> part
> of a scientific theory. We know reality because we live in the
> reality, We do not approximate reality by theories. We directly know
> reality because we live within it. Our primary knowledge is
> intuitive, historic, direct.. It is _the_ reality.
>
> A theory is a second class of knowledge about a model that
> approximate reality, maybe upto a point of an isomorphism with
> some-part-of reality, but certainly, not an isomorphism that embraces
> the whole reality, because we could never know if we have modelized
> the entire reality, nether if this modelization is accurate.
>

Let us imagine that we have a mathematical model that isomorphic with
the whole reality. Let us say that this model is before you as some
computer implementation. The problem of coordination still remains. To
use this model, you need to find out its particular part and relate it
with reality. The model of the whole reality does not do it by itself.

Evgenii

Richard Ruquist

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Nov 4, 2012, 2:37:11 AM11/4/12
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String theory is an example of knowledge of incomplete science as for
the most part string theory has not been verified/falsified
experimentally. Richard
>
> Evgenii
>
>
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Roger Clough

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Nov 4, 2012, 7:24:50 AM11/4/12
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Hi Alberto G. Corona

The only way to know reality is subjectively, just
as Descartes found. He threw everything out until
all he could know for sure was that he could think.

Reality is what is happening now, which is what
we can only know subjectively, from inside, by
aquaintance. We cannot know "now " or reality
descriptively from any theory, only by subjective
acquaintance.



Roger Clough, rcl...@verizon.net
11/4/2012
"Forever is a long time, especially near the end." -Woody Allen


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From: Alberto G. Corona
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Time: 2012-11-03, 18:47:00
Subject: Re: Weyl on mathematics vs. reality





: Is there something that I could know to be the case, and which is not expressed by a proposition that could be part of some scientific theory?"


Yes . "I love my mother" is some knowledge that I know , and is not part of a scientific theory.?
We know reality because we live in the reality, We do not?pproximate?eality by theories. We directly know reality because we live within it. ?ur ?rimary knowledge is intuitive, historic, direct.. It is _the_ reality. ?


A theory is a second class of knowledge about a model that?pproximate?eality, maybe upto a?oint?f an isomorphism with some-part-of reality, but certainly, not an isomorphism that embraces the whole reality,?ecause?e could never know if we have modelized the entire reality, nether if this modelization is accurate.


The legitimate usage of the models is ?o refine this intuitive knowledge. But at the worst, a model can ?egate our direct knowledge and try to create an alternative reality. In this case the theorist reclaim the model as the reality. Thus the theorist .reclaim a complete knowledge of reality. In this case the theorist is outside of science, even if it is ?ithin the science industry, and becomes a sort of gnostic preacher






--
Alberto.

Roger Clough

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Nov 4, 2012, 7:36:59 AM11/4/12
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Hi Evgenii Rudnyi

Weyl makes complicated what is ultimately simple--
reality, which is subjective, which is experiencing,
which is now. Which is focussing your attention
on your breath going out and coming in. This is what
yoga teaches. Weyl does best we he touches on color.

Reality is knowledge by acquaintance. The best that science
can give us is knowledge by description. But that is
just words, code, and words are not reality. The
only reality is in experiencing, such as experiencing
your breathing.

Kierkegard said it much better than Weyl, when he
stated that truth is subjective.


Roger Clough, rcl...@verizon.net
11/4/2012
"Forever is a long time, especially near the end." -Woody Allen


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Time: 2012-11-03, 14:01:41
Subject: Weyl on mathematics vs. reality

Richard Ruquist

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Nov 4, 2012, 7:45:21 AM11/4/12
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Roger,
Is God part of your reality and if so how do you experience God, or is
god just a theory.?
For me god is described by a theory.
Richard

Evgenii Rudnyi

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Nov 4, 2012, 8:18:56 AM11/4/12
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On 04.11.2012 08:37 Richard Ruquist said the following:
Let us imagine that the superstring theory is completed and even
experimentally verified. So what's then? How the superstring theory
would change engineering practice?

Evgenii
--
p. 278 "... the regularities must derive from not just natural but
logical necessity. This sentiment is sometimes encountered still, not so
much among philosophers but in physicists' dreams of a final theory so
logically airtight as to admit of no conceivable alternative, one that
would be grasped as true when understood at all."

Richard Ruquist

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Nov 4, 2012, 9:42:29 AM11/4/12
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I am unable to predict any engineering advantage to any proposed high
energy theory even if it were to explain dark energy. That includes
comp. What I can predict is that such a valid theory may change our
conception of reality. In particular it may determine if a god is
possible and exists and/or if a Many World multiverse exists. My
personal prediction is that it is one or the other, either MWI or a
god and a supernatural realm. Richard

>
> Evgenii
> --
> p. 278 "... the regularities must derive from not just natural but logical
> necessity. This sentiment is sometimes encountered still, not so much among
> philosophers but in physicists' dreams of a final theory so logically
> airtight as to admit of no conceivable alternative, one that would be
> grasped as true when understood at all."
>

meekerdb

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Nov 4, 2012, 3:58:07 PM11/4/12
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We don't know what dark matter is, we don't know what dark energy is, we don't know how to
make GR and QM compatible,...

Brent

meekerdb

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Nov 4, 2012, 4:03:50 PM11/4/12
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That seems like an impossible hypothesis. Usually when one talks about having a model it
is a model that one created or someone else created and the correspondence with whatever
is modeled is part of the creation of the model. If you were simply presented with a model
of all reality and you didn't know who created this model so that you could ask them how
it corresponded to the thing modeled then you would be just like a scientist faced with
nature and you would proceed by creating a model of the model in terms you understood.

Brent

Roger Clough

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Nov 5, 2012, 10:21:14 AM11/5/12
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Hi Richard Ruquist

Engineering advantages ? A decade before the Wright brothers
flew their airplane, people would have said, "You're going to do WHAT ?"

Many if not all innovations like that seem at present to be crazy
or impossible.


Roger Clough, rcl...@verizon.net
11/5/2012
"Forever is a long time, especially near the end." -Woody Allen


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From: Richard Ruquist
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Time: 2012-11-04, 09:42:29
Subject: Re: Weyl on mathematics vs. reality


On Sun, Nov 4, 2012 at 8:18 AM, Evgenii Rudnyi wrote:
> On 04.11.2012 08:37 Richard Ruquist said the following:
>>
>> On Sun, Nov 4, 2012 at 2:12 AM, Evgenii Rudnyi

Roger Clough

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Nov 5, 2012, 2:03:59 PM11/5/12
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Hi meekerdb

Love is a qualia and science cannot touch qualia.


Roger Clough, rcl...@verizon.net
11/5/2012
"Forever is a long time, especially near the end." -Woody Allen


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Subject: Re: Weyl on mathematics vs. reality


Evgenii Rudnyi

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Nov 5, 2012, 2:24:21 PM11/5/12
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On 05.11.2012 16:21 Roger Clough said the following:
> Hi Richard Ruquist
>
> Engineering advantages ? A decade before the Wright brothers flew
> their airplane, people would have said, "You're going to do WHAT ?"
>

I guess this is a very good example, as the Wright brothers have just
done it. I am not sure if they based this innovation on some theory.
Hence is the question, if a superstring theory is really necessary to
drive innovations.

Evgenii

Evgenii Rudnyi

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Nov 5, 2012, 2:32:30 PM11/5/12
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On 04.11.2012 22:03 meekerdb said the following:
What you say about a historical development is exactly what Van Fraassen
offers as a part of a solution to the coordination problem.

Yet, even after the theory has been developed (let us imagine that the
science has included in its model the dark energy, the dark matter and
have found a way to make GR and QM compatible), one needs to take a
decision what a particular part of the theory is necessary to drive a
particular innovation. Even a complete scientific theory will not do it
by itself. In this sense, it will be still incomplete.

Evgenii

Roger Clough

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Nov 5, 2012, 2:46:49 PM11/5/12
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Hi Evgenii Rudnyi

I have heard it said that every year a certain mathematics
society gets together to celebrate the fact that not one of
their papers has proven to be useful.

Pragmatists on the other hand believe that only the useful is true.

Take your pick.


Roger Clough, rcl...@verizon.net
11/5/2012
"Forever is a long time, especially near the end." -Woody Allen


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Subject: Re: Weyl on mathematics vs. reality


meekerdb

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Nov 5, 2012, 3:49:51 PM11/5/12
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What exactly is 'coordination' and why is it a problem?

>
> Yet, even after the theory has been developed (let us imagine that the science has
> included in its model the dark energy, the dark matter and have found a way to make GR
> and QM compatible), one needs to take a decision what a particular part of the theory is
> necessary to drive a particular innovation. Even a complete scientific theory will not
> do it by itself. In this sense, it will be still incomplete.

I don't understand the problem; are you simply saying the model of reality is not reality
itself? That seems rather trivial.

Brent

Evgenii Rudnyi

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Nov 5, 2012, 4:19:24 PM11/5/12
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On 05.11.2012 21:49 meekerdb said the following:
An analogy would be using a map. One needs for example to locate oneself
in a map. This could be generalized.

Let us consider how an engineer for example uses Maxwell equations. An
engineer starts with a design. This design could be described by Maxwell
equations but one needs an engineer to suggest the design. Maxwell
equations on their own are not enough.

>
>>
>> Yet, even after the theory has been developed (let us imagine that
>> the science has included in its model the dark energy, the dark
>> matter and have found a way to make GR and QM compatible), one
>> needs to take a decision what a particular part of the theory is
>> necessary to drive a particular innovation. Even a complete
>> scientific theory will not do it by itself. In this sense, it will
>> be still incomplete.
>
> I don't understand the problem; are you simply saying the model of
> reality is not reality itself? That seems rather trivial.

In a way. A scientific model is after all a representation. And a
representation is

p. 21 �Z uses X to depict Y as F�

Hence even a complete scientific theory does not contain "Z uses". This
remains somehow outside of even a complete Theory of Everything.

In a way it is trivial, I agree. Yet, it seems for example Hawking in
his Grand Design does not agree with such a trivial observation.

Evgenii

Stephen P. King

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Nov 5, 2012, 10:04:28 PM11/5/12
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On 11/5/2012 2:46 PM, Roger Clough wrote:
> Hi Evgenii Rudnyi
>
> I have heard it said that every year a certain mathematics
> society gets together to celebrate the fact that not one of
> their papers has proven to be useful.
>
> Pragmatists on the other hand believe that only the useful is true.
>
> Take your pick.

Laugh out loud! Such silly narcissistic elitism!

>
>
> Roger Clough, rcl...@verizon.net
> 11/5/2012
> "Forever is a long time, especially near the end." -Woody Allen
>
>
> ----- Receiving the following content -----
> From: Evgenii Rudnyi
> Receiver: everything-list
> Time: 2012-11-05, 14:24:21
> Subject: Re: Weyl on mathematics vs. reality
>
>
> On 05.11.2012 16:21 Roger Clough said the following:
>> Hi Richard Ruquist
>>
>> Engineering advantages ? A decade before the Wright brothers flew
>> their airplane, people would have said, "You're going to do WHAT ?"
>>
> I guess this is a very good example, as the Wright brothers have just
> done it. I am not sure if they based this innovation on some theory.
> Hence is the question, if a superstring theory is really necessary to
> drive innovations.
>
> Evgenii
>
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--
Onward!

Stephen


Bruno Marchal

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Nov 6, 2012, 8:49:43 AM11/6/12
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On 05 Nov 2012, at 20:03, Roger Clough wrote:

> Hi meekerdb
>
> Love is a qualia and science cannot touch qualia.

Science can touch everything. And assuming comp science can explain
why qualia are not scientific or communicable. they still remain real
phenomena on which science can say something, even if negative.

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



Bruno Marchal

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Nov 6, 2012, 8:51:11 AM11/6/12
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String theory has made possible the discovery of new proofs of
arithmetical statement. So string theory has already lead to
innovation in number theory. For physics, we will see.

Bruno


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



Roger Clough

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Nov 6, 2012, 9:44:10 AM11/6/12
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Hi Bruno Marchal

My understanding is that qualia are subjective or 1-view,
while the realm of science is completely objective (3-view).

Roger Clough, rcl...@verizon.net
11/6/2012
"Forever is a long time, especially near the end." -Woody Allen


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Stephen P. King

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Nov 6, 2012, 11:18:16 AM11/6/12
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On 11/6/2012 9:44 AM, Roger Clough wrote:
> My understanding is that qualia are subjective or 1-view,
> while the realm of science is completely objective (3-view).
Science 'traces' out the observer and wonders why it cannot understand
the observer! LOL!

--
Onward!

Stephen


Bruno Marchal

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Nov 7, 2012, 9:22:18 AM11/7/12
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Hi Roger Clough,


> My understanding is that qualia are subjective or 1-view,
> while the realm of science is completely objective (3-view).

I agree. A qualia, like the feeling of being convinced, or like the
feeling of seeing the color red, is subjective (1p).

But now the theory saying that a qualia is 1p, might very well be
objective.

Science cannot use subjective statements in a theory, but this does
not prevent a theory to make statements on subjectivity.

If not, you would make a confusion between a level and a meta-level.
We can develop objective and even testable statements about
subjectivity.

For example, with comp, we can decode an 1p-dream from a brain 3p-
analysis.
This seems to have been partially tested:

http://www.scientificamerican.com/article.cfm?id=scientists-read-dreams&WT.mc_id=SA_WR_20121024

Bruno
>> To post to this group, send email to everything-
>> li...@googlegroups.com.

Roger Clough

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Nov 7, 2012, 10:36:20 AM11/7/12
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Hi Bruno Marchal

I think that dreams are the result of the mind's (not the brain's, as
the article cited below suggests) intelligence trying to make sense of
body signals such as from muscle relaxation, etc.

In bringing up the subject of logical abduction (as well as autopoesis),
these seem to be forms of intelligence, since intelligence per se creates
something new (as I see it) out of an existing situation.
Abduction comes to a conclusion which is a prediction not
possibly arrived at by deduction.

Abduction seems to be the heart and soul of intelligence
and being intelligence, seemingly a desirable comp activity.
In other words, comp as a form of artificial intelligence.


Roger Clough, rcl...@verizon.net
11/7/2012
"Forever is a long time, especially near the end." -Woody Allen


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Roger Clough

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Nov 15, 2012, 11:10:48 AM11/15/12
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Hi Evgenii Rudnyi
 
Perhaps strings might better model materials and their behavior
than current chemistry and materials science can. And
suggest the possibioity of creating new materials (composistes) as well
as explaining little understood materials phenomena.
 
 
[Roger Clough], [rcl...@verizon.net]
11/15/2012
"Forever is a long time, especially near the end." -Woody Allen
 
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Subject: Re: Weyl on mathematics vs. reality

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Roger Clough

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Nov 15, 2012, 11:42:40 AM11/15/12
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Hi Richard Ruquist
 
 
Since all love and all truth and all beauty comes from God,
it is hard not to experience God.
 
 
[Roger Clough], [rcl...@verizon.net]
11/15/2012
"Forever is a long time, especially near the end." -Woody Allen
 
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Time: 2012-11-04, 06:45:21
Subject: Re: truth and reality cannot be expressed in words, only experienced

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Evgenii Rudnyi

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Nov 15, 2012, 1:55:10 PM11/15/12
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On 15.11.2012 17:10 Roger Clough said the following:
> Hi Evgenii Rudnyi
>
> Perhaps strings might better model materials and their behavior than
> current chemistry and materials science can. And suggest the
> possibioity of creating new materials (composistes) as well as
> explaining little understood materials phenomena.

Chemists need numerical models to reduce the number of experiments. In
my view, it is highly unlikely that the superstring theory will furnish
better numerical models for chemists.

Evgenii
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