Re: [Fis] SYMMETRY & _ On BioLogic (was Re: The Measurement Problem from the Perspective of an Information-Theoretic Interpretation of Quantum Mechanics

[Bruno Marchal]

Dear Koichiro, dear John and Colleagues,

I bump this older post, as it is related to my recent post to Lou.

On 27 Nov 2015, at 02:06, Koichiro Matsuno wrote:


At 4:28 AM 11/27/2015, John C. wrote:

A paper by my former graduate advisor, Jeff Bub, who was a student  
of David Bohm’s.

http://www.mdpi.com/1099-4300/17/11/7374

The Measurement Problem from the Perspective of an Information- 
Theoretic Interpretation of Quantum Mechanics


   Yes, Bub’s insistence on the absolute randomness would remain  
invincible as far as third-person probabilities are taken for  
granted from the outset in comprehending what messages would QM  
convey to us. On the other hand, once one may happen to feel at ease  
with the first-person probabilities (see, for instance,  James  
Hartle’s “Living in a superposition” http://arXiv.org/abs/ 
1511.01550 ), the first-person probability of the occurrence of such  
an agent assuming the first-person status would come to approach  
unity even within the framework of the decoherent-histories  
interpretation of QM.


I think I agree (modulo some possible ambiguity perhaps).

If we take seriously that we might not be more than relative universal  
machine ourself, this extends in the "decoherent-histories" internal  
(made by the universal numbers) interpretation of Arithmetic.
I discovered the first person arithmetical probabilities before  
knowing anything about quantum mechanics. It is still possible that  
the arithmetical possibilities does not interfere like they should,  
but that is shown to be testable.


Personally, I don't think that a third person indeterminacy makes  
"interesting sense". Like Einstein, I tend to think that God does not  
play dice, and that there is no spooky action at a distance (but that  
too has not yet been derived completely from computationalism, to be  
sure).


This is my second post of the week.

Best,

Bruno






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Re: [Fis] SYMMETRY & _ On BioLogic

[Bruno Marchal]

e  
each element (a,b) as a data depository, wherein we place symbols  
that are concurrently commutative and sequential. The membership in  
a cycle is a symbol that is commutative for each of the members of  
the cycle, but confers also a sequential attribute relating to the  
sequence of place changes that are the essence of a cycle. We thus  
have both commutative and sequenced symbols on elements of a set,  
which allows utilising the extraordinarily helpful relation between  
the “now” and the “past/future: not now”, illustrated in OEIS  
A242615.


We use the cycles as basic units, not the “1” and its replicas.  
Order is a prediction about where will be what, and by generating  
all possible orders, we may generate a biggish table which contains  
all elements’ places under each possible order. The reordering from  
one of the orders into a different one of the orders happens by  
means of cycles.


Among the cycles there are some which lend themselves easily to be  
used as standard cycles. The standard cycles are simple  
implications, corollaries, of a+b=c.


5.  Geometry

The standard cycles allow building rectangular spaces modi  
Descartes. The geometry is strikingly subtle, elegant, logical and  
self-evident. The attachment handles and their topology can be read  
off some tables which detail which versions of a+b=c can coexist  
with which other versions of a+b=c. This is indeed a combinatorics  
of geometry, based on properties of natural numbers.


6.  Quantum information

By keeping an exact accounting about which predictions are being  
fulfilled to which degree we see a self-organisation evolve on  
competing interpretations of a+b=c. Using the property of an  
element to belong to a cycle with cardinality n, we can use the  
negated form of not-belonging to different other cycles to transmit  
information. Information is a statement about something that is not  
the case. We can show the impossibility of a spatial arrangement of  
arguments of a sentence to cause impossibilities of coexistence of  
commutative arguments of the same sentence.


7.  Summary

The natural numbers are ready and waiting for the user to read  
results out of their multitude. The task is for the human to be  
willing to look at patterns that evolve as the order concept  
assigns places to elements. The patterns made visible by reordering  
instances of a+b=c appear to be modelling ways Nature does business  
in a simple, easy and self-evident fashion.



Happy First Full Moon After Spring Equinox to you all.

Karl


2016-03-24 19:31 GMT+01:00 Louis H Kauffman <kauff...@uic.edu>:
Sorry Louis, but try again, please, for your address was wrong in  
the list --Pedro

(I have just discovered, in a trip pause)
BlackBerry de movistar, allí donde estés está tu oficin@
From: Louis H Kauffman <lou...@gmail.com>
Date: Tue, 22 Mar 2016 17:56:06 -0500
To: fis<fis@listas.unizar.es>
Cc: Pedro C. Marijuan<pcmarijuan.i...@aragon.es>
Subject: Re: [Fis] SYMMETRY & _ On BioLogic

Dear Plamen,
It is possible. We are looking here at Pivar and his colleagues  
working with the possibilities of materials. It is similar to how  
people in origami have explored the possibilities of producing  
forms by folding paper.
If we can make hypotheses on how topological geometric forms should  
develop in a way that is resonant with biology, then we can explore  
these in a systematic way. An example is indeed the use of knot  
theory to study DNA recombination. We have a partial model of the  
topological aspect of recombination, and we can explore this by  
using rope models and the abstract apparatus of corresponding  
topological models. Something similar might be possible for  
developmental biology.
On Mar 17, 2016, at 2:45 AM, Dr. Plamen L. Simeonov <plamen.l.simeo...@gmail.com 
> wrote:


Dear Lou and Colleagues,

yes, I agree: an artistic approach can be very fruitful. This is  
like what Stuart Kauffman says about speaking with metaphors. At  
some point our mathematical descriptive tools do not have  
sufficient expressional power to grasp more global general  
insights and we reach out to the domains of narration, music and  
visualisation for help. And this is the point where this effort of  
reflection upon a subject begins to generate and develop new  
expressional forms of mathematics (logics, algebras, geometries).  
I think that you and Ralph Abraham noted this in your  
contributions about the mystic of mathematics in the 2015 JPBMB  
special issue. Therefore I ask here, if we all feel that there is  
some grain of imaginative truth in the works of Pivar and team,  
what piece of mathematics does it needs to become a serious  
theory. Spencer-Brown did also have similar flashy insights in the  
beginning, but he needed 20+ years to abstract them into a  
substantial book and theory. This is what also other  
mathematicians do. They are providing complete works. Modern  
artist

Re: [Fis] SYMMETRY & _ On BioLogic

[Karl Javorszky]

gt; general density of material on paths and of the non-uniform speeds of the
> vehicles that are in convoys. There appear a few hundred of such
> agglomeration types, which we call *logical archetypes. *They are
> referred to usually as chemical elements and their isotopes. Some of them
> cannot exist contemporaneously, but some do.
>
> The coexistence of some logical archetypes imposes constraints on which
> other entities may be in existence and how these share the space. This is a
> Lego/Tetris type arrangement, very much in molecular geometry.
>
>
> I sincerely believe that the tautomat, the model of which has been
> presented to FIS during the last few years, here reintroduced as a skeleton
> on which one may demonstrate concepts, is a powerful and versatile tool to
> discuss questions relating to order in Nature, and offers a deictic
> definition for a concept of a minimal unit. The minimal unit can also have
> the form of a negation of a logical state of affairs. This usage of the
> concept of the minimal unit, namely to refer to something that is not the
> case, is what was meant under “quantum information”.
>
> Karl
>
>
>
> 2016-03-24 20:37 GMT+01:00 Louis H Kauffman <kauff...@uic.edu>:
>
>>
>> --
>> *From: * Louis H Kauffman <lou...@gmail.com>
>> *Date: *Tue, 22 Mar 2016 17:56:06 -0500
>> *To: *fis<fis@listas.unizar.es>
>> *Cc: *Pedro C. Marijuan<pcmarijuan.i...@aragon.es>
>> *Subject: *Re: [Fis] SYMMETRY & _ On BioLogic
>>
>> Dear Plamen,
>> It is possible. We are looking here at Pivar and his colleagues working
>> with the possibilities of materials. It is similar to how people in origami
>> have explored the possibilities of producing forms by folding paper.
>> If we can make hypotheses on how topological geometric forms should
>> develop in a way that is resonant with biology, then we can explore these
>> in a systematic way. An example is indeed the use of knot theory to study
>> DNA recombination. We have a partial model of the topological aspect of
>> recombination, and we can explore this by using rope models and the
>> abstract apparatus of corresponding topological models. Something similar
>> might be possible for developmental biology.
>>
>> On Mar 17, 2016, at 2:45 AM, Dr. Plamen L. Simeonov <
>> plamen.l.simeo...@gmail.com> wrote:
>>
>> Dear Lou and Colleagues,
>>
>> yes, I agree: an artistic approach can be very fruitful. This is like
>> what Stuart Kauffman says about speaking with metaphors. At some point our
>> mathematical descriptive tools do not have sufficient expressional power to
>> grasp more global general insights and we reach out to the domains of
>> narration, music and visualisation for help. And this is the point where
>> this effort of reflection upon a subject begins to generate and develop new
>> expressional forms of mathematics (logics, algebras, geometries). I think
>> that you and Ralph Abraham noted this in your contributions about the
>> mystic of mathematics in the 2015 JPBMB special issue. Therefore I ask
>> here, if we all feel that there is some grain of imaginative truth in the
>> works of Pivar and team, what piece of mathematics does it needs to become
>> a serious theory. Spencer-Brown did also have similar flashy insights in
>> the beginning, but he needed 20+ years to abstract them into a substantial
>> book and theory. This is what also other mathematicians do. They are
>> providing complete works. Modern artists and futurists are shooting fast
>> and then moving to the next “inspiration”, often without “marketing” the
>> earlier idea. And then they are often disappointed that they were not
>> understood by their contemporaries. The lack of They are often arrogant and
>> do not care about the opinion of others like we do in our FIS forum. But
>> they often have some “oracle” messages. So, my question to you and the
>> others here is: Is there a way that we, scientists, can build a solid
>> theory on the base of others' artistic insights? Do you think you can help
>> here as an expert in topology and logic to fill the formalisation gaps in
>> Pivar’s approach and develop something foundational. All this would take
>> time and I am not sure if such artists like Pivar would be ready to
>> participate a scientific-humanitarian discourse, because we know that most
>> of these talents as extremely egocentric and ignorant and we cannot change
>> this. What do you think?
>>
>> Best,
>>
>> Plamen
>>
>>
>>
>>
>> On Thu, Mar 17, 2016 at 8:09 AM, Louis H 

Re: [Fis] SYMMETRY & _ On BioLogic

[Louis H Kauffman]

in has said one should better leave alone, but we split 
> the background to that what we talk about, that what is the case, into one 
> part that is definitely false and one part, that which is simply unknown. 
> That what Wittgenstein has delineated as the background to rational speech is 
> now – thanks to computers – accessible. We propose to use the name 
> “information” for a logical statement which details facts that are not the 
> case, belong to the background in Wittgenstein’s sense. Information is a 
> description of the background to that what is the case.
> 
> d) Unit of what
> 
> Now we arrive at what an accountant would term the minimal accounting unit. 
> The concept may well be called a quantum by people outside the accounting 
> world. In the tables, one may point to an increased degree of exactitude 
> which one arrives at having picked the i-th element. What this minimal degree 
> of increased exactitude refers to exactly, appears not that easy to put in 
> spoken words of a rational language. We do not restrict its meaning to what 
> is the case, but also may refer to something that is now more not the case 
> than before, and specifically we cannot say whether this increased exactitude 
> refers to a linear, spatial or material or temporal (mis-) match. The general 
> idea of a match (or its mirror experience, the mis-match) or a Zero (in case 
> we refer to the contents of the Gray Table) may well be what is targeted by 
> speakers who use the word quantum. That the concept is not easy to catch 
> appears to root in its referring to a mixture of observations that refer to 
> consistent, but also to non-consistent appearances.
> 
> e) Vectors, agglomerations and directions  
> 
> By using the standard reorders, one can build two Euclid spaces. These can be 
> merged into one Newton space with the axes (a+b), (a-2b), (b-2a) for z, y, x. 
> The cycles create a web which is very much directed and oriented.
> 
> Within this web, spatial geometry and topology is of paramount importance. 
> The picture is, however, overlaid by two additional planes, created by 
> standard reorders, that transcend the spaces created by the rectangular axes 
> of standard reorders. It may be a wild guess to suggest the words 
> “electro-magnetic” to be used while describing the effects these two planes 
> cause.
> 
> Influenced or not by the two extra planes, the general tendency of cycles in 
> space is to attribute density unevenly along their paths. There appear 
> agglomeration points in space, where the probability that on this spot 
> material exists continuously contemporaneously is higher than elsewhere.
> 
> These assemblies can be visualised as traffic jams that appear out of the 
> general density of material on paths and of the non-uniform speeds of the 
> vehicles that are in convoys. There appear a few hundred of such 
> agglomeration types, which we call logical archetypes. They are referred to 
> usually as chemical elements and their isotopes. Some of them cannot exist 
> contemporaneously, but some do.
> 
> The coexistence of some logical archetypes imposes constraints on which other 
> entities may be in existence and how these share the space. This is a 
> Lego/Tetris type arrangement, very much in molecular geometry.
> 
>  
> I sincerely believe that the tautomat, the model of which has been presented 
> to FIS during the last few years, here reintroduced as a skeleton on which 
> one may demonstrate concepts, is a powerful and versatile tool to discuss 
> questions relating to order in Nature, and offers a deictic definition for a 
> concept of a minimal unit. The minimal unit can also have the form of a 
> negation of a logical state of affairs. This usage of the concept of the 
> minimal unit, namely to refer to something that is not the case, is what was 
> meant under “quantum information”.
> 
> Karl
> 
>  
>  
> 
> 2016-03-24 20:37 GMT+01:00 Louis H Kauffman <kauff...@uic.edu 
> <mailto:kauff...@uic.edu>>:
> 
> From: Louis H Kauffman <lou...@gmail.com <mailto:lou...@gmail.com>>
> Date: Tue, 22 Mar 2016 17:56:06 -0500
> To: fis<fis@listas.unizar.es <mailto:fis@listas.unizar.es>>
> Cc: Pedro C. Marijuan<pcmarijuan.i...@aragon.es 
> <mailto:pcmarijuan.i...@aragon.es>>
> Subject: Re: [Fis] SYMMETRY & _ On BioLogic
> 
> Dear Plamen,
> It is possible. We are looking here at Pivar and his colleagues working with 
> the possibilities of materials. It is similar to how people in origami have 
> explored the possibilities of producing forms by folding paper.
> If we can make hypotheses on how topological geometric forms should develop 
> in a way that is resonant with biology, then w

Re: [Fis] SYMMETRY & _ On BioLogic

[Karl Javorszky]

 of a match (or its mirror experience, the
mis-match) or a Zero (in case we refer to the contents of the Gray Table)
may well be what is targeted by speakers who use the word quantum. That the
concept is not easy to catch appears to root in its referring to a mixture
of observations that refer to consistent, but also to non-consistent
appearances.

e) Vectors, agglomerations and directions

By using the standard reorders, one can build two Euclid spaces. These can
be merged into one Newton space with the axes *(a+b), (a-2b), (b-2a) *for *z,
y, x. *The cycles create a web which is very much directed and oriented.

Within this web, spatial geometry and topology is of paramount importance.
The picture is, however, overlaid by two additional planes, created by
standard reorders, that transcend the spaces created by the rectangular
axes of standard reorders. It may be a wild guess to suggest the words
“electro-magnetic” to be used while describing the effects these two planes
cause.

Influenced or not by the two extra planes, the general tendency of cycles
in space is to attribute density unevenly along their paths. There appear
agglomeration points in space, where the probability that on this spot
material exists continuously contemporaneously is higher than elsewhere.

These assemblies can be visualised as traffic jams that appear out of the
general density of material on paths and of the non-uniform speeds of the
vehicles that are in convoys. There appear a few hundred of such
agglomeration types, which we call *logical archetypes. *They are referred
to usually as chemical elements and their isotopes. Some of them cannot
exist contemporaneously, but some do.

The coexistence of some logical archetypes imposes constraints on which
other entities may be in existence and how these share the space. This is a
Lego/Tetris type arrangement, very much in molecular geometry.



I sincerely believe that the tautomat, the model of which has been
presented to FIS during the last few years, here reintroduced as a skeleton
on which one may demonstrate concepts, is a powerful and versatile tool to
discuss questions relating to order in Nature, and offers a deictic
definition for a concept of a minimal unit. The minimal unit can also have
the form of a negation of a logical state of affairs. This usage of the
concept of the minimal unit, namely to refer to something that is not the
case, is what was meant under “quantum information”.

Karl





2016-03-24 20:37 GMT+01:00 Louis H Kauffman <kauff...@uic.edu>:

>
> --
> *From: * Louis H Kauffman <lou...@gmail.com>
> *Date: *Tue, 22 Mar 2016 17:56:06 -0500
> *To: *fis<fis@listas.unizar.es>
> *Cc: *Pedro C. Marijuan<pcmarijuan.i...@aragon.es>
> *Subject: *Re: [Fis] SYMMETRY & _ On BioLogic
>
> Dear Plamen,
> It is possible. We are looking here at Pivar and his colleagues working
> with the possibilities of materials. It is similar to how people in origami
> have explored the possibilities of producing forms by folding paper.
> If we can make hypotheses on how topological geometric forms should
> develop in a way that is resonant with biology, then we can explore these
> in a systematic way. An example is indeed the use of knot theory to study
> DNA recombination. We have a partial model of the topological aspect of
> recombination, and we can explore this by using rope models and the
> abstract apparatus of corresponding topological models. Something similar
> might be possible for developmental biology.
>
> On Mar 17, 2016, at 2:45 AM, Dr. Plamen L. Simeonov <
> plamen.l.simeo...@gmail.com> wrote:
>
> Dear Lou and Colleagues,
>
> yes, I agree: an artistic approach can be very fruitful. This is like what
> Stuart Kauffman says about speaking with metaphors. At some point our
> mathematical descriptive tools do not have sufficient expressional power to
> grasp more global general insights and we reach out to the domains of
> narration, music and visualisation for help. And this is the point where
> this effort of reflection upon a subject begins to generate and develop new
> expressional forms of mathematics (logics, algebras, geometries). I think
> that you and Ralph Abraham noted this in your contributions about the
> mystic of mathematics in the 2015 JPBMB special issue. Therefore I ask
> here, if we all feel that there is some grain of imaginative truth in the
> works of Pivar and team, what piece of mathematics does it needs to become
> a serious theory. Spencer-Brown did also have similar flashy insights in
> the beginning, but he needed 20+ years to abstract them into a substantial
> book and theory. This is what also other mathematicians do. They are
> providing complete works. Modern artists and futurists are shooting fast
> and then moving to the next “inspiration”, often without “mar

Re: [Fis] SYMMETRY & _ On BioLogic

[Louis H Kauffman]

Dear Folks,

I am sending this again, just the quantum part, with typos removed.

Best,
Lou

Quantum Theory in a Nutshell

1. A state of a quantum system is a vector |psi> of unit length in a complex 
vector space H. 
H is a Hilbert space, but it can be finite dimensional. 
Dual vectors are denoted by  is a complex number and 
 is a positive real number.

2. A quantum process is a unitary transformation U: H ——> H. 
Unitary means that the U* = U^{-1} where U* denotes the conjugate transpose of 
U.
Unitarity preserves the length of vectors.

3. An observation projects the state to a subspace. The simplest and most 
useful form of this is to 
assume that H has an orthonormal basis { |e_1> ,|e_2>,…} that consists in all 
possible results of observations.

Then observing |psi> results in |e_n> for some n with probability ||^2.
Note that the Sum_{n} ||^2 = 1 since |psi> is a vector of unit 
length.

This description shows that quantum theory is a dynamic sort of probability 
theory.
The state vector |psi> is a superposition of all the possibilities for 
observation, with complex number coefficients.
Via the absolute squares of these coefficients, |psi> can be regarded as a 
probability distribution for the outcomes that correspond to each basis 
element. 
Since the coefficients are complex numbers and the quantum processes preserve 
the total probability, 
one has room for complexity of interaction, phase, superposition, cancellation 
and so on.











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Re: [Fis] SYMMETRY & _ On BioLogic

[Karl Javorszky]

 that are the essence of a cycle.
We thus have both commutative and sequenced symbols on elements of a set,
which allows utilising the extraordinarily helpful relation between the
“now” and the “past/future: not now”, illustrated in *OEIS A242615.*

We use the cycles as basic units, not the “1” and its replicas. Order is a
prediction about where will be what, and by generating all possible orders,
we may generate a biggish table which contains all elements’ places under
each possible order. The reordering from one of the orders into a different
one of the orders happens by means of cycles.

Among the cycles there are some which lend themselves easily to be used as
standard cycles. The standard cycles are simple implications, corollaries,
of *a+b=c*.

5.  Geometry

The standard cycles allow building rectangular spaces modi Descartes. The
geometry is strikingly subtle, elegant, logical and self-evident. The
attachment handles and their topology can be read off some tables which
detail which versions of *a+b=c* can coexist with which other versions of
*a+b=c*. This is indeed a combinatorics of geometry, based on properties of
natural numbers.

6.  Quantum information

By keeping an exact accounting about which predictions are being fulfilled
to which degree we see a self-organisation evolve on competing
interpretations of *a+b=c*. Using the property of an element to belong to a
cycle with cardinality *n, *we can use the negated form of not-belonging to
different other cycles to transmit information. Information is a statement
about something that is not the case. We can show the impossibility of a
spatial arrangement of arguments of a sentence to cause impossibilities of
coexistence of commutative arguments of the same sentence.

7.  Summary

The natural numbers are ready and waiting for the user to read results out
of their multitude. The task is for the human to be willing to look at
patterns that evolve as the order concept assigns places to elements. The
patterns made visible by reordering instances of *a+b=c* appear to be
modelling ways Nature does business in a simple, easy and self-evident
fashion.



Happy First Full Moon After Spring Equinox to you all.

Karl

2016-03-24 19:31 GMT+01:00 Louis H Kauffman <kauff...@uic.edu>:

> Sorry Louis, but try again, please, for your address was wrong in the
> list --Pedro
> (I have just discovered, in a trip pause)
> BlackBerry de movistar, allí donde estés está tu oficin@
> --
> *From: * Louis H Kauffman <lou...@gmail.com>
> *Date: *Tue, 22 Mar 2016 17:56:06 -0500
> *To: *fis<fis@listas.unizar.es>
> *Cc: *Pedro C. Marijuan<pcmarijuan.i...@aragon.es>
> *Subject: *Re: [Fis] SYMMETRY & _ On BioLogic
>
> Dear Plamen,
> It is possible. We are looking here at Pivar and his colleagues working
> with the possibilities of materials. It is similar to how people in origami
> have explored the possibilities of producing forms by folding paper.
> If we can make hypotheses on how topological geometric forms should
> develop in a way that is resonant with biology, then we can explore these
> in a systematic way. An example is indeed the use of knot theory to study
> DNA recombination. We have a partial model of the topological aspect of
> recombination, and we can explore this by using rope models and the
> abstract apparatus of corresponding topological models. Something similar
> might be possible for developmental biology.
>
> On Mar 17, 2016, at 2:45 AM, Dr. Plamen L. Simeonov <
> plamen.l.simeo...@gmail.com> wrote:
>
> Dear Lou and Colleagues,
>
> yes, I agree: an artistic approach can be very fruitful. This is like what
> Stuart Kauffman says about speaking with metaphors. At some point our
> mathematical descriptive tools do not have sufficient expressional power to
> grasp more global general insights and we reach out to the domains of
> narration, music and visualisation for help. And this is the point where
> this effort of reflection upon a subject begins to generate and develop new
> expressional forms of mathematics (logics, algebras, geometries). I think
> that you and Ralph Abraham noted this in your contributions about the
> mystic of mathematics in the 2015 JPBMB special issue. Therefore I ask
> here, if we all feel that there is some grain of imaginative truth in the
> works of Pivar and team, what piece of mathematics does it needs to become
> a serious theory. Spencer-Brown did also have similar flashy insights in
> the beginning, but he needed 20+ years to abstract them into a substantial
> book and theory. This is what also other mathematicians do. They are
> providing complete works. Modern artists and futurists are shooting fast
> and then moving to the next “inspiration”, often without “marketing” the
> earlier idea. And then they are often disa

Re: [Fis] SYMMETRY & _ On BioLogic

[Louis H Kauffman]

From: Louis H Kauffman <lou...@gmail.com <mailto:lou...@gmail.com>>
Date: Tue, 22 Mar 2016 17:56:06 -0500
To: fis<fis@listas.unizar.es <mailto:fis@listas.unizar.es>>
Cc: Pedro C. Marijuan<pcmarijuan.i...@aragon.es 
<mailto:pcmarijuan.i...@aragon.es>>
Subject: Re: [Fis] SYMMETRY & _ On BioLogic

Dear Plamen,
It is possible. We are looking here at Pivar and his colleagues working with 
the possibilities of materials. It is similar to how people in origami have 
explored the possibilities of producing forms by folding paper.
If we can make hypotheses on how topological geometric forms should develop in 
a way that is resonant with biology, then we can explore these in a systematic 
way. An example is indeed the use of knot theory to study DNA recombination. We 
have a partial model of the topological aspect of recombination, and we can 
explore this by using rope models and the abstract apparatus of corresponding 
topological models. Something similar might be possible for developmental 
biology. 
> On Mar 17, 2016, at 2:45 AM, Dr. Plamen L. Simeonov 
> <plamen.l.simeo...@gmail.com <mailto:plamen.l.simeo...@gmail.com>> wrote:
> 
> Dear Lou and Colleagues,
> 
> yes, I agree: an artistic approach can be very fruitful. This is like what 
> Stuart Kauffman says about speaking with metaphors. At some point our 
> mathematical descriptive tools do not have sufficient expressional power to 
> grasp more global general insights and we reach out to the domains of 
> narration, music and visualisation for help. And this is the point where this 
> effort of reflection upon a subject begins to generate and develop new 
> expressional forms of mathematics (logics, algebras, geometries). I think 
> that you and Ralph Abraham noted this in your contributions about the mystic 
> of mathematics in the 2015 JPBMB special issue. Therefore I ask here, if we 
> all feel that there is some grain of imaginative truth in the works of Pivar 
> and team, what piece of mathematics does it needs to become a serious theory. 
> Spencer-Brown did also have similar flashy insights in the beginning, but he 
> needed 20+ years to abstract them into a substantial book and theory. This is 
> what also other mathematicians do. They are providing complete works. Modern 
> artists and futurists are shooting fast and then moving to the next 
> “inspiration”, often without “marketing” the earlier idea. And then they are 
> often disappointed that they were not understood by their contemporaries. The 
> lack of They are often arrogant and do not care about the opinion of others 
> like we do in our FIS forum. But they often have some “oracle” messages. So, 
> my question to you and the others here is: Is there a way that we, 
> scientists, can build a solid theory on the base of others' artistic 
> insights? Do you think you can help here as an expert in topology and logic 
> to fill the formalisation gaps in Pivar’s approach and develop something 
> foundational. All this would take time and I am not sure if such artists like 
> Pivar would be ready to participate a scientific-humanitarian discourse, 
> because we know that most of these talents as extremely egocentric and 
> ignorant and we cannot change this. What do you think?
> 
> Best,
> 
> Plamen
> 
> 
> 
> 
> On Thu, Mar 17, 2016 at 8:09 AM, Louis H Kauffman <lou...@gmail.com 
> <mailto:lou...@gmail.com>> wrote:
> Dear Plamen,
> I do not know why Gel-Mann supported this. It is interesting to me anyway. It 
> is primarily an artistic endeavor but is based on some ideas of visual 
> development of complex forms from simpler forms.
> Some of these stories may have a grain of truth. The sort of thing I do and 
> others do is much more conservative (even what D’Arcy Thompson did is much 
> more conservative). We look for simple patterns that definitely seem to occur 
> in complex situations and we abstract them and work with them on their own 
> grounds, and with regard to how these patterns work in a complex system. An 
> artistic approach can be very fruitful.
> Best,
> Lou
> 
>> On Mar 16, 2016, at 9:43 AM, Dr. Plamen L. Simeonov 
>> <plamen.l.simeo...@gmail.com <mailto:plamen.l.simeo...@gmail.com>> wrote:
>> 
>> Dear Lou, Pedro and Colleagues,
>> 
>> I have another somewhat provoking question about the "constructive" role of 
>> topology in morphogenesis. What do you think about the somewhat artistic, 
>> but scientifically VERY controversial theory about the origin and 
>> development of life forms based on physical forces from classical mechanics 
>> and topology only, thus ignoring all of genetics, Darwinism and Creationism:
>> 
>> http://www.ila

Re: [Fis] SYMMETRY & _ On BioLogic

[Louis H Kauffman]

Sorry Louis, but try again, please, for your address was wrong in the list 
--Pedro
(I have just discovered, in a trip pause)
BlackBerry de movistar, allí donde estés está tu oficin@
From: Louis H Kauffman <lou...@gmail.com>
Date: Tue, 22 Mar 2016 17:56:06 -0500
To: fis<fis@listas.unizar.es>
Cc: Pedro C. Marijuan<pcmarijuan.i...@aragon.es>
Subject: Re: [Fis] SYMMETRY & _ On BioLogic

Dear Plamen,
It is possible. We are looking here at Pivar and his colleagues working with 
the possibilities of materials. It is similar to how people in origami have 
explored the possibilities of producing forms by folding paper.
If we can make hypotheses on how topological geometric forms should develop in 
a way that is resonant with biology, then we can explore these in a systematic 
way. An example is indeed the use of knot theory to study DNA recombination. We 
have a partial model of the topological aspect of recombination, and we can 
explore this by using rope models and the abstract apparatus of corresponding 
topological models. Something similar might be possible for developmental 
biology. 
> On Mar 17, 2016, at 2:45 AM, Dr. Plamen L. Simeonov 
> <plamen.l.simeo...@gmail.com <mailto:plamen.l.simeo...@gmail.com>> wrote:
> 
> Dear Lou and Colleagues,
> 
> yes, I agree: an artistic approach can be very fruitful. This is like what 
> Stuart Kauffman says about speaking with metaphors. At some point our 
> mathematical descriptive tools do not have sufficient expressional power to 
> grasp more global general insights and we reach out to the domains of 
> narration, music and visualisation for help. And this is the point where this 
> effort of reflection upon a subject begins to generate and develop new 
> expressional forms of mathematics (logics, algebras, geometries). I think 
> that you and Ralph Abraham noted this in your contributions about the mystic 
> of mathematics in the 2015 JPBMB special issue. Therefore I ask here, if we 
> all feel that there is some grain of imaginative truth in the works of Pivar 
> and team, what piece of mathematics does it needs to become a serious theory. 
> Spencer-Brown did also have similar flashy insights in the beginning, but he 
> needed 20+ years to abstract them into a substantial book and theory. This is 
> what also other mathematicians do. They are providing complete works. Modern 
> artists and futurists are shooting fast and then moving to the next 
> “inspiration”, often without “marketing” the earlier idea. And then they are 
> often disappointed that they were not understood by their contemporaries. The 
> lack of They are often arrogant and do not care about the opinion of others 
> like we do in our FIS forum. But they often have some “oracle” messages. So, 
> my question to you and the others here is: Is there a way that we, 
> scientists, can build a solid theory on the base of others' artistic 
> insights? Do you think you can help here as an expert in topology and logic 
> to fill the formalisation gaps in Pivar’s approach and develop something 
> foundational. All this would take time and I am not sure if such artists like 
> Pivar would be ready to participate a scientific-humanitarian discourse, 
> because we know that most of these talents as extremely egocentric and 
> ignorant and we cannot change this. What do you think?
> 
> Best,
> 
> Plamen
> 
> 
> 
> 
> On Thu, Mar 17, 2016 at 8:09 AM, Louis H Kauffman <lou...@gmail.com 
> <mailto:lou...@gmail.com>> wrote:
> Dear Plamen,
> I do not know why Gel-Mann supported this. It is interesting to me anyway. It 
> is primarily an artistic endeavor but is based on some ideas of visual 
> development of complex forms from simpler forms.
> Some of these stories may have a grain of truth. The sort of thing I do and 
> others do is much more conservative (even what D’Arcy Thompson did is much 
> more conservative). We look for simple patterns that definitely seem to occur 
> in complex situations and we abstract them and work with them on their own 
> grounds, and with regard to how these patterns work in a complex system. An 
> artistic approach can be very fruitful.
> Best,
> Lou
> 
>> On Mar 16, 2016, at 9:43 AM, Dr. Plamen L. Simeonov 
>> <plamen.l.simeo...@gmail.com <mailto:plamen.l.simeo...@gmail.com>> wrote:
>> 
>> Dear Lou, Pedro and Colleagues,
>> 
>> I have another somewhat provoking question about the "constructive" role of 
>> topology in morphogenesis. What do you think about the somewhat artistic, 
>> but scientifically VERY controversial theory about the origin and 
>> development of life forms based on physical forces from classical mechanics 
>> and topology only, thus ignoring all of genetics, Darwinism

Re: [Fis] SYMMETRY & _ On BioLogic

[Pedro C. Marijuan]

Dear FIS Colleagues,

For my taste the ongoing conversation is running too fast. We have 
passed, via Louis, Plamen, and other colleagues, along essential themes 
on the relationship between life and formal approaches, perhaps too 
cavalierly.


I am still stuck with the problem of explanation in biology and the role 
of Darwinism as a supposed central theory of the biologic, motivated by 
the initial exchanges. The apparent centrality of natural selection when 
confronted with biomolecular, physiological, developmental, 
populational, and ecological arenas becomes often the overstretching of 
a paradigm (of not so brilliant performance in my opinion), and also the 
lack of alternative general frameworks to reflect more consistently on 
the knowns and unknowns of the whole biological complexity. The parallel 
with mechanics in physics could be illustrative--classical, statistical, 
fluid, quantum... what is finally "mechanics"? For Wilczek, a successful 
"culture".


More explanatory dimensions are needed in biology, and herein we have 
been commenting on topology, morphology, and other lateral points. 
Living systems have discovered and introjected so many laws of nature 
and emergent morpho-geometric constraints, that a whole signaling pack 
devoted to deal with mechanical force (mostly via cytoskeleton and 
adhesion molecules) has become essential for organismic development. 
Stress and adhesion dictate gene expression, powerfully. That some 
coding counterparts have to exist is OK, but the explanatory burden 
belongs to the very morpho-topological phenomena and to the functional 
tricks that realize it cellularly on the biomolecular and physiological 
scales. The same regarding the amazing emergences derived from the 
handling of electrical and electromagnetic fields.  A doctrinarism close 
to the sectarian takes the existence of the encoding --by natural 
selection, and what else?-- as the only significant point to reiterate, 
endlessly. In an equivalence with modern technology, would we talk about 
market competition as the only creative engine of inventions?


The sort of explanatory art needed (quite OK with Plamen's call and Dr. 
Pivar's exploration), would mean following the appropriate disciplinary 
tributaries, irrespective of their origins, and not only the officially 
established main course. In my view, we maintain explanatory styles of 
other epochs, with far less complicated systems of knowledge.


An interesting point, perhaps more concrete, would rely on the 
capability of the cellular "engine" to attain a quasi universal 
problem-solving capability. Whatever the problem at hand, the adequate 
mixing of positional, differentiating, and mecano-morphological 
capabilities of cells will produce adequate inventions. The ways and 
means to achieve those inventions is our explanatory problem. A little 
detail is why prokaryotes were unable to conquer morphology, while 
eukaryotes excelled. Was it because of the lack of cytoskeleton and the 
associated lack of mechano-topological mastery (or mainly for lacking 
DNA handling virtuosity)? More other expl. branches to the "river"?


Anyhow, excuse these torpid attempt to rekindle a discussion that for me 
is very important, yes, in informational matters.


best regards--Pedro

--
-
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
Instituto Aragonés de Ciencias de la Salud
Centro de Investigación Biomédica de Aragón (CIBA)
Avda. San Juan Bosco, 13, planta X
50009 Zaragoza, Spain
Tfno. +34 976 71 3526 (& 6818)
pcmarijuan.i...@aragon.es
http://sites.google.com/site/pedrocmarijuan/
-

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Re: [Fis] SYMMETRY & _ On BioLogic

[Dr. Plamen L. Simeonov]

Dear Lou and Colleagues,

yes, I agree: an artistic approach can be very fruitful. This is like what
Stuart Kauffman says about speaking with metaphors. At some point our
mathematical descriptive tools do not have sufficient expressional power to
grasp more global general insights and we reach out to the domains of
narration, music and visualisation for help. And this is the point where
this effort of reflection upon a subject begins to generate and develop new
expressional forms of mathematics (logics, algebras, geometries). I think
that you and Ralph Abraham noted this in your contributions about the
mystic of mathematics in the 2015 JPBMB special issue. Therefore I ask
here, if we all feel that there is some grain of imaginative truth in the
works of Pivar and team, what piece of mathematics does it needs to become
a serious theory. Spencer-Brown did also have similar flashy insights in
the beginning, but he needed 20+ years to abstract them into a substantial
book and theory. This is what also other mathematicians do. They are
providing complete works. Modern artists and futurists are shooting fast
and then moving to the next “inspiration”, often without “marketing” the
earlier idea. And then they are often disappointed that they were not
understood by their contemporaries. The lack of They are often arrogant and
do not care about the opinion of others like we do in our FIS forum. But
they often have some “oracle” messages. So, my question to you and the
others here is: Is there a way that we, scientists, can build a solid
theory on the base of others' artistic insights? Do you think you can help
here as an expert in topology and logic to fill the formalisation gaps in
Pivar’s approach and develop something foundational. All this would take
time and I am not sure if such artists like Pivar would be ready to
participate a scientific-humanitarian discourse, because we know that most
of these talents as extremely egocentric and ignorant and we cannot change
this. What do you think?

Best,

Plamen




On Thu, Mar 17, 2016 at 8:09 AM, Louis H Kauffman  wrote:

> Dear Plamen,
> I do not know why Gel-Mann supported this. It is interesting to me anyway.
> It is primarily an artistic endeavor but is based on some ideas of visual
> development of complex forms from simpler forms.
> Some of these stories may have a grain of truth. The sort of thing I do
> and others do is much more conservative (even what D’Arcy Thompson did is
> much more conservative). We look for simple patterns that definitely seem
> to occur in complex situations and we abstract them and work with them on
> their own grounds, and with regard to how these patterns work in a complex
> system. An artistic approach can be very fruitful.
> Best,
> Lou
>
> On Mar 16, 2016, at 9:43 AM, Dr. Plamen L. Simeonov <
> plamen.l.simeo...@gmail.com> wrote:
>
> Dear Lou, Pedro and Colleagues,
>
> I have another somewhat provoking question about the "constructive" role
> of topology in morphogenesis. What do you think about the somewhat
> artistic, but scientifically VERY controversial theory about the origin and
> development of life forms based on physical forces from classical mechanics
> and topology only, thus ignoring all of genetics, Darwinism and Creationism:
>
> http://www.ilasol.org.il/ILASOL/uploads/files/Pivar_ILASOL-2010.pdf
>
> What part of this can be regarded as science at all, and If there is
> something missing what is it? Why did a person like Murray Gel-Mann support
> this?
>
>
> Best
>
> Plamen
>
> 
>
>
> On Tue, Mar 15, 2016 at 12:00 PM, Pedro C. Marijuan <
> pcmarijuan.i...@aragon.es> wrote:
>
>> Louis, a very simple question: in your model of self-replication, when
>> you enter the environment, could it mean something else than just providing
>> the raw stuff for reproduction? It would be great if related to successive
>> cycles one could include emergent topological (say geometrical-mechanical)
>> properties. For instance, once you have divided three times the initial
>> egg-cell, you would encounter three symmetry axes that would co-define the
>> future axes of animal development--dorsal/ventral, anterior/posterior,
>> lateral/medial. Another matter would be about the timing of complexity,
>> whether mere repetition of cycles could generate or not sufficient
>> functional diversity such as Plamen was inquiring in the case of molecular
>> clocks (nope in my opinion).  best--Pedro
>>
>>
>> --
>> -
>> Pedro C. Marijuán
>> Grupo de Bioinformación / Bioinformation Group
>> Instituto Aragonés de Ciencias de la Salud
>> Centro de Investigación Biomédica de Aragón (CIBA)
>> Avda. San Juan Bosco, 13, planta X
>> 50009 Zaragoza, Spain
>> Tfno. +34 976 71 3526 (& 6818)
>> pcmarijuan.i...@aragon.es
>> http://sites.google.com/site/pedrocmarijuan/
>> -
>>
>> 

Re: [Fis] SYMMETRY & _ On BioLogic

[Pedro C. Marijuan]

Louis, a very simple question: in your model of self-replication, when 
you enter the environment, could it mean something else than just 
providing the raw stuff for reproduction? It would be great if related 
to successive cycles one could include emergent topological (say 
geometrical-mechanical) properties. For instance, once you have divided 
three times the initial egg-cell, you would encounter three symmetry 
axes that would co-define the future axes of animal 
development--dorsal/ventral, anterior/posterior, lateral/medial. Another 
matter would be about the timing of complexity, whether mere repetition 
of cycles could generate or not sufficient functional diversity such as 
Plamen was inquiring in the case of molecular clocks (nope in my 
opinion).  best--Pedro


--
-
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
Instituto Aragonés de Ciencias de la Salud
Centro de Investigación Biomédica de Aragón (CIBA)
Avda. San Juan Bosco, 13, planta X
50009 Zaragoza, Spain
Tfno. +34 976 71 3526 (& 6818)
pcmarijuan.i...@aragon.es
http://sites.google.com/site/pedrocmarijuan/
-

___
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Fis@listas.unizar.es
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Re: [Fis] SYMMETRY & _ On BioLogic

[Francesco Rizzo]

Caro Pedro e cari Tutti,
allego un file .doc di alcune pagine di "Etica dei valori economici o
economia dei valori etici" scritte nel 2002 e pubblicate nel 2004
(FrancoAngeli, Milano), il cui contenuto è, a mio giudizio, congruente e
pertinente al tema che si sta affrontando. Naturalmente, chiedo scusa a
tutti per la lunghezza dello scritto e per la pazienza che Vi chiedo di
avere nei miei confronti, dato che uso la lingua italiana. In modo
particolare a Pedro che mi deve sopportare pur essendo, in un certo qual
modo, un diverso che naviga in molti campi del sapere e chiede
semplicemente di trovare, come sempre è accaduto nella Fis, uno spazio per
me prezioso, provvidenziale e  compensativo di tante congiure del silenzio
di cui sono stato oggetto. Ecco perché, fino a quando il mio "pensiero
pensante" funzionerà farò il possibile e l'impossibile per comunicare con
il mondo che amo, conservo e custodisco nel mio cuore. Comunque, io voglio
bene a Tutti perché ho sempre avuto da Dio Padre una misericordia che mi
abilita a per-donare e ad essere per-donato.
Grazie quaresimale e pasquale.
Vostro Francesco


2016-03-11 14:09 GMT+01:00 Pedro C. Marijuan :

> Dear FIS Colleagues,
>
> Let me start by announcing the *special session on **INFORMATION &
> SYMMETRY*, in the Symmetry gathering this Summer in Vienna (18-22 July)
> http://festival.symmetry.hu/ The deadline for abstract reception in this
> session has been enlarged until beginnings of next month. Tentatively, it
> will be chaired by our colleagues Jerry Chandler and Abir Igamberdiev. A
> special issue has been planned in cooperation with the journal
> "Information" too. We will celebrate the near 20th anniversary of the first
> joint session with FIS on information and symmetry (Washington 1995) and
> the subsequent special issues (Symmetry & Culture, 1996 and 97). It will be
> a good occasion to meet again and pass over the views developed in this
> period. Old FISers and members of this list are invited to attend.
>
> And then about the ongoing discussion--responding to the exciting
> exchanges by Louis and Plamen. This type of abstract discussion is rarely
> fertile for biological fundamentals, where structure and function become so
> intertwined that the concrete mechanisms obliterate the quest for too
> far-reaching generalizations, but it may be interesting for approaching
> problems such as "distinctions". Some time ago I tried an approach not so
> different from Spencer Brown's. It was based on "multidimensional
> partitions", a development of Karl Javorszky (of this list) for set theory
> out from classical Euler's partitions (the different ways to decompose
> additively a natural number). It was very interesting finding a natural
> limit for the total distinctional between members of given set, finding a
> curious info dynamics of distinctional gains and losses after addition of
> just one sign or a few signs in the set, a sort of power law in the total
> decomposition, etc. (most of this was coming from previous works by
> Karl--we somehow improved the algorithmic, with a few colleagues here in
> Zaragoza). Then we tried to apply it to prokaryotic complex receptors (2CS,
> 3CS) and to the "language of cells"... but we reached our math limits very
> soon (anyhow, some elementary drafts and publc. were left). I keep thinking
> that it was a serious approach to cellular "distinctions" that could be
> escalated upwards. Later on, in a couple of papers in BioSystems (2010, 99,
> 94-103; and  2013, 114, 8-24) we roughly described prokaryotic and
> eukaryotic signaling machinery in relation with the intelligent advancement
> of the life cycle of each cell.
>
> About viruses in evolution, we could listen in Vienna (IS4IS & FIS 2015
> Conference) to one of the most advanced thinkers, Guenther Witzany. What
> Plamen suggests about a virus theory from the viewpoint of viruses is not
> science fiction. It is astonishing what a few crucial proteins of HIV
> "know" about hundred molecular components of our lymphocytes. It is as if
> they had conspired with structurally enslaved pieces of former viruses
> temporarily joining them to create havoc in the machinery of the cellular
> host. If just 30% of what Guenther says is right, we have to revise the
> Symbiotic Theory, the Central Dogma, the RNA (inner) cloud, gene
> expression, biosemiosis, etc.
>
> Echoing the final debates of the previous session, description should go
> first. And in bio-informational matters there is still plenty to describe.
>
> Best regards--Pedro
>
>
>
>
> --
> -
> Pedro C. Marijuán
> Grupo de Bioinformación / Bioinformation Group
> Instituto Aragonés de Ciencias de la Salud
> Centro de Investigación Biomédica de Aragón (CIBA)
> Avda. San Juan Bosco, 13, planta X
> 50009 Zaragoza, Spain
> Tfno. +34 976 71 3526 (& 
> 6818)pcmarijuan.iacs@aragon.eshttp://sites.google.com/site/pedrocmarijuan/
> 

[Fis] SYMMETRY & _ On BioLogic

[Pedro C. Marijuan]

Dear FIS Colleagues,

Let me start by announcing the *special session on *_*INFORMATION & 
SYMMETRY*_, in the Symmetry gathering this Summer in Vienna (18-22 July) 
http://festival.symmetry.hu/ The deadline for abstract reception in this 
session has been enlarged until beginnings of next month. Tentatively, 
it will be chaired by our colleagues Jerry Chandler and Abir 
Igamberdiev. A special issue has been planned in cooperation with the 
journal "Information" too. We will celebrate the near 20th anniversary 
of the first joint session with FIS on information and symmetry 
(Washington 1995) and the subsequent special issues (Symmetry & Culture, 
1996 and 97). It will be a good occasion to meet again and pass over the 
views developed in this period. Old FISers and members of this list are 
invited to attend.


And then about the ongoing discussion--responding to the exciting 
exchanges by Louis and Plamen. This type of abstract discussion is 
rarely fertile for biological fundamentals, where structure and function 
become so intertwined that the concrete mechanisms obliterate the quest 
for too far-reaching generalizations, but it may be interesting for 
approaching problems such as "distinctions". Some time ago I tried an 
approach not so different from Spencer Brown's. It was based on 
"multidimensional partitions", a development of Karl Javorszky (of this 
list) for set theory out from classical Euler's partitions (the 
different ways to decompose additively a natural number). It was very 
interesting finding a natural limit for the total distinctional between 
members of given set, finding a curious info dynamics of distinctional 
gains and losses after addition of just one sign or a few signs in the 
set, a sort of power law in the total decomposition, etc. (most of this 
was coming from previous works by Karl--we somehow improved the 
algorithmic, with a few colleagues here in Zaragoza). Then we tried to 
apply it to prokaryotic complex receptors (2CS, 3CS) and to the 
"language of cells"... but we reached our math limits very soon (anyhow, 
some elementary drafts and publc. were left). I keep thinking that it 
was a serious approach to cellular "distinctions" that could be 
escalated upwards. Later on, in a couple of papers in BioSystems (2010, 
99, 94-103; and  2013, 114, 8-24) we roughly described prokaryotic and 
eukaryotic signaling machinery in relation with the intelligent 
advancement of the life cycle of each cell.


About viruses in evolution, we could listen in Vienna (IS4IS & FIS 2015 
Conference) to one of the most advanced thinkers, Guenther Witzany. What 
Plamen suggests about a virus theory from the viewpoint of viruses is 
not science fiction. It is astonishing what a few crucial proteins of 
HIV "know" about hundred molecular components of our lymphocytes. It is 
as if they had conspired with structurally enslaved pieces of former 
viruses temporarily joining them to create havoc in the machinery of the 
cellular host. If just 30% of what Guenther says is right, we have to 
revise the Symbiotic Theory, the Central Dogma, the RNA (inner) cloud, 
gene expression, biosemiosis, etc.


Echoing the final debates of the previous session, description should go 
first. And in bio-informational matters there is still plenty to describe.


Best regards--Pedro




--
-
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
Instituto Aragonés de Ciencias de la Salud
Centro de Investigación Biomédica de Aragón (CIBA)
Avda. San Juan Bosco, 13, planta X
50009 Zaragoza, Spain
Tfno. +34 976 71 3526 (& 6818)
pcmarijuan.i...@aragon.es
http://sites.google.com/site/pedrocmarijuan/
-

___
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