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<DIV><FONT face=Arial size=2>Dear Mark and Colleagues (for which latter I attach
Mark's message),</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Thank you, Mark, for reminding us of your
discussion, especially, on p. 104 "energy is a kind of information". As we have
discussed previously, however, adding that "information is a kind of energy"
does not resolve the problem completely:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>1. You yourself define information as
'multi-faceted', but this begs the question of which facet energy is a
kind.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>2. We may agree that, if they are not
identical, energy and information always accompany one another and may have
emerged together from some as yet incompletely defined substrate. However, they
may not be, do not have to be and for me are not at the same ontological level,
and energy is primary being less abstract.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>3. Even the sophisticated mathematics of your
<EM>Theory of Information</EM> does not capture, any more than any other
mathematical theory, the complex qualitative properties of information
processes for which no algorithm can be written. On the other hand, these
processes do follow the logical laws for the evolution of energetic processes.
</FONT><FONT face=Arial size=2>To state this in other terms, whatever the entire
complex set of properties of information, one of them is that it reflects the
underlying duality of a universe constituted by physical
matter-energy.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>4. As a further example of the importance of
ontological priority, one that is consistent with 'informational thinking', I
mention the theory of Michael Graziano, <EM>Consciousness and the Social
Brain</EM>, Oxford, 2013*. According to this, consciousness does not result in
attention but is a consequence of the reflexive processing of information
obtained through attention. The 'hard problem' of an isolated, subjective
experience falls out. This is consistent with the principles of my logic which I
will not repeat here.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Comments welcome,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Joseph</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>*Reviewed in <EM>SCIENCE</EM>, 345:6193, p. 147, 11
July 2014</FONT></DIV>
<DIV>
----- Original Message
----- </DIV>
<BLOCKQUOTE
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=mburgin@math.ucla.edu href="mailto:mburgin@math.ucla.edu">Burgin,
Mark</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=joe.brenner@bluewin.ch
href="mailto:joe.brenner@bluewin.ch">Joseph Brenner</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Friday, August 01, 2014 9:19
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [Fis] Krassimir's
Information Quadruple and GIT. Quintuples?</DIV>
<DIV><FONT face=Arial size=2></FONT><FONT face=Arial size=2></FONT><FONT
face=Arial size=2></FONT><FONT face=Arial size=2></FONT><FONT face=Arial
size=2></FONT><FONT face=Arial size=2></FONT><FONT face=Arial
size=2></FONT><FONT face=Arial size=2></FONT><FONT face=Arial
size=2></FONT><FONT face=Arial size=2></FONT><FONT face=Arial
size=2></FONT><BR></DIV>Dear Joseph and Colleagues,<BR>An answer to "t<FONT
face=Arial size=2>he perhaps badly posed question of whether information or
energy is more fundamental</FONT>" is given in the book M.Burgin, Theory of
information. The answer is a little bit unexpected:<BR>Energy is a kind of
information and information is a kind of energy.<BR>It's a pity that very few
researchers read books with advanced theories based on sophisticated
mathematics.<BR><BR> Sincerely,<BR>Mark Burgin<BR><BR><BR><BR>
<DIV class=moz-cite-prefix>On 7/31/2014 2:40 AM, Joseph Brenner
wrote:<BR></DIV>
<BLOCKQUOTE cite=mid:65F859D7557B404EAEA1B1B767A04D81@PCdeJoseph
type="cite"><META content="MSHTML 6.00.6002.19114" name=GENERATOR>
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<DIV><FONT face=Arial size=2>Dear Krassimir and Colleagues,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I have followed this discussion with interest
but not total agreement. As I have commented to Krassimir previously, I feel
that his system, based on symbols as outlined in his paper, is too
static to capture the dynamics of complex information processes and their
value (valence). </FONT><FONT face=Arial size=2>It suffers from the same
problems as that of Peirce and of set-theoretic approaches,
namely, a certain arbitrariness in the selection and number
of independent elements and their grounding in nature (or rather
absence of grounding).</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>If you will permit a naïve but well-intentioned
question, why not have a theory whose elements are quintuples? Would this
not be a 'better', more complete theory? This opens the possibility of
an infinite regress, but that is the point I am trying to make: the form of
the theory is, to a certain extent, defining its content.</FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>The /development/ of any GIT should, from the
beginning I think, recognize the existence in real time, so to speak, of any
new suggestions in the context of other recent contributions of a different
form, such as those of Luhn, Hofkirchner, Marijuan, Deacon, Dodig-Crnkovic,
Wu and so on. Several of these already permit a more directed
discussion of the perhaps badly posed question of whether information or
energy is more fundamental. Otherwise, all that work will need to be done at
the end. In any case, the GIT itself, to the extent that it could be
desirable and useful, would also have to have some dynamics capable of
accepting theories of different forms. </FONT><FONT face=Arial size=2>20th
Century physics sought only identities throughout nature and the balance is
now being somewhat restored. I think keeping the diversity of theories of
information in mind is the most worthwhile strategy. </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>One of the values of Krassimir's approach is
that it recognizes the existence of some of these more complex questions
that need to be answered. I simply suggest that process language and a
recognition of dynamic interactions (e.g., between 'internal' and
'external') could be part of the strategy.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Best wishes,</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Joseph</FONT></DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<BLOCKQUOTE
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=markov@foibg.com href="mailto:markov@foibg.com"
moz-do-not-send="true">Krassimir Markov</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=jerry_lr_chandler@me.com
href="mailto:jerry_lr_chandler@me.com" moz-do-not-send="true">Jerry LR
Chandler</A> ; <A title=fis@listas.unizar.es
href="mailto:fis@listas.unizar.es" moz-do-not-send="true">FIS</A> ; <A
title=pridi.siregar@ibiocomputing.com
href="mailto:pridi.siregar@ibiocomputing.com" moz-do-not-send="true">Pridi
Siregar</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Saturday, July 26, 2014 10:42
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [Fis] Information
quadruple</DIV>
<DIV><BR></DIV>
<DIV dir=ltr>
<DIV style="FONT-SIZE: 14pt; COLOR: #000000; FONT-FAMILY: 'Calibri'">
<DIV><FONT face="Times New Roman">Dear Jerry, Pridi, and
Colleagues,</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="Times New Roman">Thank you for the nice
comments!</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="Times New Roman">To answer to questions I have to present
next step from the GIT (General Information Theory) we are
developing.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="Times New Roman">Let remember in words (below “Infos” is
abbreviation from “Information Subject”, it is an intelligent natural or
artificial agent (system)):</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="Times New Roman">Information is quadruple (Source,
Recipient, Evidence, Infos) or formally </FONT><FONT
face="Times New Roman"><EM>i = (s, r, e, I)</EM> </FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="Times New Roman">The nest step is to define elements of
the quadruple:</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="Times New Roman"><STRONG><EM>s</EM> and <EM>r</EM> are
structured sets;</STRONG></FONT></DIV>
<DIV><FONT face="Times New Roman"><STRONG><EM>e</EM> is a mapping from
<EM>s</EM> in <EM>r</EM> which preserves (all or partial) structure of
<EM>s</EM> and resolves any <EM>information expectation</EM> of
<EM>I</EM></STRONG></FONT></DIV>
<DIV><FONT face="Times New Roman"><STRONG></STRONG></FONT> </DIV>
<DIV><FONT face="Times New Roman">I expect new questions:</FONT></DIV>
<DIV><FONT face="Times New Roman">- what is an “intelligent
agent”</FONT></DIV>
<DIV><FONT face="Times New Roman">- what is “information
expectation”</FONT></DIV>
<DIV><FONT face="Times New Roman">- ...</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="Times New Roman">If it is interesting, answers to these
questions may be given in further letters.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="Times New Roman">***</FONT></DIV>
<DIV> </DIV>
<DIV>Now I want to make some comments to letters received (their full
texts are given below my answers).</DIV>
<DIV> </DIV>
<DIV>Pridi: “information cannot be viewed in any absolute sense but as
internal representations of "external patterns"”</DIV>
<DIV>Kr.: Yes, the “reflection” is a property of Matter,
“information” is a reflection for which the information quadruple exists.
But information is not “internal representations of "external patterns" ”.
It is result from resolving the<EM> subjective information
expectation</EM> which is process of comparing of internal and external
patterns. I know, this will cause new questions <IMG
class="wlEmoticon wlEmoticon-smile"
style="BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: none; BORDER-BOTTOM-STYLE: none"
alt=Smile src="cid:4B906538DEB54013801AA23670F2B594@PCdeJoseph"></DIV>
<DIV> </DIV>
<DIV>Pridi: In this framework then, it seems that "information" cannot be
conceptualized without reference to the both "something out there" and the
"internal structures" of the receptor/cognitive system. </DIV>
<DIV><FONT face="Times New Roman">Kr.: Yes.</FONT></DIV>
<DIV> </DIV>
<DIV>Pridi: How can we really quantify meaningful (semantic) information
... ?</DIV>
<DIV>Kr.: By distance between "external patterns" and “information
expectation” (sorry to be not clear but it is long text for further
letters).</DIV>
<DIV> </DIV>
<DIV>Pridi: All "objective" measures (entropy, negentropy,...) are
actually totally dependant of I1 and I2 and can never be considered as
"absolute". </DIV>
<DIV><FONT size=4>Kr.: Yes, but the world humanity is an Infos and its
information expectations we assume as <FONT
style="FONT-SIZE: 14pt">"absolute".</FONT></FONT></DIV>
<DIV> </DIV>
<DIV>Pridi: ... some researchers that posit that "information" may be more
fundamental than the fundamental physical (mass, time, space, amps).
</DIV>
<DIV><FONT size=4>Kr.: Yes, there are other paradigms which are useful in
some cases, but in our paradigm “information” is not fundamental but
“reflection” is the fundamental.</FONT></DIV>
<DIV> </DIV>
<DIV>Pridi: ... no "absolute truth" (whatever this means) is really
gained. "Only" a richer more complete (subjective but coherent) world-view
.</DIV>
<DIV><FONT size=4>Kr.: Yes.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=4>Jerry: ... assertion of a quadruple of symbols is rather
close to the philosophy of C S Peirce (hereafter "CSP") </FONT></DIV>
<DIV><FONT size=4>Kr.: Our paradigm is nor opposite to what science has
explored till now. All already investigated information theories
(Shannon,<FONT style="FONT-SIZE: 14pt">Peirce, etc) </FONT>have to be a
part or intersection of a new GIT.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=4>Jerry: ... </FONT>moves these 'definitions' of
individual symbols into the subjective realm. (CSP's notion of
"interpretation?)</DIV>
<DIV>Different researchers have the freedom to interpret the evidence as
they choose, including the relationships to engineering terms such as
"bandwidth".</DIV>
<DIV><FONT size=4>Kr.: Yes. But not only researches, everybody has such
freedom. Because of this there exist advertising processes ... but for
this we have to talk in further letters. </FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=4>Jerry: Pridi's post appropriately recognizes the tension
between objective scientific theories and subjective judgments about
evidence by different individuals with different professional
backgrounds and different symbolic processing powers. </FONT></DIV>
<DIV><FONT size=4>Kr.: Yes, there will be tension if we assume world as
plane structure. But it is hierarchical one and what is assumed as
“subjective” at one level is assumed as “objective” for the low
levels.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=4>Jerry: ... to show that these definitions of symbols
motivate a coherent symbol system that can be used to transfer information
contained in the signal from symbolic representations of entities. It may
work for engineering purposes, but is it extendable to life?</FONT></DIV>
<DIV><FONT size=4>Kr.: The goal of work on GIT is to create a coherent
symbol system which is equal valid for life creatures and artificial
agents.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=4>Jerry: ... this requires the use of multiple symbol
systems and multiple forms of logic in order to gain the functionality of
transfer of "in-form" between individuals or machines.</FONT></DIV>
<DIV><FONT size=4>Kr.: Yes, at least on three levels – Information, Infos,
Inforaction (Information interaction)</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=4>Jerry: Anybody have any suggestions on how this
quadruple of symbols can be formalized into a quantitative coherent form
of communication?</FONT></DIV>
<DIV><FONT size=4>Kr.: A step toward this I give above in the beginning of
this letter but it is very long journey ...</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=4>Thank you for creative discussion!</FONT></DIV>
<DIV><FONT size=4>Friendly regards</FONT></DIV>
<DIV><FONT size=4>Krassimir</FONT></DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>-----Original Message----- </DIV>
<DIV>From: Jerry LR Chandler </DIV>
<DIV>Sent: Wednesday, July 23, 2014 8:57 PM </DIV>
<DIV>To: FIS </DIV>
<DIV>Cc: Krassimir Markov ; Pridi Siregar </DIV>
<DIV>Subject: Re: [Fis] Re to Pridi: infinite bandwith and finite
informationcontent CS Peirce and Chemical Nomenclature </DIV>
<DIV> </DIV>
<DIV>Pridi, Krassimir, List:</DIV>
<DIV> </DIV>
<DIV>(In order to place this comment in context, and for reference, I have
copied Krassimir's "definition" of information below. My comments follow
the excellent post of Pridi.)</DIV>
<DIV> </DIV>
<DIV>> In physical world there exist only reflections but not
information. </DIV>
<DIV>> </DIV>
<DIV>> Information “ i " is the quadruple: </DIV>
<DIV>> i = (s, r, e, I) </DIV>
<DIV>> where </DIV>
<DIV>> s is a source entity, which is reflected in r </DIV>
<DIV>> r is the entity in which reflection of s exists </DIV>
<DIV>> e is an evidence for the subject I which proofs for him and only
for him that the reflection in r reflects just s , i.e. the evidence
proofs for the subject what the reflection reflects . </DIV>
<DIV>> I is information subject who has possibility to make decisions
in accordance with some goals – human, animal, bacteria, artificial
intelligent system, etc. </DIV>
<DIV>> </DIV>
<DIV>> In other words, information is a reflection, but not every
reflection is information – only reflections for which the quadruple above
exist are assumed as information by the corresponded subjects. </DIV>
<DIV>> </DIV>
<DIV>> For different I , information may be different because of
subjects’ finite memory and reflection possibilities. </DIV>
<DIV>> Because of this, a physical event with an infinite bandwidth may
have finite information content (for concrete information subject) .
</DIV>
<DIV>On Jul 23, 2014, at 6:45 AM, Pridi Siregar wrote:</DIV>
<DIV> </DIV>
<DIV>> Dear Krassimir,</DIV>
<DIV>> </DIV>
<DIV>> Thank you for your explanation. It does give me a better
understanding of how information (beyond Shannon) can be formalized!
However, a closer look at the formalism and its semantic does raise new
questions:</DIV>
<DIV>> </DIV>
<DIV>> From the definition you have given, it appears that information
cannot be viewed in any absolute sense but as internal representations of
"external patterns" whose meaning depends on the subject
capturing/interpreting/storing the said patterns. In this framework then,
it seems that "information" cannot be conceptualized without reference to
the both "something out there" and the "internal structures" of the
receptor/cognitive system. </DIV>
<DIV>> </DIV>
<DIV>> In other words the concept of "information" lies within some
"subjective" (albeit rational) realm. I'm sure that I'm stating the
obvious for most of FIS members but a question arised upon reading your
formalism: How can we really quantify meaningful (semantic) information
beyond Shannon (that disregards semantics) and his purely statistical
framework? Or beyond Boltzmann's entropy/Information based on micro-macro
states ratios?</DIV>
<DIV>> </DIV>
<DIV>> When we formalize i = (s, r, e, I) there is a "meta-level"
formalisation that is only apparent since even (s,r) reflect our own
(human) subjective world-view. We could actually write (I1(s), I1(r), e,
I2) where I1 and I2 are two distinct cognitive systems and both of which
lie at the OBJECT level of the formalizing agent which is NEITHER I1 or
I2. All "objective" measures (entropy, negentropy,...) are actually
totally dependant of I1 and I2 and can never be considered as "absolute".
</DIV>
<DIV>> </DIV>
<DIV>> </DIV>
<DIV>> This leads me to a second question (sorry for the lengthy
message): there are some researchers that posit that "information" may be
more fundamental than the fundamental physical (mass, time, space, amps).
This appears (and perhaps only appears) to be at the opposite end of the
above-mentioned view. Indeed, in this framework some kind of "universal"
or "absolute" notions must be accepted as true.</DIV>
<DIV>> </DIV>
<DIV>> One apparent way out would be to demonstrate that information
somehow logically entails the fundemantal physical entities while
accepting that we are still within a human-centered world view. And
thus no "absolute truth" (whatever this means) is really gained. "Only" a
richer more complete (subjective but coherent) world-view .</DIV>
<DIV>> </DIV>
<DIV>> Am I making anys sense? Any thoughts?</DIV>
<DIV>> </DIV>
<DIV>> Best</DIV>
<DIV>> </DIV>
<DIV>> Pridi </DIV>
<DIV>> </DIV>
<DIV> </DIV>
<DIV>Pridi's comment concur with many of my views wrt the concept of
information. </DIV>
<DIV> </DIV>
<DIV>Krassimir's assertion of a quadruple of symbols is rather close to
the philosophy of C S Peirce (hereafter "CSP") in one context.</DIV>
<DIV> </DIV>
<DIV>S as symbol represents an external source of signal, that which is
independent of the individual mind and being. This is analogous to
CSP's term "sinsign".</DIV>
<DIV> </DIV>
<DIV>R is a thing itself. That is, R generates S.</DIV>
<DIV> </DIV>
<DIV>E as evidence is a vague term which infers an observer (2nd Order
Cybernetics?) that both receives and evaluates the signal (S) from the
thing (R). CSP categorizes evidence as icon, index or symbol with
respect to the entity of observation.</DIV>
<DIV> </DIV>
<DIV>I as Krassimirian information is a personal judgment about the
evidence. (Correspondence with CSP's notion of "argument" is
conceivable.) </DIV>
<DIV> </DIV>
<DIV>Krassimir's assertion that: </DIV>
<DIV>> For different I , information may be different because of
subjects’ finite memory and reflection possibilities. </DIV>
<DIV>> Because of this, a physical event with an infinite bandwidth may
have finite information content (for concrete information subject) .
</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>moves these 'definitions' of individual symbols into the subjective
realm. (CSP's notion of "interpretation?)</DIV>
<DIV>Different researchers have the freedom to interpret the evidence as
they choose, including the relationships to engineering terms such as
"bandwidth".</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>Pridi's post appropriately recognizes the tension between objective
scientific theories and subjective judgments about evidence by
different individuals with different professional backgrounds and
different symbolic processing powers.</DIV>
<DIV> </DIV>
<DIV>The challenge for Krassimirian information, it appears to me, is to
show that these definitions of symbols motivate a coherent symbol system
that can be used to transfer information contained in the signal from
symbolic representations of entities. It may work for engineering
purposes, but is it extendable to life?</DIV>
<DIV> </DIV>
<DIV>(For me, of course, this requires the use of multiple symbol systems
and multiple forms of logic in order to gain the functionality of transfer
of "in-form" between individuals or machines.)</DIV>
<DIV> </DIV>
<DIV>Pridi writes:</DIV>
<DIV>> How can we really quantify meaningful (semantic)
information beyond Shannon (that disregards semantics) and his purely
statistical framework?</DIV>
<DIV> </DIV>
<DIV>One aspect of this conundrum was solved by chemists over the past to
two centuries by developing a unique symbol system that is restricted by
physical constraints, yet functions as an exact mode of communication.
</DIV>
<DIV> </DIV>
<DIV>Chemical notation, as symbol system, along with mathematics and data,
achieves this end purpose (entelechy) of communication, for some entities,
such as the meaning of an "atomic number" as a relational term and hence
the meaning of a particular integer as both quantity and quality. </DIV>
<DIV> </DIV>
<DIV>This requires a dyadic mathematics and synductive logic for
sublations.</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>Pridi writes:</DIV>
<DIV> </DIV>
<DIV>> It does give me a better understanding of how information
(beyond Shannon) can be formalized! </DIV>
<DIV> </DIV>
<DIV>Can you communicate how this "better understanding... ...
foramlized" works? </DIV>
<DIV> </DIV>
<DIV>It is not readily apparent to me how Krassimirian information can be
formalized.</DIV>
<DIV> </DIV>
<DIV>Anybody have any suggestions on how this quadruple of symbols can be
formalized into a quantitative coherent form of communication?</DIV>
<DIV> </DIV>
<DIV>Cheers</DIV>
<DIV> </DIV>
<DIV>Jerry </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV></DIV></DIV>
<P></P>
<HR>
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