Re: [Fis] Revisiting... --From Dieter Gernert

2010-09-29 Thread Pedro C. Marijuan
(herewith a very interesting text received off-line from a newcomer to 
our list --welcome Dieter!---Pedro)



--

1. For many years I highly estimate the work of Michael Conrad -- whom I 
never could see or hear in person. So the study was restricted to 
reading some papers, and to store them as a separate file. I am very 
glad for the references to more recent work.


2. Before making any comment on the transmitted text, I must admit that 
I do not have sufficient knowledge on biology to give convincing remarks.


3. Modern physics must necessarily be physics at the Planck scale. I 
do not know whether in this moment there is a sufficient, explicit 
physics at the Planck scale such that one build up on this basis. 
Anyway, it must be a theory of processes, not of particles.


4. Anti-entropy or negentropy are children of the classical 
Shannon-Weaver theory, which is incorrectly (only due to a certain 
historical development) called information theory. There are specific 
(narrow, local) situations in biology where Shannon-Weaver is 
sufficient. But in the general case -- and for a modern, futuristic 
theory -- it can really be doubted whether Shannon-Weaver (here it is 
always meant: together with extensions and ramifications) will be 
sufficient. It seems to me that the comprehensive theory is needed, 
which (again for historical reasons) is named theory of pragmatic 
information. This is not opposed to Shannon-Weaver, but the latter is 
included as a special case (one can state conditions under which Sh.-W. 
will be adequate for a situation). An overview (including the historical 
development) can be found:


Gernert, D., Pragmatic information: historical development and general 
overview. Mind and Matter, vol. 4 no. 2 (2006) 141-167.


Here I am really only a reporter and historian -- I did not make 
concrete contributions. The article can be downloaded  (google
dieter gernert).


5. For any concept setting out to connect the manifest and the 
unmanifest a mathematical structure is required which permits us to 
describe the manifest and the nonmanifest and the interaction between 
both realms, or more precisely: conditions for an influence to occur in 
a single situation. It seems to me that one can do this along the lines 
sketched in my paper:


Gernert, D., Formal treatment of systems with a hidden organizing 
structure, with possible applications to physics. Int. J. of Computing 
Anticipatory Systems 16 (2004) 114-124.


It will become inevitable to use a vector space on the basis C (the 
algebraic field of complex numbers). Best candidates in this moment are 
C^3 and C^4 (such that we have 6-  or 8-parametric manifolds -- not 6 or 
8 dimensions!). Equally important is a measure for the similarity 
between complex structures. To both issues I published proposals, and if 
there will be better ones, I shall quickly adopt them.


6. Models like particle/anti-particle pair production is a matter of the 
underlying physical structure; it will not contribute to explain the 
interaction or non-interaction between two complex structures. Any 
answer to the question interaction between these two or not? must take 
into account the entire structure of those two.


7. I do not believe that consciousness has something to do with rather 
elementary processes like the unmasking mentioned in the text. From 
the viewpoint of a research strategy one can put off this question and 
first try to understand the processes.



Kindest regards,

Dieter Gernert
Professor of Computer Science
Technical University of Munich


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Re: [Fis] FW: Fluc replies - more

2010-09-29 Thread Robert Ulanowicz
Quoting Pedro C. Marijuan pcmarijuan.i...@aragon.es:

 About the formalism to deal with entropies: How does the treatment of
 entropies by Michael in his Adaptability Theory --extended by the
 fluctuon model into the microphysical realm-- relate with the
 contemporary quantum information theory, and the qubits stuff? Given
 that it was initially conceived from the ecological perspective, can it
 be connected with Bob Ulanowicz's conceptualization of energy flow and
 diversity (and his tentative variational principle?) The paper by Kevin
 on Biological adaptibilities and quantum entyropies (BioSystems 64,
 2002, 33-41) is an excellent portal for this question.

I must confess to all that I have never read Michael's work on  
fluctuons. In 1984, however, I was honored to review Michael's book,  
Adaptability for Mathematical Biosciences (69:153-154). I have  
lost an ecopy of the review, but I remember expressing much sympathy  
for Michaels discourse on the use of conditional entropy to quantify  
adaptability. My one note of reserve about the work was that Michael  
made no effort to explain how one could put numbers on his formulae. I  
was trained as an engineer not to discuss anything to which one could  
not attach a measurement (a stricture I have since come to ignore.  
[Stan Salthe says that if you can attach a number to a concept, it's  
too simple to merit discussion!]:)

Nevertheless, Michael's work helped motivate my attempts to  
quantitatively describe the relationship between efficiency and  
reliability, or between adaptation and adaptability, as I put it in my  
contribution to the 2002 Memorial issue to Michael (BioSystems  
64:13–22 [2002]).

For me this question came to somewhat of an empirical resolution, once  
I had abandoned the notion that ecosystems always developed to  
increase their adaptation and looked at the data, which said that real  
ecosystems actually crowded into a narrow window of vitality. (See  
Fig. 5 on p92 of Int. J. of Design  Nature and Ecodynamics 4(2):83-96  
[2009].)

The enigma remains as to why the ratio of organization:complexity so  
tightly favors the value (1/e)?

Regarding fluctuations in the quantum vacuum, I have my doubts as to  
how far up the scale they reach. (I also have grave doubts about  
coupling gravitation with quantum phenomena, as the Planck constant  
and the gravitational constant differ by some *43* orders of  
magnitude! An engineer would *never* touch such a disparity!  
Apparently, Hawking gave up on it as well, even though I doubt he's  
ever been exposed to dimensional analysis. :)

There are some physicists who claim that the coherence domains such  
as one sees among collections of molecules of water (which apparently  
are kept in coherence by signals propagated in the quantum vacuum by  
phasings that can propagate there faster than the speed of light)  
apply to the brain and even to ecosystems! (See Ecological Modelling  
220: 1865–1869 [2009].) I think this hypothesis is wrong. The  
dimensions of the brain and certainly those of the ecosystem are  
simply too far removed from the quantum level to entertain such a  
thought. (Again, my engineer's familiarity with dimensional analysis  
suggests such infesability.)

That doesn't mean that an analogous scenario isn't at work in the  
brain, however. Typically, brain synapses function on the time scale  
of tenths of a second. While this might seem fast to the lay person,  
it is far too slow to explain any synchrony. One doesn't have to go  
down to the quantum level, however, to find a phenomenon that might be  
capable of synchronizing brain activity. To synchronize a set of  
processes, it is not necessary that the communication be of high  
amplitude. It can be rather faint. The means of synchrony must,  
however, act very quickly with respect to the phenomenon being  
synchronized.

Well, when a synapse fires it creates a weak electromagnetic field.  
Although weak, there are usually many, many other synapses in the  
vicinity that could receive this weak signal. I.e., the local  
electromagnetic field could reasonably serve to synchronize brain  
behavior at a larger scale than the synapse. It should be possible to  
observe the brain acting in synchrony as a *macroscopic* coherence  
domain.

Such coherence would agree with our common notions of consciousness.  
When we are conscious, we are aware of many things at the same time --  
even our own brain activity. When part of the brain becomes  
dysfunctional, it cannot participate in the coherence domain -- ergo  
the loss of recognition by a patient with aphasia of, say, the left  
arm as belonging to him/her.

Well, I digress! These thoughts rattle around in my brain  
(incoherently? :), and I welcome the opportunity to put them into  
writing.

The best to all,
Bob

-
Robert E. Ulanowicz|  Tel: +1-352-378-7355
Arthur R. 

Re: [Fis] Fluc replies - more. Reply to Gordana

2010-09-29 Thread Joseph Brenner
FW: Fluc replies - moreDear Gordana and All,

Gordana's note is very useful, as I think it makes possible a further 
discussion of what is at the heart of information. The following, partially 
negative comments, should be seen only as an attempt to get closer to that 
heart.

1. Floridi indeed claims that reality is an informational structure, but if the 
reality of information - its structure and constitutive elements  - has not 
been defined, we are in full tautology. If there are really fluctuons down 
there (the theme of this discussion), this may have consequences for all of 
our theories, mine included.

2. This judgment is confirmed :-) by the citations: a) One can agree (I do) 
with Floridi's interpretation of reality as the totality of structures 
interacting with one another, but we still do not know what a structure is, 
ontologically, and there is a caesura with the implication for information; b) 
Referring to physicists who say that reality is fundamentally informational 
is begging the question at issue.

3. It is not quite accurate to say that Floridi's Levels of Organization (LoOs) 
give access to an ontological side that will enable us to see an 
informational reality for two reasons: a) we have not established that reality 
is primarily informational nor what this might mean (see above); b) LoOs, to 
quote Floridi do support an ontological approach, according to which systems 
for analysis (my emphasis) are supposed to have a structure in themselves de 
re, which is allegedly captured and uncovered by its description. For example, 
levels of communication, of decision processing and of information flow can all 
be presented as specific instances that can be analyzed in terms of LoOs. 
However, I submit that we are still dealing, here, with epistemological 
constructions.

4. It is not necessarily true that an ontological informational structures 
should be seen in conjunction (sic) with computational processes. Let us 
consider, quite seriously, that there is a /disjunction/ between ontological 
informational structures and computational processes.

5. On the question of it 'or' bit, I suggest that bits are the simplest, most 
abstract elements of information, constitutive of its lowest semantic level. 
Its are something more, for example, as Kevin Kirby said, fluctuons can 
perfectly well be looked at as its, given their apparent interactive 
characteristics. Understanding the relationship (one or more ?) between 
information and matter/energy may be easier if we consider that we might be 
talking about the same thing from two perspectives.

Cheers,

Joseph  
  - Original Message - 
  From: Gordana Dodig-Crnkovic 
  To: Kevin Kirby ; fis@listas.unizar.es 
  Sent: Wednesday, September 29, 2010 1:38 PM
  Subject: Re: [Fis] Fluc replies - more


  Dear Kevin, Dear all!

   

  What I was thinking about, referring to Floridi's Informational Structural 
Realism is his claim that reality is an informational structure

  A preferable alternative is provided by an informational approach to 
structural realism, according to which knowledge of the world is knowledge of 
its structures. The most reasonable ontological commitment turns out to be in 
favour of an interpretation of reality as the totality of structures 
dynamically interacting with each other. Floridi [11] p. 151. 

  http://www.mdpi.com/1099-4300/12/4/878/pdf

  I could have referred to physicists Zeilinger, Lloyd, or Vedral and number of 
other authors who would say that reality fundamentally is informational.

   

  Now, the question of objective vs. subjective levels (levels of organization 
vs. levels of abstraction). One may be interested in the first place in the 
epistemological aspect and then focus on what an agent can see from that 
informational reality. On the other hand one may put the focus on the 
ontological side and ask what informational reality an agent can see. Those two 
things are closely related. I agree with you that if we only focus on levels of 
abstraction we will miss something, as LOA only reflect epistemological side. 
Besides epistemology we need ontology, which is reflected in Levels of 
organization LOO. 

   

  What I find interesting is the interplay of epistemological and ontological 
informational structures. Those informational structures should be seen in 
conjunction with computational processes. All of that is also closely connected 
to the question of it or bit, or the relationships between information and 
matter/energy.

   

  Present FIS discussion shows that there is an interest and a lot of things to 
do in order to elucidate our current understanding of the relationship. 

  I would like to kindly invite you to contribute to the following special 
issue of the journal Information:

  . http://www.mdpi.com/journal/information/special_issues/matter/

   

  With best regards,

  Gordana

   

   

  From: fis-boun...@listas.unizar.es [mailto:fis-boun...@listas.unizar.es] On 

Re: [Fis] Revisiting... --From Dieter Gernert

2010-09-29 Thread Guy A Hoelzer
Hi all,

I have been enjoying the current discussion and appreciate Dieter’s focus on 
process.  I am an evolutionary biologist, not a physicist, but I would like to 
suggest one way in which some of the views expressed in different posts might 
be reconciled.

From a simplistic point of view, I think it is fair to posit that spatial 
pattern (e.g., the existence of particles) is manifested information, and that 
pattern is generated by process (e.g., particle interaction).  Process itself 
can also be viewed as information in the form of temporal pattern.  Pattern 
and process are inextricably linked in self-organizing dissipative systems, 
which represent a special class of “its”.  Other kinds of “its” include 
artifacts of dissipative system dynamics, which stumble from one local entropy 
peak to another under thermodynamic constraints.  Of course, particulate 
artifacts can also be swept up in other thermodynamic cascades, including 
those exploited by other dissipative systems.

The Prigogine notion of dissipative systems provides a compelling case, in my 
view, for including both pattern and process in generic treatments of 
information.

Regards,

Guy
--
Dr. Guy A. Hoelzer
Department of Biology, MS 314
University of Nevada Reno
Reno, NV  89557



On 9/29/10 3:38 AM, Pedro Clemente Marijuan Fernandez 
pcmarijuan.i...@aragon.es wrote:

(herewith a very interesting text received off-line from a newcomer to our list 
--welcome Dieter!---Pedro)


--

1. For many years I highly estimate the work of Michael Conrad – whom I never 
could see or hear in person. So the study was restricted to reading some 
papers, and to store them as a separate file. I am very glad for the references 
to more recent work.
2. Before making any comment on the transmitted text, I must admit that I do 
not have sufficient knowledge on biology to give convincing remarks.
3. Modern physics must necessarily be physics at the Planck scale. I do not 
know whether in this moment there is a sufficient, explicit physics at the 
Planck scale such that one build up on this basis. Anyway, it must be a theory 
of processes, not of particles.
4. Anti-entropy or negentropy are children of the classical Shannon-Weaver 
theory, which is incorrectly (only due to a certain historical development) 
called information theory. There are specific (narrow, local) situations in 
biology where Shannon-Weaver is sufficient. But in the general case – and for a 
modern, futuristic theory – it can really be doubted whether Shannon-Weaver 
(here it is always meant: together with extensions and ramifications) will be 
sufficient. It seems to me that the comprehensive theory is needed, which 
(again for historical reasons) is named theory of pragmatic information. This 
is not opposed to Shannon-Weaver, but the latter is included as a special case 
(one can state conditions under which Sh.-W. will be adequate for a situation). 
An overview (including the historical development) can be found:
 Gernert, D., Pragmatic information: historical development and general 
overview. Mind and Matter, vol. 4 no. 2 (2006) 141-167.
 Here I am really only a reporter and historian – I did not make concrete 
contributions. The article can be downloaded  (google   dieter gernert).
 5. For any concept setting out to connect the manifest and the unmanifest a 
mathematical structure is required which permits us to describe the manifest 
and the nonmanifest and the interaction between both realms, or more precisely: 
conditions for an influence to occur in a single situation. It seems to me that 
one can do this along the lines sketched in my paper:
Gernert, D., Formal treatment of systems with a hidden organizing structure, 
with possible applications to physics. Int. J. of Computing Anticipatory 
Systems 16 (2004) 114-124.
 It will become inevitable to use a vector space on the basis C (the algebraic 
field of complex numbers). Best candidates in this moment are C^3 and C^4 (such 
that we have 6-  or 8-parametric manifolds – not 6 or 8 dimensions!). Equally 
important is a measure for the similarity between complex structures. To both 
issues I published proposals, and if there will be better ones, I shall quickly 
adopt them.
6. Models like particle/anti-particle pair production is a matter of the 
underlying physical structure; it will not contribute to explain the 
interaction or non-interaction between two complex structures. Any answer to 
the question interaction between these two or not? must take into account the 
entire structure of those two.
 7. I do not believe that consciousness has something to do with rather 
elementary processes like the unmasking mentioned in the text. From the 
viewpoint of a research strategy one can put off this question and first try to 
understand the processes.


Kindest regards,

Dieter Gernert
Professor of Computer Science
Technical University of Munich

Re: [Fis] Fluc replies - more. Reply to Gordana

2010-09-29 Thread Rafael Capurro

 dear Joseph

I very much agree with your views and criticisms of Floridi's 
tautologies. One main problem I have with Floridi is that he does not 
distinguish between ontology and metaphysics (in the Heideggerian sense 
of these terms). This leads to the question of trying to identify the 
nature of it which is, I guess, another term for what metaphysics 
called beings (or das Seiende im German, i.e. everything that is). 
Metaphysics is the project of trying to fix the nature of beings in 
their being (or on he on as Aristotle said). But this is exactly the 
problem, that in every intent to fix this is (or it) there is always 
an AS. In other words, we have no possibility of taking a metahistorical 
and meta-physical (our of the world in which we are involved as 
being-in-the-world) position and overview forms AS being only this and 
not that. Neither through levels of abstraction (LoA) which is the 
classic method of metaphysics since Plato, nor through levels of 
communication nor... On the other hand, what we say when we say that 
it is AS this and this (including the digital perspective when we say 
that it AS bit) is one possible perspective. The fluctuation of AS 
co-rresponds to the fluctuation of its. To say that reality is 
fundamentally this or that is to repeat the ambitions of metaphysics.


best regards

Rafael



Dear Gordana and All,
Gordana's note is very useful, as I think it makes possible a further 
discussion of what is at the heart of information. The following, 
partially negative comments, should be seen only as an attempt to get 
closer to that heart.
1. Floridi indeed claims that reality is an informational structure, 
but if the reality of information - its structure and constitutive 
elements  - has not been defined, we are in full tautology. If there 
are really fluctuons down there (the theme of this discussion), this 
may have consequences for all of our theories, mine included.
2. This judgment is confirmed :-) by the citations: a) One can agree 
(I do) with Floridi's interpretation of reality as the totality of 
structures interacting with one another, but we still do not know what 
a structure is, ontologically, and there is a /caesura /with the 
implication for information; b) Referring to physicists who say that 
reality is fundamentally informational is begging the question at issue.
3. It is not quite accurate to say that Floridi's Levels of 
Organization (LoOs) give access to an ontological side that will 
enable us to see an informational reality for two reasons: a) we have 
not established that reality is primarily informational nor what this 
might mean (see above); b) LoOs, to quote Floridi do support an 
ontological approach, according to which systems /for analysis /(my 
emphasis) are supposed to have a structure in themselves /de re/, 
which is allegedly captured and uncovered by its description. For 
example, levels of communication, of decision processing and of 
information flow can all be presented as specific instances that can 
be analyzed in terms of LoOs. However, I submit that we are still 
dealing, here, with epistemological constructions.
4. It is not necessarily true that an ontological informational 
structures should be seen in conjunction (sic) with computational 
processes. Let us consider, quite seriously, that there is a 
//disjunction// between ontological informational structures and 
computational processes.
5. On the question of it 'or' bit, I suggest that bits are the 
simplest, most abstract elements of information, constitutive of its 
lowest semantic level. Its are something more, for example, as Kevin 
Kirby said, fluctuons can perfectly well be looked at as its, given 
their apparent interactive characteristics. Understanding the 
relationship (one or more ?) between information and matter/energy may 
be easier if we consider that we might be talking about the same thing 
from two perspectives.

Cheers,
Joseph

- Original Message -
*From:* Gordana Dodig-Crnkovic mailto:gordana.dodig-crnko...@mdh.se
*To:* Kevin Kirby mailto:ki...@nku.edu ; fis@listas.unizar.es
mailto:fis@listas.unizar.es
*Sent:* Wednesday, September 29, 2010 1:38 PM
*Subject:* Re: [Fis] Fluc replies - more

Dear Kevin, Dear all!

What I was thinking about, referring to Floridi's Informational
Structural Realism is his claim that reality is an informational
structure

/A preferable alternative is provided by an informational
approach to structural realism, according to which knowledge of
the world is knowledge of its structures. The most reasonable
ontological commitment turns out to be in favour of an
interpretation of reality as the totality of structures
dynamically interacting with each other. /Floridi [11] p. 151.

http://www.mdpi.com/1099-4300/12/4/878/pdf

I could have referred to physicists Zeilinger, Lloyd, or Vedral
and number of other authors who would say that reality

Re: [Fis] Revisiting... --From Dieter Gernert

2010-09-29 Thread Robert Ulanowicz
Dear Guy,

I, too , was enthused by Dieter's emphasis on process, although I  
don't quite share your concern about neglecting structural pattern. As  
an ecologist, I spent my career studying *patterns of processes*,  
i.e., networks of ecological interactions. Furthermore the information  
embodied in the pattern of processes is quite amenable to  
quantification.

A process-first ontology would view particles and their related  
structures as outcomes of configurations of processes. Such was a  
major thrust of my process view of evolution, as espoused in my last  
book, A Third Window.

The chief benefit of a process-based narrative of evolution is that  
one can consistently view evolution going forward. The particle-law  
conventional metaphysic always entails a great deal of backtracking.

Doubtless, many of you will disagree, but that's part of the fun of FIS!

The best to all,
Bob U.

Quoting Guy A Hoelzer hoel...@unr.edu:

 Hi all,

 I have been enjoying the current discussion and appreciate Dieter´s  
 focus on process.  I am an evolutionary biologist, not a physicist,  
 but I would like to suggest one way in which some of the views  
 expressed in different posts might be reconciled.

 From a simplistic point of view, I think it is fair to posit that  
 spatial pattern (e.g., the existence of particles) is manifested  
 information, and that pattern is generated by process (e.g.,  
 particle interaction).  Process itself can also be viewed as  
 information in the form of temporal pattern.  Pattern and process  
 are inextricably linked in self-organizing dissipative systems,  
 which represent a special class of its.  Other kinds of its  
 include artifacts of dissipative system dynamics, which stumble  
 from one local entropy peak to another under thermodynamic  
 constraints.  Of course, particulate artifacts can also be swept up  
 in other thermodynamic cascades, including those exploited by other  
 dissipative systems.

 The Prigogine notion of dissipative systems provides a compelling  
 case, in my view, for including both pattern and process in generic  
 treatments of information.

 Regards,

 Guy
 --
 Dr. Guy A. Hoelzer
 Department of Biology, MS 314
 University of Nevada Reno
 Reno, NV  89557



 On 9/29/10 3:38 AM, Pedro Clemente Marijuan Fernandez  
 pcmarijuan.i...@aragon.es wrote:

 (herewith a very interesting text received off-line from a newcomer  
 to our list --welcome Dieter!---Pedro)


 --

 1. For many years I highly estimate the work of Michael Conrad -  
 whom I never could see or hear in person. So the study was  
 restricted to reading some papers, and to store them as a separate  
 file. I am very glad for the references to more recent work.
 2. Before making any comment on the transmitted text, I must admit  
 that I do not have sufficient knowledge on biology to give  
 convincing remarks.
 3. Modern physics must necessarily be physics at the Planck scale.  
 I do not know whether in this moment there is a sufficient, explicit  
 physics at the Planck scale such that one build up on this basis.  
 Anyway, it must be a theory of processes, not of particles.
 4. Anti-entropy or negentropy are children of the classical  
 Shannon-Weaver theory, which is incorrectly (only due to a certain  
 historical development) called information theory. There are  
 specific (narrow, local) situations in biology where Shannon-Weaver  
 is sufficient. But in the general case - and for a modern,  
 futuristic theory - it can really be doubted whether Shannon-Weaver  
 (here it is always meant: together with extensions and  
 ramifications) will be sufficient. It seems to me that the  
 comprehensive theory is needed, which (again for historical reasons)  
 is named theory of pragmatic information. This is not opposed to  
 Shannon-Weaver, but the latter is included as a special case (one  
 can state conditions under which Sh.-W. will be adequate for a  
 situation). An overview (including the historical development) can  
 be found:
  Gernert, D., Pragmatic information: historical development and  
 general overview. Mind and Matter, vol. 4 no. 2 (2006) 141-167.
  Here I am really only a reporter and historian - I did not make  
 concrete contributions. The article can be downloaded  (google
 dieter gernert).
  5. For any concept setting out to connect the manifest and the  
 unmanifest a mathematical structure is required which permits us to  
 describe the manifest and the nonmanifest and the interaction  
 between both realms, or more precisely: conditions for an influence  
 to occur in a single situation. It seems to me that one can do this  
 along the lines sketched in my paper:
 Gernert, D., Formal treatment of systems with a hidden organizing  
 structure, with possible applications to physics. Int. J. of  
 Computing Anticipatory Systems 16 (2004) 114-124.
  It will become inevitable to use a 

Re: [Fis] Fluc replies - more. Reply to Gordana

2010-09-29 Thread karl javorszky
Dear FIS,

the discussion here is excitingly interesting from the standpoint of formal
logic. The points that one may comment on regard:
 tautology
 structure
 totality of structures interacting with one another
 epistemological constructions
 relationship between matter/energy
 perspectives of descriptions
 philosophic relativity
to name but a few.

Formal logic addresses all these points and introduces a neutral web of
well-defined concepts, the relations of which allow quite exact definitions
of the above terms.

We find empistemologically clear and well-defined explanations for these
terms by taking recourse to the words of a formal language (in the sense of
Wittgenstein), namely to the natural numbers. We may be in the situation of
those of our forefathers who have felt that there is a comprehensive
explanation to spatial arrangements they observed but lacked the exact
understanding of the words height, distance, angle and so forth. I
don't know who proposed using simple calculations regarding the sides of
triangles to arrive at trigonometry, but the principles that can be read off
the tables of trigonometry demonstrate that numbers do have a use outside of
mathematics, too.

The concepts of sinus and cosinus and tangent etc. could be understood
after one has seen how these concepts are generated by simple numeric
procedures.

Please allow me to propose for general usage some tables based on natural
numbers. The concepts can prove to be well usable and versatile, after one
has seen how the concepts are generated.

The Table to be introduced into this discussion is quite simple, in fact not
more complicated (from the level of its intellectual principles) as dividing
the lengths of sides of triangles. It uses following novelties in the
dealings with natural numbers:

1) we discuss the instances of a+b=c for values of a,b 1..16;
1.1. This yields 136 cases of additions, from 1+1=2 to 16+16=32
1.1.1 we alsways assume a=b
2) we concentrate on the symmetry of a and b, that is on u=b-a;
2.1 u can be in the range of 0 to 15
3) we generate measures for the relation of u to a and b
3.1. we build k=u-a
3.2. we build k+u=t
3.2.1 we make an addition ((b-a)-a)+(b-a)=2b-3a
3.3. we build -u=a-b
3.3.1 we do this for reasons of commutativity
3.4.  we build q=-u-b
3.5.  we build w=q+(-u)
3.5.1. we make an addition ((-u-b)+(-u))=((a-b-b)+(a-b))=2a-3b
3.6. we thus have 4 additions:
3.6.1. a+b=c
3.6.2. k+u=t  =((b-a)-a)+(b-a)=2b-3a
3.6.3. q+(-u)=w  =((-u-b)+(-u))=((a-b-b)+(a-b))=2a-3b
3.6.4. reading column 3 down we see c+t=-w=(a+b)+(2b-3a)= -
(2a+3b)=3b-2a
3.7. we propose to investigate, which of the 4 additions is generally
relevant in each case of a,b
3.8. we call the terms a,b,c,k,u,t,q,w, and and measure s=17-{a+b|c}
aspects of a+b=c
4. we introduce the conept of order
4.1. we order the set of 136 additions by sorting them
4.1.1. we use the procedure sort() from excel or any other software to do
so
4.2. we sort the collection on two of the aspects
4.2.1. we have then 72 sorting orders, 9 aspects once as 1st, 8 aspects once
as 2nd sorting key
4.3. each case of a+b has then a specific sequential place in the sequence
1..136
5. we re-sort from sorting order alpha,beta into sorting order gamma.delta
5.0.1. alpha,beta,gamma,delta are any of the 9 aspects
5.0.2. alpha#beta, gamma#delta
5.1. we investigate the place changes of the individual cases of a+b
5.2. those cases that move together we call a thread
5.2.1. the term thread may possibly be the concept behind the word
string used in Physics
5.3. some resorts yield no changes, some do
5.3.1. those resorts that yield no changes we call the structure
5.4. there are resorts that offer themselves as unit resorts
6. The unit resorts allow constructing two Euclid spaces
6.1. the two Euclid spaces differ slightly
6.2. the two Euclid spaces can be merged into one Euclid space
6.2.1. in this merged space one loses either the position's exactitude or
the extent's exactitude
6.2.2. the differences of the two Eulid spaces may well be the concept
behind the word information
7. there are several - but by no means an infinite number of - realities of
orders' consequences
7.1. the terms relevance and importance of ordering concepts can easily
be defined.
8. The term logical archetype is defined by those standard rearrangements
that are geometrically representable in an Euclid space
8.1. the term logical archetype may well be the concept behind the words
chemical element.

This is of course only a very cursory introduction. The idea is new but it
seems to be quite useful to contribute to a discussion within FIS. The usage
of this kind of approach to words is, that one may well point out: this is
what I mean as I say 'structure' or 'information' or 'ordering principle'.

Exact science has to be rooted in solid logic, where the words one uses do
have a clear and unmistakable definition. Nothing is better suited to be