The issue of simultaneity also has some relevance to Gerald Werner's
"long post on objectivity" which I found very good and I will reply to
it seperately.
To continue my reply to Don Miculecky's question:
>> .... a living or cognitive system could be approximated as a network
>> of event sequences where each event may or may not have *simultaneous
>> translations* within the operation of neighbouring event sequences.
>> It is precisely these "simultaneous translations" which cannot be reduced
>> to a mechanistic system, and they are necessary if a system is to be "alive".
>
>This is very suggestive....can you tell us more about this idea?
I first came across this idea from a rather unusual and difficult paper
by the late German (or Austrian?) philosopher Gotthard Guenther:
"Cybernetic Ontology and Transjunctional Operations". (I think it originally
appeared in 1960 or so). His idea was that 2-valued logic was not sufficient
to describe a system interacting with its environment. For an outside
observer, an event may constitute "information". From the point of view of
a living system, this "information" takes the form of a "disturbance" which
does NOT belong to its (2-valued) "universe" or current context. His argument
was basically: we need two values to define/specify the whole system. For its
environment (that is seen from THE SYSTEMS's point of view, not ours) we need
a third!
The third logical value should refer to a simultaneously existing context
which is not the current one. As an operation to produce such a value,
Guenther introduced a hypothetical logical operator called the "transjunction".
This is any operator which, when "given" two different values returns a third
value. Guenther derived this using a rather unusual method, which I will try to
summarize at the end of this posting.
First of all I wish to say how the idea (which I called "simultaneous
translation" for lack of a better term) was shown in his paper.
He refers to the famous paper by von Foerster on "Self-organising Systems
and their Environments" (from a conference in 1960) where an experiment
with magnets in a hidden box is carried out. The box is shaken and when
it is opened there suddenly appears this beautiful sculpture! In a sense,
the hidden "order" of each individual magnet expresses itself in a
totally unexpected way when the magnets are allowed to interact freely.
(This is the "noise" which was added by the shaking).
I think it was von Foerster who called the phenomenon "order from noise"
and Guenther reinterpreted it as "order from (order + disorder)" to make
more explicit the two simultaneously existing "systems" (one external and
one internal). The internal "order" (the magnetic poles of each magnet)
which is hidden to the outside observer, expresses itself simultaneously as
a "work of art" for the external observer.
Transjunction as a hypothetical operator:
Effectively Guenther described this operator as a simultaneous logical
connection between two systems. His argument was that a formalisation
of this principle may be possible and if this were so it may become
"computable". He came to this conclusion by a rather unusual manipulation
of truth tables (I didn't take it seriously at first). I will try
to summarize it here.
Instead of using classical "truth" values such as 0 and 1 (or F and T),
Guenther introduced the concept of "kenogram". That is an "empty slot"
which indicates only that it should contain a value the same or different
from the neighbouring slots - without referring to the value itself.
A truth table can then be converted into columns of abstract patterns.
We start by taking into account the value patterns (for example, TFFF is
the pattern for AND). With two values there are 16 value-patterns.
If we ignore the values themselves and consider only the "slots", this reduces
to 8 (because then TFFF is equivalent to FTTT, i.e. *+++). Such abstract
patterns (which merely reflect distinctions - not positive identifications)
are called "morphograms". (Actually I think in some of his papers he used
digits but that does not matter).
Guenther then came to a rather astonishing conclusion: 2-valued logic
is morphogrammatically incomplete. This is because the 8 patterns do not
exhaust all the possible combinations. One can add two new symbols which
indicate "foreign" values, leading to 7 new patterns. These patterns
define a class of hypothetical operators called "transjunctions".
(For example, *^^+ corresponds to a "complete" transjunction because
it always "rejects" both values when they are different, i.e. ** gives *,
*+ gives ^, +* gives ^ and ++ gives +)."Partial" transjunctions only
sometimes reject both values. The last combination is *^v+, i.e. two
"foreign values" are introduced.
Incidentally this has nothing to do with fuzzy logic which deals with
values BETWEEN 0 and 1 WITHIN the one system. Other systems (simultaneously
valid contexts) are not taken into account at all in fuzzy logic.
The above only deals with 2 variables and binary operators. In later papers
Guenther generalized this scheme for n-ary operators and n variables.
In this way more general patterns of distinction are derived known as
"kenogrammatics" (where the original morphograms are a special case).
The "multi-system" logic itself came later to be known as the
"polycontextural" logic with multiple negations as well as transjunctions.
There is no successful formalisation as yet.
I know that this all sounds totally crazy on a first reading. For that
reason Guenther's work tends to be ignored or not taken seriously. I had to
read the paper several times before I came to the conclusion that there
was some deep sense in it. It is interesting that Rosen seems to have
similar ideas developed from a different perspective.
Many problems remain with the hypothetical "transjunction". One of the most
important is the linguistic problem. How does one specify a system with
transjunctions? All the existing logical operators (and formal systems
for that matter) are based on natural language. When we are making
statements we are always talking within a system (or we change systems
sequentially). How do we talk *about* the simultaneous interwovenness
of systems? To solve this problem Guenther is said to have proposed the
idea of a "negative language", but I'm not sure exactly what he meant by it.
How to obtain the paper (and Guenther's other works):
The original paper is available (in English) in a collection
of works by Gotthard Guenther. The collection is mostly in German, but I can
give a complete reference for anybody who is interested. In the U.S. it is
probably better to look for the paper in the historical archive of the
Biological Computer Laboratory (BCL) where I believe Guenther worked.
Incidentally, does anyone know where I could find this archive? (I have heard
that it exists on Microfiche somewhere).
regards,
Catharina
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Catharina Kennedy, ck@ics.inf.tu-dresden.de,
PhD student, Institute for Artificial Intelligence,
Faculty of Computer Science,
Technical University of Dresden,
01062 Dresden, Germany.
Tel: +49 351 4575 490
Fax: +49 351 4575 335
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