Dear Organlearners,
Don Dwiggins < d.l.dwiggins@computer.org > writes
AM de Lange writes:
>>But when the whole is made up of three or even more parts,
>>our languages have not yet caught up with these possibilities.
>>For example, we do not yet speak of a "complementary trials"
>>or a "complementary triality". In fact, we use the word "trial"
>>for something else, namely examination.
>Don't sell our languages too short. My little online Webster's
>includes dyad, triad, tetrad, pentad, hexad, heptad, and octad.
>(I couldn't find nonad or decad, and gave up there, although it's
>pretty clear what a hexadecad would be).
Greetings Dwig,
I was definitely thinking aboud dyads, triads, tetrads, pentads, etc, when
I was writing the above. However, they are words formed from Greek
numerals. The corresponding Latin words for the numerals begin to differ
remarkedly from number 4 (quattuor), 5 (quinque) onwards. Thus, when
using the word "complementary" which has a Latin etymology, we should
speak of binary, ternary, quaternary, quintenary , ... complementarities.
I still remember as a student how these counting words with a Latin
etymology made me stumble in organometallic chemistry, for example
"sextanary" (6). To think of the seven essentialities of creativity as a
"septanary complementarity" sounds almost like a septic complication ;-)
>In his book "The Journey of the Software Professional",
>Luke Hohmann builds a conceptual framework based
>on the complementary triad of structure-process-outcome,
>which he uses to motivate a lot of his points and advice.
>(The book might be worth reading for anyone in a
>project-oriented organization -- he incorporates a lot of
>organizational and psychological material, although he
>doesn't make any references to Senge or learning
>organizations.)
Yes, it is a very interesting book to read and gives one much food for
thought.
But likewise is the modern development in mathematics called Category
Theory. In category theory two sets (cat objects) are linked by a functor
(cat arrow). You will find that much of Hohmann's insights are also
refelected in Category Theory.
But there is something just as important to learn as Hohmann's conceptual
framework, namely that one can connect two processes (input process and
output process) with a structure in between. The overall result is a
"becoming" rather than the "being" of the "structure-process-outcome"
scheme (the "outcome itself a structure). I had to use exactly these
"becomings" (procedures linked by a structure between them) to create a
utility in my lesson authoring system with which I could analyse the
creative inputs of students. (I call it the Creation Processing Structure
or CPS.)
In other words, I want to stress that for me it is the web between
structures and processes which are important, not the fact that we employ
ternary (triadic) complementarities. However, eventually, when we have a
whole web of structures and processes linked together, it becomes very
important to know what we are dealing with when thinking about the web
itself. It can be a structure (being), or a process (becoming), or a
processing-structure (becoming-being). I find much more harmony in overall
becoming-beings than in a overall being (such as in Hohmann's framework)
or a overall becoming (such as in my CPS).
Quantume mechanics, especially the work of Niels Bohr and his Copenhagen
school of thought, opened my eyes as a student some thirty years ago to
dual complementarities. For a long time I played with higher
complementarities merely out of curiosity. However, it was, as I have
noted in another contribution, the Creation Processing Structure (CPS)
which opened my eyes to the vast untouched terrain of complementarities
(binary, ternary, quaternary, quintenary, sextanary, septanary, .......)
reflected in our mental creations. I am now very cautious of reducing
complementarities into a binary or ternary scheme.
The 2x2 matrix (unconscious, conscious, uncompetent, competent) which
formed such a great thread for a couple of weeks, is an example of a
quaternary complementarity.
Irreversible Self-organising Systems (Prigogine's terminology) or Complex
Adaptive Systems (Kaufmann's terminology) are essentially "becoming-being"
systems. This is what makes liveness ("becoming-being") such an
interesting essentiality of creativity.
Dwig, by the way, I like your quote of Charles Pierce in your signature
very much.
>The very first lesson that we have a right to demand that
>logic shall teach us is how to make our ideas clear.
> C S Pierce
He was one of the first persons to note that the logical pair
induction+deduction do not form a complete complementarity. He suggested a
third member (I think he called it adjunction) to make the complementarity
more complete.
He was also the first person to point out how important the NOR
function is to the elucidation of thoughts. The NOR function is
defined as follows
OR(x,y) = NOT ((NOT x) AND (NOT y))
NOR(x,y) = NOT (x OR y)
He was certainly a fine candiate for complementarity thinking.
It is possible to create a logical system which uses only the NOR function
as J P G Nicod eventually has shown. In today's design of the logical
microchips which computers use, we cannot do without the so-called NOR and
NAND gates, thus vindicating Pierce's work. The definition of NAND is
simple:
NAND(x,y) = NOT (x AND y)
Best wishes
--At de Lange <amdelange@gold.up.ac.za> Snailmail: A M de Lange Gold Fields Computer Centre Faculty of Science - University of Pretoria Pretoria 0001 - Rep of South Africa
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