>Date: 02 Jul 96 12:25:06 EDT
>From: "Milton L. Dawes" <102362.1465@CompuServe.COM>

   A  Universe of Rhythms.   Relative Invariance under Transformation.

To paraphrase Korzybski: In a world of diversity and change, when we discover 
something that seems to remain relatively invariant, (relatively unchanged),
then we are unto something of  great  significance  and importance to us in
understanding ourselves-and-our-world. The formulation "relative invariance
under transformation" addresses such invariances. (Read Chapter X1X  Science and
Sanity). "Relative  invariance under  transformation" is a general-semantics
generalization of the important scientific and mathematical principle
"Invariance of principles and laws under transformation of  frames of
reference".(The addition of  "relative" in the  formulation serves to emphasize
the  basic  general-semantics principle of "non-identity" - no two things are
the same in all respects)  I  propose that "rhythms'' like ''structure''
(another general-semantics formulation)  constitute such an invariance. But
first let's explore the relative invariance principle.

 You could think of ."Relative invariance under transformation" as a fancy way of 
saying something "A'' is  structurally similar to,  is like,  some other thing
"B". And also another way of saying  "Although  "A" has changed,  broadly
speaking, there are some  features we can abstract from  "A"  that have
remained relatively unchanged. In brief we are saying ''a this is like a that''.
We are "talking relative invariance" when we say   "Like father, like
son"..Laws, rules,  constitutions, regulations, policies, mission statements,
habits, attitudes, notions of personality and self,   consistency, complacency,
etc., can all be considered examples of  the relative invariance principle.. For
example,  A law or regulation, is designed to remain operative in different
places and different times. . Metaphors, similarities, analogies, models,
examples,  explanations, constants, correspondence, maps,   fractals, theories,
names, labels, words,  etc., can also be considered examples of the relative
invariance principle. When we give an explanation,  for instance,  we are in
effect proposing that there are  some similarities, some resemblance, between
imagined structures,  and some other reality.  

To facilitate  understanding of the principle, here is an example of an
application  illustrating  analogy, example, explanation, hypothesis, structural
similarity, and so on.  It answers the question "How is our perception of
objects (a this)  like a swarm of bees?" (a that).  In addition to the various
ways we have been writing and 'thinking' about objects, and  our perception of
objects,  we can also apply  the relative invariance   principle to  increase
our understanding of this process. . To facilitate this approach,  I invite you
to imagine you are observing  a very densely packed swarm of bees. Imagine  that
you don't know, and cannot see,   that there is  an invisible barrier (let's
say,  a star trek-like  force field) that surrounds and move with this swarm;
creating a boundary  which cannot   be crossed by a bee. Now visualize what you
might  observe watching  this swarm from a distance , far enough away  so that
you are unable to see individual bees darting here and there in all directions.

 Now imagine  a  very large number of  densely packed interacting and
interrelating  subatomic particles, each moving at tremendous speeds in diverse
directions. Also imagine some kind of force field accompanying this  'swarm of
particles' . This force field prevents most of the particles from flying off in
all directions as  the bees would without their surrounding force field. (Now
don't be picky here.. I know that a swarm of  bees tends to stay together. So
imagine an unruly  swarm that ignores the rules of  swarming).  In terms of
"relative invariance "  this eventful subatomic activity, this swarm of
particles,  can be likened to  that swarm of bees.   We could now consider an
object  as  "A structure  that remains and  appears to us  relatively unchanged
through all the  various changes of directions and movements of its constituent
'parts-ticles' : A  structure that remains topologically  relatively invariant
through all the tremendous activities and energetic  interactions of its
constituents.".  Now for a  change of rhythm. (By the way. I invite you to see
if you can sense other changes in your rhythm while reading this story. Keep in
'mind' that  "rhythm'' is not only about sounds and music). 

"Relative invariance" is very much involved in the communication process.
Communication works well when what I think-feel is well represented by what I
say. And what I say,  or intend,  is well received, and  represented,  by a
listener's interpretations and  meanings. The principle is also useful in
helping us to improve our general  understanding of various,  seemingly
unrelated features,  of our world. If  for instance, we know that  something
"A",  is like some other thing "B", then knowing something about  "A" can help
us to understand, expect,   and even make predictions about "B".  Our models,
expectations,  and predictions,  imply relative invariance between structures we
imagine and structures in the world outside our heads. 

The principle of relative invariance under transformation constitutes a
fundamental characteristic of  scientific activities. Scientific laws  as
statements about  what we can expect  regarding the behaviour of  physical
systems at different times and different places,  would not make much sense ,
would not be very useful, without an underlying principle of relative
invariance.    Living and non-living systems  exhibit the relative invariant
cycle of  coming  into being,  growing, and  eventually declining or going out
of being. We often, to our distress, ignore this  relative invariant  rhythm,
when we expect  "a good thing to last" or remain the 'same'.  And  we could
better manage ourselves in many stressful situations by also remembering this
factor of changing rhythms of our own, and others' psycho-physical being. 

We could define a culture in terms of  relative invariant behaviors of a
'people' in terms of beliefs, speech patterns, music, dance,  and so on.  The
dynamics of  societies could be understood, as ways 'we' have found, through,
institutions,  laws, rules, regulations, roles, functions, etc., to organize and
regulate (keep relatively invariant) to some degree,  the diverse rhythms (range
of behaviors) of  large numbers of interacting individuals. Without such
regularizations, societies would not exist. 

In business,  when times, location, personnel,  demands,  social norms,
political variables,  significant international factors, etc., have changed -
while  attitudes, approaches, policies, rules, etc., are not  updated,  but
remain relatively  unchanged (invariant)  - businesses usually do not prosper.
And in problem-solving, whether in our personal, social, or professional lives,
asking ourselves "In what ways, or how is this problem  like others I have faced
before?" could provide helpful clues toward solving the current problem...
There are cameras that produce sharp pictures, despite shaky hands. Although I
know  little about  the technology involved, I would take a bet that the
invariance principle has been applied. Our own visual processes would not work
well without some underlying biological activities, based on the relative
invariant principle,  enabling us to see things clearly and sharply, while we
were moving our heads around, walking,  running, jumping up and down, and so on.
The recording industry  would  not exist  without  technological applications of
the relative invariance principle: There are  transformations  involving
patterns of air movement  from voice or instrument - to voltage and current
changes in microphones - to voltage and current changes in magnetic heads and
lasers - to magnetic and structural changes in tapes and compact discs - to
vibrations in speakers - to patterns of air movement  which we respond to as
sounds.  Without some relative invariance mechanism incorporated in the
technological systems, pitch, timbre, rhythmic patterns, etc, of the origin
voice or instruments  would not be maintained. A song or musical piece would be
unrecognizable.

We can very easily translate  our notion of  "wisdom" in terms of the relative
invariant principle. In this respect we could propose that the "wise" person  is
one who has accumulated a wide range of knowledge (relative invariant factors)
of  our world; and has developed an ability to  consistently (relatively
unvarying) respond  to a wide variety  of  situations ( a diversity of rhythms)
with a high level  of appropriateness ( a relatively invariant degree of
effectiveness). 

Another area where the relative invariance principle can be useful  has to do
with our  notion of  "self".  So let's suppose the 'object'  we are examining
is our ''self''.  In  terms of the principle,  a  ''self'' can be considered as
''Those aspects of a human  organism that remain  relatively unchanged through a
diversity of changes and  transformations of other aspects of the organism''.
Each one of us can determine for ourselves,  what we have discovered in our own
thinking-feeling-   behavior-attitudes-beliefs-values-needs-fear-pleasures-and
so on, that have  remained relatively unchanged over the years, and places. .
(The  hyphens serve to emphasize the interrelatedness of these various factors).


Rhythms. 

In a world of change, processes, and diversity,  we need some kind of stability,
something we can rely on:  We have to have something that helps us to make sense
of, give meanings to, ground our expectations, make predictions,  and  so on.
Without this, we could not  understand what's going on in and around us.  The
principle of  relative invariance under transformation  labels a process by
which our limited nervous system evolved to cope in a universe of diverse
rhythms. 

Speaking for 'my self',  what  I have discovered as a relative  invariant over
the many  years and  different places,  involves what I describe as a
"Persistent drive" to understand two things: "What this universe is about. And
the structure of  consciousness." .And following this, and applying the relative
invariant principle,  I have arrived at a place where  I evaluate "rhythms" as
one of  the most invariant  characteristics of universe -our selves included. (I
am still working  on consciousnss).

  In Science and Sanity,  Korzybski advanced  a  proposition that  "Structure is
the only  content of  knowledge". Well if we include  the time factor,  this
statement can be translated to "Rhythms  (structure and structural changes) are
the only content of knowledge":  With regard to the proposition that "structure
is the only content of knowledge  here are a few words of explanation:  We don't
know anything directly. What we know involves relationships between  our nervous
system structures, and their responses (how they order, how they relate to, how
they  structure)  structured information (light waves and sound waves, etc., of
particular frequencies, and patterns). In other words,  what we know involves
relationships between our inner nervous system structures,  and structures
outside our nervous systems. . When we forget that our nervous systems
structure data it receives, we come to  believe  - and  usually  to our distress
-  that  what we  know or believe,  is absolutely so; instead of what we know or
believe,  has been structured by us so.  When we recognize that we structure our
experiences, we give ourselves the power to re-structure our  evaluations:  we
become more creative. 

 "Rhythms'' can be considered in terms of  " a measure of structural
transformation"  And ''structural transformation'' can be considered in terms of
how  a system changes  with respect to different times and places. . Terms
related to ''measure of structural transformation", include "frequency,
vibration, pitch, cycle,  wave,  recurrence, periodicity, pulsation,  variation,
rate of change, patterns of change,  resonance, harmony, dissonance,
fluctuations,  undulation, speed, (change of position with respect to time),
how often, ups and downs, going with the flow, to everything a season, comings
and goings, growth and decay,  among others. 

As individuals, we constitute a complex of rhythms immersed and interacting with
a universe of rhythms: A universe of rhythms ranging from  the indeterminately
high frequencies of sub-atomic activities, to the immeasurable long cycles of
cosmic processes. Our personal  and more easily observable rhythms involve our
swing and sway, and various  other movements when we walk, for instance. When we
are abroad, criminal types recognize us by the way we walk,  talk, look around,
and so on.  Our rhythms  are easily recognized as being  different from (varying
relative to) the rhythms of the 'natives'.  We  recognize  friends,
acquaintances, and  others,  from a distance,  and in not so well lit places, by
the relative invariance of their movement  rhythms. The pitch of our voice, our
intonation, our speaking speed, when we are being affectionate, or when we are
excited, angry, distressed, nervous, and so on, illustrate variations in
rhythms. These variations are important variables in developing our
communication skills.  In terms of  "moods" we move around differently when we
feel good, compared to how we move when we are not feeling so good. (By the way:
We can sometimes, through a neuro-semantic feedback process,  change our mood.
For example,  doing an exercise (rhythm change) can affect our state of
mind-body). We  listen,  learn, understand, eat, sleep, do  a variety of things,
and so on, at our own pace, by  our own rhythms.  We recover from  physiological
and psycho-logical injuries, at our own pace. (Some  of us  may be very
forgiving. And others may  hold a grudge for a lifetime. Some  groups hold a
grudge for centuries.)  In our  many  relationships, personal, intimate,
social, cultural, political,  international, etc., an invariant  source of a
variety  of problems,  conflicts,  disagreeableness and  dissatisfaction, etc.,
can be attributed to a "clash of rhythms''.: A clash resulting from not being
aware of one's own rhythms;  insensitivity  to  the rhythms of others; and how
these different rhythms  interfere, hinder, impede, collide, and so on. 

 Our personal,  domestic, social, work related  and other  habits and
activities, age differences, social standing,  and so on,  find expressions in
our rhythms.  When we say or 'think'  things like "Act your age", we are
implying that someone should behave according to the rhythms we expect.  When we
find ourselves  waiting impatiently for someone, or an important letter or
telephone call;  or when in a hurry  and  anxiously  waiting for the elevator,
bus, taxi or train; or when our expectations aren't met, and we feel
disappointed; and when things don't happen as we would like, when we would like,
and as often as we would like them to happen   we can be sure that there are
differences in rhythms involved.  Notice your own rhythms, and change of rhythms
while reading this piece. 

Here is another way to get a 'feel' of rhythms. Imagine a tree,  or better yet,
look at one:  a tree with lots of branches and leaves. .Observe'  the variety of
movements and rhythms. If there is a light breeze, the leaves might be doing a
fluttering dance like the leaves of an aspen.. This will be different from the
rhythms  of the smaller branches; which will be different from the rhythms of
the bigger branches.  If it is a very big tree,  the trunk may not show much
movement , or any movement  - but it also has its complex of  rhythms, although
not as easily recognized as the rhythms of the leaves and branches.  Can you
specify a rhythm for the trunk? And other rhythms  of  the leaves?  And can you
'think' of any structure  that cannot be associated with  a  complex  of
rhythms?. What are some of the rhythms you see expressed in your home, at social
gatherings, in  your workplace, in and around you?  Would you consider it a fact
that if something isn't seen to be moving, there are no rhythms involved?

 In the workplace, more and more employers are beginning to recognize that  some
individuals do not shift easily  from night shift to day shift.  In the world of
business, those who invest in stocks usually do well when they have learned to
read the rhythms of the stockmarket . The attractiveness of cities can be
attributed mainly to the wide range of rhythms they attract and  accommodate.
.'Nations' exhibit rhythms, observable in their  level of  economic, population,
international stature,  military, etc., growth and decline.  In  international
politics, many politicians,  not having a  knowledge of, or caring about
differences  in rhythms, often create social-cultural-economic-and other
problems that persist for many years. This usually  occurs when certain
practices or policies are imposed on another,  without  alloting sufficient time
for a change in that culture's well established  rhythms. A simple example
involves  teaching  men to farm in a culture where the women do most of the
farming - and the men like it that way.. A more troubling example involves
efforts  to hurry a country with centuries of  other forms of political systems,
into one's version of  'democracy'.This could be as disturbing and disruptive as
the drastic change of rhythms imposed on a society by a revolutionary group. 

 On the road, many accidents occur when  a driver makes a sudden stop, or lane
change, or change in speed. In general,  sudden changes in rhythms, that  do not
allow sufficient adjustment time for others often  create problems.  In
medicine,  some doctors are beginning to recognize that some medication and
treatment and 
operations are more effective at certain times of the day. The rhythms of adults
are usually very different from the rhythms of  little children. Compare  the
rhythms of  grandparents  with their grandchildren. How is it that grandparents
often  seem  so adaptable to the rhythms of  their grandchildren when they are
with them? 

  In our everyday living and interactions, our communication with others, in our
efforts toward  self-development  and self-improvement, etc.,  how often  we are
conscious of our abstractings  (remembering that we have not included all in our
experience, interpretations, beliefs,  verbalising, etc.) can make a very big
difference.  In setting out  to resolve our personal, social,  international,
and other problems, we often forget about the changes in rhythms that our
solutions will generate. Our resistance to change ( a preference for relative
invariance in the frequency,  timing, numbers,  and kinds,  of  our activities)
has a lot to do with a tendency to resist a change to our rhythms - especially
when those changes are initiated by someone else. 

 As human individuals, we  literally disturb each other's rhythms: In becoming
more sensitive to rhythms, this can be avoided, but only to a certain degree.
(See yourself  in a hurry on  a crowded sidewalk, or in  slow moving traffic) If
we live in the 'same' world,  and  interact with each other,  we literally get
in each other's way. We  will  'disturb' each other's rhythms to lesser and
greater  degrees. Here is a simple example of a way we can move toward more
rhythmic harmony.  In terms of "rhythms", we could specify that   a
characteristic of a 'good' houseguest is,  "a  person who does not move things
around, leave things lying around, do things etc., which requires a host to put
things back, pick up things, undo things, and so on. In other words,  a
characteristic of a 'good'  houseguest  is, "a person  who is sensitive to, and
does not unduly disturb the  rhythms of a host". The above example can be
generalized to many other situations. 
 
 Sometimes, we react quite strongly to  disturbances to our rhythms. .  And then
there are also those times when we experience satisfaction and calm  - a harmony
of rhythms - at least for a while. Seeing ourselves as a complex of rhythms  in
a universe of infinitely many rhythms,  could  help us a great deal in
minimizing and  managing the  stress in our lives that  could come from a clash
of  our rhythms,  with  a multitude of other rhythms.  

Sometimes, we even disturb our own rhythms when we push ourselves too fast, and
too much. And when we take on more than our psycho-physiological systems can
adapt to in a given time period. When things don't  go the way we expect them
to, or happen as fast as we want them to, look for a difference in rhythms as a
possible source of the problem, and also as a possible factor in the resolution
of the problem.   We often create much problems for ourselves as individuals and
as a species,  when we attempt to hurry the universe, or "push the river" -  and
sometimes when we dam it. . . But through awareness of, and a sensitivity to
rhythms,  we can some times create a harmony of rhythms - at least for a while:
For would you believe it?  Rhythms have rhythms. In other words "rhythms'' like
anything else also change.

By now you might suspect that  I am proposing that, ''Everything, as far as we
know, can be  thought of  in terms of  rhythms". And that   'thinking ' in terms of
rhythms is not   just a  'philosophical'  or 'intellectual' exercise,  but also
has many diverse practical benefits. 'Thinking'. in terms of   rhythms can be
very helpful in  improving our   personal  and other relationships. Including
"rhythms" as one  of our management  tools  can help us better avoid and manage
stress; become more patient with ourselves,  and  develop more  patience,
tolerance, and understanding in interacting with others. In solving  problems,
and making  decisions,  including 'rhythms" as a variable could  be an important
move. For instance in many everyday situations, we often create our own
problems by not asking ourselves such questions as "How often has this happened?
Is this something that is likely to happen again? "Is there a major difference
in rhythms involved?" Am I in synch?  And so on".   A sensitivity to "rhythms"
can help us recognize trends; help us to anticipate and manage change; recognize
and minimize stress; avoid many disagreeable situations and  many problems;
improve our judgment; improve our  communication skills; improve and increase
our understandings of our selves, our friends and acquaintances, and the diverse
structures of our world; and help us to feel and be more at home in our worlds.


Scientists define "power" in terms of  "rate of work done" or "work done in unit
time". And  "work" is defined as "movement in a specified direction". "Movement" and
"time'' are factors in the structure of rhythm.  Applying the relative invariant
principle, (this, is like that)  we could  define "power"  in general, (
political,  physical, economical, intellectual,  etc.) as "The degree to which
individual/s or group/s can dictate, restrain, determine, control, etc.,  the
rhythms (speech, movements, activities, behaviors, etc., ) of other individuals
or groups". And we could 'think' of  . "personal power"  as "The degree to which
one is able to determine his or her own rhythms", (literally degree of  freedom
of movement) in a universe of diverse rhythms).  

And now for another  change of rhythm. You may recall the wise old folk sayings
"You can take a horse  to water, but you can't  make it  drink" .  "Don't cross
the bridge,  'till  you come to it".  "A stitch in time saves nine". These were
about rhythms - Don't you think?.  In a world of change, our chances for success
and effectiveness in our activities  depend  on our skills in  anticipating,
managing , and creating changes. But this I propose is not enough.  In meeting
challenges in  a world of change, we  do better by being up to date,  not only
about what is going on (first order changes);  but  we also have to be  up  to
date  in terms of  changes to what is going on (second order changes).  A
sensitivity to  rhythms  keeps us alert. . 

With good timing, we can keep a swing going with very little effort.  If our
timing is bad, we could get knocked over. In a similar manner,  in  meeting the
many challenges of living,  satisfaction and success depend not only on our
knowledge , skills, and experience, but also on our good timing. And good timing
is not just a matter of good luck, but develops from a sensitivity to one of the
most constant and important variable in our world  " rhythms":  our rhythms,
the rhythms of others, and the rhythms of the world we live in. 

 Our sensitivity to rhythms helps us to focus, not on how things  "are", or how
someone  "is",  but on what we  have  learned about  how someone or something
has been behaving; what we observe of their present behavior; and what we can
infer in terms  of how they might  behave.  This is quite in keeping with the
general-semantics principle of "non-identity". This states that  "No two things
are identical." And that "A thing is not identical with itself". A sensitivity
to rhythms helps us to treat a situation, person, or thing, not in  the more
restrictive sense of what  we say they are (our names, stereotypes, labels, etc.
) but more in terms of  their actions, and our interpretations of their actions.


Scientists have  helped us realize  that there are a wider range of rhythms in
our world than we can directly experience. By  improving our listening, our
looking, our sense of touch, and so on,   each one of us  through our own
experiences,  can develop more sensitivity to our rhythms and the rhythms of
others. This could go a long way to improving our personal, social,
professional,   national, international, and other relationships. But more
importantly we could improve our relationship with ourselves. After all,  how
can we expect to have a good relationship with others, if we are having a poor
relationship, if we are not in harmony  with ourselves? 


                                                                                 
Milton Dawes/96