PRECISION OF FIT
Posted by Laurence J. Victor on August 18, 2007
I am sorting though old floppies, to dispose of, and chanced to look at a BU file of an essay composed in 1986. The concept of “precision of fit” remains critical, and I often couple it with the concept of “sufficient action”. I copy/paste my old essay – which goes into some of the precision of physics and biology to make the point that we need to consider such precision and complexity in social systems. It was probably composed on the outliner GrandView and stored as an AskSam file.
filename[precfit1.mf2]
date[11-05-86]
domains[educ] domains[meta] domains[doing]
topics[pub] topics[semeh]
concepts[fit] concepts[precision] concepts[chromosome]
type[ type[essay]
rank[10]
names[Eddington]
~
title[PRECISION OF FIT] by Laurence J. Victor
^^^^^^^^^^^^^^^^ 11-05-86
This is so significant a concept, that a whole book should
be devoted to it. It is important that the concept be
experienced in detail, with many clear examples from the
sciences so that it is comprehended to a high level of
complexity, and not “just understood” with a ho-hum, “nice
idea”.
~
A. PURPOSE OF THE CONCEPT.
This concept is important because it illustrates how
much farther we must go in detailing the design of
socio/cultural systems for them to be viable. The
physical, chemical and biological systems of the known
Universe work (are viable) because of the “extra-
ordinary” precision of fit of components with the
system.
1. Actually, the precision of fit for these “real”
systems is
quite ORDINARY, which is the point I want to make.
It is our naive conception about complexity that is
causing the trouble. The Universe is “simply” not
that simple.
~
a) The physicists who are attempting to develop a
“unified field theory” fall into this same trap
(of over simplification) — illustrating that the
problem does not lie soley with the scientifically
illiterate. These physicists believe that if they
can reduce the four (known) primary forces into
one logically consistent mathematical formulation
they will have “explained everything” — that all
else will follow logically and simply from this
universal formulation.
~
1) What is wrong with this “application” of their
work is beyond the scope of this discussion.
2) However, their work DOES ILLUSTRATE the
precision of fit at work at this fundamental
level of physical reality: the four forces
probably will be discovered to fit together in
a precise way, which is another way of saying
their very natures are — to some extent —
inter-dependent.
~
2. If socio/cultural systems are as complex as these
other systems (and they may even be more complex),
then it seems logical that they will need as much (or
more) precision of fit for their components.
a) Consider one illustration at this point. The
parts that are assembled in constructing a modern
house must be shaped to fit each other. They are
also selected to have material properties needed
for strength, durability, etc. The relationship
between the parts is significantly determined by
the shape and properties of each part, designed to
functionally fit together in a larger whole — the
system of a house. The same kind of consideration
is needed when designing a large skyscrapper, the
space shuttle, or DisneyWorld.
~
The businesses or human systems that do this kind
of designing and construction must work with this
level of detail; the parts don’t make themselves
to fit. Their own organizational structure is
usually not, itself, of this detail. However,
there are great variations in detail in
organizational structures of agencies,
institutions, corporations and governments. Much
of this social organization is bureaucratic and
oppressive; yet the degree of organizational
detail cannot be eliminated (although it could be
organized differently — e.g. organistically
instead of mechanistically — later on this). If
what we are trying to create is a socio/cultural
system, then we must consider in detail the
precison of fit for its components (persons and
teams).
~
Now think on what NewAge, Humanist, futures-
oriented movements and organizations are doing.
What they are attemting to create (as new forms of
human socio/cultural organization) are naively
simple. They do not think in detail, either about
the world they wish to build or the
structure/process of their own organization. In
particular, they give little to no thought to how
they, as components of these organizations are to
fit together so that their organization can become
a viable system. They remain so highly
individualistic that they view interpersonal
relationships ideally as between two inert objects
that somehow get on well with each other, where
the “fit” is “natural” and “they” don’t need to
“do” anything about it.
~
If individuals change, it must be as to their
personal self-interest; certainly not to “fit”
into a larger system, even if it be a marriage or
family, let alone a community or society. Harmony
comes from good feelings and intentions, not by
“doing” anything. This sounds a bit harsh, and
with intention of caricature. Later we will
explore the reasons for this avoidance of
precision and what we might be able to do about
it.
~
B. PERSONAL NOTE — ON FINE STRUCTURE.
My interest in precision of fit and quantitative detail
goes back a long way to my early interests in physics
and my reading of the philosophy/physics of Sir Arthur
Eddington in high school. Eddington, professionally a
reknowned astrophysicist, was also a “general systems
mystic” (before general systems was invented). His
views on FUNDAMENTAL THEORY have never been accepted by
the physics community, and whether they are “true” is
not really an issue. His ideas continue to stimulate
vital thinking much the way Kepler’s discovery of the
HARMONY OF THE SPHERES did to earlier planetary
astronomy.
~
1. The Ultimate Fit: MACRO TO MICRO TO MACRO TO MICRO…
Eddington believed in an ordered Cosmos. He
speculated that the detailed structure or the micro
world — of atomic structure — was intimately
intertwined with the detailed structure of the macro
world — the expanding universe of galaxies. He went
so far as to develop a detailed mathematical theory
for this ultimate fit. a) A metaphor often used to
illustrate one nature of this fit,
was to a bug crawling on the surface of a regular
solid.
~
1) Now, there are only FIVE regular solids in this
Universe (a marvel itself). A regular solid has
faces that are congruent (same size and shape).
The cube (with 6 square faces) is the best
known regular solid. The tetrahedryon has four
faces that are each equilateral triangles. The
other three regular solids have 8, 12 and 20
faces, two with triangular and one with
pentagonal faces. Why there are only five is a
consequence of space being three dimensional –
a very deep example of fit.
~
2) Incidently, Kepler’s 6 spheres circumscribed
and inscribed the five regular solids, each
sphere representing the orbit of the six
planets around the sun, with relative
distances-from-sun the same (to the accuracy of
measurement of Kepler’s day) with the relative
radii of the six spheres. This discovery
“blew” Kepler’s mind !
~
b) Back to our bug. Imagine it comes to one corner
of a regular solid and makes measurements of the
angles at the corner. Then the bug creatively
assumes that it is on a regular solid, and from
the measurements of one corner can decide which of
the five regular solids it is on, and the exact
number of corners without having to go to them.
~
c) Eddington took the hydrogen atom in vacuum as one
corner of a model of the “regular” universe (he
called it a Uranoid -a cosmological universe with
a uniform density of hydrogen atoms everywhere –
actually not a bad approximation). The
measurements of that corner were the properties of
the hydrogen atom. From this, using his model,
Eddington computed the “exact” number of atoms in
the Uranoid. He opened one lecture with writing
that number on the board, 80 digits long. What is
to be of interest here, is that the formula for
his computation contains the number 137.
~
d) In another domain of his model, Eddington was an
epistemologist, wondering how the knower
influences what is known. He uses the following
metaphor to illustrate this.
1) Imagine a scientist as an ichthyologist (a
student of fishes) who dips his net daily into
the ocean and carefully measures each catch.
Eventually the ichthyologist arrives at a
universal statement about fishes >> they are
all longer than two inches! BUT, is this not a
condition of the weaving of the net, and not a
characteristic of fishes ?
~
2) Eddington set for himself an ambitious program
to consider how our theoretical pre-
suppositions about reality (systems with
components) acted to influence our scientific
“discoveries”. His initial model was a simple
one, considering only two-body systems
(hydrogen atoms) in a statistically expanding
universe (Uranoid) >> which lead to a matrix of
possible structures for which there were
exactly 136 degrees of freedom. Using this
model Eddinton deduced that ALL the laws of
physics AND all the unitless parameters of
scale were “filter factors”, characteristics of
our scientific methods and NOT characteristics
of the universe (except that we are within and
of the universe)!
~
a> Obviously this conclusion did/does not fit
well with our contemporary beliefs on the
empirical-deductive model of the scientific
method. To ridicule Eddington, physicists
have pointed out that he first selected the
number 136 as his “fine structure constant”,
and at the time he did it, the empirical
value was very close to 136. Later the
value shifted slightly upward to 137.009 .
Then Eddington said that he forgot to
include one more degree of freedom for his
system, that was the whole universe itself.
~
Eddington also had a calculation correction
that he applied to empirical values to
adjust them to the Uranoid — taking into
account the the measuring instruments are
themselves within the universe. When this
correction is applied, ALL the constant
parameters of the physical universe fit
Eddington’s model.
~
2. As some of you may have already recognized, my power
number is 137. It is my ID number on PCNC, and has
coincidently appeared at many times in my life. This
is called the FINE STRUCTURE CONSTANT (actually, it
is the reciprocal 1/137 that is often given this
name). In conventional physics, it is the ratio of
three other most significant parameters of the
physical universe.
FSC = h x c / e2 = 137
h times c divided by e squared (e times e)
where
h >> Is Planck’s constant, a measure in quantum
theory of the ultimate uncertainty of measurement
itself.
~
For example, the product of the
uncertainties of measurement of the location and
movement of a particle must ALWAYS be greater than
this number. This is the “scale factor” for the
empirical knowlability of the universe. (Actually h
divided by 2 pi).
c >> Is the velocity of light in vacuum, which is the
“scale factor” for our ability to interact and
communicate.
e >> Is the charge on the electron, the fundamental
“scale factor” for forces, that leads to all other
structure.
In this ratio, the measurement units (e.g.
centimeter, seconds, etc.) all cancel out and leaves
the ratio a PURE number.
~
3. None of the above is explicitly relevant to the issue
of precision of fit, which would exist had there been
no Eddington and no Fundamental Theory. His work
“smacks” of mysticism and numerology (of which
“normal” physicists accuse him of). When at Yale I
was deciding between two PhD thesis projects. One
was to unpack Eddington and attempt to update his
work (he died in 1945 before completing the book,
Fundamental Theory, not having written the general
introductory or summary chapters). I even have a
collection of his earlier drafts and unpublished
manuscripts. I just didn’t have the fortitude of
scholarship into another’s work. So I chose my
second option: to challenge Einstein’s claim that the
velocity of light was a limiting velocity for ALL
interaction. Even this was eventually defeated by
disciplinary politics.
~
Yet, this early work set the
stage in my mind to appreciate complexity, relativity
of perspective, and holism — in the sense of
Eddington’s attempt at a mathematical theory for the
ultimate fit: micro within macro within micro with
macro. And, that this fit was not a “wishy-washy
right-brain, Eastern holism in resistance to explicit
conceptualization”, but involved complexity,
precison, and attendence to detail. I often
transcend this detail, and experience the UNITY IN
DIVERSITY holistically — with an intensity that
depends on the deeper patterns of analytical thought.
~
C. DEFINITIONS.
Although I am opposed to the contemporary concept of
“definition of terms”, I do wish to comment on some
evolving ideas that are often labeled by the terms:
PRECISION, QUANTITATIVE, and FIT.
1. PRECISION:
I will talk around this concept in metaphor. The fit
of a key into a lock is an excellent example of
precision. If the key duplicator is sloppy, there
will be no fit, meaning the lock and key will not
work as a functional whole.
~
a) Note that when a key is copied, the “master” is
used as a “template” for the duplication process.
One does not make “measurements” of “quantative”
aspects of the key. However, if your high
security strong box arrived in New Zealand and had
to be opened within the hour, and it was designed
to resist the efforts of locksmiths, you would
have to communicate a quantative description of
the key to a keymaker in Auckland. Quantification
occurs ONLY when we need to communicate precise
pattern — more on this later.
~
b) How different can keys be to work in the same
lock? Mass production in industry occured only
after we were able to machine parts to a
sufficient precision that they could be inter-
changable !
1) In elementary particle physics, one type of
particle –the Fermion, of which the electron
is a member — are cosmologically
indistinguishable. This fact is taken into
account in the theory and is confirmed by
experiments. Electrons are ABSOLUTELY
indistinguishable from each other (which leads
some to speculate that there is only ONE
electron that has “reflections” in many
different places.
~
c) The lock-key model is popular today. Neuro-
transmitters are small protein molecules (three
dimensional structures) that serve as “keys” into
the receptor sites (also protein molecules on the
receiving membrane of the synapse). When enough
keys are inserted into locks, “circuits” are
activated, that catalyzes a pulse to start moving
doing the neuron.
~
1) The CHROMOSOME can also be visualized in a
lock/key model. The basic component of the
chromosome is the nucleitide, a binary molecule
composed of two bead molecules. A bead
molecule is really a multi-nucleated atom
(rather than our usual view of molecule as an
assembly of atoms) where the electrons are
truly shared by all the different nucli in the
bead molecule. The nucleitide has two parts,
let me call them the “base” and the “prong”.
For all nuceitides, the bases are identical.
The bases are capable of attaching to each
other into a chain, with the prongs sticking
out as prongs on a single side of a zipper.
~
There are four different prongs, let me call
them A, B, C, D. Now prongs A and B are shaped
so that they fit together (in 3-D) as lock and
key (which is the key and which is the lock is
not relevant). Likewise for prongs C and D.
AND, the lengths of the whole system A+B and
C+D are EXACTLY the same.
The chromosome is then an advance lock-key
system, with two single strands “zippered”
together. When transcription occurs, a
segments unzippers exposing the prongs as a
template onto which “free” nucleitides attach
making a “mirror image” RNA copy of the DNA
gene.
~
What is important here, is the role played by
“precision of fit”. This is a very intricate
system, far more dependent on precison than our
industrial technology for mass production.
~
2) PROTEINS are the basic threads in the tapestry
of cellular structure. Proteins are a family
of chain molecules, which are folded into
definite 3-dimensional shapes. Proteins are
chains of bead molecules, of which there are 24
different types, where each of the 24 can link
into a chain with any other of the 24,
including itself. This is like 24 letters to
an alphabet, where there is no limitation on
what letters can be together forming “words”.
~
There is an awesome “fit” between the proteins
and the DNA in the chromosome. Given the four
“letters” of the DNA alphabet, we can make 24
triplets (AAA, BBB, CCC, DDD, ABA, ABB, ACD,
DCA, etc.) — exactly 24 by the combinational
rule: 4x3x2. In the cell, each of these RNA
triplet FITS precisely with only one of the 24
protein beads (called amino acids). In the
cytoplasm of the cell are ribosomes (woven
fabrics of protein) that take in RNA copies of
DNA genes (sequences of inheritance language
coded with a four letter alphabet into three
letter words) and assemble proteins from the
RNA-AminoAcid pairs in the vicinity.
~
After the protein chain is formed, it “folds”
according to its “sequence of amino acids” into
a 3-dimensional structure that has a specific
role to play in cellular functioning (a role
played by the “fit” of its shape with the
shapes of other proteins).
~
3) This precision of fit is everywhere there is
life ! The structures composed of proteins
(called organelles in analogy with organs of
the physiological body) are finely tuned
systems dependent on the precise fit of their
protein components. The recent literature on
molecular biology is truly awesome. The
complexity of cellular membranes to regulate
the flow of many different types of molecules
in and out of the cell makes a typical factory
operation appear simplistic. The ion pumps
that enable pulses to move down neural fibers
is another example of an intricate system that
works ONLY because of the phenomenal fit of its
components.
~
The immuneological system of the body/blood and
the organization of the brain itself are other
examples. Occasionally one mispelled gene
gives rise to a cascade upward of dysfunction
to the whole organism, another example of the
critical nature of precise fit.
~
d) I will not go on in further detail here. I
believe that to fully UNDERSTAND this precision
within complexity, each person must study a few
real systems in detail. Then they can appreciate
this level of precision in all systems in the
Universe. If no systems are actually experienced
at this level of detail, the person is really
unable to aprreciate the universe AS IT IS, and
instead attempts to impose their simple-minded
views on the rest of us.
~
2. QUANTATIVE.
There is much confusion today between the concepts of
the “qualitative” and the “quantative”, and I won’t
go deeply into it here. What is important is a new
view that there is NOT a “qualitatively” sharp line
between the two. QUANTIFICATION does NOT ALWAYS
involve the use of NUMBERS.
a) USEFUL DESCRIPTIONS OF PRECISION MUST INVOLVE
QUANTIFICATION. As discussed above, precision
itself does not involve numbers, only 3-D fits
between locks and keys. Only when we want to
describe these fits, do we need mathematics and
numbers — which are characteristics of symbolic
language.
~
b) “Mathematics”, in this context, is but a family of
specialized human languages, specifically designed
for describing, thinking and communicating about
specific types of systems where precision is
critical. Each different mathematical language
(and many do not involve numbers) have structures
that enable the precise structures of real systems
to be represented within the language. The
symbolism of mathematical languages are concrete
(real marks on paper, that can be manipulated) and
thus enable us to represent abstractions in
material forms that can be perceived thru the
senses.
~
c) The design of and planning for new systems that
involve the precise fit of components requires the
use of quantification, requires attending to
detail. In the “real world” you can’t just slop
together anything just because it feels good and
expect it to work.
~
3. FIT TO WHAT? FOR WHAT? WITH WHAT?
The concept of “fit” seems inseparable from the
concept of “precision”. At least, above, we used the
METAPHOR of fit (lock/key) for our explication of
“precision”. Is “fit” a primitive, or is there more
to be said about it ? Where does this “fitness” come
from — to some it appears as evidence of a creator,
to others it demonstrates the power of emergent
creativity.
a) COMPONENT-COMPONENT FIT.
What was discussed above was primarily the fit of
two components of a system, as lock/key, to form a
functional whole. Many of these were dyads, while
it was implied that many components could mutually
fit together to form a more complex wholes.
~
b) COMPONENT-SYSTEM FIT.
This is the fit to the role a component of a
system must assume to be a functional member of
the whole. This is manifest in the component-
component fits, but the many component-component
fits together are organized that give “meaning” to
the concept that the components are functional to
the system as a whole.
~
c) COMPONENT-SYSTEM-METASYSTEM FIT.
This can be viewed a just bumping up component-
system fit another level. However, we want to
imply here that there can be “fit” in the system
“mediating” a functional relationship between the
components at one (inner) level and the
environment (metatsystem at an outer level).
Fitness in the evolutionary sense of organism
within species within biome may be examples at
this level. It should be emphasized the “survival
of the fittest” has much more to do with “fitting
in with the whole”, rather than being superior in
component-component competition.
d) HOLARCHICAL FIT.
Here we might consider the fit (role) a holon
plays in the “whole” eco-holarcy. COSMIC
RELEVANCE !
~
D. CONSEQUENCES OF THE CONCEPT: “PRECISION OF FIT”
As stated in the first section, our purpose is not to
educate about biological or molecular systems, but to
examine the role of attending to detail re complexity of
systems and the precision of fit as it relates to human
efforts to organize their thoughts/actions to create a
better world-system. However this need for percision
cannot be appreciated without seeing the awesomely
significant role it plays in the Universe.
~
1. IS HUMANKIND EXPEMPT FROM THE LAWS OF THE UNIVERSE ?
We often act as if we are. We were put here to
exploit the universe, and we might need to know her
laws so as to better exploit her, but we need not
consider ourselves part of the universe or need to
obey her laws. Thus, we humans are exempt from the
need to attend to such “left brain” detail. Indeed,
it is such attention that has got us into such a
pickle already. Relax and flow with your “feelings”,
insist that the universe be squeezed into your narrow
brain.
~
2. This is not the PRACTICE of those social systems that
must work within the real world. If we want to
travel in the air, we must be be concerned with the
precise details of flight. If we want to make a
profit on a business venture we must attend to the
necessary details. It is no mystery that the
academic discipline of BUSINESS ADMINISTRATION has a
math requirement into advanced statistics and the
calculus (the natural languages for thinking with
complex systems).
a) The problems with these systems is that they have
considered only component-component and component-
system fit, and have ignored component-system-
metasystem fit (worker/consumer-firm/market-
society) and holarchical fit (ecological and
humanistic).
~
3. There are many people who are concerned with those
types of fit ignored by contemporary societal
practice. However, they somehow feel that they
can/should not be concerned with precision of fit at
the “lower” levels. They naively attempt to move
mountains with thimbles and good intentions.
4. I propose that any serious venture in the humanist,
NewAge, futures-oriented movement must consider their
internal organization within an evolving system that
will eventually (soon) be MORE sophisticated than the
systems of NASA ! We have ample of what it takes to
get there, we only need the realization of the true
magnitude of the task, and then set for ourselves the
goal. Dreaming that somehow the universe will do it
all for us is denying our knowledge of how the
universe works. How we go about doing this will be
the topic of other essays.
@@
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