Mapmaker, mapmaker, where's the topography
in a complex system?
Why, in the pattern, of course, and it's all mathematics.
Virgil J. Seutter,D.C.
Mathematics in the biological sciences is not something taken lightly. Certainly
it's much more complex and wonderful than I can imagine, let alone figure
out. Somehow it deals with models. For the chiropractor, this doesn't mean
too much. Focused on the subluxation, he doesn't see any pattern to his ritual
that makes any sense except what he feels with his hands. On the other hand,
for the embryologist, it means something more; like the formation of structure
as a morphogenesis of cellular development (1,2). It gives
the embryologist an idea of how the embryonic form might be created by
understanding the pattern of development. In other words, it gives him
"insight" into something relatively obscure (3).
Complexity Science and the Weather:
Mapping a Map
Pattern generation has been linked to the Turing chemical pre-pattern approach
where pattern and morphogenesis take place sequentially. Form in morphogenesis
is important in understanding the emergence of structural changes from a
cellular beginning. All this is based on reaction diffusion mechanisms as
a mathematical model to understand the development of patterns in or on the
body. Mathematical modeling can be used to study motion in biomechanics
(4) as well as applications to geographic contour maps
of the earth (5,6), the universe, or even
to structural design of mechanical objects.
The real idea behind all this business about topographical mapping is the
possibility of extracting information, useful information. That's sometimes
difficult to envision. However, I might be able to give the reader some idea
how this could be possible.
An eternity ago, when I was in the air force, I plotted weather maps. It
was an education and an experience. The meteorological world has changed
from my day using sophisticated computers and doppler radar and goodness
knows what. In my day, plotting weather maps, whether surface
(7) or upper air (8), was a tedious business.
A surface map
contained dots that represented the different cities
with a weather station. Each dot was plotted with the necessary information.
The data on the left contains only a portion of the data: city/town letter
identification on the right bottom, barometric pressure top right, high
temperature top left, and low temperature bottom left. A stick flag with
little barbs pointing the direction of the wind and speed was symbolic to
all maps. More was included: a symbol representing the type of cloud and
whether it was overcast or clear, and much more. Now, mind you, all this
had to be plotted within a circle no bigger than the size of a dime. Talk
about eyeball strain! I'm not sure if a distant relative had similar problems
as a cartographer (
9,10,11), but he did
an a-o-kay job.
Now, all this business about plotting maps is more than the eye can see for
the moment. All the data on each city plot, when plotted for its similarities
dot to dot or plot to plot, provided information that normally would not
have been seen. After all, looking at each city plot meant nothing except
that it was either hot or cold, windy or calm. Nothing exciting about that!
However, if we began to connect our dots to cities with the same information,
we began to literally 'see' a pattern develop. Our cognitive minds grasped
the significance of this pattern formation (it's exciting just to know our
minds can do that!). This pattern began to show the areas of land mass in
which the temperature was the same as it was at home, where the wind was
blowing just as hard as it was at home, and where the clouds obscured the
sun just as much as it did at home. That was nice to know, that other areas
had the same weather as I did - at home. But what was noticed was that by
visualizing all these patterns, it was possible to tell when the next mass
of air might slide our way. It's wonderful to know something ahead of time.
Sometimes it's just wonderful to know something!
Of course, I'm being facetious. But I'm trying to make a point. It's really
a jab, you know, at how to acquire information without making a big fuss
about it. It doesn't have to be absolutely right, you know. It's really just
a theoretical projection of probable relationships. What it is though, is
the ability to acquire information that might make some projection of a probable
event or action down the road. And...
Of course it works, all the sciences are using
it. But how does it apply to chiropractic?
Well, it seems to me that chiropractors are having the same problem as some
of the other sciences: the inability to find relationships between an action
and an outcome (or reaction; now where have I heard that
before?)(note1). What the chiropractor interprets as
an entry point into body function is based upon either touch or palpation
(12). The latter is similar to touch, just probably poking
a little harder to find contour changes on a local area of the body, often
the spine. He does a pretty good job, at least the patients seem to acknowledge
some feeling of change and well-being as the result of some action called
But the problem is one of credibility and absolutes. On the one hand, the
credibility is based upon a philosophy and a theory - a philosophy called
"vitalism" that can't really be proved since innate function is just a
description, not an answer to explain things. It has no life of its own,
or no form that can provide a basis for the patient's response to a physical
action on the body like an "adjustment;" there is nothing absolute to tie
it down to a cause - effect relationship. And how it's all tied in is the
pickle. How it all interrelates hasn't been found, probably because noone
has a really good idea (or at least not very original), and ideas are just
ideas with no substance.
On the other hand, the theory, more or less states that much of our body
ills are due to something called a "subluxation" (a bone out of place) that
sort of pinches on a nerve coming out of the spinal column. Well, that sounded
good at one time when the reducibility of the anatomy could view a bone sort
of pinching on a nerve... at least that was the thinking of the time. Lately,
however, something called "ion channels"
how it relates to touch as a molecular basis for explanation
(16) suggests that a nonlinear system of communication
exists in the nervous system as well. In other words, the old explanations
can no longer support the neat explanations of a wiring system schema; it
deals with something more nonlinear (and that ain't half the pickle if we
can understand that it all ties into the brain cortex somewhere. Now that
could reduce the importance of the spinal column even more!).
Oh, well, I'll be in more of a pickle unless I can spit out another idea.
At least this idea can create something a little more substantive than just
an innate something or other. Of course, this idea and the substantive form
of the idea may have no real existence any more than the innate idea. But
at least it can be plotted, that's more than one can do with the innate.
In other words, it gives an "insight" into something relatively obscure.
But the trick of it is the implications of an idea. In other words, an idea
is an abstraction. Now, the innate idea is also an abstraction. But the defining
thing about it all is that an abstraction defines or expresses a quality
that's apart from an object. The innate does a pretty good job at this. But
it's something that can't be pinpointed without getting into heaps of trouble.
And there's probably more to it since something abstract may have intrinsic
form but relatively little or no pictorial representation. Now, that's a
real problem since it implies that substance is virtually absent and very
likely non-representable since even a picture perfect representation isn't
Well, perhaps it's time to leave the innate and get with the program. Something
plottable might work. At least it gives me something to picture, as well
as something to think about, as well as something abstractly curious. What
it means is that abstractions can be examined by science but only if we can
translate it into something representational, something pictorial. Now, that's
substance without form, i.e., it doesn't really exist except as an idea;
more precisely, it isn't reducible since it's existence is somewhere in a
nonlinear world and that means we have to jump into something that uses
mathematics to translate the abstraction to understand the dynamic processes
involved in the everyday world of function and form.
Well, let's try. Mathematics is about the only way to represent something
tangible and yet, not tangible. That's a riddle in itself. But mathematical
descriptions are not explanations, merely useful in presenting models of
And here's the meat of it: that a mathematical model is useful in providing
a basis to simulate experiments and to get approximate quantitative solutions.
Well, that's nice, but how do we ask the right questions unless we ask...
How does the leopard change its spots?
Now, that's a silly question, the leopard can't change its spots, or can
it (21)? Of course this is a riddle and of course its got
something to do with complexity science, and mathematics, and abstractions,
and the whole ball-of-wax of nonlinear inquiry; it's got to do with mathematical
modeling, simulating experiments and getting approximate quantitative solutions;
that animal coat patterns can be generated with morphogen based reaction
hypothesis for consideration is this:
that biomathematical applications based on the principles of Turing space
(as a form of aberrant spatial patterning) may provide information for
understanding provocative muscle testing procedure and its relation to therapy
localization contact points. It assumes that the spots on a leopard can be
mathematically correlated as instabilities in the diffusion of morphogenetic
chemicals in the animals skins
Recent findings involving touch link the importance of ion channels as a
chemical or molecular basis for touch. While linear mechanisms exist, speculation
would suggest a nonlinear basis for analysis of the less tangible phenomena
of therapy localization as somehow chemical related and nonlinear dependent
as an information system. It attempts to delineate a neurocognitive component
to the subluxation complex as distinct from the motor/sensory components
of the physical (wiring) system. It attempts to examine the cognitive
(programing) system as a constantly changing system of neuro-networking
communication. It is an attempt to provide an innovative model for theoretical
Now, there you have it; got it, right? Well, don't worry about it, I'm still
mulling it over myself. I'll need the whiz kids to take the quantum
leap to really get down to business. For now, ole Simon says "keep it simple."
So, Simon says, "what's so different about a plot on a dot or a spot with
a plot?" My question has to be simple since complexity seems to be a
remote idea for some. My mapmaker background prompts the question whether
plotting a contour map of relative complexity on weather data should be much
different from plotting the imaginary spots (therapy localization
(25)) on a virtual body? Is it possible to generate meaning
(and that's precisely what we do, 'generate' meaning, since it is an implied
function of the mathematics)?
Now that we know a little about complexity science, reaction - diffusion
mechanisms, and plotting imaginary lines on weather maps, it should only
be a stepping stone away to plot the body surface and extract some
information from the process.
Method: data gathering
Of course, there's one big problem, a huge problem, really: how do we get
the data? and what kind of data? Well, this is a problem since I'm not a
researcher, I really didn't have access to tools that permit technical inquiry
that could document the data as a recordable test or access to academia who
could help me. But that was of secondary importance at this point since my
objective was to determine whether the procedure of therapy localization
used by techniques such as "Applied Kinesiology" might hold some water. The
implication was that I had to use muscle testing (26) because
at this point in time there didn't seem to be any other method to test muscle
testing except by using it.
Furthermore, I suspected that a feasibility study could still be performed.
A differentiating feature in this procedure was the consideration that while
previous research attempts to compare consistency and/or reliability between
different people challenging the test subject, my premise was that a coarse
the body surface might yield a form of data that could be analyzed for
probability rather than absolute consistency
(30,31,32). This is
used in complexity science and computational analysis.
However, another problem had yet to be addressed: that was that if a change
was to be obtained on the ventral body surface as a distal contact challenge
to the cord level, a method had to be found to alter the impulses at the
cord level in relation to the distal, ventral portion of the body. Previous
search for information on methods to alter muscle testing in therapy localization
challenges suggested the use of a electromagnetic influences to modify the
test (33). A negative polarity strip magnet was found and
taped to the side and level of the spinal column being tested. The rationale
was that if magnetic influences had some effect upon muscle testing, that
blocking a proximal nerve root ought to influence the muscle testing by creating
an aberrant effect on the spatial patterns tested on the ventral or distal
contact site as it correlated to the spinal level.
The procedure involved blocking the spinal cord level, then muscle testing
the subject by having the subject contact each topographical ventral contact.
These contact areas were designated by number for purposes of computer
designation and followed the dots represented on figure 1. These were arbitrary
contact sites complying with therapy localization sites often used by some
of the techniques but also spatial parameters for referencing future testing
Each contact point was tested. Those contact points that demonstrated aberrant
response (i.e., a positive test) were recorded. This took days since the
test subject had to demonstrate a relative neutral response before the test
challenge was deemed valid (i.e., no other interference). Also, because of
constraints, i.e., fatigue, etc., only a few levels were tested each day.
|Table 1. Subluxation Pattern for reference point (above glabella
|Graphic simulation pattern below from computationally correlated
data. This was derived from topographical spatial reference points in therapy
localization. It represents a behavior pattern of associated neurological
probabilities in subluxation patterns. In an information context, the data
provides an ability to graphically or visually associate tentative levels
of influence. The clinician's intervention in manipulative procedure does
not encompass awareness of associated levels of subsystem activity, i.e.,
the clinician is not always aware of the muscle groups that are recruited
in a demonstration of compromise. Using computational methods, subsystem
activity can be further elaborated visually to demonstrate possible muscle
involvement as it relates to levels of the spinal cord. Computational approaches
to information gathering could assist both the clinician and researcher by
creating an awareness of the probable extent that manipulation might effect
a muscle grouping, etc. It encourages a global perspective of clinical findings
by referencing muscle groups, neurological pathways, etc. so the clinician
can make more informed decision in either treatment or in research
Graph 1 - therapy localization site above glabella.
The raw data was essentially unintelligible.
In other words, testing the C1 level produced aberrant responses at more
than one level of the ventral topography as did testing levels in the lumbar
region. Analysis of the data produced identification of spinal levels as
graphic display of these levels in graph 1. This represents the test site
or therapy localization site on the forehead above the glabella.
I couldn't be sure what this meant and was disappointed to find that levels
of the spine were represented throughout the analysis. The graphical display
provided some visual insight indicating that some areas were more prominent
with a higher percentage of the data in relation to other levels.
Application of the Data
However, the next step was to use the data by manipulating and/or adjusting
the level of the spine according to the data. This required more precise
adjusting than manual manipulation offers, so instrumentation was used to
localize the level to adjust. I adjusted from the high percentage level to
the low, i.e., adjusting all the levels indicated by the data but in a sequence
starting with the highest percentage.
Finding the Subluxation by
Objective changes: The ability to detect neuromuscular pattern changes required
examination of the patient's posture while standing along with muscle testing,
rather than laying prone and palpating the spinal column. The inquiry eventually
led to experimenting with postural evaluation as the patient therapy - localized
the contact area.
In so doing, I became more aware of posture changes as different contacts
were made by the subject on the ventral surface of the body. Postural evaluation
included viewing the level of the iliac crests or innominates, the level
of the scapula, shoulders, ears, occiput, position of the head, etc.
What was noted was that when the subject changed contact positions (therapy
localization) at various locations on the ventral spatial reference, changes
were noted on the level of the iliac crests, etc. In other words, as the
subject moved to different areas of the ventral spatial reference point,
changes could be detected in the way in which the patient changed posture.
Treatment using a manual instrument to the spine altered the deviation noted
in postural examination. Objective changes could be noted in the posture
but also in the subject's range of motion as well as the subject's subjective
remarks that indicated they were either standing straighter, feel looser,
can move better, etc.
Often preceding the objective changes, however, the patient began to describe
subjective changes while laying on the table. Since chiropractic data reveals
little about how a patient describes the treatment except "feeling better,"
"more relaxed," "no pain," etc., I was surprised by remarks the patients
began to relate. Descriptions like "the sinuses are opening up," "I feel
tingling in my arms, (legs, etc.). Other remarks included feeling warmth
in the shoulders, neck, or the feet starting to warm up, or the stomach relaxing,
or the headache easing, etc. These are sensations I had no way of measuring
except by listening to the patient after the treatments as they lay on the
table. These also appeared different from what I had experienced in diversified
treatment of the spine.
The possibility that pattern analysis of spatially referenced topographical
contact points on the ventral surface of the body could reveal information
that relates to a neuro - reflexive mechanism may need to be considered for
further research. However, the nature of the information suggests that both
the philosophy and the theory may need revision before the chiropractor can
understand that a transition from linear to nonlinear mechanisms is taking
place. Furthermore, the ability to unveil the existence of patterns to variable
spinal column levels reveal a deeper mechanism that might be more precise
and predictable in treatment application. The advantage in the detection
of patterns is that identification of multiple levels of lesion areas permit
treatment of all levels rather than testing single levels either through
muscle testing or leg length differentiation.
My original endeavour to uncover information about muscle testing protocols
was to apply my understanding of mapmaking with a meager understanding of
complexity science. I felt that topographical mapping could be possible as
a way of extracting information. I also felt that the profession needed some
method whereby information could be extracted that might provide an insight
into something that has been relatively obscure in our ability to understand
how or why things happen with the manual therapy protocols. Considering that
a common denominator in all techniques involves "touch," I speculated that
it might be possible that techniques could be analyzed on that basis if patterns
could be demonstrated on the body surface.
What has become functional as a technique is not complete at this point since
further experimentation and research is needed. However, what may have emerged
in this pilot effort is the possibility that the techniques might be open
to examination and/or question in a way that has not previously been possible.
In other words, if the researchers can begin to think in terms of finding
patterns to the subluxation idea, it might be possible to analyze how a technique
might affect the body as a reflexive effect.
Beginning of Questions
In experimenting with the above, I have already commented in other
(34)about the following observation:
that both muscle testing and leg length checks are an
(35); that mere touch to a body surface
can change the appearance of body posture as well as leg length. In other
words, while the purist would view leg length changes as an unadulterated
procedure relating to strict biomechanical explanation, I suggest that it
engages mechanisms similar to those engaged in muscle testing and that the
whole business is an illusion. This does not mean that the protocols cannot
be used, merely that we need to understand what they "really" do rather than
following more assumptions that lead us in the wrong direction.
HOW TO CITE THIS ARTICLE
Seutter, V. "Mapmaker, mapmaker, where's the topography in a complex
system? Why, in the pattern, of course, and it's all mathematics." Chiropractic
Resource Organization. 20 May 2001. ChiroZine ISSN1525-4550
http://www.chiro.org/ChiroZine/clnrvw/article/topo_anal.html (c) 1997-2001
Chiro.org. All rights reserved.
Visual Models of Morphogenesis: A Guided Tour biological
structures and visualization simulation of development. procedural techniques
for realistic image synthesis.
Mathematical Biology Text
Planar Machines' web site. An invitation to Topology
basic machines and topology.
Topographic Maps Geographical examples.
Maps of Earth
Surface temperature map
Air 500 mb height/temperature map
Old Maps of Japan Georg Matthaeus Seutter
The Trails of the Explorers THE
SEUTTER MAP OF THE PROVINCE OF LOUISIANA, PUBLISHED IN NUREMBERG, GERMANY,
IN 1727, FROM FATHER HENNEPIN'S NOTES OF HIS EXPLORATIONS IN 1687.
As An Island ^
Review: Touch Perception
Ion Channel Webpage
Ion Channel Dogpile Search
Kinetics of Ion Channels as a Substrate for Adaptation
Discover Molecule That Detects Touch
(sciencedaily; 26 Oct 2001)
of a Reaction-Diffusion System Modeling Man--Environment--Man
Inc. Motion Capture Research and Development
Computer modeling and Simulation
THE LEOPARD CHANGED ITS SPOTS The Evolution of Complexity.
Brian Goodwin. London, 1994.
Reaction Diffusion - animal coat patterns
Creating Synthetic Texture - zebra
Murray, JD. Reaction Diffusion Equations and Animal Coat
Graining and Renormalization in Material Diffusion
automata with coarse-graining invariant orbits
on Statistical Inference Initial Report
Introduction to statistical inference
33. Walther, DS. Applied Kinesiology. Meridian Therapy.
1976; SystemsDC,, Pueblo, CO. p157-158.
Topic: An Inquiry into Chiropractic Theory (and Alternative
Commentary: Philosophy/Research: Are chiropractors asking
the right questions? How to demonstrate that muscle testing and
leg length inequality may be an illusion.
Somewhere in our basic understanding of science is the idea that for every
action there is a reaction. For the health sciences, the emphasis has been
placed on "outcome" as equivalent to the reaction one might view as a result
of a specific action. For the chiropractor, the action is equated to a manual
therapeutic application whereas for the medical community the action is also
associated with a procedure of sorts or the introduction of a pharmaceutical
Somehow I must be missing something. Somewhere
the transition from an action to a reaction doesn't seem to have been answered.
That which represents "outcome" often appears as a glossover of intermediary
reactions that noone really understands, especially me. For the chiropractor
to satisfy the outcome as a direct result from an action (i.e., manipulation),
I would think it important to understand more about what happens the minute
an adjustment is performed than to assume that the outcome is a direct effect
of the adjustment. In other words, I'm more interested about what goes on
between the action and reaction, what changes the objective findings of postural
alteration after an adjustment. Or, for medicine, what changes occur that
constitute an outcome as a direct reaction to a substance? Somewhere in-between
the action and reaction is the elusive placebo that noone seems to understand,
even though one might suspect that noone will ever understand the nature
of outcome as a result of an action until one understands placebo.
The nature of graphic displays of data is important in nurturing the cognitive
visualization of patterns. If chiropractic is to inquire into the theoretical
nature of its protocols, visual graphic pattern recognition should improve
the ability to ask questions as a result of the graphic display. In other
words, the graphic display ought to be able to inspire questions that normally
would not have been conceived as a possible mode of action previously.
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