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Gravity, Strange Attractors, Hausdorff Dimensions and Collagen


Note:  I really understand that upper cervical doctors may not be looking at many of these topics that I am putting on my blog.  I have come to think that they are however, important topics for some of us to look at as we try to understand exactly what it is that we are doing in our clinical work.  Again, these are just my own notes to myself as I try to educate myself regarding various topics that present themselves as potentially important to understand the vast landscape that this work constitutes.   




The one constant for any creature who ventures beyond the water’s edge is gravity.  Structure and function in any land-based organism is closely related to the effects of the Earth’s gravitational field. 


Gravity is a constant force of attraction between two bodies.  Unless you are one of the intrepid travelers aboard the space station, every action you make must take gravity into account (even at 300 km above the earth, gravitational forces remain substantial (approximately 0.9 G).   The reason for the apparent weightlessness in the space station is that the centrifugal and centripetal forces are almost balanced, canceling each other –and the effects of gravity- out.  (resultant gravitational forces range from 10-3 to 10-6 G).  [ from: Klaus DM. (2001) Clinostats and bioreactors. Gravitational and Space Biology Bulletin 14:55-64].  Microgravity (defined as 10-6 G) requires approximately 1000 earth radii or 6.37 x 106 km.)  This is because the universal gravitational constant (6.67 x 10-8 cm 3/g.s2 is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. [Morey-Holton ER. “The Impact of Gravity on Life”, in Evolution on Planet Earth 2003 Elsevier. Edit. Rothschild. P. 144]


Physics has identified four fundamental forces.  Gravity is by far the weakest.  For example, if gravitational force is given an arbitrary value of 1, the relative value of the weak nuclear force is 1026, electromagnetic force is 1038, and strong nuclear force is 1040. [http://learn.lincoln.ac.nz/phsc103/lectures/intro/4_forces_of_physics.htm] However, the great mass of the earth (approx. 6.0 x 1024 kg) and the relatively miniscule distances involved, creates continual loading, pressing any object against the surface. And so, humans, with their bipedal stance, must contend with gravitational force every time they move about. 


As noted above, dynamic, non-linear systems tend toward certain states over time.  A pendulum is often used as an example of an attractor.  Regardless of where it is released, the pendulum will end at the same point, perpendicular to the ground.  Gravity is the unseen force that gradually brings the pendulum to its final position of equilibrium.  Dissipative dynamic systems tend to give rise to strange attractors.  Again, strange attractors are not completely defined, but are often described as having non-integral Hausdorff Dimensions (or else dependant on initial conditions). [ Note:  Hausdorff Dimension represents a way to measure the dimensions of a mathematical object.  A point has a dimension of ‘0’.  A line occurs in ‘1’ dimension, a plane has ‘2’, three-dimensional space obviously has ‘3’.]   Such (non-integral) attractors are non-periodic (never exactly repeat themselves) and are fractal in nature. 


Because gravity is a constant and biologically significant force, it is a critical component in the ongoing calculations of the central nervous system as it continually effects ‘new’ postural strategies.  Gracovetsky writes about the constraints of the fascial envelope and the strategies of the central nervous system in dealing with varying loads:


“The continuously loading and unloading of collagen requires the CNS to rapidly re-direct forces.  It is known for quite some time that there exist many combinations of muscles and ligaments that correspond to a single posture.  A “steady” erect stance can be kept because the musculo-skeletal system oscillates from one combination to the next in such a way that no structure ends up being continuously loaded.”…


He continues:


“It could be argued that the need to switch from one muscular combination to the next is determined by the properties of collagen.  In a series of studies in Sweden, Kazarian (1968) realized that collagen has a complex time dependent response to loading.  The most important factor for the purpose of this discussion is the fact that collagen has at least two time constants.  One of them is about 20 minutes and another one of about one third of a second.”


Gracovetsky, S. (2005).Personal communication –data from his latest paper accepted for publication by Elsevier LTD, UK.

[ Note:  Kazarian L; 1968.  Acta orthopedic Scandinavia supplemental.  ]


This means that even standing erect posture is an inherently dynamic state which develops from constantly updated integration of afferent input and which is then made possible by the constantly shifting postural strategies which load and unload the joints and fascial envelope, in order to minimize and equalize stress throughout the organism in a tensegral manner.  As Gracovetsky further notes:


“Stability at minimum energy cost is essentially a collagen issue, and the forces that shaped us cannot be left out of the equation.  I believe that sooner or later we will end up being confronted with the need to understand the relation between the visco-elastic properties of collagen and gravity.”


Gracovetsky  2005. ibid.


The effect of gravity on the human body is profound.  In the standing neutral position, the alignment of the human frame is most biomechanically efficient when consistent with the vertical axis.  The vertical axis represents the greatest stability with respect to gravity in the upright position.  Obviously, a horizontal posture (lying flat on the ground) would constitute the most stable position (equilibrium) but it also represents the least potential for kinesis.  Standing upright on two legs with our center of mass some distance above our feet is an inherently unstable configuration.  This instability may however, be the point.  Gracovetsky writes:


“Interestingly, engineers purposefully construct unstable machines.  The modern jet fighter is one of them.  This machine can be flown because there are dozens of computers forcing that instable machine into stable flight.  Why not design a stable fighter in the first place?  Survival is the short answer: a stable fighter may not be agile enough to escape an incoming missile.  It takes less time to execute a maneuver by letting go an unstable machine than force a stable fighter into an evasive maneuver at a considerable energy cost.”   


Gracovetsky, 2005 ibid.


Gracovetsky reminds us that even standing posture is not static but extremely dynamic as the central nervous system constantly recalculates muscle strategies to deal with the time constants of the fascia.  Our agility too, is greatly enhanced by the inherent instability of the bipedal stance, allowing rapid shifts in posture and weight balance with movement.