"The mind is a compact, multiply connected thought mass with internal connections of the most intimate kind. It grows continuously as new thought masses enter it, and this is the means by which it continues to develop."

Bernhard Riemann On Psychology and Metaphysics ca. 1860

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Friday, April 29, 2011

Pacemaker or Autowaves, Biophysical and Noetic Curvature, and Shockwaves

For the first time, it has been shown by researchers at UC San Diego that regular electrical oscillatory waves in the brain are a requirement for the proper firing of neurons that provide a nodal grid that acts as a conformal mapping as a kind of spatial sensory compass. There are a number of profound implications of this development which I will attempt to illustrate here.

The first broad implication has to do with the concept of a conformal mapping per se. Gauss showed that the natural alternation of negative to positive curvature of surfaces that we encounter everywhere in nature may be conformally mapped via normals to a tangent plane onto a unit hypersphere. (Hilbert gives a visual illustration of this in his book Geometry and the Imagination.) Riemann continued and expanded upon this concept to evolve the so-called Riemann surface function, which provides a framework for a rigorous network of nodes or branch points that allow functional passage from imaginary sheets (imaginary understood here in the sense of the complex plane) on this Gaussian unitary sphere. Now, pause here and consider how this non Euclidean geometric model might apply to the research cited above. What do we have but such a one to one mapping by our mental sensorium of the "outer space" through which we must navigate. As we move through this space, neurons can fire appropriately to provide layer upon layer of continuous maps that we may consciously access a memory of through the processing of  the electrical impulses at these nodes. I will return to this theme shortly after a necessary ellipsis below.

This, I hope, aptly illustrates what to most readers is a remarkable sort of prescience of the genius of a Gauss and a Riemann. However, this quality of thinking needs to be demystified, if humanity is to meet the pressing requirements of the mission of getting off this planet and colonizing space, such that these apparently inaccessible powers of mind become the common property of all. Gauss and Riemann built upon the revolution in scientific methodology introduced by Cardinal Nicholas of Cusa. Here, I must point out that the attempt to characterize Cusa as a Christian "mystic" by modern academics is a completely obfuscatory slander, either resulting from ignorant incompetence or worse intentional premeditated malevolence. Ironically, it is Cusa's concept that the microcosm and the macrocosm are necessarily intimately connected in their mutually evolving creative development that laid the foundation for breaking the chains of the intentionally destructive and insane precepts of Ptolemaic/Euclidean mystical scholasticism. This too, followed upon Dante's revolutionary ecumenical characterization in the Paradisio, where he foreshadowed Kepler's and Einstein's relativity by placing his frame of reference on the moon and , thereby dispelling the mythology that there is some mystical priority of earth's place somehow mirrored  in a pantheon of fixed feudal relationships. Thus, Cusa promoted the return to the Platonic/Pythagorean  measurement of the curvature of the earth by the very same Gaussian normal vector to the tangent plane method by Eratosthenes in Egypt some 1700 years earlier. It is no accident, that Cusa recognized that what was to become the colonization of the new world was a necessary flanking precursor of the universal rights of humanity for development that he enunciated in his writings. This method of Cusa of comprehending and hypothesizing the underlying continuous creative composition of the physical macrocosm and noetic microcosm then, constitutes the basis for a true scientific method of investigation. This revolutionary method so challenges the authority of the establishment arbiters of  the second law of thermodynamic plodding, Ockhamite sense certainty method that  it is all but forbidden for in  accepted "peer reviewed" publications to merely allude to the actual facts.

Returning to the matter at hand, I turn next to the question of the pacemaker wave referenced above or what many Russian scientists have labeled the autowave. Again, here in writing of wave phenomena, I must return to the towering figure of Bernhard Riemann. Before there was any physical proof of sonar/pressure shockwaves, Riemann used his method of starting from elements of known physical constraints to adumbrate how shockwaves would develop. He reasoned in his paper  from 1860 "The propagation of planar air waves of finite amplitude" that there is a sort of limit imposed for the propagation of waves through a medium. Furthermore, if the source of propagation of wave exceeded this limit a bunching up of waves would occur that might disrupt the medium itself. This we know today, of course, as the familiar sonic boom.

Let us extrapolate this principal given what we have uncovered of some other wavelike phenomena since Riemann's time. The general phenomena of solitonic waves, I believe are examples of extreme wave formations that tend to bridge what Vernadsky characterized as the disparate domains of the lithosphere and biosphere (and as I believe also have a correlative in the noosphere.) It has recently been hypothesized for instance that soliton/anti soliton energetics in phage dynamics can account for transitions from active lysogenic to dormant lytic states. Long lived relatively stable wave phenomena that underlie the proper functioning of the biosphere are evident, whether they be aortic pacemaker waves, calcium brainwaves or quantum wave phenomena along the double helix of DNA

A question that we may pose, building upon Riemann's work, is what happens in the biophysical domain when the velocity of wave propagation tends to surpass the transparency for propagation in that medium? Certainly, the catastrophic malfunction of a heart attack and epilepsy, for example, are evidence that  these pacemaker waves have dynamically overloaded the biological medium. The means to solving such anomalies, is of course the appropriate province of medical research. Further we see similar destructive such anomalies in the domain of Vernadsky's lithosphere, for what are hurricanes but a kind of soliton dynamic, similarly earthquakes are characterized by disruptive gravity waves, solar flares as plasma wave events, and are not the very phenomena of black holes that can rip apart the center of galaxies themselves a type of soliton? Likewise here, it must be a mission of science to secure humanity against such threats.

Now, finally let us drive the analogy with these anomalous soliton-like formations into the domain of the noosphere. One can think of the radiation of technology in human society over time as operating similarly to the kind of standing waves in the brain. For a society, the successive "waves" of transmission of knowledge through culture and education provides the preconditions  for its continued functioning and survival. However, a crisis is encountered whenever there is a limit of resource transparency for the prevailing mode of technology. As LaRouche has shown, what constitutes resources must be redefined via a breakthrough in scientific creativity. This is the quality that uniquely distinguishes the noosphere. This is what Cusa characterizes as an immanent power of humanity. But it is a mission which is also a choice. Nowhere else is there freedom in this sense. And it is truly this gift that Cusa proffered when he collaborated with Toscanelli to revive Eratosthenes non Euclidean method to send Columbus to the new world so that humanity might escape the clutches of those that would have us be slaves.

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