Real Science for a Change

To this I say: bravo. As I have noted the remarkable feature of the ATP synthase engine in the past is that it rotates clockwise or counterclockwise for aerobic or anaerobic synthesis for the creation of cellular free energy. Now, a new feature is discovered that this wonderful enzyme also is capable of switching from use of ionic hydrogen and sodium at the extreme thermodynamic boundary condition in the "methanogenic archaeon Methanosarcina acetivorans." It is precisely in the study of these types of such extreme anomalous domains that true scientific progress is secured.

Promiscuous archaeal ATP synthase concurrently coupled to Na⁺ and H⁺translocation

1. Katharina Schlegel^a, 
2. Vanessa Leone^b, 
3. José D. Faraldo-Gómez^b,^c,¹, and
4. Volker Müller^a,¹

+Author Affiliations

1. ^aMolecular Microbiology and Bioenergetics, Institute of Molecular Biosciences, Johann Wolfgang Goethe University Frankfurt am Main, 60438 Frankfurt am Main, Germany;
2. ^bTheoretical Molecular Biophysics Group, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany, and
3. ^cCluster of Excellence ”Macromolecular Complexes,” 60438 Frankfurt am Main, Germany

1. Edited* by E. Peter Greenberg, University of Washington, Seattle, WA, and approved December 2, 2011 (received for review September 27, 2011)

Abstract

ATP synthases are the primary source of ATP in all living cells. To catalyze ATP synthesis, these membrane-associated complexes use a rotary mechanism powered by the transmembrane diffusion of ions down a concentration gradient. ATP synthases are assumed to be driven either by H⁺ or Na⁺, reflecting distinct structural motifs in their membrane domains, and distinct metabolisms of the host organisms. Here, we study the methanogenic archaeon Methanosarcina acetivorans using assays of ATP hydrolysis and ion transport in inverted membrane vesicles, and experimentally demonstrate that the rotary mechanism of its ATP synthase is coupled to the concurrent translocation of both H⁺ and Na⁺across the membrane under physiological conditions. Using free-energy molecular simulations, we explain this unprecedented observation in terms of the ion selectivity of the binding sites in the membrane rotor, which appears to have been tuned via amino acid substitutions so that ATP synthesis in M. acetivoranscan be driven by the H⁺ and Na⁺ gradients resulting from methanogenesis. We propose that this promiscuity is a molecular mechanism of adaptation to life at the thermodynamic limit.

Energy Dynamics: The Key to Scientific Progress and Survival

 Lately, I have been urged to clarify some principals with which every citizen should be familiar that are critical to humanity's survival. If we as a society fail to understand and act upon these principals we will not provide the economic means for our future generations to live in increasing freedom from want and disease. Therefore, those among us that can grasp the truth must lead the way out of the errors in policies we have adopted. 

Usually, the idea of economics is thought of as the use of money to purchase things. However, money has no real value if there is nothing to purchase with it. Of course that would be an extreme rather Hollywood dystopian scenario. It is easier to see how in a nation that has a collapsed economy, money rapidly loses its value. 

Perhaps one way to approach the lack of understanding due to the prejudice that money has value in itself is through the idea of the need to provide energy to sustain the economy. Recently I came across some interesting and worthy studies regarding energy dynamics. 

Now, one may look at this issue in regard to differing realms of reality. What I mean by this for instance is we can for example view the engine of cellular processes which use ATP. This would be what a very great Soviet era scientist Vladimir Vernadsky called the biosphere. Scientists at the Gladstone Institute carried out an audit of how every gene in human beings have a role in either making or consuming energy in the form of ATP. This study is absolutely critical because the cellular energy throughput is central to biophysics just as it is to the functioning of the physical economy. Our understanding of these functions effects whether we can treat or cure a whole host of human diseases. 

At a totally different realm of reality "a team of physicists from University College London measured the separation between two specific energy levels of positronium, what’s known as its fine structure." This strata is obviously inorganic and would fit into Vernadsky's system as part of the lithosphere. However, this is extremely critical as well for humanity. Why is this so? 

To unravel the answer takes some examination of the progress in providing the energy requirements for the functioning of human economy. As we have moved away from the use of fuel from wood burning to heat our homes and cook our food. (Although we may still use them of course.) However, to propel human industrial mass production we have via technological discoveries and inventions moved through coal for steam power, hydroelectricity and petroleum, to nuclear fission. What has remained constant throughout these changes is an increase in the density and flow of the energy. The so called energy-flux-density throughput.  What this means for our economy is that we can now have more power than at any time in human history. This is what sustains our standard of living and gives value to money! 

Getting back to the research on positronium, we must first understand that the next higher level for energy-flux-density is controlled nuclear fusion. If you read articles at all on the background of this research, usually this issue is not mentioned. However it is absolutely crucial as to why it is so important to the global economy to achieve because we will have at our disposal not only a virtually inexhaustible form of energy using fusion of the most abundant elements in the universe, we will have the highest energy-flux-density we have ever achieved by a so called order of magnitude. This will make previously nearly unbelievable benefits for humanity possible such as providing enough electricity consumption to pull all countries on the face of this planet out of poverty.

However the story does not end with fusion. And this is where the positronium research comes in. This is because theoretically we know that what are called matter/anti-matter reactions can be even a step beyond fusion energy. This research is however merely in its infancy. But discovering that there is something we don't understand about the structure of such states of the lithosphere, a so called anomaly, is the necessary way forward for humanity. 

The Struggle to Survive and Energy Throughput of Species

The differentiation of species is characterized overall by the energetic means through which they are perpetuated. If a global shift in conditions vitiates the predominate form of energy capture and utilization of a species or group of species, then that type of life form is supplanted so long as it is possible for new species to achieve a harmonic metastability.

The function of mitochondrial ATP synthase is a universal limiting factor for such energy reduction across all biological domains. It is analogous to a constant for the inorganic such as the speed of light or fine structure. The ATP enzymatic development of energy reduction in living monads represents a singularity which separates the organic from the  inorganic. It represents a qualitatively superior and distinct organizing principle comparable metaphorically to Cantor's treatment of transfinite infinities.

The only continuation in this higher order of energetic speciation that we know of up to now, is the strictly unique human development to further evolve by the acquisition of the knowledge to control fire for cooking food. It is the only way the human brain's relative enlargement over other primates were possible. This is what differentiates our species uniquely from all less evolved life. However, it does not end there. Given the shift in conditions wrought by the advent of such Promethean evolution, the need to acquire new technological means to further improve the conditions of human health and lifespan requires a continuous non-linear improvement in control over energy throughput via more condensed forms.

To deny all this, as do the fanatic proponents of the back to nature dogmatists, is to deny our unique humanity. This is the only fundamental conflict that operates as a driving motif in the history of mankind. The oligarchical worldview is a desperate mandate to put the genie back in the bottle and to deny that there is a higher universal ordering purpose for humanity. Thus the mythical figure of Zeus seeks to perpetually enchain and punish the quality of mind that Prometheus represents. Any nation or group that seeks to continue the inescapable development of energy must be defeated by such bestial logic. Thus today as China leads in an effort to mine Helium 3 from the moon for the heretofore most energy dense form of controlled nuclear fusion, the inheritors of the bestial outlook must seek and destroy that very development.

Re: Less life: Limited phosphorus recycling suppressed early Earth's biosphere

The recent work "Biomass recycling and Earth’s early phosphorus cycle" is precisely correct. The throughput energy density of phosphorus in the biosphere directly effects the potential for ATP synthase, the molecular engine of life, to power evolution. This energy density throughput (as identified by Lyndon LaRouche and co-thinkers, myself included) is the critical component for human economic activity as well. The difference is that for the human economy the measure of energy density throughput is of a higher Cantorian transfinite order that subsumes previous technologies. For example, energy derived from wood burning subsumed by coal, then oil, natural gas, nuclear fission. The next step in this sequence is nuclear fusion, and beyond that matter-anti-matter reactions.

On the down side we have the entropic philosophy of the doomsayers "green" agenda. It assumes falsely that that is only so much stuff on our planet so therefore we must "invest" in "renewables." This is mad and criminally so. It is relegating future generations to increasing levels of poverty both economically and culturally. Thus we have today's opioid addiction crisis. 

The principle of Cantorian transfinite subsumption goes back to Nicholas of Cusa and his collaborators in the Florentine renaissance (which Cantor readily admitted.) However, the foundation of this quality of noesis can be found in Dante Alighieri's Divine Comedy. If good reader you will overcome your silly adopted "modernist" assumptions about the separation of left brain/right brain hermetically distinct categories of science versus art, then you will conceive that great poetry going back to Plato's dialogues is science. And as Dante quite rightly demonstrated that even in the very uttermost depths of hell such as we have ravaging our society there always exists an ordered pathway out of that hideous cave toward the light. This is the pre-established dynamic harmony Leibniz propounded. 

Contrary to the childish science fiction epigones of H.G. Wells, the "space age" by necessity, as Ibn Sina so succinctly argued in his proof of the "Necessary Existent," is the common ennobling destiny of humanity. Only then will we put away our infantile playthings of yesteryear and enter into a new self reflective transfinite domain of that which Dante and Cusa profoundly depicted as the Vision of God.

Update: this excellent research shows the unique role of fungi in producing soluble phosphorus and compares differing possible rates of its throughput. 

Endosymbiosis of Mitochondria as Nicholas of Cusa's Principle of Contracted Maximality

 As I have insisted within these pages and elsewhere, Nicholas of Cusa is not a mystic. In fact, the truth is precisely the opposite. And anyone professing to identify Cusa's works as such, merely demonstrates his of her intellectual shortcomings. 

By the phrase "just the opposite" I mean to say that the method of philosophic dialogue that Cusa develops is the basis not for mysticism but rather it is the basis for scientific investigation. I shall demonstrate this in what follows. 

We do not know, and will never know precisely when and how the mechanism of cellular energy throughput came about in the history of the biosphere. We do know that the remarkable near universality of the mitochondria as the locus of the energy throughput via the engine of the enzyme ATPase supplying ATP as the source of energy to the cell. We know that this constitutes an endosymbiosis, in which the cell's nuclear DNA is separate and distinct from the encapsulated mitochondrial DNA. This constitutes a unity as the basis for the very organization of life across the boundaries of its aerobic and anaerobic forms. 

The principle for this process of development of our organic existence is twofold. One is the necessity of the capture and useful reduction of energy underlying and differentiating the living and non-living states of matter. The second principle is the process of subsumption of opposites in the manifold contractedness of substance.  This occurs via that which Riemann established as the equivalence of degrees of freedom through added dimensionality. This is understood as the orthogonal movement of n dimensions to n + 1 dimensions. 

Thus for all history, the subsumption of the mitochondria into the cell, constitutes a nodal event that rather efficiently demonstrates that which Cusa identified as learned ignorance. For we will never know precisely how this came about, however by investigating this very biophysical irony, if you will, we know that we shall progress upon the pathway of humanity's necessary mission of conquering disease and extending our "healthspan." We do this not as an isolated goal, but instead as the complement for humanity's larger mission of space colonization.

It is likewise not accidental that the scientific progress in the investigation of the inorganic realm hinges upon a subsumption of a different, restricted kind. That is both matter and anti-matter somehow are related as a basis of energy throughput of that nonliving realm. How it is that there is a sort of directionality of the priority of matter over anti-matter in the evolution of the cosmos will never be precisely known. However, we know that in investigating this, we will likewise afford humanity the ability to achieve a new degree of freedom in energy throughput. For it is known that the potential of matter/anti-matter reactions will bring about a new regime for providing thrust for that very same mission of space colonization identified above. 

Once again, we as a unique species are by our nature fitted out to carry out these scientific investigations. In any one historical epoch of such necessary endeavours, we understand that we are merely providing guidance and a potential pathway for what future generations must achieve to further the true mission for humanity. And once again, we return to the principle of "investigation" cited above for both the inorganic and organic realms. This time however we are applying the principle of subsumption of opposites as Cusa develops in his Docta Ignorantia in a different manner. 

Firstly, even though the history of mankind pivots around two different and opposed principles, it is only by the utter defeat of one upon which our continued existence hinges. The organization of society by an irrational oligarchy whose goal is itself destructive of the means and ends of civilization's necessary missions must be once and for all overcome. Now, achieving that does require an uplifting of humanity out of such infantile irrationality. It means extinguishing forms of oppression such as the mechanisms of financial looting of the physically productive economy. In this case it is not a relation of symbiosis that we are dealing with so much as parasitism.

However, there is a precise meaning for the unity of opposites as Cusa developed in his great work De Docta Ignorantia. It is in the national language cultures and philosophical and religious beliefs that apparent opposites can and must be overcome. The ongoing cooperation of eradicating poverty, defeating disease and colonizing space is the basis of creating a new degree of freedom for humanity. Moreover it is by the production of beauty in the arts that we inspire progeny to take up that very same mission. This represents the principle of the Contracted Maximum in human history and as such qualifies the philosophy of Cusa as the basis for scientific progress. 

Nicholas of Cusa (1401-1464), detail of relief ‘Cardinal Nicholas before St. Peter’ on his tomb by Andrea Bregno, church of St. Peter in Chains, Rome

Some Thoughts on Issues Arising from Leibniz' Monadology

 One of the principles of Leibniz' great Monadology is the proposition that lower or simple monads have no "windows through which anything could come in or go out."  However they do possess confused perceptions of what is near to them:

7. Further, there is no way of explaining how a Monad can be altered in quality or internally changed by any other created thing; since it is impossible to change the place of anything in it or to conceive in it any internal motion which could be produced, directed, increased or diminished therein, although all this is possible in the case of compounds, in which there are changes among the parts. The Monads have no windows, through which anything could come in or go out. Accidents cannot separate themselves from substances nor go about outside of them, as the ‘sensible species’ of the Scholastics used to do. Thus neither substance nor accident can come into a Monad from outside.

Now our representations of cells is that "things," i.e. proteins, do come in and go out continuously via the cellular surface gates. And indeed that there are protein enzymatic engines of ATP supplying internal energy to all cells. So in Leibniz' Monadology the study of these changes would have to place cells and their proteins including those signaling molecules Intergrins that permit cellular communication as mere ephemera that come into and out of being, constantly being reduced and recreated as constituents of "cellular automata."

61. And compounds are in this respect analogous with [symbolisent avec] simple substances. For all is a plenum (and thus all matter is connected together) and in the plenum every motion has an effect upon distant bodies in proportion to their distance, so that each body not only is affected by those which are in contact with it and in some way feels the effect of everything that happens to them, but also is mediately affected by bodies adjoining those with which it itself is in immediate contact. Wherefore it follows that this inter-communication of things extends to any distance, however great. And consequently every body feels the effect of all that takes place in the universe, so that he who sees all might read in each what is happening everywhere, and even what has happened or shall happen, observing in the present that which is far off as well in time as in place: σύµπνοια πάντα [sympnoia panta], as Hippocrates said. But a soul can read in itself only that which is there represented distinctly; it cannot all at once unroll everything that is enfolded in it, for its complexity is infinite.

62. Thus, although each created Monad represents the whole universe, it represents more distinctly the body which specially pertains to it, and of which it is the entelechy; and as this body expresses the whole universe through the connexion of all matter in the plenum, the soul also represents the whole universe in representing this body, which belongs to it in a special way.

And yet that which separates a simple lower monad absolutely from human monads is our unique ability to mirror the necessary existence of the ongoing potential of universal perfection.

   29. But it is the knowledge of necessary and eternal truths that distinguishes us from the mere animals and gives us Reason and the sciences, raising us to the knowledge of ourselves and of God. And it is this in us that is called the rational soul or mind.

So as I have looked to Riemannian surface biophysical models in the past with the "poles" of branchpoints being proteins, it must be kept in mind that these are not lower living Monads but mere chemical compound constituents that come into and out of being. And therein lies the research of the division of the living from the non living. This particular connection is the most necessary aspect of progress in biophysics. For exploring these interconnected protein functions will make all advances of biophysics quest to extend our life and "health-spans" possible, in the analogous manner in which exploring the energetics of elemental constituents of matter will propel our species into space colonization.

Further, it is the division of non-monadic elements into groupings of Vernadsky's domains of inorganic, organic and noetic and their potential interactions that should inform the metatheoretical design for scientific research. For instance, in the domain of the noetic must be included the philosophic purpose for setting research agendas. Is it a requirement that we by necessity must increase the secular healthy lifespan of humanity? How is this to be achieved per capita and overall? Does the defense of society against inevitable impacts from meteors and comets figure in? 

Moreover, it is the historical quality of hypothesis that mediates future deployment of noetic resources. In this regard, these hypotheses "live" beyond their attachment to being produced by an historical person. Among these higher hypotheses, Plato's demonstration of the universality of geometrical knowledge triggered a proven truth about the necessary changes of governance for the survival of society. That is, the breakdown of the irrational barriers to advancement and perfection of knowledge imposed by arbitrary rule by oligarchical families maintained by usurious financial interests of pantheons of pagan cults.  

 

Cooperative Evolution

 Contrary to the Hobbesian schema of survival by a war of isolated species (and bogus "races") each on a war against all, symbiosis seems to be yet evolving at the extreme cellular level. Here is the abstract about this alternative respiratory symbiont that differs from the nearly ubiquitous mitochondria. 

The endosymbiont Candidatus Azoamicus ciliaticola was proposed to generate ATP for its eukaryotic host, an anaerobic ciliate of the Plagiopylea class, fulfilling a function analogous to mitochondria in other eukaryotic cells. The discovery of this respiratory endosymbiosis has major implications for both evolutionary history and ecology of microbial eukaryotes. However, with only a single species described, knowledge of its environmental distribution and diversity is limited. Here we report four complete, circular metagenome assembled genomes (cMAGs) representing respiratory endosymbionts inhabiting groundwater in California, Ohio, and Germany. These cMAGs form two lineages comprising a monophyletic clade within the uncharacterized gammaproteobacterial order UBA6186, enabling evolutionary analysis of their key protein complexes. Strikingly, all four cMAGs encode a cytochrome cbb3 oxidase, which indicates that these endosymbionts have the capacity for aerobic respiration. Accordingly, we detect these respiratory endosymbionts in diverse habitats worldwide, thus further expanding the ecological scope of this respiratory symbiosis.

 My first impression is that this is indicative of ongoing cosmic evolutionary anomalies on par with the discovery of  transcendental numbers. Both are analogues of the transfinite ordering of the power of infinite possibilities for forward problem solving cooperative biophysical evolution. Thus Leibniz dictum in his Monadology that we as finite beings cannot grasp the full scope of such infinite potential due to our necessarily limited yet progressively developing vision. I leave it to the reader of this blog to unpack the implications. 

Detection of the Azoamicaceae 16S rRNA gene sequences in publicly available 16S rRNA gene amplicon sequencing datasets shows a global distribution across all continents. Points represent amplicon datasets, and are colored according to their affiliation with the Azoamicaceae genome that have > 95% 16S rRNA gene identity to reads in the dataset. The hotspots in the global north likely reflect sampling bias.

Good Science Bad Politics

Everything goes through the PC lens of climate change change these days. Sort of like the the cosmological gravitational lens, it creates spots in the front of your mind...Reminds one of traveling to a cave to have a very disturbed wild girl pronounce gibberish because of fumes from poisonous gases and call her an oracle. Anyway on the front of ATP some progress is for real. By the bye, I only use Michelangelo's depiction because it was the one state of mind he knew.

Biophysical Self Similarity as a Negentropic Higher Ordering Principle

Since the mission of combating disease and aging are anchoring research to reality in biophysics much progress is being made as a result, despite limitations of investigative methods adherence to philosophical biases. The difference with the Quixotic quest for an unverifiable unified field theory of everything in physics is stark in contrast. 

I contend that much of the brilliant hypothesizing that created the non Euclidean, Riemannian spacetime manifold geometry is just as applicable, if not more so, to biophysics. In the broadest overview within the domain of the biosphere we encounter nested sequences of functional dynamic orderings. To seek to bring these into coherence we must locate the progression of evolutionary sequences in capability of nonlinear improvements in energy flux density of negentropy. The biosphere itself is bounded by the inorganic and human noetic power analogous to Dirichlet's principle in least action bounding dynamics for topology. 

Within that biosphere we can investigate how the divisions of life types adhere to the intake and transformation of useful energy. It is the interaction with the inorganic domain that limits the development of both. For example, the organic carbohydrates that comprise the biosphere require for their dynamic life sustaining elements to be incorporated to resolve their ability to reproduce. Thereby the uptake of phosphorus by mitochondria as catalytic in providing energy reduction by the enzymatic framework of ATP was evolved for the different branches of cellular life.

One intriguing direction would be developing a rigorous geometrical framework for the protein "interactome." There exist multiply connected functions within that interactome and there are coherent classes of cases of proteins acting as singularities that bridge them. For example, the scaffolding functions of actin and myosin might be bridged in some cases by multifunctional proteins interacting with signaling entities like sonic hedgehog. There appears to be a scale of closer integrated cellular functions enmeshed with these multifunctional proteins with some that are referred to as moonlighting seemingly unrelated such functions. Topologically, these disparate states might be thought as Riemannian non deformable surfaces of higher ordered connectedness.  

However within such extended topologies there also exist the equivalence of multi sheeted polarities whereby the multifunctional proteins exhibit the characteristic of operating as branch points. This physical geometric framework was supplied toward the end of 19th century by Riemann and Abel among others. The problem is that the further development of this physical geometry was vitiated by the usage of the statistics of entropy as a fundamental principle for scientific research. 

It should have been apparent that a negentropic higher ordering principle contradicted the materialist assumptions of limited resources. This proceeds from the top down via human creative breakthroughs that reorganize and redefine what constitutes resources for economic survival of society. That principle of moving beyond the relatively fixed limits of reproduction within that economic topology is equivalent to the emergence of life from the fixed limits of the inorganic domain. It is representative of a higher harmonic class of ordering.

In that context, I came across a rather startling bit of brilliant research bearing upon morphogenesis yesterday evening. The apparent random process of cellular reproduction are controlled by "morphogens" that admit self organization in embryogenesis. It is my contention that such agents of self organization apply as a limiting principle to the entirety of the domain of biophysical interactions. Thus we see cohesin and topoisomerase functions operating upon the mitotic DNA reproductive process, for instance. This represents a principle of self similar harmonic ordering that "closes" the boundaries of structure of the biophysical domain that Dirichlet provided for compact manifolds. 

Motivation for a New Direction in Mathematical Modeling

(DNA Topology as a Dual Function of Homotopy Induced Solitonic and Discrete Resonance)

This quality of duality cannot be resolved merely by assuming a stochastic frame of reference for the unique problem inherent in phase space transformations. This is as true for the field quantum physics; and in general self organization theory that induces the formation of discrete attractor and emergent states from any “arbitrary” random preconditions. The toroidal dynamics (hence torsion, chirality, asymmetry, as well as orientation) of n dimensional Riemannian space as it undergoes homotopy to Costa Surface of n degree embedded in such space, is the equivalence of subsumption of transfinite ordinals extended outside the simple number theoretical domain of the “continuum.” The Vernadskyian definition of a modular continuum, delimited by irreducible boundary conditions into interoperating domains, i.e., the inert, biotic, and noosphere conforms to this conception. Further, the Hopf positively curved minimal surface’s connection with Costa in the sense of phase transformation allows for the orientability via Cartan Repere Mobile construction of Kiehn to evolve naturally, rather than stochastically. (It is of no small note that Vernadsky references Cartan’s geometry within his text explicating the Noosphere.) The model for the positively curved space wave function transformation to the hyperbolic horn (Mach cone) is Riemann’s paper on shock wave propagation. Toroidal action is a metastable configuration of Alfven’s plasma cosmogony in the macrocosmic scale and is invariant down to the infinitesimal. In this context, the metastable formation of solitons of determinate orderings is properly located. The connection these have with catalysis, DNA replication, and far from equilibrium systems in general is instructive. (See Davia) The fact that autowave dynamics are differentia specifica in the biotic domain as in contrast with the inert is not negligible and is suggestive of a further refinement of possible wave dynamics within the higher transfinite dimension of the noosphere. The application of Hausdorff fractional dimension and its fractal sequelae does not conform with my use of term transfinite dimension in the foregoing. However, it does properly situate the question of induced singularities from a continuous manifold.

Neurogenesis and conformality resonance

It is proven that an enriched environment is directly related to adult neurogenesis in certain cortical regions. As classical music is the semi-mediated expression of human creativity, the case for sonic resonance in this instance is not a trivial topological problem. Again, the connection at the cosmological scale of star formation and topological invariance is intriguing. This, if you will, is the true locus of “connectionism.” It is decidedly not the theory of “encoding” prevalent in academia today. (As a matter of fact the craze of trying to undo the relevance of Goedel’s proof among logicians and information theorists has led to a rather degenerate embracing of non-reality as substance. This has its approximate correlative in the attempt at ergodic modeling and distribution theory as a replacement for causality.) In this light, it is intriguing that current studies show that the orientation of the plane of cleavage in neurogenesis that regulates brain tissue growth. The Gbetagamma subunits of heterotrimeric G proteins are likely causal elements. Additionally, the vortical-like chiral nature of the enzyme ATP synthase is well understood. It is further evidence of a topological refinement for the biological equivalent of the model of toroidal torsion. It is also astounding that this enzyme exhibits nearly 100% mechanical chemical efficiency as an engine that makes possible the cellular consumption of free energy for the biosphere, including both aerobic and anaerobic types. (Also, separation in these two domains is defined as counter- or clockwise rotation on the mitochondria, exclusively (!)) All of which further reflects on the need for a model that can account for the formation of solitonic singularities within this transfinite hierarchical domain. Another qualifying refinement of in the arena of bioenergetics is that the quantum mechanical “laws” governing regimes of possible spin topologies are violated by biophysical macromolecular states.

Dynamics of Human Thought

Media of transmission for human thought are certainly of the most complex and excitable types imaginable. The first question to be addressed is that of the quality of hylozoic monism of this subject matter. We can view many different aspects or dimensions of human thinking and their impact upon various portions or manifolds of relationships of the continuum of reality. (This notion of continuum is not restricted to the idea of linear extension and types of number, as will be developed further on.) However, it is essential to comprehend that there exists a world line of development whereby ideas are characterized as ordered in the sense of Cantor’s transfinite. In this sense, the entirety of human history of advancement of thought and praxis is invariantly self similar. (By the way, in this regard the principle of fractal generation is simply a convenient mathematical device for producing discreteness out of such self similarity. It is not the generating principle but merely a relic of that generation, in reality the generation of singularities rarely proceeds by such a uniformly simple manner.)
For humanity, it is the ability of scientific discovery to overcome the relatively fixed limits or boundary conditions of any particular mode of functioning of society from the standpoint of thermodynamic disequilibrium, i.e. negative entropy. By this, it must be understood that due to the necessary nature of directedness or hylozoism, if you will, one mode must be superceded by another. This quality of the vectoring of society is not merely accidental, but is built into the very ordering of the inorganic and biological substrates. For example, the fact that there exists a birefringent axis or anisotropy for electromagnetic propagation in the universe, which at the most macroscopic regime exhibits precisely this quality. Similarly, the anti-racemic and optical chirality distinguishing the dynamics of living systems is a further higher ordered transfinite development of this same anisotropy that characterizes the inorganic. Electromagnetic propagation is now ordered once again according to a new lawfulness. Now, human thought or what Vernadsky labeled the Noosphere, is of a yet further transfinite such ordering distinguished by its own particular power over the lower two subsumed realms. It is only here, that an awareness for consciousness of these ordering principles has any meaning.

As to the question of interaction of wave functions and the excitable media: firstly the approach of Riemann in his groundbreaking paper on the principle of the dynamics of propagation of sound and pressure in a physical medium. In this, he established the principle that the medium itself possesses a boundary of rate of transmissibility. The resulting shockwave formation induces a change in the quality of curvature of wave propagation. (For astrobiology compare galactic ram pressure.)The so-called Mach cone, taken as an accelerated series as the speed of sound (pressure) continuously surpassed, represents in its entirety a negatively curved hyperbolic horn. That is, what was a propagation of a radiative spherical kind now has gone over through a shockwave formation into a different species of curvature. In the instance of the propagation of electromagnetic at the speed of light, the medium is not able to rectify itself as for sound and instead, a transformation of a different sort occurs via Einstein’s equation. This being a different transfinite species of boundary.

This same principle certainly applies to the two remaining substrates, i.e. the biosphere and the noosphere. Mutagenic transformations, I contend, are nothing but the same shockwave principle applied to the biological realm. When an organization of life develops an ability to reduce energy through a new quality hitherto unknown, this is nothing but the surpassing of the previously fixed rate of transmissibility of the medium. In the same way that the speed of light represents a higher kind of boundary condition for the inorganic, the boundary separating humanity from all other biology is a sort of speed limit, if you will, for mutagenic transformations. This again, of course, is of a higher ordered transfinite than Einstein’s principle was for the inorganic.

Now, you are probably asking yourself, how might this same shockwave principle apply to human thought? In any mode of functioning of society there exists an active “media/manifold” of a set of relationships created by the successive discovery of principles of underlying organization of the three substrates, i.e. inert, biota, and human cognition and interrelationships among these (see for example the role of Deinococcus radiodurans). The human individual’s cognitive development occurs, of course in an historically concrete/discrete context. The previous associated development of society has made the medium of cognition transparent for the mental development of this individual. For example as a thought experiment, consider the following: (along the same line of dialectic of mnemonics from Plato’s Meno) how is it possible that a gifted young child in the modern era is able to seemingly intuitively grasp the principles of projective geometry and readily apply them in drawing? View the historical artifacts of the lengthy and arduous development of these principles; compare Massacio’s nearly completed perspectival artwork with that of DaVinci. So, I posit that the substrate of the mind is also a developing organic “compact” type of n + m dimensional manifold, a multi-sheeted hyper-surface, connected through topological singularities, (unfortunately sometimes referred to analytically as defects) and exhibiting negative and positive regions of curvature. Now, crucial scientific discoveries necessarily create for human practice free energy that allows society to overcome the bounding conditions of this thermodynamically relatively fixed reactive medium. This signifies the movement from n dimensions to n + m (topological cobordism.) Further, the geometrical transformation of such a succession, I posit, also acts upon the principle of least actional, minimal surface, topological constraints. For example, the latest in a centuries’ long mathematical development in this arena is the remarkable discovery of the Brazilian geometer Celsoe Costa of a principle of generation of such surface by way of homotopic deformation of toroidal types. Here, from this perspective, are properly situated considerations of self similar, relatively “force free” species of action, found in the subsumed substrates we have been considering, i.e. solitons and cellular automata or autowaves. Such species of hypertori and their deformations are intimately connected with what has come before as the geometrical analysis situs of instantiations of “compact” manifolds as a substrate capable of resolving and emerging whole the principle of shockwave transformations. Topological singularities that are either discovered in nature, e.g. Falaco, morning glories, hurricanes, spiral nebula, Davidov, aorta autowaves etc. or produced in the laboratory under extreme circumstances, e.g. plasma kink instabilities, light bullets, BEC breathers, sonoluminescence etc. are representative of anomalous conditions, which when their principles of organization are made explicit through scientific investigation act to transform the domain of human practice and create new thermodynamic boundary conditions.

Such qualities of human thinking themselves may be cognized as having a wavelike nature in terms of propagation through the medium of human practice. Consider for example, how the historical personage of Plato was directly and mediately responsible for sparking off a methodological renaissance centuries after his death. His opus may be viewed as propagating itself historically in two senses from the standpoint of curved space. In his own epoch, his attempts to win over the Syracusan tyrant to his system, create an academy, etc. represent a radiative propagation of his method analogical to the previously instanced propagation of plane waves below the limits that the medium is capable of supporting. Why? Primarily because his efforts failed to transform his own society. That is to say, even though the ideas were effectively transmitted in the medium of language and otherwise of his day, the power (potential energy) inhering in them failed to catalyze the desired transformation of society. However, centuries later Plato’s class of ideas were able to transform the practice of society very much in principle as a shockwave. So then, human thought, although it is insubstantial from the perspective of spatial extension, except as it adheres in some way to the nervous system, cortical manifold is able to act in a particular sense to transform the geometry of human practice. In the same oriented/vectored characteristic of action that birefringence has for electromagnetic inert propagation, chiral or helical enantiomorphisms for the biotic, thought has but on a transfinitely higher ordering for human practice.