"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

Today's Elites


Sunday, September 17, 2017

Kepler's Method is Alive and Well

The situation with dark matter and dark energy that astronomy confronts today is eerily reminiscent of Ptolemaic epicycles. Upon founding the mission for the moon at NASA John Kennedy remarked "The greater our knowledge increases, the greater our ignorance unfolds."

What was the method that allowed Kepler to overcome the roadblock along the pathway toward resolution of the ordering of planetary orbits? He pronounced that method openly and forthrightly. The principle of the universal composition must be comprehensible to humanity. That is there must be a higher order that would allow coherence to seemingly random pathways that celestial bodies take. At first he envisioned an ordering subsumed by the geometrical system of embedded regular Platonic solids. This bold hypothesis derives from Kepler's insistence that any planetary order must not be algebraic but constructive. Which is to say that the scheme of the composition of the universe could not be merely arbitrary but by necessity must be well reasoned. 

The harmonic elliptical function that Kepler next hypothesized also adumbrated the very same idea of a lawful higher ordering subsuming universal motion of matter. For elliptical conic sections are geometrically projective. In its own way this elliptical principle is a type of relativity. And it is no coincidence that the same method of strictly basing any hypothesis upon geometrical analysis in fact did underlie Einstein's breakthroughs. The four dimensional complex geometry that Einstein utilized was made possible by Gauss and Riemann's advancements. 

Firstly, Gauss resolved the whole matter of apparent universal cyclical randomness with his grand opus on higher arithmetic. Which is to say that at the granular level of comparative relative celestial motion a higher principle of cyclic remainders or higher arithmetic  is necessary by the very composition of substance. 

Next Riemann boldly established whole new types of geometrical projection in his dissertation on the hypotheses underlying the foundations of geometry and in his work on pressure shock waves. First Riemann showed that dimensionality was analogically projective from n + 1 dimensions to n dimensions.  This allowed Einstein to suppose that time itself was quasi dimensional as the fourth dimension. (As I showed earlier, this assumption in a way was already given birth by Kepler's elliptical principle which itself stood outside of time by subsumption.) Just as importantly for Einstein was Riemann's development of the ordering of universal curvature. (This was foreshadowed also by Gauss as Riemann admitted.) 

Further, it has been my lifelong contention that Riemann's revolutionary reworking of geometry has much more to bequeath to today's scientific problems. His branch point surface function itself  is evidently a coherent pathway toward establishing a biophysical type of ordering. Riemann himself deeply delved into this realm with his paper on the mechanics of the ear. We see in research everywhere that at the very small biophysical order a protein or some other biotic monad or branch point singularity has a manifold of functions completely in line with the sheaves of functional space that Riemann developed. 

In this way, the principle of projective relativity takes another non linear step from the merely inert physical dead matter to the living realm. In the very same way that for instance we witness microtubules functioning communicatively biophysically, may we not hypothesize that intergalactic dust lanes might be a sort of macrotubule for the creation of star systems? It is a question that goes directly back to Kepler's method that instead of the frankly dreadful assumption that mere randomness underlies all motion in physics in the small and large, living systems and noetic systems must subsume from a higher order that which appears to the senses. Or as Kepler would have it, the mind of the Composer of universal substance

Monday, August 21, 2017

Beauty's Secret Snare

What secrets has thou kept these many years
Upon a mountain top in China
Lovely Iris, from humanity's prying eyes?
Though beauty as the dawn's sweet light does bathe
Your winsome hues in rainbow petals grace:
Sweet sacrifice of nectar
You now make with measured guile.
For rudely mating sawflies
Entranced to merely dine
Yet leave untouched both stigma and stamen
For the sake of your flower progeny
That yet will delight with blues and purples
Up in the rarefied heights
New generations of friend and foe alike.



By Kogo (Own work) [CC BY-SA 3.0 
(http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

Wednesday, June 21, 2017

The Universal Relative Process of Becoming

Nicholas of Cusa over half a millennium ago propounded a principle that should have governed scientific inquiry to this day. He called it learned ignorance or docta ignorantia. To restate this: the principle is that as humanity discovers successive breakthroughs regarding the organizational constitution of the physical, biophysical and psychological functioning of our universe, we paradoxically discover that we are just as far if not farther from understanding what lies beyond.

This train of thought is based upon a methodology of Platonic dialog. It is a rigorous determination regarding the ontology of the power of the infinite process of becoming. For instance, how can we surmise that if humanity lifts our civilization off this planet we can be confident that we will collectively discover new sources of energy to propel us forward? (A progressive energetic series of fission, fusion, matter-anti-matter, etc.) This is just because we can hypothesize that the potential entirety of human history is concomitant with this very infinite such power. To think otherwise is irrationally absurd.

And yet society has been in the throes of such "thinking" over the ages. The magical belief in the power of a pantheon of immortals who arbitrarily rule over human affairs is unfortunately prevalent in the tide of history to date. It is synonymous with the infantile worship of money for instance: the magic of the marketplace. It is the equivalent of the belief in renewable energy sources as somehow constituting progress rather than regress -- i.e. that there is only so much stuff to go around on this lifeboat earth.

It is nearly miraculous that since we have been imprisoned intellectually by such infantile poppycock that we have somehow not managed to blow our whole planet to smithereens several times over. Which indeed is as close as I can come to an otherwise impossible proof that the continuing process of creation is harmonically composed of what can only be described as a nurturing or loving governance. Never has the choice of mutual development of nations versus destruction been more stark.

Sunday, May 07, 2017

Human Brain Surface Topology

If one were to perform a normal conformal mapping of the surface of the human brain to a Gaussian unit sphere, there would be the equivalent of a Riemannian surface function that has a multiplex sheath of sheets. This mapping is on the complex mathematical domain and counts every bit as much for the human brain's quality as the intricate axonal branching that supposedly carry "information." Whatever that is...









Wednesday, April 19, 2017

Nonlinear discontinuities are the characteristics of substance

The absolute and unbridgeable separation among the realms of the non living, biophysical and human creativity points to the idea that rather than assuming that substance is merely located within those boundaries, substance is rather the movement from one to another.

The paradox of humanity's forever finite yet evolving knowledge of such infinitely powerful sources of universal creation rightfully situates the solution to the current baleful consequences of the false ideologies of geopolitics and limited resources.

For there can be no possible limits to human technological progress which revolutionizes the very definition of what constitutes a resource. The proof of this potential can only be grasped negatively in the same way that the ironic nature of substance is addressed above. While we as a species are constrained to operating within the confines of existing modes of sustenance, it is only when the necessary orientation of discovery permeates our science and art that we truly exhibit our whole and uniquely creative nature.


Sunday, March 19, 2017

What Prevents Science from Achieving Accelerated Breakthroughs

The edifice of assumptions regarding the DNA code as the program that is determinate for life is fatally flawed. The reality is that life is of a higher order of transfinite than the non living. Likewise human creative reason is of a higher such order than the domain of lower life forms. The question is why do the vast majority of scientists not know what transfinite ordering is?

Edgar Allan Poe, whence the name of this blog, in his Eureka presaged this lack of epistemological clarity thus:

"Now, my dear friend," continues the letter-writer, "it cannot be maintained that by the crawling system, exclusively adopted, men would arrive at the maximum amount of truth, even in any long series of ages; for the repression of imagination was an evil not to be counterbalanced even by absolute certainty in the snail processes. But their certainty was very far from absolute. The error of our progenitors was quite analogous with that of the wiseacre who fancies he must necessarily see an object the more distinctly, the more closely he holds it to his eyes. They blinded themselves, too, with the impalpable, titillating Scotch snuff of detail; and thus the boasted facts of the Hog-ites were by no means always facts -- a point of little importance but for the assumption that they always were. The vital taint, however, in Baconianism -- its most lamentable fount of error -- lay in its tendency to throw power and consideration into the hands of merely perceptive men -- of those inter-Tritonic minnows, the microscopical savans -- the diggers and pedlers of minute facts, for the most part in physical science -- facts all of which they retailed at the same price upon the highway; their value depending, it was supposed, simply upon the fact of their fact, without reference to their applicability or inapplicability in the development of those ultimate and only legitimate facts, called Law.



"Than the persons" -- the letter goes on to say -- "than the persons thus suddenly elevated by the Hog-ian philosophy into a station for which they were unfitted -- thus transferred from the sculleries into the parlors of Science -- from its pantries into its pulpits -- than these individuals a more intolerant -- a more intolerable set of bigots and tyrants never existed on the face of the earth. Their creed, their text and their sermon were, alike, the one word 'fact' -- but, for the most part, even of this one word, they knew not even the meaning. On those who ventured to disturb their facts with the view of putting them in order and to use, the disciples of Hog had no mercy whatever. All attempts at generalization were met at once by the words 'theoretical,' 'theory,' 'theorist' -- all thought, to be brief, was very properly resented as a personal affront to themselves. Cultivating the natural sciences to the exclusion of Metaphysics, the Mathematics, and Logic, many of these Bacon-engendered philosophers -- one-idead, one-sided and lame of a leg -- were more wretchedly helpless -- more miserably ignorant, in view of all the comprehensible objects of knowledge, than the veriest unlettered hind who proves that he knows something at least, in admitting that he knows absolutely nothing.



"Nor had our forefathers any better right to talk about certainty, when pursuing, in blind confidence, the a priori path of axioms, or of the Ram. At innumerable points this path was scarcely as straight as a ram's-horn. The simple truth is, that the Aristotelians erected their castles upon a basis far less reliable than air; for no such things as axioms ever existed or can possibly exist at all. This they must have been very blind, indeed, not to see, or at least to suspect; for, even in their own day, many of their long-admitted 'axioms' had been abandoned: -- 'ex nihilo nihil fit,' for example, and a 'thing cannot act where it is not,' and 'there cannot be antipodes,' and 'darkness cannot proceed from light.' These and numerous similar propositions formerly accepted, without hesitation, as axioms, or undeniable truths, were, even at the period of which I speak, seen to be altogether untenable: -- how absurd in these people, then, to persist in relying upon a basis, as immutable, whose mutability had become so repeatedly manifest!



"But, even through evidence afforded by themselves against themselves, it is easy to convict these a priori reasoners of the grossest unreason -- it is easy to show the futility -- the impalpability of their axioms in general. I have now lying before me" -- it will be observed that we still proceed with the letter -- "I have now lying before me a book printed about a thousand years ago. Pundit assures me that it is decidedly the cleverest ancient work on its topic, which is 'Logic.' The author, who was much esteemed in his day, was one Miller or Mill; and we find it recorded of him, as a point of some importance, that he rode a mill-horse whom he called Jeremy Bentham: -- but let us glance at the volume itself!



"Ah! -- 'Ability or inability to conceive,' says Mr. Mill very properly, 'is in no case to be received as a criterion of axiomatic truth.' Now, that this is a palpable truism no one in his senses will deny. Not to admit the proposition, is to insinuate a charge of variability in Truth itself, whose very title is a synonym of the Steadfast. If ability to conceive be taken as a criterion of Truth, then a truth to David Hume would very seldom be a truth to Joe; and ninety-nine hundredths of what is undeniable in Heaven would be demonstrable falsity upon Earth. The proposition of Mr. Mill, then, is sustained. I will not grant it to be an axiom; and this merely because I am showing that no axioms exist; but, with a distinction which could not have been cavilled at even by Mr. Mill himself, I am ready to grant that, if an axiom there be, then the proposition of which we speak has the fullest right to be considered an axiom -- that no more absolute axiom is -- and, consequently, that any subsequent proposition which shall conflict with this one primarily advanced, must be either a falsity in itself -- that is to say no axiom -- or, if admitted axiomatic, must at once neutralize both itself and its predecessor.



"And now, by the logic of their own propounder, let us proceed to test any one of the axioms propounded. Let us give Mr. Mill the fairest of play. We will bring the point to no ordinary issue. We will select for investigation no common-place axiom -- no axiom of what, not the less preposterously because only impliedly, he terms his secondary class -- as if a positive truth by definition could be either more or less positively a truth: -- we will select, I say, no axiom of an unquestionability so questionable as is to be found in Euclid. We will not talk, for example, about such propositions as that two straight lines cannot enclose a space, or that the whole is greater than any one of its parts. We will afford the logician every advantage. We will come at once to a proposition which he regards as the acme of the unquestionable -- as the quintessence of axiomatic undeniability. Here it is: -- 'Contradictions cannot both be true -- that is, cannot coexist in nature.' Here Mr. Mill means, for instance, -- and I give the most forcible instance conceivable -- that a tree must be either a tree or not a tree -- that it cannot be at the same time a tree and not a tree: -- all which is quite reasonable of itself and will answer remarkably well as an axiom, until we bring it into collation with an axiom insisted upon a few pages before -- in other words -- words which I have previously employed -- until we test it by the logic of its own propounder. 'A tree,' Mr. Mill asserts, 'must be either a tree or not a tree.' Very well: -- and now let me ask him, why. To this little query there is but one response: -- I defy any man living to invent a second. The sole answer is this: -- 'Because we find it impossible to conceive that a tree can be anything else than a tree or not a tree.' This, I repeat, is Mr. Mill's sole answer: -- he will not pretend to suggest another: -- and yet, by his own showing, his answer is clearly no answer at all; for has he not already required us to admit, as an axiom, that ability or inability to conceive is in no case to be taken as a criterion of axiomatic truth? Thus all -- absolutely his argumentation is at sea without a rudder. Let it not be urged that an exception from the general rule is to be made, in cases where the 'impossibility to conceive' is so peculiarly great as when we are called upon to conceive a tree both a tree and not a tree. Let no attempt, I say, be made at urging this sotticism; for, in the first place, there are no degrees of 'impossibility,' and thus no one impossible conception can be more peculiarly impossible than another impossible conception: -- in the second place, Mr. Mill himself, no doubt after thorough deliberation, has most distinctly, and most rationally, excluded all opportunity for exception, by the emphasis of his proposition, that, in no case, is ability or inability to conceive, to be taken as a criterion of axiomatic truth: -- in the third place, even were exceptions admissible at all, it remains to be shown how any exception is admissible here. That a tree can be both a tree and not a tree, is an idea which the angels, or the devils, may entertain, and which no doubt many an earthly Bedlamite, or Transcendentalist, does.



"Now I do not quarrel with these ancients," continues the letter-writer, "so much on account of the transparent frivolity of their logic -- which, to be plain, was baseless, worthless and fantastic altogether -- as on account of their pompous and infatuate proscription of all other roads to Truth than the two narrow and crooked paths -- the one of creeping and the other of crawling -- to which, in their ignorant perversity, they have dared to confine the Soul -- the Soul which loves nothing so well as to soar in those regions of illimitable intuition which are utterly incognizant of 'path.'



"By the bye, my dear friend, is it not an evidence of the mental slavery entailed upon those bigoted people by their Hogs and Rams, that in spite of the eternal prating of their savans about roads to Truth, none of them fell, even by accident, into what we now so distinctly perceive to be the broadest, the straightest and most available of all mere roads -- the great thoroughfare -- the majestic highway of the Consistent? Is it not wonderful that they should have failed to deduce from the works of God the vitally momentous consideration that a perfect consistency can be nothing but an absolute truth? How plain -- how rapid our progress since the late announcement of this proposition! By its means, investigation has been taken out of the hands of the ground-moles, and given as a duty, rather than as a task, to the true -- to the only true thinkers -- to the generally-educated men of ardent imagination. These latter -- our Keplers -- our Laplaces -- 'speculate' -- 'theorize' -- these are the terms -- can you not fancy the shout of scorn with which they would be received by our progenitors, were it possible for them to be looking over my shoulders as I write? The Keplers, I repeat, speculate -- theorize -- and their theories are merely corrected -- reduced -- sifted -- cleared, little by little, of their chaff of inconsistency -- until at length there stands apparent an unencumbered Consistency -- a consistency which the most stolid admit -- because it is a consistency -- to be an absolute and unquestionable Truth.



"I have often thought, my friend, that it must have puzzled these dogmaticians of a thousand years ago, to determine, even, by which of their two boasted roads it is that the cryptographist attains the solution of the more complicated cyphers -- or by which of them Champollion guided mankind to those important and innumerable truths which, for so many centuries, have lain entombed amid the phonetical hieroglyphics of Egypt. In especial, would it not have given these bigots some trouble to determine by which of their two roads was reached the most momentous and sublime of their truths -- the truth -- the fact of gravitation? Newton deduced it from the laws of Kepler. Kepler admitted that these laws he guessed -- these laws whose investigation disclosed to the greatest of British astronomers that principle, the basis of all (existing) physical principle, in going behind which we enter at once the nebulous kingdom of Metaphysics. Yes! -- these vital laws Kepler guessed -- that it is to say, he imagined them. Had he been asked to point out either the de ductive or in ductive route by which he attained them, his reply might have been -- 'I know nothing about routes -- but I do know the machinery of the Universe. Here it is. I grasped it with my soul -- I reached it through mere dint of intuition.' Alas, poor ignorant old man! Could not any metaphysician have told him that what he called 'intuition' was but the conviction resulting from de ductions or in ductions of which the processes were so shadowy as to have escaped his consciousness, eluded his reason, or bidden defiance to his capacity of expression? How great a pity it is that some 'moral philosopher' had not enlightened him about all this! How it would have comforted him on his death-bed to know that, instead of having gone intuitively and thus unbecomingly, he had, in fact, proceeded decorously and legitimately -- that is to say Hog-ishly, or at least Ram-ishly -- into the vast halls where lay gleaming, untended, and hitherto untouched by mortal hand -- unseen by mortal eye -- the imperishable and priceless secrets of the Universe!



"Yes, Kepler was essentially a theorist; but this title, now of so much sanctity, was, in those ancient days, a designation of supreme contempt. It is only now that men begin to appreciate that divine old man -- to sympathize with the prophetical and poetical rhapsody of his ever-memorable words. For my part," continues the unknown correspondent, "I glow with a sacred fire when I even think of them, and feel that I shall never grow weary of their repetition: -- in concluding this letter, let me have the real pleasure of transcribing them once again: -- 'I care not whether my work be read now or by posterity. I can afford to wait a century for readers when God himself has waited six thousand years for an observer. I triumph. I have stolen the golden secret of the Egyptians. I will indulge my sacred fury.'"

Saturday, March 11, 2017

Leibniz and Einstein: an Equation of Sorts

To wit: Leibniz' revolution was f=ma and he wrote the Theodicy. Einstein's revolution was e=mc2 and he wrote that God doesn't play dice.


Thus does genius operate as a force upon history via hypothesis of the continuing order of creation with humanity at its summit.

Life After Death: A reflection upon the issue of brain death.

Human creative thought generates an infinite array of potential for the continued development of civilization. These waves involved are quite real. Indeed, the most powerful dialogues of this type are in perpetual synchronicity with the totality of human history, past and future.


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