The Heart of the Matter
Indulge my infrequent optimism concerning the imminent resolution of the metaphysical problems of immaterialism and the BPW. Taking our cue from Ms. Grandin, let us suppose that matter is the means to the resolution of cosmic conflict.
Before venturing further, however, allow me to acknowledge another member of the idealism club. This is an excerpt from the NYTimes 1/4/05, "God (or Not), Physics and, of Course, Love: Scientists Take a Leap: Fourteen scientists ponder everything from string theory to true love:"
Cognitive scientist, University of California, Irvine; author, Visual Intelligence.
I believe that consciousness and its contents are all that exists. Space-time, matter and fields never were the fundamental denizens of the universe but have always been, from their beginning, among the humbler contents of consciousness, dependent on it for their very being.
The world of our daily experience - the world of tables, chairs, stars and people, with their attendant shapes, smells, feels and sounds - is a species-specific user interface to a realm far more complex, a realm whose essential character is conscious. It is unlikely that the contents of our interface in any way resemble that realm.
Indeed the usefulness of an interface requires, in general, that they do not. For the point of an interface, such as the Windows interface on a computer, is simplification and ease of use. We click icons because this is quicker and less prone to error than editing megabytes of software or toggling voltages in circuits.
Evolutionary pressures dictate that our species-specific interface, this world of our daily experience, should itself be a radical simplification, selected not for the exhaustive depiction of truth but for the mutable pragmatics of survival.
If this is right, if consciousness is fundamental, then we should not be surprised that, despite centuries of effort by the most brilliant of minds, there is as yet no physicalist theory of consciousness, no theory that explains how mindless matter or energy or fields could be, or cause, conscious experience.
Now from the first chapter of his book:
But wait. If you construct all you see, then since you see this book, you construct it as well. And if that's so, then why should you buy it and why should I get royalties? What right have I to copyright your construction?
This question has more than passing interest to me as an author, and I shall have to raise a distinction to rescue my royalties. [...]
The except from Amazon leaves us hanging, and I could not get the search function working to retrieve more pages. I would like to hear more.
Ms. Grandin points out that 'normal' humans are uniquely prone to ambivalence, apparently in the furtherance of our quest for coherence. I happily construct a cosmology on this simple observation. The doctrine of apokatastasis posits restitution in the future. Various fundamentalist eschatologies rather posit Armageddon and division at the Omega. Let me suggest that they have made the common mistake of transposing the Alpha and the Omega. The paradisiacal zodiacal circuit is broken. It requires atomic metabolism and the human proclivity toward concrescence and coherence to make restitution. We finally internalize the predator/prey dynamic.
There is the primordial rupture: felix culpa. It has something to do with the primal sacrifice and subsequent theophagy as reenacted in the X-event. Sexual dimorphism is one small part of this cosmogonic event. We have had to eat and, yes, fornicate our way out of our predicament. We have grown so acclimated to our via metabolis that we can scarcely contemplate its abeyance, not quite the same as abstinence. Are not our own cells quite beyond copulation? Now we partake as if there would be no tomorrow: not an unreasonable posture under the circumstances.
Does this help in our understanding of atoms? Where would we be in our miscegenation without our recombinant DNA? Please note that organicity does not imply homogeneity. It is about the rainbow coalition. DNA, for all it's worth, need be little more than the logical detritus or our morphogenetic proclivity. Logic and love are our only glue. We come to the point where pure imagination can bridge the remaining gap in our cosmic circuit. Behold the spark gap.
Logic begins with the primal 'mark of distinction'. We can come home again, but only via the Riemann Hypothesis. It has been a struggle. Nothing will be wasted, not even our squeals.
A critical mass was exceeded. We are the fallout from the chain reaction. Atoms are the retarded cores of the primal circuit.
Keeping with the spirit of the quantum, it could have been a 'measurement' event which precipitated the rupture. We may still be in the throes of realizing that event, of reifying the possibilities.
Another way to look at cosmogenesis is in terms of a phase change within the matrix being precipitated at some critical juncture. That precipitous phase change is Alpha, involving a separation. From Alpha up to Omega, the cosmic partition is internalized within the microcosmic egos. This gradual historic process of internalization leads up to the final restitution that is completed within a couple of generations. I doubt that we have yet entered this final stage, but I would expect that the Internet will play a significant role in the initial phase of the apokatastasis. The Y2X event will signal its commencement. This website is intended to facilitate that event.
Does this sound too mechanistic? Well, no point in having God do busy work.
Suppose we switch from beach to forest. Fallen leaves replace sand. The trees are each teleological, and so are the blades of grass in the lawn. How do these differ from the sandy beach? Only in the associated teleology.
With the forest we can still tell the trees, if not the leaves. On the new mown lawn, there are only blades and grains, very similar to the beach. How may we move seamlessly between the two?
But we can tell the forest for the trees. It and the lawn are essentially systems. But then there is the petrified forest turning into a beach. Whose system is that in our young earth scenario?
We need not inherit the hobgoblin of Plato and Descartes: that true ideas must be clear and distinct. This shibboleth is a procrustean bed for relational, systemic thought. However, we must not belittle the individuality of each and every blade of grass. Each is a microcosm like ourselves.
What of the individuality of the archaeopteryx? Did her heart never beat? I have said that it is we who personify nature. I may have to stick with that. It is we who individuate. We do that because we are individuated chips off the cosmic block. We do this to numbers, as none others can. Numerology is not something gratuitous, juxtaposed against mathematics. It is the heart of the matter.
How do personification and abstraction coexist for us? Are they not antinomies? There must be combinatorics involved, but there is also integrity. Integrity is no abstraction, it is our soul. This may be where we come back to Temple Grandin. She points to the links between animal and human consciousness that are adumbrated by autism. Is Ms. Grandin lacking in integrity? Certainly not in honesty. Her refreshing honesty shines through every sentence. Is she lacking in humanity or personality? Perhaps she is correct in her self-diagnosis of lacking in cosmic ambivalence or multi-valence? The personal and cosmic are two poles of the chain of being. The world is suspended betwixt them. They are the Alpha and Omega in a slightly shifted perspective. Music is a link. It ties into both our emotions and abstractions. This is something lacking in animals. Temple has little to say on this score. Pythagoras had more to say. Temple says that we and the whales are latecomers to the musical scene (p. 278).
Is there nothing abstract about emotions? Is there nothing emotional about numbers. What would Srini say? Is there not a music of the spheres? How great can be the difference between the mental lives of Wolfgang and Srini? How far can either be removed from God? Did not Jesus have perfect pitch when it came to the Golden Rule, and how far is that removed from the Golden Section? Abstraction, microcosm and our social nature come intact. These come together in our linguistic skills.
There was nothing clear and distinct about atoms until we came along. Now we know the limits of distinction. There are phenomenal regularities that seem to require atomic action. No, we did not invent the atom, but someone conceived it. We partake and amplify that conception in a crucial way. We are a cog in the wheel. We internalize the wheel. The petrified jungle grows in our dreams. We and it are the essence of the Creator. The graininess of the beach, the atomicity of the ocean are equally essential.
Organic teleology is limited by individuality. Does that individuality require atoms, or can it be subsumed under the dialectic? Persons are more than combinations.
We have here a reprise of the Newton incident. What happens when the apple falls from the tree? Yes, gravity, but what else? Can we make the teleology seamless? How do we survive so well on our pseudo distinctions? From whence do they come? Even the symmetry breaking must have a telos. At what point does the apple detach from the telos of the tree to become a statistic, and what does that mean?
What kind of phenomenology is this? How does it differ from that of Husserl and Heidegger? Theirs is a species of psychology. This is cosmology. The emphasis is on the system.
Perhaps the first phenomenologist was:
OETINGER, FRIEDRICH CHRISTOPH (1702-1782), German divine and theosophist, was born at Goppingen on the 6th of May 1702. He studied theology at Tubingen (1722-1728), and was much impressed by the works of Jakob Böhme. On the completion of his university course, Oetinger spent some years in travel. In 1730 he visited Count Zinzendorf at Herrnhut, remaining there some months as teacher of Hebrew and Greek. During his travels, in his eager search for knowledge, he made the acquaintance of mystics and separatists, Christians and learned Jews, theologians and physicians alike. At Halle he studied medicine. After some delay he was ordained to the ministry, and held several pastorates. While pastor (from 1746) at Waldorf near Berlin, he studied alchemy and made many experiments, his idea being to use his knowledge for symbolic purposes. These practices exposed him to the attacks of persons who misunderstood him. " My religion," he once said, '' is the parallelism of Nature and Grace."
Fred was a student of the 'divine system of relations'. I couldn't have put it any better.
What is the phenomenology of death, be it of you, me, apple or mountain? Plato's ideas are eternal. That is the burden of distinct ideas. Ours are purely relational and nodal, always dynamic, and nothing if not. Can numbers die? Where do they go when they fall out of use? No wonder that mathematicians are Platonists to the core. No wonder that I fear the Monster! The mountain goes down to the beach, but the beach goes back to Shell Mountain, all in the eternal divine system of relations. Sand is the spawn of mountains. Binary digits and neural pulses are the spawn of meaning. All things are one at the atomic level and in the Telos. Plato could never tolerate shells on his mountains, nor craters on his moon.
Deadly and Yet Necessary, Quakes Renew the Planet,
By WILLIAM J. BROAD,January 11, 2005:
But despite such staggering losses of life, said Robert S. Detrick Jr., a geophysicist at the Woods Hole Oceanographic Institution, "there's no question that plate tectonics rejuvenates the planet."
Moreover, geologists say, it demonstrates the earth's uniqueness. In the decades after the discovery of plate tectonics, space probes among the 70 or so planets and moons that make up the solar system found that the process existed only on earth - as revealed by its unique mountain ranges.
In the book "Rare Earth" (Copernicus, 2000), which explored the likelihood that advanced civilizations dot the cosmos, Dr. Peter D. Ward and Dr. Donald Brownlee of the University of Washington argued in a long chapter on plate tectonics that the slow recycling of planetary crust was uncommon in the universe yet essential for the evolution of complex life.
"It maintains not just habitability but high habitability," said Dr. Ward, a paleontologist. (Dr. Brownlee is an astronomer.) Most geologists believe that the process yielded the earth's primordial ocean and atmosphere, as volcanoes spewed vast amounts of water vapor, nitrogen, carbon dioxide and other gases. Plants eventually added oxygen. Meanwhile, many biologists say, the earth's first organisms probably arose in the deep sea, along the volcanic gashes.
"On balance, it's possible that life on earth would not have originated without plate tectonics, or the atmosphere, or the oceans," said Dr. Frank Press, the lead author of "Understanding Earth" (Freeman, 2004) and a past president of the National Academy of Sciences.
The Lord giveth, and the Lord taketh away, but who can take back the MG?
We are God going to seed. Our Creation is her recreation. We are God's spawn. Atoms are a necessary part of the recombinatoric ouroboric circuit. In some essential way, God must be both mortal and immortal, and so must we. No individual tree is immortal. A given tree does not have an individual soul, the Wye Oak being a possible exception. Souls are not Democritian atoms. They, like everything else, have only a relative existence.
And will the Monster be restored to God? I have little doubt that it can be unraveled into the fabric of love, into the synaesthesia of God. What we know of it now is a pale shadow, a merest skeleton. It will be subsumed into the cosmic system in a far more robust manner than we could presently imagine. A world without the Monster and without the Wye would be flawed. The only possible and the best possible are not the same here. They came through a sacrifice that we also cannot imagine. It was not the only possible sacrifice. That datum is about a sure as any can be. It is like asking if I am the only possible Dan Smith. That question takes us well beyond our depth. Possible worlds exist only to the degree necessary, keeping in mind that necessity is nobody's mother. We think of the MG as something fixed. Only in God will it come to life. We are seeing a projection of it: a shadow on the wall. Its apparent fixture is another measure of our ignorance. We could say the same of the petrified forest. It comes to life not in the eon, but in the Aion. Don't be confused. We don't trifle with the cosmic semantics.
In the divine system of relations, what is the relation of the atom to the Monster, and how do they both relate to us and God?
Permit me to explore a cellular analog of the matrix. In this analog the microtubular cytoskeleton, along with the genetic material, plays the role of mathematical logic. We must understand that the role of math may be changed between the Alpha and Omega. We might also wonder about the structuring of our ideas that leads to coherence. Are ideas transported the way organelles are, on tubular networks.
Coherence is something rooted in biology and teleology. The cytoskeletal matrix that supports biological coherence, generally remains out of sight. I wonder what supports coherence in the psyche. The neural net may point to something more metaphysical. Certainly logic and symmetry are part of the skeleton. If logic is the hardware, then ideas and feelings are the software, and ultimately this distinction is transcended. There are atoms in the phonemes, sense data and letters, but these are not generally attended to. It is the functionality that counts, and functions are strictly relational. The data bits aid in the communicative metabolism of thoughts. Atoms exist no more definitely than do sense data, and the latter have fallen out of favor. Neural pulses and atoms may not be the bedrock of reality. Analysis does not come naturally. It is something that we impose on the world. Something that comes with its own costs and benefits. There is a logic of atoms. Those two constructs are mutually supportive. They cannot be separated, as the quantum demonstrates. It is less clear how atoms are necessary for logic. It might have to do with reversibility and other symmetries.
Space, time and atoms are mutually dependent. Numbers are not conceivable without space and time. Numbers and atoms are equally dependent upon the concepts of space and time, and this puts them into a logical proximity. Atoms, number, space and time play a major role in the coherence of the world. The idealist will want to turn this dependency around so that the former emerge form the latter. Should this direction of emergence be problematic? I would think not. Causality, entropy and evolution can emerge in a very similar fashion out of the primal coherence. This is to say then that the Zodiac is numerically indefinite outside of this support. Z may be the nexus of the emergence. The dialectic is instrumental here.
The Matrix may be supposed to harbor a primal state of virtual coherence from whence the world is realized, under the guidance and instigation of a Creative intelligence. Our dreams may be the stuff of which the world is made. Our dreaming may constitute the making of it. The world emerges as our collective dream. The source of the real world is the dream world. That realm is the connecting link between us and the Matrix, between the real and the virtual.
The main strategy for the creation was to foster a self-sustaining process, i.e. biological reproduction, and various other cycles. Coherence is translated into networks of mutual dependency.
It is not clear whether the phenomenology of bodies should be taken as logically prior to the existence of atoms. The relations between atoms and bodies is likely to be complex. Consider the phase changes between ice, water and vapor. This phenomenon could well be regulative of the properties of atoms. What is the metaphysics of ice? Ice, per se, has a diminishing climactic role. Life can get on without it, but not without the related peculiarities of water, such as its high surface tension, boiling point and heat capacity, and its role in the many organic hydrates and biological solutions, etc. Water is the basis and mediator of all biological systems. Bodies and atoms are mutually stabilizing, as in the manner of homeostasis. Biological bodies/systems necessarily maintain a state of dynamic (non-)equilibrium, e.g. see Ilya Prigogine and his 'dissipative structures'.
There is the mutual exclusion of solid bodies to explain. Is this necessarily mediated at an atomic level? It is an electro/quantum force, based on atomic rigidity. That same rigidity must give way to chemical reactions and recombination. Atoms are the sole carriers of properties, determining the genus of each physical substance.
There is no unalterable physical substance. This distinguishes the physical and abstract realms, and does promote a dualist metaphysics. But atoms have mainly abstract properties, that are open to recombination. The same may be said of our ideas. Atoms are the logical link between the two realms. Mental and physical substance find a common ground in the atom, as they must, despite the fact that atoms are not directly perceivable. Or it could even be because of their imperceptibility!
Then we have to deal with the corruptibility of the flesh, and the incorruptibility of the spirit. I can only refer back to the atom. This is part of our genetic immortality. That leaves the eschaton unaccounted for.
The atom mediates between the physio- and teleo- logics. As the physics presumably drops out in the restitutional phase, where does that leave the atom? We might suppose the observational effects to increase, without modifying the relative value of q. It may be a case of out of sight and out of mind, and we do not wish to disrupt the physio- or techno- logics prematurely or at all. It is no mean feat to arrange for the physics to quietly fade away. The ending of metabolism can hardly be painless. 'Woe be unto them that is with child'? This is where I have felt the need for a 'stargate' or 'portal' (see 7/16ff) style of 'transmigration'. That was an attempt to localize the dislocations. 'Alien abduction' is a case in point, and so may be lucid dreaming. The question is narrowed to the mechanics of in- and out-of-body effects. The body becomes something of a phantom limb that we drag along for the ride. It is peculiar, however, that the abduction accounts often contain instances of perceived physical trauma. What's a body to do? We are then left to offer a rational account of 'survival'. What will full restitution look like, if, indeed, it will look like anything. Where is Dante Alighieri when we need him? Our guidance in this area is singularly lacking, but not for no good reason, we have to presume. The rationale for our ignorance might be as good a place to start as any.
Yes, we remain on a need to know basis. The need in this case is to simply argue in favor of the logical possibility of an alternate reality, which can stand beyond our historical reality, and, yet, remain an integral part of the BPW. For this purpose, we do not need clairvoyance, but simply an imaginative use of logic. A major challenge is to incorporate a non-linear time scheme. At least as important is the future of the ego. The dependence of the ego on linear time will certainly relate these two issues. Clairvoyance concerning the eschaton would be tantamount to an eschatological event in itself. It might not be inducive to the gradualism espoused for the BPW. Clairvoyance is not something that should be dropped upon us. It is something for us to work up to in an organic fashion.
Allow me to note that the demands of the BPW may easily overdetermine the physics. How far can the rules of physics be bent to accommodate the telos? The bending of the rules is expected to be greatest in the proximity of the Alpha and Omega.
When we go to the other side we are reverting to the conditions of the pokatok court and Jurassic Parc. These are simplified realities where that status of atoms is less relevant. That world is the lucid dream of the Zodiac. I don't recall if there was a scenario for bootstrapping metabolism. How do we ensure that our Xcaret becomes a self-sustaining dream world? What is the big attraction. How much do the zodiacal angel investors have to put up for 'seed money', before we can go to the IPO?
The virtual 'Xcaret culture' does not become historical, in the sense of acquiring a linear time scale, until it goes megalithic and global. That would be c. 4-2,000 BC.
I may have hinted at it before, but let me say more explicitly that our metabolic bodies could be very effective homeostats for the properties and logic of atoms. This is a variation on our already reversed anthropic principle in which our proactive consciousness rides herd on reality. The feedback from our consciousness is a primary element in the bootstrapping and maintenance of the world. After all, the world is our folie a deux. Now our bodies may be added into that loop. Catching a cold may also serve for debugging the universe. The makers of antibiotics are a partial addition to that loop, as are scientists and engineers in general, as well as we consumers thereof. The white knuckled airline passenger is holding up more than just the airplane. Much of our homeostatic exertions somehow become vested in the atomic logos. Where better to be vested? As such, we also become the usually unwitting conduits of the Telos. This is the atomic suspension bridge holding up history. As we approach the distant shore, the atomic logos gives up the ghost. Our autopilot is turned off. Reality becomes more fluid and lucid. All of these effects will be greatly magnified in the vicinity of portals, up until the Omega, at which point the entire world becomes our portal.
Consider our investment in language, and then the influence that language has on our world, particularly on our social reality. The focused attention of the alchemists shaped our eventual chemical reality. Note the explicitly spiritual telos in much of their opus.
Direct perception and direct realism (also 1, 2, 3, etc.) have not been considered for some time. These ideas are tied up with the notions of presence (see 2/12/04) and gnosis (1/12/04). We perceive things directly in terms of their functionality, i.e. the Telos supports all of our perceptions. With misperceptions there is always a reason, as per the PSR. With an autoimmune disease there is a biological misperception.
It seems that all we directly see are surfaces, but vision and perception need not be the same thing. Vision is optical, and it is hardly the end of perception. Also we do not ordinarily read minds, but we do make inferences. Inferences are corrigible and are frequently modified. It is a cumulative kind of perception. Inferences have duration and durability. They are highly functional.
Vision is essential to our spatial orientation, but we tend to overrate its epistemological significance. Our perception of facial expressions is almost entirely inferential or intuitive. The autistic person does not generally have this ability, despite perfect vision. Directness has to do with presence, which is something more profound than temporal immediacy. Intuitions tend to be immediate and direct.
Our retinal images, if taken by themselves, present only a chaotic jumble of colors. The stability and functionality of our world 'image' is what points to our real powers of direct perception. This perception may well include metaphysical dimensions, although we need not always be conscious of them. Our ocular kaleidoscope is simply some frosting on the cake. We idealists need hardly begrudge it.
Next we take up the perception of atoms. We directly perceive the logic of atoms, the way that Srinivasa perceives the logic of numbers. The Greeks and other natural philosophers had an intuition for atoms, long before science came on the scene. The logic was there all along, whether or not we chose to consciously recognize it. I would now say the same for the logic of God and the BPW. We will kick ourselves afterwards for not having recognized it sooner. On the surface we are social/political animals. Deeper down we are gnostics, one and all. We keep our gnosis on a short leash.
So much for the epistemology, what about the ontology? That is if we are able to make the distinction. What I seem to be getting at here is a variation on the notion that to be is to relate. Our conscious knowledge covers mostly the periphery of the network of being. This is where knowledge seems more indirect. As we probe deeper in the ground and potency of being, we come into a more direct contact with the Ontos. It is as if Srinivasa were personally acquainted with the living organism that is vital substance that is know to the rest of us only by its shadows. This sounds like an Aristotelian coloring of Plato.
We used to have a more collective and functional or pragmatic understanding of the ontos, before we became individuated to the degree we are now. Now we can look forward to achieving a more consciously or deliberately integrated gnosis. Thus do we take on a more cosmic perspective. We thusly transcend our primordial street smarts.
The core of being remains beyond the reach of our ego consciousness. That is a stretch that we will be taking sooner rather than later. The ground or core of being is the cosmic self. In that case our factual or analytic knowledge resides at the base of a pyramid, with the cosmic 'I' at its peak. Our modern materialist picture of the world is about to undergo an inversion. Is the atom then a mini me? I would have to say it is a reflection of the cosmic self, reflected in the base of the pyramid, giving the impression of an inverted pyramid resting on the atom. This is the scientific view. Their confusion is understandable, and must be a major factor in the plan of history. The atom is God as reflected on the wall of our material cave. It is time for us to look and move toward the source. Mathematical physics is actually leading us part way back to God. The MG is God's skeleton. Srinivasa's muse was able to put some flesh on those bones. As God's resurrection, it is up to us to breath life back into that body. We shall be doing so in a nonce, with some help from our heavenly host. It remains to provide a better rationale for this ontological scheme. The scheme needs to be related particularly to the circumstances of the Alpha and Omega. The plane of reflection needs to be better specified. That mirror could be human consciousness itself. Which are the active and passive elements? Where does the math come in? And while we're at it, what does the sky reflect? And what about the Zodiac? How does this relate to JPc, or to biological cells? The notion of the microcosm is crucial, but it has not been developed. Can anyone imagine a world without atoms, i.e. one based solely on phenomenal cycles? What we strive for is atomic logic without physical atoms. The 'cloning' of God into egos, does not stop at that level.
I wonder if there might be someway to apply the above notion of metaphysical 'cloning' to a non-biological system such as atoms? Does the reproductive cycle of a cell make it any more or less real than an atom? Organisms participate in ecological systems. Their metabolic regimen ensures this outcome. This is their network of being. I am attempting to construct a network for atoms, without benefit of metabolism. But can we not just subsume the ontology of atoms into the existing metabolic framework. Maybe I'm making this problem too difficult. Metabolism makes no sense without them. Were physics and biology conceived of separately, or were they all of a piece? How do we avoid over-temporalizing this conceptual/creative process?
It is at about this point in my thinking that I have become stuck on previous occasions. It feels as though there is a particular idea that I am not quite able to grasp. Permit me to take a slight detour and come at this 'problem' from a different angle. I put 'problem' in quotes because I have not yet even been able to specify upon what it is that I become stuck, but whatever else it is, it feels like it is close to the heart of the matter.
My detour is to Peter van Inwagen and his book, Material Beings (1990 Cornell). Here is a review. He admits that the philosophy he presents is a strange one. I gather that he is some kind of materialist. He takes persons seriously, but only as living systems, so he takes bacteria just as seriously. What he dismisses is the objectivity of all non-living objects, apart from atoms (actually he specifies quarks and electrons). His thesis is that only simples exist, and the only simples, i.e. irreducibles, are either (living) beings or atoms. Only in retrospect does he take up the problem of relative identity, that is the view that (two?) things can be both the same and distinct, depending on one's perspective.
I am sympathetic with Peter, to a certain extent. His systemic view of existence goes only as far as his materialism allows. I push his systemics well beyond that point. We are both left with an atomic residue.
Atoms stick in my throat. They are hard to swallow, and harder to spit out.
I am intrigued with Van Inwagen and the Possibility of Gunk (Theodore Sider). Where do I stand on 'gunk'? In some sense, the BPW is an irreducible hunk of gunk. That is especially true of the Matrix. The partitioning of the BPW/Matrix is a very functional illusion. Atoms are the logical bedrock of that illusion. Necessity is the mother of all things atomic. Atoms are the tail-end of the network of being. We just don't want that tail to wag this dog.
Atoms conform to the Monster Group (MG), and the MG conforms to the BPW. More directly, atoms conform to vitalism. Atoms are pliable to the optimal degree. Atoms exist only to the necessary degree. Otherwise they are out of sight and out of (the cosmic) mind. It is the master phenomenological cycles that count. Atoms are merely their virtual counters or logical tokens. This goes back to my organic view of math. Numbers exist because of the telic property of the MG. The MG is not an accident of numbers. Numbers are the logical detritus, the tokens of the MG. I believe the the Riemann Hypothesis will have more to say about this. We could play poker without the chips, but who wants to bother? Atomic being devolves from our laziness. Scientists suppose that the atoms have mutinied, that they have turned anarchic and nihilistic.
But we should not look down our noses at the atoms, for we too are the mere tokens of God. It is all smoke and mirrors, but, by that same token, it is the only show in town. Did God have to conjure the atoms? Did she have to conjure us? When it comes to Creation, God is the 'chairman of the board', and we are all the vice presidents. She was not stingy with the vice.
Is this the heart of the matter? The point seems to be that the BPW is not a slam dunk. It will grow on us as we have grown on it. However, from a more popular perspective, there will come the straw that breaks the back of materialism and dualism, and all their ilk. I can only hope to live to see that day.
What stands in our way are all the absolutes to which we feel compelled to cling. The foremost amongst these is our own absolute identity. We have trouble discerning God in the briar patch of relativity. Rather than follow Brer' Rabbit, we sit on our log and get tarred.
The quantum paradoxes should be weaning us away from our compulsive absolutism. They have, but only to a barely perceptible degree.
Yes, we are trapped in our own language games. Our verbally dominated, left hemispheric brains, are much too susceptible to artificial categorization. Words, we can't live with them, nor without them. They are our stepladder to the higher reality. At some point we will have to transform or transcend them. That is a feat almost impossible for us to imagine. We can use words to point to, but not to grasp, a larger reality.
What remains problematic is our ability to recruit our virtual atoms to do our own heavy lifting when it comes to maintaining the natural order. There is still much to be explained or rationalized.
It could be said that the atoms are not doing any work. Their work has been done in logically coordinating the initialization of the phenomenological cycles, which then proceed on their own mimetic inertia. This same rationale could be applied to the artifactual cycles introduced through technology. Again, I have in mind the MG. The numbers had to do their work only once, but not at any definite time. It is our own, mostly subconscious, monitoring of the phenomenology that keeps the world on track. The scientific enterprise has extended the range of the phenomenology to which we attend. But this extension does not differ in kind from the continuing discoveries of mathematicians. I suspect that the we are, in this eschatological epoch, reaching the end of the discoverable mathematical and physical phenomena. As the novelty of math and physics wanes, our attention will inevitably turn toward the metaphysics. That is certainly what happened in my case. I had the available resources to strike out on my own. My less fortunate colleagues will have to contend with the political inertia that will continue to keep them on a shorter intellectual leash, until such time as comes the final straw.
The atomic logic helps to ensure that the vital, telic force acts as a very widely distributed intelligence. Sufficiently so as to remain off of our analytic radar screens. Our experience of it is only subjective. Subtle are the ways of God, and that subtlety in ensured by the atomic logic. No matter how closely we inspect the atoms, we will not see a living cell. No matter how closely we inspect the individual numbers, we will not see the MG. The MG is pulled out of our mathematical intuition, rather like Athena from the head of Zeus, and its demonstration comes then through deduction, not induction. This is the trick the we must perform with God. We must allow her to spring from our forehead. She will not do so unless properly courted. That is all I can attempt here. A cattle prod will not suffice.
Another problem to consider is the interaction between the cycles. Materialists suppose that these interactions are all mediated at the atomic level, thus producing the observed unlimited variability of the resulting phenomena. One alternative is to make liberal use of fractal structures as a simulation of atomic chaos.
Considerable progress has been made in the use of meteorological models on a global scale. Adding a fractal dynamics at the fine scale could go a long way in verisimilitude. However, I do not want to advance the notion that we are living inside a cosmic computer. That would in no way ameliorate the problems of materialism. It does suggest that we do not need to rely on atoms in order to produce weather on an ongoing basis. The hydrological processes therein can simply be reproduced from the combination of medium grained cycles. We can operate on a purely phenomenological level.
Another place to distribute intelligence would be to the phenomena, on the generic level, but then we need a scheme to apply the generic intelligence to the specific cyclic interactions. This need not be a great problem if we consider the relative simplicity of the effective models now in use. They work well on a coarse grained three dimensional grid, each node with its specific set of rules and nearest neighbor interactions. This would not account, however, for the phenomena of specific clouds. I am tempted to treat clouds and storms as organisms. This tack runs afoul of the work of Peter van I. Next we would have to account for the babbling brook.
Perhaps there is not such a need to distribute the intelligence. Is that not acceding too much ascendancy to the space-time manifold? Here is an opportunity to apply direct realism. What Peter doesn't quite get is that the world behaves as a super-organism. Behind the phenomena there is an ecos. Our dialog with the ecos unfolds it into a global ecology within history. The intelligence only appears to be distributed. It is all a reflection of the one Telos. The Ecos is one part of the Telos and it is our job to unfold it in a seamless manner. The seamlessness is not fortuitous, however. It reflects the monism of the Matrix. The intelligence then resides in the dialectic between us and the Matrix. Thus must the final restitution occur through us. May we not suppose that the intersubjective consistency of our experience also owes itself to the monism?
With the Zodiac in mind we can think of the world as a folie a douze. The Zodiac is a dialectical reflection of the one intelligence. With the Matrix, unity is more natural than plurality. There is an effort to maintain a degree of separation. That effort is aided by the conception of space, along with its concomitant time. Unity remains in the overarching Presence/present, but they and we become mesmerized by the kaleidoscopic possibilities, which we pursue with abandon. We become ensnared in our own collective illusion and mind games.
Metabolism and the concomitant atoms seal the lid on our self-imposed cage. It keeps us off the cosmic streets and out of worse trouble while we pursue our individual and collective lessons. The atoms is the seal affixed to our box. We cannot break that seal without deconstructing the atom. That is what I have been attempting here. Our atom smashers have been of assistance in this regard. They have led us to the Monster Group which casts its shadow on the super-strings and M-branes. To expedite its deconstruction, I attempt here to recapitulate the construction of the atom.
The atom is primarily a logical construct. The exigencies of any spatial combinatorics and even a rudimentary anthropics, gives rise to it. Atoms do seem to come to us with their own paleological pedigree, i.e. an astrophysics complete with a starry sky, wherein there also resides the shadow of the Zodiac. We might think of the sky as something like an x-ray diffraction pattern of the primal zodiac.
In immaterialism, rationale replaces mechanism. This is difficult to get used to. We forever attempt to rationalize our lives and the world. Our failures in this regard are not an indictment of the world, rather they result from the incompleteness of our understanding. Atoms derive simply from the coherence of mind. They are its most significant manifestation. From whence derives coherence? That may not be answerable. What are its limits? Does the BPW represent that limit?
This is a relatively simplistic explanation of atoms. We must see how it will stand up.
Coherence becomes the most powerful force in the world. It plays the role of Atlas in holding up the world. God is its source. Hers is the face that is upon it.
Coherence is another expression of relationalism. Relationalism is a necessary property of mind. Relationalism expresses the necessary subjectivity of mind. By that I simply mean that there can be no experience without an experiencer, no thought without a thinker, no feeling without a feeler. This grounding of the mind is so pervasive and profound that we sometimes find ourselves overlooking it. Materialism provides numerous excuses for overlooking what ought to be excruciatingly obvious. Mystics are also intent upon the path of denial. This comes well after they deny the existence of atoms. My point is that atoms are not entirely optional or dispensable. The self is dispensable only vis a vis its grounding in the Matrix. The Matrix, however, is not the nirvana of the mystics. It is, rather, pure potency, something very different.
Atoms are indispensable to the coherence of life, and so to Creation and the BPW. Be very clear that what we need of atoms is not their objectivity, but rather their anthropic logic, particularly their manifestation of the MG. The MG and the RH may represent the limits of coherence as alluded to above. Am I placing a limit on the intelligence of God? No, this is a self-imposed limit, it is the best of all possible limits. By the same token it becomes virtually necessary. I am also saying that it is not possible for numbers to be hiding a complexity that is beyond the limit of comprehension. There cannot exist unobservable complexity. That is a basic aspect of relational existence, of which numbers constitute the purest example. This statement might be construed as implying the existence of a largest prime number, contrary to the 'plain facts'. But hold on. Beyond a point, primes become probabilistic, while their density decreases. Their existence becomes increasingly virtual. As individuals, they loose relationality. The become hypothetical tokens of the Riemann hypothesis. Their complexity is purely quantitative rather than qualitative as with the MG and RH. These are subtle points that need fleshing out.
Prime numbers provide another model to aid our understanding of the virtual, relational existence of atoms and distant stars. Primality becomes increasingly abstract and subjective, once we stop to think about it and are willing to set aside our Platonic compulsions. When I take a Bayer aspirin to alleviate my headache, it is not a gesture toward the objectivity of atoms, but a gesture toward their subjective relationality, as is ultimately the nature of the headache itself. Should we be good Christian Scientists and dispense with medical treatment? Like other potentially good ideas, it should be employed in moderation and with a firm grip on the pragmatic side of cosmology and eschatology. Is that a quibble? I say that we can celebrate the coherence of atomicity without idolizing atoms. The celebration will ultimately obviate the idolatry. I am suggesting that we are simply in the protracted process of thinking our way through materialism. We thought our way into it, we can think our way out of it. We need only allow ourselves to aspire to coherence. It is there for the asking. There is plenty to go around.
It is not so difficult to understand forests, or treeness, from an immaterial perspective, but how do we explain unique peculiarities of every individual tree, without resorting of objectivity? There are random internal processes which can be covered by generic fractal models. Otherwise there are systemic interactions, i.e. interactions between individual systems. Those interactions necessarily have specificity as between predator and prey. The fox eats a specific rabbit, the caterpillar a specific leaf. As with an individual organism or system, there are variable patterns of interaction. We get into the issue of cause and effect and the PSR. The creation of the pattern need not differ from the creations of a painting, representational or otherwise. Each stroke is accounted for, and once applied, need not be actively sustained.
Cause and effect and the PSR need not and should not be associated with materialism. In a dream state these principles are loosened considerably, if they weren't it wouldn't be a dream. In our social waking state, the principles become tighter. Is the relative tightness a warrant for materialism? I suggest it is simply a warrant for coherence.
Creation is the way of maximizing coherence up to the optimal point of the BPW. Coherence is finite, and our world defines that limit. It is our job to push that envelope. Let us hold in abeyance the issue of an eschatological realm. There may be a tendency for us to overestimate its role in the cosmic scheme. It might be more of a vestigial organ: a safe house for us creatures.
In the formation phase, coherence acts something like gravity. The greater the relational charge the stronger the attraction. The cosmic self takes center stage. The total 'mass' increases up to the limit as the potentialities are realized and integrated into the expanding network of being. As the limit is approached, there occurs an eschatological phase change. This might be something like the formation of a black hole. The sky falls as the space-time manifold is finally dissolved or deconstructed. Elsewhere I have spoken of the space-time manifold as our cocoon, and then the eschaton is a metamorphosis. It has been some time since I have examined this latter model. It was never brought under the larger rubric of coherence. The separation of the stages does not lend itself immediately to the relationalist perspective. Our egos represent the individual cells as they redistribute themselves in the chrysalis. The primal Zodiac is our larval (tribal?) stage. Linear history is the crystal/chrysalis/pupal stage. This is where atoms and biology predominate. It is a time of seeming anarchy and chaos. We have to integrate this seeming discontinuity into the cosmic coherence. How much weight can we give to the biological metaphor? Why do we have to endure this stage of cosmic decoherence.
The old explanation for the decoherence, which may have dated back to my first website, envisioned a more chaotic style of matrix, more like a quantum potential. I spoke of human consciousness as like a seine net cast upon those waters. That may not be in keeping with my more organic, or self-centered matrix.
I may be overdue for a reevaluation of my ouroboric/metamorphic/microcosmic model of cosmology. If there does exist a transcendental realm beyond space and time, why do we need to take this detour through materialism? Can we not short-circuit or bypass the present stage? What is the point of stages, if the temporal dimension is only an artifact in the first place? Is it from here to eternity? Then let's skip the 'here' part. If the measure of all things is coherence, why mess around with all the decoherence implied by the space-time manifold?
I have spoken often of the microcosm, without having bothered to justify it in the BPW scheme. An appeal to the microcosm seems to be an appeal to quantity over quality. Why bother with all the replication when we can go for the gold? If the Matrix is self-organizing, why does it need our help? Why does it need to mess with all this combinatorics, when it has all the potency? If we take mere diversity and sheer quantity as ends in themselves, does that not compromise the BPW rationale? Why do we need all these mean streets, why not just masterpiece theater? Recognize that another reason for this excursus is to develop a rationale for heaven, if such there be.
I'm inclined to simply point out that when it comes to heaven, half the fun is getting there, especially if the Telos is a 'do it ourselves' proposition. However, if there were not such an expansive Creation, we would not be around to have any preferences.
It is hard to imagine a creation without a material/physical aspect at all. Would that not be impoverished from almost any perspective? The only reasonable complaint concerns the quality and/or quantity of that aspect. Is it not possible that quality was sacrificed for quantity? But is this not an egregious case of Monday morning quarterbacking? Well, not if it is the very fact of Creation that is ultimately up for grabs.
If materiality is supposed to be so important, why then should so many of our fellow creatures be materially impoverished? If all this is just meant to impress upon us the relative merits of matter vs. spirit, then are we not entitled to say, 'Alright, already!'? There must be something more fundamental at stake, and I suspect that it does have to do with coherence. It is our perspective that is lacking.
What is being suggested here is that the BPW might more plausibly have consisted of a spiritual paradise with a more modest material appendage. When it came to creating the Earth, maybe God carried a good idea a bit too far. Or was it our fault? All 10^10 of us were just dying to get in here, and God didn't have the heart to turn us away, as if God had no control over the length of the queue. Is there some qualitative aspect of 10^10 that we don't appreciate? Perhaps 10^10 is the limit of coherence. Coherence may not be fully realized if its limits are not tested, but is that not contrary to the notion of optimality, which rather suggests a golden mean? The human situation now has the aspect of extremity. Birth pangs may be essential to metamorphosis. God is not one for half measures. It is of its essence that Creation be an all out affair. If we, altogether, only go around once, we go with gusto, and this is one gutsy world. No one will deny that. What it lacks in creature comforts, it more than makes up for in many other ways, drama being a major component.
I think we may well suppose that there cannot be coherence without incoherence. There must be an optimal balance. If that is the case, then every bit of seeming incoherence that we experience here is a portent for the coherence that lies beyond space and time.
Yes, I am Chicken Little, but it is not often that I get to play the part, so here goes: the sky is falling! I even have a picture for you. There is a heliocentric anomaly in the cosmic microwave background (CMB). I am not aware of any more cosmologically deconstructive piece of evidence since Copernicus deconstructed the Ptolemaic cosmology. Is it time to head for the hills? I doubt it. Materialism will be a tough nut to crack. We may not hear more about the CMB until another WMAP is launched, but don't let anyone tell you that the hand is not writing on the wall.
And while we're at it, how about them birdbrains? Does the discovery of avian intelligence(/consciousness?) put a hole in our anthropocentrism? Is it no skin off our backs? It helps to underscore the universality of mind, and the ability of mind to find accommodations in many different forms. When will we realize that the brain is just a docking station, not to give it too dualistic a slant? There is more than enough mind to go around. It is not a zero sum game. The eschaton remains our baby.
I keep wanting to think of the microcosm, e.g. the human self, as a test-bed for cosmology, but that is detracting from the overarching potency of the Matrix. The BPW has an eternal potency within the Matrix. It could be, though, that it is the role of the microcosm to serve as and manifest the potency of the Matrix. Creation and the Matrix may be two sides of the same coin, but don't ask me what that coin is. OK, then, the Matrix is to Creation somewhat as Creation is to the microcosm. One relation is the inversion of the other. This ought to help explain the Ouroboros, but don't ask me how. Only when we realign our microcosms will the Matrix be rejoined, and only then can Creation be unraveled. Until then it is unrivaled. In such fashion does Creation dissolve back into the Matrix. The Matrix has turned itself inside out via the microcosm, and don't ask what that is good for, but it must be an aspect of the cosmic coherence. At that point we may revert to the zodiacal state, or to a kind of Adam Kadmon. The circle is unbroken. And will we not come this way again? Will we not revisit Creation? That may not be the right question to pose to the Matrix. Creation can at once be both temporal and eternal, without actually repeating itself. Dimensionality is not something that our egos may readily transcend. Eternity is with us always in the shining present/Presence.
I'd like to know what will happen to the 10^10 of us when we revert back to the 'twelve'. Such numbers can live on in the MG. There is coherence in the many scales of 10^10, such as the number of neurons in our brains. It is hard to know what to make of this circumstance. It likely has something to do with an optimal complexity. Given a finite world, it is very important to know how far to push the finitude. The MG probably has something to do with that, but otherwise it may be a rather subjective matter. There are likely to be functional considerations that would apply mainly to the eschatological regime, which would be very difficult for us to fathom.
If one were going to err with this crucial number, would one aim high or low? Would there be anything like right to life considerations? To what degree might we be willing to compromise on quality here in deference to quality there? We should suppose that there are many conflicting demands and constraints to be placed on this master quantity. The AIDS epidemic ought to tell us something about this issue, or at least about its complexity. That epidemic argues to the point that God is motivated by considerations other than political correctness concerning the meaning of human life. Does this imply a devaluation of life, human or otherwise? I hardly think so. It rather implies a cosmic perspective, which is not likely to correspond with our more parochial views.
Presently I am reading Apology for the proof of the Riemann hypothesis by Louis de Branges de Bourcia (6/10/2004), a paper which I found through the archives of Science Daily, a source I commend to you. The proof is supposed to be contained in the companion paper: Riemann zeta functions, but I have not found any discussion as to the merits of this 'proof'', beyond the skepticism generated by his initial claim. [2/3 - Here is a prior critical comment on Louis' method of proof. Louis fails to mention this critique in his recent publications. See also here. Refer to an earlier page concerning the possible significance of the RH.]
With regard to the network of being, there cannot be a major divide between the mundane and supra-mundane. There can be no unobserved phenomena. But what does that mean? There also can be no isolated observations. Our eidetic memories must be eternally stored, and not just passively. They must be coherently incorporated into the cosmic self or zodiac or whatever. That is the whole point of the network. Our notion of private experience is something oxymoronic.
Undoubtedly our personal memories contain much overlapping and redundant material, so that what is eternal is not just the sum of mundane experience. It is, at once, both more and less than that. It may be more like the interference pattern from all the individual experiences. As with a hologram, the individual experiences can be reconstructed from the whole pattern. We might then suppose that some lives are virtually redundant. I can only imagine that such a view implies a limitation of our mundane perspective.
These considerations must also speak to the source and being of atoms. There surely is a redundancy in our materialist perspective of them. We appeal to the higher powers to minimize that redundancy. There is finally one world and one self. The self is grounded in the world, and the world in the self. It is all in service to the Dialectic, MDX/Z.
I can observe a unique pattern of cracks in the pavement. Must this pattern be registered for all eternity? What is the source of the pattern? Would it not be simplest just to blame it on the atoms. Can the atoms not just keep track of their own processes? All they have to do is act naturally. But things get more complicated when we introduce the quantum. Then we have a non-local accounting system to attend to. The non-locality includes the effects of countless virtual gravitons from the most distant galaxies. Can we not just make approximations? We can, but the whole point of materialism is that atoms don't approximate. With them, reality is all or nothing.
With immaterialism, I am an observer in a functional loop of interacting processes, all of which have a timeless aspect. The combinatorics will have unique instances. I have a memory of that pattern which seems to be eidetic, but if I were to attempt to reproduce it, I doubt that it would be accurate. Or I could have taken a picture of the pattern and posted it to this website.
I am observing aging and an increasing entropy from the telic origin of the road as it reverts back to a chaotic state. This is another form of metabolism. But then suppose we are talking about the crack in the Liberty bell. The crack itself becomes the icon. It loses any semblance of being a generic property.
Processes that do not contribute to the coherence do not get recorded in the cosmic or akashic memory. The road will continue to crack and break up until it is repaved. That process has no reason to violate the PSR. Non-violation of the PSR is simply one aspect of the Telos. The anti-teleology of deconstruction is an essential part of a metabolic system. Still the road has to decide when and where to crack, without direct input from individual atoms. This is not a problem if the anti-telos is implicit in the telos. My own aging is equally essential to the larger scheme. A related issue is that of fire that was discussed on the previous page on 11/30/04 &f.
Progress here continues. It is a question of tying up the loose ends, and tightening up the arguments. It will be necessary to indicate how this progress may be continued in a systemic fashion, without the prospect of encountering insurmountable obstacles.
When one line of thought is temporarily exhausted, I pick up what seems to be the next loosest end and pursue that. What comes to mind now is photosynthesis. This phenomenon may be treated under several rubrics, e.g. cycles, metabolism, heliotropism, symmetry and atomism. Permit me to start over in attempting to locate the foundational issue. I will take a tack that may, in part, go back to the previous incarnation of this website.
A likely point of departure is Ilya Prigogine, but keep in mind some skepticism. He speaks of irreversible processes and dissipative structures far from equilibrium. This is what metabolism is about. What then is the role of energy conservation and dissipation?
But let us take a step back and have a look at metabolism. It is about the metamorphosis of matter and energy. This is just where immaterialism is likely to encounter its most serious challenge. Metabolism provides the basis of the interactions that make up ecosystems. Its processes determine the rules of the 'game' of life.
Why rules? Rules provide for coherence. The interactions become intelligible. Cycles can be maintained. Over on the other side, it is supposed that rules are less prevalent and rigid. They are more likely to be merely conventional. Coherence comes about more by consensus. There are fewer independent actors.
Down here we creatures are self-reproducing. Our interactions tend not to be morally constrained. Other constraints are required that will be conducive to cooperative behavior.
Given the natural symmetries of space and time, energy will be a conserved quantity that is a measure of matter in motion. There will then be ergonomics. There will be sources and sinks of energy. As in any economic system, sources tend to be monopolized to the extent possible. One way to restrain monopolistic behavior is to arrange for a remote source of energy. The sun fits that role quite nicely, thank you. Many ecological niches are made available for heliotropes, herbivores and carnivores. The possibility of visual optics creates more opportunities. Empty space becomes the ultimate sink for the solar energy.
The point here is to provide a rationale for the given phenomenology. The next step it to minimize our reliance on the physics. I would just as soon have photosynthesis without the photons, as we have striven for matter without atoms. The atoms are there, but only in a virtual and logical sense.
I am partial to the logic of photons, but reluctant to commit to the mechanics of it, and thus become mired in dualism or materialism. The idea with atoms is to have atomic phenomenology available as needed.
It is not immediately apparent how we can maintain the rules without the mechanics. I appeal to logic, math, PSR, cycles, memory, habits, socialization, teleology, etc.
It might seem that the objective particularity of atoms and photons would be essential to the conservation of matter and energy. The classical theory of electromagnetic fields, however, does not require photons in order to conserve energy. Photons were invented only in order to account for the phenomenology of 'black-body' radiation. But what then of chemistry? How can we ensure the conservation of matter undergoing chemical transformations, without resorting to the objectivity of atoms? I appeal mainly to the metabolic cycles. The chemicals are recycled indefinitely without sources or sinks. The overall conservation need only be appropriate to the phenomenological situation, keeping in mind the PSR. Matter and its elemental constituents will not appear or disappear without sufficient reason. Atoms are the phenomenal tokens of the necessary logic of metabolism. Metabolism rests on the phenomenal continuity of its cycles. It is discontinuity that demands special circumstances and explanations.
Back to photosynthesis. Most plants are able to grow and reproduce by transforming solar energy into chemical processes. If the sunlight is removed, their metabolism will be interrupted, and they will eventually die. The same will occur if certain chemicals are depleted. Consider water. Cacti will hoard what little water they can get. That water is conserved with great biological assiduity. Otherwise we rely on a relatively constant sea level to provide our phenomenal determination of conservation.
Animals require food, air and water. A few minutes without oxygen and it is all over for us. Why does breathing have to be such a big deal for us? Why such a stringent chemical dependency? It is just an intrinsic part of metabolism. Oxidation is our source of energy, but oxygen is highly toxic to cells. Carbon is the primary food for plants. The habitat of plants would be greatly restricted if carbon, water (and sunlight) were not widely dispersible and available. Respiration and atmospherics is the simple solution to these metabolic constraints. Life is the phenomenal conservator of these materials: no conservation, no phenomena.
Instead of sunlight, we might imagine manna falling from heaven. Would not the resulting ecosystem be radically impoverished? I should think that this design would be a non-starter, but don't let me discourage anyone from ruminating on this possibility.
We often consider the constraints of metabolism to be a great hindrance. One of the big attractions of heaven has been the lack of such constraints, with death being high on that list. The science of ecology and the anthropic principle have given us a much greater appreciation for the many hidden virtues of metabolic systems, and impressed upon us the notion of Rare Earth. Now our biggest concern might well be that Rare Earth is going to be a hard act to follow. How rare will heaven be? What will be the systematics that will keep heaven running on an even keel? Eternity is a long time for contending with a design failure. Once you get past the golden gates and the seventy-two virgins, the literature on this subject is very short on specifics. Perhaps the Creator put all her energy into Creation. Heaven might be an afterthought. I spend a lot of time touting relationalism, but I hardly have a clue on the relation between heaven and earth. Am I in a state of avoidance?
My point on these many pages is that the cosmos can be self-organizing, and that mind is a more logical basis for that organization than is matter. Given a minimal starter system, on the order of the JPc, the remaining rules of Creation will naturally fall into place more on the basis of (teleo-) logic than mechanics. Mind provides an excellent feedback system for the maintenance of ecologic and metabolic order, better than atoms ever could, even as in the dreams of the materialists.
But so what, you are quick to ask. So, mind over matter. Yes, and then what? Then everything. There is something decidedly unnatural about the human mind. The same may be true for the minds of the other creatures, but we are not in as good a position to pass judgment. The upshot with humans is that we are increasingly, and mainly by choice, dependent upon unnatural environments. Most of us spend our time in places from which 'nature' is barely accessible. When we do venture into the wilderness, we are very well equipped. Very few of us aspire to the special skills of a John Muir. We humans are homo faber, the great fabricators. We are also the great imaginators. Put together these two primary traits, and see how unnatural it would be for us not to aspire to heaven. Heaven is the Telos of mind and spirit over matter. The natural goal of immaterialism is that telos. John Muir speaks of the eternal beauty of a nature undisturbed by homo faber. Yes, it will be a hard act to follow. Imagine a wilderness without mosquitoes.
Are we then the primary link between heaven and earth? We bring with us a pot-load of unrealized ideas. They should keep us occupied for the first few days of eternity. Let me hasten to add that eternity is meant to be a qualitative state rather that a quantitative one. If I had to choose one descriptor it would be gemeinschaft or community. One might think of something tribal or clannish, but both of these have metabolic foundations. Perhaps the closest historical model would be the communalism of the early christian church, but one in which the lion lies down with the lamb. The anti-metabolic aspect of that picture points to our challenge.
Here is a caveat concerning that model. It was a decidedly eschatological community. Its coherence was based on a set of shared expectations and aspirations concerning the eschaton. It was forward leaning. How might this translate into a post-eschaton aeon?
I'm wondering whether in the best possible world, this website would be blocked from searches. Within the last month or two, all but one page, the one titled 'Crisis', have been removed from the Google data base. Every page has been removed from the MSN data base. Alta Vista seems to have been unaffected, but how many people do we know who still use that search engine? Am I supposed to imagine that this is all for the best, or am I being goaded into intervention? How long do I wait before calling Ron on this? [not long at all.] I cannot imagine that any self-respecting intelligence organization would not retain a preemptive ability to arbitrarily block certain types of sensitive information. Now, I am not claiming that as the reason in this case, but I would be very naive not to wonder about it. In any case, that same department would surely know how to remedy this little problem. Back to our little stairway to heaven. Who ever may have been assigned to monitor these scribblings, please take note! I have been told that there are folks who do pay attention, believe it or not.
OK, I have spoken with another individual about this problem. Here is an innocent explanation, which once pertained to the organization for which she works: the Google web crawler happens to hit your server when it is down, maybe if that is only for a few minutes, then the site (server?) is dropped. She said that this happened to them, and it happened with more than one search engine at the same time. I am having some problem with this explanation. Comcast is one of the biggest servers in the world, people would immediately start screaming from all over, the oversight would be easily corrected within hours. Am I to believe that Google and Microsoft are using the same crawler? That would be a virtual collusion.
So let me try another search on the Comcast site. I try 'site:home.comcast.net money' and get 16,000 hits. Well, does that shoot down that theory, or does the (universal?) crawler look for different websites on the same server at different times? I have gone ahead and resubmitted my URL to Google. It may take them 6-8 weeks before they can schedule another crawl. In the meantime, am I not to be vouchsafed a modicum of paranoia?
Growing and building things is not much of a problem for the immaterialist. There is plenty of direct and indirect teleology at work. It's when things fall apart that there may be more difficulty. To some degree the thanatos (anti-telos) is built into the telos, but in general this latter stage seems much more arbitrary and mechanistic. Is the mechanistic devil in the details of the thanatos? I would much rather take on the burden of explaining incoherence than having to explain coherence. I would much rather have an immaterial cosmology based on the telos, than a material one based on thanatos.
The materialist would have us suppose that the entropic 'heat death' is the most natural state of affairs. It is the final equilibrium for any closed system. Life is an embarrassment to the materialist. Death is an embarrassment to the immaterialist. That is one reason for heaven. If this is not the heart of the matter, then I don't know what is. Death is supposed to be the transition from a state of low probability to a state of higher probability.
I want to fall back on the PSR, but I'm not seeing how to do that. It needs to be expanded. If I drop a glass on the floor, the PSR tells me that it will break, but does not provide any details. In principle, materialism could provide an analysis of the breakage, but that is seldom realized. Destruction is mainly a random process. That randomness is supposed to be traceable back to its basis in atomic chaos. We are not afforded that fallback.
Even within physics, however, there is a problem of providing a fundamental explanation for irreversible processes or for the directionality of time. Irreversibility is strictly a macroscopic phenomenon. No microscopic explanation exists. Once again we see the 'benefit of the doubt' being afforded to materialism, but not to immaterialism. It is partly my job to turn that table, and provide a more level playing field, at least for anyone who is seeking the truth of the matter.
Our best explanation for irreversibility may simply be that it is an essential part of any metabolic process, now with the sense of metabolism extended beyond the merely organic realm to include cyclical processes in general. That is our extension to the PSR. This puts us ahead of the physicists in terms of providing a fundamental explanation for thanatos.
This high level explanation still leaves me feeling uneasy about those cracks in the pavement. It is probably these gut feelings, more than any intellectual problem, that stand between us and immaterialism, and it is those feelings that are the most difficult to address.
Water pipes break. They do so where the pipe is the weakest and the stress is the greatest. Wherein resides that particular information, and how is it applied to the phenomenon? Here we seem to be talking about cause and effect. Once again we are dealing with a macroscopic concept which has no place in the terminology of modern physics. The concept of cause and effect is certainly amenable to the PSR. Causes and effects never ceased, they just went over to immaterialism.
The breakage must reside in the concept of the pipe and its support structure. These items are 'designed' and prepared to meet certain limiting criteria. If the design limits are exceeded, the pipe will fail. This is true for both organic and inorganic systems. Who watches the limits? No phenomenon is real unless observed. But what counts as an observation? It need not be direct, and there's the rub. Reality is a network of phenomena and observations, while not taking this distinction too seriously.
Are we dealing simply with planned obsolescence? That is a thought that could use some analysis, but hold on to it for now.
Part of the telos of paving is just the prevention of cracking. The design of the materials and structures keeps that in mind. Indeed, this is where a notion of planned obsolescence arises. As we study the biology of ageing, we see evidence of similar 'planning' or programming in organisms.
OK, we know its going to crack and we'll have a pretty good idea of when, but not where. That will depend on any structural faults and on the history of insults. An analysis of the pavement would indicate stresses and strains that portend fractures. This is all part of materials science. We are still dealing with a generalized teleology. With proper design, as in safety glass, the fractures will be jagged, and in as random a manner as possible. The pavement acts also as a primitive recording device, in that it retains a partial record of the incidents that impact it. It is not designed specifically to do this, but it comes as no surprise. The fracture patterns, when they finally do appear, will have no further intrinsic meaning. They will not be memorable, unless there are additional circumstances as with the Liberty bell or the 'Abraham Lincoln' french fry. Once the random pattern appears, the PSR tells us that it will tend to retain its shape while the process of ageing continues. The only surprise would be if the cracks did not appear.
We are delving here in to the realm of noise, while the PSR is concerned mainly with signal. When the noise takes over from the signal, as it does in ageing processes, we may then usefully employ the mathematics of fractals. This is the science of 'fractures'. It will provide for us a range of examples of fractures that we are likely to encounter in varying circumstances.
So here we have a nearly complete science of materials, without resorting to materialism. The test will be to see if this line of reasoning will suffice to ameliorate my uneasiness when I next go jogging on the 'payment'. I'll be sure to report back here.
Noise happens, but we want to make sure that it can live comfortably alongside the PSR and the Telos. How does noise fit into the big picture? Noise is logically integral to metabolism. Metabolism relies on fluidics, and that circumstance brings Brownian motion to the fore. Those motions are quintessentially fractal. The diminutive size of the atoms speeds up that thermal motion and leads to an efficient metabolic transport of molecules.
The cell serves as a microcosm for the combinatoric processes occurring on much larger scales. Many social and economic phenomena have the appearance of stochasticity. Stochastic interactions are the primary function of our three-dimensional world.
Then there is synchronicity and serendipity. One function of the stochasticity is to conceal the synchronicity. Why conceal? This is partly how we are able to maintain our exaggerated estimations of our free will. This is how the vital hidden hand is able to remain hidden on all phenomenological scales. The vital and divine forces are able to operate effectively below the noise level. The stochastic dice are loaded. Subtle are the ways of God. The noise is what gives us and God room to maneuver. The noise acts almost as a lubricant for (the reconstruction of) the signal. The stochasticity delivers to us the pieces of the puzzle which we reconstruct to form the Telos, which then becomes our own. The virtual Telos is thus realized.
Without its fractal patterns, nature would not be natural. These fractal patterns are very easy to program into virtually any system. What we see phenomenally are seldom the pure fractals, but fractals that have been modified or constrained by their interactions with other processes.
How does matter maintain its identity without atomic objectivity? Water vapor mixes in with the rest of the air, but at the condensation point the water is able to reaggregate itself. How do we explain this without appealing to individual molecular identities?
If matter were, in general, not conserved, life would certainly not be possible. It would not be possible to observe such an unruly world. Atomicity bears directly on this issue. The problem is highlighted by the quantum fluctuations. All of physics would collapse if such were the case. This is somewhat like asking why the prime numbers are conserved. Otherwise there would be a collapse of logic and math. It is just the relationality and rationality of being which holds this 'physical' world together.
Numericity and atomicity are of the same ilk. That's my story, and I'm sticking to it. I don't think this is the first time I've made this observation (see above, at least); however, I do note that 'numericity' is new to my spell checker. This may be the crux of my story. We'll have to look into it.
Atoms are physical; numbers are abstract, or so we are told. This dichotomy has been greatly exaggerated in the course of our sojourn into materialism. The early Greeks certainly did not adhere to this dichotomy. It is just this artificial dichotomy that leaves us so puzzled by the 'unreasonable effectiveness of mathematics'. Why have we become so resistant to seeing this linkage? It is the supposed dualism of mind and matter, the very foundation of modernity, that leaves us so susceptible to every possible incoherence. And why have we fallen, so unwittingly, into the incoherence trap? Has science been the cause or the effect? Or did it have something to do with monotheism?
Why is it that we have come to regard God as an artisan rather than an artist? Monotheism has come to be antagonistic to monism, which has become the province of pantheism. This is not the first time I have raised this issue. Why are we so intent upon separating ourselves from God? Is this not the basis of all duality?
Without atoms, there could be no numbers. Without numbers, there could be no atoms. Does this imply that neither exist in heaven? Perhaps. Is this the heart of the matter?
How did we come to suppose that there could be a Creator without a Creation? Is not creatorhood an essential attribute of God? In the MDZ scheme, I have set M&D above Z, and the Zodiac is a far cry from being monotheistic. X is the basis of my claim to monotheism. I hold onto a Quaternity. Otherwise there is a slide into pantheism.
The greatest duality in the BPW scheme appears to be that between Earth and Heaven. To get into heaven, we have to forget the multiplication table. There may be more to this than meets the eye. Down here it's atomicity, up there it's organicity. Atoms, get 'em while they last! What then is the analog of metabolism? It is something like D & Z and the ouroboric/psychic circuit. That is from whence we came and whither we shall go. We will have progressed from tail to head, from tribal to communal.
It is noteworthy the extent to which abstractions hold sway in this supposedly 'physical' realm. We may suppose that they will be less prevalent elsewhere. Our adherence to duality is a measure of our ignorance of metaphysics. It is part of the separation mandated by Creation itself. The duality is temporary and epistemic, rather than ontic.
I suggest the Deus faber came from Homo faber, which in turn came from the industrial revolution, or culminated therein. That economic reality, along with monotheism, was the main source of the dualistic impulse of modernism. It is only with postmodernism that we begin to overcome that dualistic worldview.
A question to consider: why is the complicated end of math, e.g. the MG, connected to the simple end of matter, i.e. the 'elementary' particles? Is there something ouroboric about this? Does this imply that simple math attaches to the complicated matter? In a sense, it does. Counting can be a very sophisticated feat. Something that animals decidedly do not engage in, nor would gods without access to atomic brains. Only the most complicated material structures can support simple numericity. Is there something passing odd in these juxtapositions of the simple and complex?
There seems to be something oddly ouroboric about these juxtapositions, but I'm having difficulty in providing any further specification of it. It is not making sense. The ouroboros does not make a whole lot of sense. It pushes rationality to the limit, something that is bound to happen when rationality attempts to chase its own tail.
It requires a great deal of abstraction to specify a simple logic. The simplest logic rests on the most complex of grammatical constructions. The very process of abstraction remains shrouded in mystery. OK, here is a possible analogy: mating act vs. mating ritual. Having the former without the latter is considered the most serious violation of the social order. This analogy might bring us back to the provenance of the Zodiac. There are involved here the profound issues of identity, along with the problem of the microcosm and of part vs. whole.
There is the simplicity of Fermat's last theorem vs. the complexity of its proof. It is in the self that the simple and complex are united to an unprecedented degree. This unification is the basis of all coherence, even of all being, with only the potency of being in the Matrix that is left unaccounted.
These juxtapositions are reminiscent of the self that is at the heart of the matter. Each of the other juxtapositions is a reflection of the self. If we understand one, we understand all. That would be something, indeed. The best understood conjunction is that of the FLT and its proof. First we might wonder if the proof is essential to the FLT. It might have been unprovable, and so could have been treated as an independent axiom, like the continuum hypothesis, which becomes a mere appendage to the mathematical corpus. This may well be the fate of the Riemann hypothesis, although the smart money says it won't be. This is certainly not how we envision the role of the cosmic self.
What is the 'proof' of the self? Well, the proof is in the pudding. The proof of anything is in the coherence that it brings to the world. The FLT, CH and RH combine to amplify the coherence of mathematics. The self is a concept of proven social utility. So too was the concept of the tribe, in its time, but has that construct not outlived its usefulness?
Creator and creation is another juxtaposition of this type. It is generally supposed that downward causation also flows from the simple to the complex, as teleology is translated into functionality. And then came love. What sort of juxtaposition have we there? It is a vital and creative force. All this seems far removed from the FLT: a^n + b^n /= c^n for n>2. Evidently the FLT serves as an organizing principle. It is also telling us that sporadicity is a rare feature. The MG and its finite family may be the only examples. The powered triple has either infinitely many solutions or none. Having a finite number would violate some version of the PSR. That the proof is so convoluted is pointing to the profundity of sporadicity. The BPW is sporadic. It is the organicity of the number system that ensures this. And there is a trinitarian component to this organicity as witnessed in the power of the elliptic functions. Between the quadratic and the cubic lies all of creation.
Then there is the self-referential quality of the construction used by Godel in his incompleteness theorem. I doubt that the meaning of the construction could be recognized by any mechanistic system: it does not compute. This construction has become a mainstay of logic. Embedded in math is a rudimentary concept of self.
There cannot be identity without identicality, and there cannot be identicality without a finite quantum basis with built-in space-time symmetries. Observation and self-reference are intimately involved, as we have seen. The numericity of identicality will not be supported without sufficient metabolic complexity. The ouroboric circuit is closed with complexity of the MG matching the metabolic complexity. What qualifies this as the optimal degree of complexity remains undetermined. God's self-referential identity depends on this outworking or outsourcing, if you will.
The juxtaposition of the simple and complex may be a manifestation of the microcosmic construction of the world. Even the most simple items, e.g. numbers and particles, must reflect the complexity of the world. This is the basis of relational being.
The FLT may be interpreted as a statement of the fractal dimensionality of the world. This is a bit like Bekenstein's holographic bound for entropy, which also gives space a fractal dimension. Fractality does epitomize the juxtaposition of the simple and complex. Recall that the Mandelbrot set is generated by z' = z^2 + C. The notion of the microcosm is holographic in spirit. This is also the statement that the world is a projective construct. The particles generate the MG, and the MG projects the particles. The holograph provides a bootstrap. I'm not sure how the observer fits in.
The Creatures have to hold up their end of the Dialectic. Then how does the dialectic enter into the other juxtapositions? Can anyone see a dialectic component of the Mandelbrot? There is at least something very compelling about the Mandelbrot. There is an aesthetic component to it which resists mathematical analysis. Fractals have been very effective in lending a natural quality to virtual realities.
There is something organic about the Mandelbrot. There is a peculiar aesthetic unity to the beast. It seems to possess a kind of ecological or functional coherence, while every piece of it retains a unique identity. At the same time, each piece contains a microcosmic recapitulation of the whole. The natural and unnatural, the simple and complex reside together in a perfect harmony. Then there is the mystery. From whence did this beast come? What is its provenance? But once we finally see it, we begin to recognize it everywhere. I claim that the mystery reigns. There is more than pantheism in the Mandelbrot. There is also coherence. Coherent pantheism = theism. The Mandelbrot is one very high resolution snapshot of God, caught in the act of creation. It is a vector to the higher intelligence. It is a cairn on the path of transcendence. Materialists claim our world is flat in some mechanistic sense, but with the Mandelbrot, we come to the end of mechanism and keep on sailing. Imagine finding this gem in the midst of a computer. Never discount the divine ubiquity.
But how is the Mandelbrot something other than merely self-generated (sua sponte! Fenn)? How does it connect? How do we defend monotheism in light of the Mb? The Mb is born of God, as are we. Ergo, we do not need to be baptized. Suggesting otherwise is the sin of the Christians. Has Jesus not saved us? I say that Jesus is the lynchpin of our salvational/eschatological economy. He does his job, we do ours. You may take that for what it is worth.
How then does God manage to intervene in the Mb generating formula: z' = z^2 + C? How does God manage to intervene in any conception? It is coherent vitalism. It is the dialectic in action. As I pointed out on the Mb page, using the term 'generator' is a misnomer. It is more like an aperture that is allowing the vital coherence to shine through. One could argue about whether there is a finite or infinite amount of information contained in the Mb, but no doubt it is vastly greater than the information in the 'generator'. What then are we to surmise concerning the provenance of that information? Perhaps I have misspoken. Could not the origin have been the Matrix? With minimal coherence in the Mb, only a minimal participation of God is required for the Mb. The MG is another matter. The anthropic principle requires more coherence on the part of the MG. Perhaps the generator is to the Mb as God is to the world. God places the optimal constraints on the natural effusions of the Matricial potency. One of God's tools in this process is the MG. We creatures are the other 'tool' of Creation. We are simply the co-Creators.
Benoit Mandelbrot, one of the world's mathematical giants on fractals, said that "fractal shapes of great complexity can be obtained merely by repeating a simple geometric transformation, and small changes in parameters of that transformation provokes global changes." In essence--through a predictable, orderly process the "simple iteration appears to liberate the complexity hidden within it, thus giving access to creative potential."
Thus, in that misnomer called chaos theory, mathematicians and physicists have discovered an *underlying order, a kind of memory operating in non-linear, evolving systems. Fractal geometry illustrates that shapes have self-similarity at descending scales. In other words, the form, the *information,* is enfolded--already present in the depths of the cosmos. So this is reminiscent of the Implicate Order. Iteration liberates the complexity hidden within it. It is not dissimilar to Bohm's law of holonomy: a "movement in which new wholes are emerging."
Ostensibly, our brains also provide an aperture into that 'implicate order', referred to here as the Matrix. This may be particularly the case if one is under the influence of an hallucinogen.
Speaking of apertures, there was a time when I subscribed to a 'quantum aperture'. This was back in the early days of my metaphysical sojourn, 1975-'84, when I initially adopted a Cartesian/quantum dualism of mind and matter. Lately, the idea of a quantum aperture has gone mainstream under the rubric of the quantum mind (19,800 hits) (and follow this link to other references to 'quantum mind' herein). On this view, instead of Descartes' suggested pineal gland, it is the non-local strangeness of the quantum realm that provides a connecting link between our minds and bodies. Now that I have adopted the much greater coherence of monistic immaterialism, I see the quantum as just another symptom of immaterialism, rather than having any direct functional role. It is now ours and God's creative love and rationality which is the aperture between the Matrix and the rest of Creation. Under the influence of drugs, or in some other altered state, we individually confront an unfiltered Matrix.
Where does this place us with regard to the Mandelbrot? There is still the question of how there could be an external influence upon the seemingly closed system described by the Mb generator.
The Mandelbrot lies on the tenuous boundary between structure and chaos. This is the same borderline inhabited by living systems, and so the Mb exhibits its organic quality. Novelty reigns in its interacting patterns as one form mutates into the next. There is much replication, but it is never exact. It is themes and variations. A good symphony or poem has these qualities. One wonders if there is any conceivable pattern that could not be discovered in the MB or one of its cousins. I don't believe that anyone has discovered anything resembling a face. Prove me wrong! Invertebrates are represented almost to the exclusion of us vertebrates.
Here is a worthy attempt at rationalizing the Mandelbrot. Significantly the site is maintained by an extropian, shades of transhumanism. (This is one of the best, aesthetic, Mb Explorer. (This one computes externally, most of the others are applets.) Beware, though, that it rounds off the edges as compared with this explorer, rendering it of dubious analytic value!)
It is noteworthy that there are many claims concerning the infinite complexity of the Mandelbrot (420 hits), and I see no attempts at refutation, beyond those implied by Robert Munafo noted above. There is no doubt that there is an (uncountable) infinity of patterns contained in the Mb, none of which is derivable from the others. And what are we to make of this? Here is Robert Curry's suggestion:
I do not know exactly how to convey the degree to which this entire harangue utterly fails to impress anyone who has ever taken time to explore a few portions of the Mandelbrot set, which is a mathematical model of infinite complexity derived from a simple (one might say "mindless") recursive process.
Mathematical proof is less disputable and far more reliable than the ravings of any creationist lunatic: complexity can and does derive from simplicity, just as simplicity can and does arise from complexity.
The issue is one of self-organization or autopoiesis vs. externality. There seems to be no way for there to be non-physical or non-mathematical influence upon objects of biological or mathematical provenance. The mere existence of the mind, however, ought to cause us to think twice about this issue.
Here is an excellent Mandelbrot show and tell. Be sure to see this analytic (lemniscate) approach to the Mb. The point is that ultimately the Mb, for all its depth of structure, is neither analyzable nor computable. Are we left to contemplate our navels? There is no mechanism to point to an explanation. There was no forewarning when we fell into this monster. There was this much warning: Gaston Julia. (More fractal art.) Here is an applet showing the iteration process for the Mb. A more erudite collection of pages may be found by searching on Fatou & Julia & theorem (4,300 hits). THE MANDELBROT MONK is a must see:
While Udo himself is little-known, one of his works is far more familiar. This 13th century German monk was the author of a poem called Fortuna Imperatrix Mundi (Luck, Empress of the World) in the collection of mediaeval underground verses now known as the Carmina Burana.
[...] In Salus, Udo describes how he used these numbers: "Each person's soul undergoes trials through each of the threescore years and ten of allotted life, [encompassing?] its own nature and diminished or elevated in stature by others [it] encounters, wavering between good and evil until [it is] either cast into outer darkness or drawn forever to God."
When Schipke saw the translation, at once he saw it for what it was: an allegorical description of the iterative process for calculating the Mandelbrot. In mathematical terms, Udo's system was to start with a complex number z, then iterate it up to 70 times by the rule z -> z*z + c, until z either diverged or was caught in an orbit. [*4]
Below the description was drawn the first crude plot of the Mandelbrot, which Udo called the "Divinitas" ("Godhead"). He set it out in a 120x120 frame he termed a "columbarium" (i.e. a dovecote, which has a similar grid of niches) and records that it took him nine years to calculate, even with the newly imported technique of ‘algorism', calculation with Arabic numerals rather than abacus.
"It tends to be taken for granted," Schipke says, "That the Mandelbrot is too calculation-intensive to be done without computers. What we have to remember is the sheer devotion of the monastic life. This was a labour of faith, and Udo was prepared to work for years. Some slowly-converging pixels must have taken weeks."
This anecdote ought to give us pause. [2-25: Yes, indeed! Although the story is still being carried by ABC News, it is apparently too good to be true.]
Here is a further iteration of the lemniscate approach to the Mb, taking N to 25. (Here is a another iteration scheme. On this one you can set the iterations from 5 to >500K.) Is this the closest we can get to an analytic version of the Mb? How much does it give away? To what degree is the Mb an artifact? How do nature's versions of it differ from the computer's in terms of the generators? Robert Munafo provides a synopsis of the computing algorithms. (Yet another viewer, about the best general viewer. )
(Pardon me while I note an area w/o structure: -0.7528656865, -(+?)0.0418538316i from this last viewer. The size is 10^-8.) Usually it is possible to recognize even a minimal pattern. This seems to be a dead zone between patterns. There should have been a four-fold pattern with the usual minibot, but it was split in three parts. It took me about an hour to relocate this section. It's just on the other side of the lake, not quite one width east of the upside-down minibot. The bulb on the right points to it. There are at least two similar areas just to the north and east. Each non-pattern has a minibot near its center of gravity, and there is some repetition at smaller scales. Across each of the eight lakes surrounding the central minibot are similar areas of confusion. This area is repeated, along with the central minibot, on repeating unit of this large spiral deep in seahorse valley. On a sister spiral, several clicks above, there are similar areas surrounding the central minibots.
What seems to be happening in these ill formed areas is that there is a prominent minibot nearby which is robbing these neighboring sites, where you would usually expect to find a minibot, of sufficient coherence or symmetry to produce one. Instead the area is split into three dissimilar areas, and there is a much smaller minibot in the central region. This three-fold non-pattern is repeated as you go to smaller scales.
The canonical pattern may be seen near the minibots out in front of the Mandelbrot along the negative real axis. Each one is found at an apparent cross-roads with a fourfold symmetry. It is not a real cross-road because the filaments cannot intersect, they can only branch out. This has to do with the fact that the Mandelbrot set is simply connected. This is related to the fact that we are dealing with a flow system in 'complex dynamics' (q.v.). Your arteries never intersect, they only branch out. If you look along the 'crossing' filaments, you will see 'S' curves, with two main branches on each side. This is what gives rise to the threefold symmetry observed above. There is a confusion between the three and four-fold symmetry. The same confusion is seen in the threefold Mandelbrot, the cardioid portion having two halves, at the intersection of the real and imaginary axes. What I am coming to here is a rationalization for the Mb. Its generator, z' = z^2 + C has a quasi-fourfold symmetry. The generator would like to twist the Cartesian axes into an 'S' curve, but that is not allowed, and the result is the Mandelbrot. The cardioid is performing the function of the heart in attaching the arterial to the veinal system. Also, recall what I said above about the ritualization of the intersection of the sexes. All of this is being recapitulated chez minibot. A critic would say that I am using the Mandelbrot as a Rorschach. Perhaps it is a cosmic or zodiacal Rorschach.
It is said that the Mb is a connected set. That is true, but only in a technical sense. A primary connecting 'link' is a non-link. It is the ubiquitous infinite inward double spiral. The two arms of the spiral never meet, yet there is no topological way to separate them. It then becomes a mathematical convention to suppose that the two parallel arms meet at infinity, like the two parallel lines. It would be more intuitive to say that the Mb is inseparable. The suggestion is that the Mb has a microcosmic aspect.
Here is a ubiquitous feature of the minibots. As you step down in scale each succeeding generation tends to dissolve into own lace work of veils. There is an apparent trend toward self-censorship of the successive generations. I was able only to go out to the fourth or fifth generation before reaching the 10^14th magnification limit of Neal Ziring's explorer. To see this effect, simply pick up the filamentary thread in any spiral or lattice structure. Because of the simple connectedness, there will be bottlenecks/bridges through which the single filament must pass. It is near the center of such structures that you will find a minibot. But then within each bottleneck, by self-similarity, there will be several smaller bottlenecks/bridges of perhaps one-tenth of the width; however, the central minibot in these substructures will be orders of magnitude smaller relative to that bottleneck. Is there any larger significance to this fact? Can it be rationalized?
There are significant trends to observe on venturing into seahorse and elephant valleys. The seahorse valley/canyon walls are studded with minibots. With each minibot is a associated an increasingly dominant triplet structure consisting of two distinct objects. One of these is a spiral and the other is a circular lattice also decreasing inward, let's call it a 'millipede'. On one side of the canyon there is a millipede sandwiched between two spirals, with the reverse arrangement on the other side. In elephant valley there is, on both the floor and ceiling, a looser triplet structure consisting of a relatively large minibot with a spiral on one side and a millipede on the other.
With the disappearing minibots noted yesterday, they seem to be attempting to turn themselves into millipede, without a central structure. This trend is seen continuing down to a magnitude of 10^25 in the series of snapshots taken by Bengt Månsson. Please forgive me if I now give in to the temptation to try my hand at deep zooming. The main issue is the degree to which novelty appears at the deeper levels. Or will it just be variations on the established themes. I suspect the latter.
Using Fractint, the next smaller generation of minibots that I could locate was at a magnification of 10^23 employing a 28 decimal floating point precision. This was the first minibot I could find in the vicinity of its much larger parent. This tend to confirm my suspicion about the disappearing minibot. Fractint runs mainly in DOS mode, with marginal graphics, but it can calculate up a storm. The final image took about half an hour to generate at 1.5 gig.
Yesterday I gave up on the DOS running of Fractint, and have since been using an evaluation copy of Ultra Fractal, which is easily worth its sixty bucks. What a relief! So now I'm eyeball to eyeball with the Mandelbrot.
(Udo of Aachen may be a fiction, but I suspect the hoax will outlive its author. Do I then have to give credit to Ray Girvan?)
The Rorschach test continues. I am not the only one to be fascinated by the Mb. What is its psychological charm? Clearly it is something more than a mathematical tool. There is a game of hide and seek. The minibots are quite clever at hiding. In the process of looking for them in all the strangest places, it is hard not to get the impression that there is some kind of intelligence behind the game.
Yesterday my nephew, Toby, discovered a whole new class of bots. His first one was at the center of what looked like a spiral from a distance, but at high magnification the spiral split apart, with a bot between its two branches. For some spirals, then, the two arms are connected well short of infinity. Now we have more places to look. I'm calling these bots the 'missing links'. This class of bots evolves from a linear triplet of minispiral-bot-minispiral that gets sucked into a master spiral, and in that process, the two companions effective rotate around the bot, swallowing it, while they in their turn are swallowed by the main spiral. Now I am using 'mini-spiral' to designate both the canonical spirals and its cousins that I have variously called amoebas or gopher holes.
What is there to be learned? Toby's discovery bolsters the cosmic interpretation of the Mandelbrot. The minibots' effectively being swallowed by the Mandelbrot is very much in keeping with our old acquaintance, the Ouroboros. The Mb is being both head and tail, Alpha and Omega. In the process, it is turning itself inside-out.
In parallel with the above action there is the more visible bot 'parade' out of elephant gulch and back into seahorse canyon, with considerable mutation and evolution along the way.
Here are some good Mandelbrot pedagogy sites: Mb vs. Julia Set applet using iterations, an iteration of the Mb boundary (the previous applet can also do iterations), Julia star trip, Math World, Wikipedia. Be sure to see the Julia star trip on the Ibiblio site.
There is astonishing detail in the Mb. It is coordinated as far as the eye can see. From whence does the order come? Is the PSR at work? Can we speak of causation? Is it upward or downwardly acting? Is it just one darned iteration after another? What might the appearance of this order tell us about the world, keeping in mind the difficulties we have in explaining the spontaneous emergence of order.
Outside the Mb the Julia set is disconnected. It is at the points of disconnection of the JS where one finds the minibots in the Mb. As one progresses toward greater detail, the minibots grow more hair, while become smaller relative to their corona of filaments. The central ordering feature of the Mb is to be found in those minibot halos. The halos have either circular or polygonal shapes in powers of two, alternating without any obvious sequence. How these larger structures are formed out of the microscopic filaments is the issue here.
Relative to the filaments, there are sources and sinks. If the minibots are the sources, then the spirals are the sinks. The filaments retain the option of spontaneously ending in thin air, this being their most common fate. Thus are the coiffures maintained. The spirals, however, will consume whatever comes their way, including even the most smartly tonsured minibots. Any measurable segment of filament includes an infinity of minibots.
A very significant source of order is the singly connected attribute of the Mb. There are no holes. The filaments can only branch outward, or die-off, but they can never reconnect with anything. This restriction ensures considerable regimentation. In other words, there are no puddles in Mandelbrot land. All the convoluted 'streams' must flow into the ocean.
The proof of single-connectedness relies on the over-arching principles of complex variables. Almost all mathematical proofs are deductive in nature. The four-color map theorem was a notable exception in that it relied on a computer to perform an exhaustive tabulation of all possible configurations. Such a negative requirement is a long way from providing a positive account of the complexity. In exploring the Mb, one finds clusters of minibots of similar size. There is no reason to limit the complexity of these clusters as one progresses to greater detail. The computing power limits Ultra Fractal to a magnification of about10^33on present-day pc's. The dimension of the visible universe is about 10^28 cm. If the Mb were the universe, our viewer could discern the period at the end of this sentence.
My interest in the Mb lies in its microcosmic aspect. Mb is the Creator. The minibots are the creatures, and the external portion represents the rest of the world. This demonstrates how the creatures act as the co-creators. What is outside represents what is inside. The world is elicited from the cooperative effluence of the creatures. It demonstrates how an overarching coordination could be obtained in a relatively democratic fashion. Is this the BPW? Well, it is the mother of all fractals. There is also the ouroboric quality, with the spirals serving as the tail of the cosmic serpent.
(Permit me to speculate that the M-bulbs represent the Zodiac, in which case the Cardioid is the Matrix, and the primary bulb is the X-factor. Each bulb is a perfect circle [12/18/06 - no, only the primary one], and this shows the place of Pi in AZO/X/QRP. The Mandelbrot is then the archetype of archetypes. The unit circle and triune syzygy, e^i*pi = -1 (and here &ff), is implicit in the complex construction. It appears that the fictional 'Udo of Aachen' may have the last laugh.)
In an immaterial, holographic world, every part necessarily represents the whole. The generator, z' = z^2 + C, creates a blank space or vacuum that can only be filled by the cosmos, in accord with the PSR. This should be no more controversial than pointing out that every number is a microcosm of mathematics, with Pi holding the place of pride. This, in turn, is a recapitulation of Quine's holism. We stir in the anthropic Monster Group (MG), and we have the primordial Matrix soup. We are left to wonder how the multiplication of two numbers can have cosmic significance. Is this not the same problem of how the mind can emerge from atoms swerving in the dark? Where is the hidden hand? We might even settle for a 'God of the Gaps' if there were any gaps. What could have fewer gaps than the multiplication table?
How then do we explain e^i*pi = -1? If we didn't know any better, we would never guess that the multiplication table could generate the Mb or the MG. Then again, the Pieta was carved out of a block of marble. The microcosm of numbers, syzygys and all, is laid bare by an indefatigable process of chipping away at the |z| < 2 block. What is left is the coherence of the syzygous numbers. These are the numbers that have stable orbits under the fundamental operation. So does the solar system carve itself out of the primordial dust cloud.
Mathematics, generally, is a testimonial to the complexity hidden in the multiplication table. As to the provenance of this complexity, we have no explanation. Mathematicians merely catalog it. Srinivasa had an unsurpassed numerical intuition, but asking him about the source of that intuition would be like asking a fish about the source of water. The Mandelbrot is one more demonstration of that hidden complexity.
Should we suppose that the source of mathematical beauty differs from that of truth and beauty generally? Is it an accident of nature? Did it evolve? Do we ascribe to a correspondence theory of truth or a coherence theory? The coherence of the Mb is evidence against the former. The anthropic principle and the role of mathematics in it, should already have settled this argument.
The skeptic would argue that it is we who have carved coherence out of the numbers, but this explanation falls far short of explaining the Mb or the MG and mathematical physics generally. In retrospect, we need not have been surprised by the Mb. We can see now that it fits the cosmic pattern. And is this not the heart of the matter? Platonism is inescapable. Theism is then just a fact of the living, shining Presence of the Forms. When it comes to incarnation there are only three historically viable choices. The first two are the Buddha and Mohammed, and neither of them claimed to be that. This is not rocket science or brain surgery. This is waking up and smelling the coffee.
How can even the simplest of integers not be integral to the cosmic coherence? Integers can only reflect the integrity of the world. This is not a play on words, it is integral to the cosmic play. Think about it, my friends. Think about one and zero and e^i*pi = -1. Is this the AZO/X/QRP, or what? Does the Mb not incarnate the AZO/X/QRP? Does anything else come so close? How could the cosmic coherence fail to fill that void?
We don't need to invoke a deus ex machina, or a God of the gaps to explain the Mb. It is rather the hidden hand of mathematical coherence. It is the same as the order of the seemingly random prime numbers that is exposed by the Riemann hypothesis. It is the hidden intricacy of Fermat's last theorem, exposed in Wiles' proof based on elliptic analysis. All of this intricacy had to be incarnated for the world to witness. That is an essential aspect of the observer principle. And what better place? What better raison for our computer technology? It is all wrapped up in the strangely familiar beauty of the Mandelbrot: Exhibit B!
That's my story, and I'm sticking to it. Is there a better explanation? The only alternative is for us to poke out our eyes like Oedipus. But we, unlike Oedipus, are able to know that we are forgiven. It goes with the territory of truth and beauty.
How does the observer principle work with the Mandelbrot? This seems now to be the biggest issue. Is there any way the observancy can be incarnated within the Mb? I would guess that it has something to do with the single connectedness of the mini-Bs. I suppose, also, that the notion of the microcosm is tied up with observancy. This, in turn, has to do with direct perception. We can perceive only that which is of us. We are God perceiving herself. And there is only one God, as there is only one Mandelbrot, and it is the best of all possible such.
The optimality is reflected in the simplicity of the generator. What would be the optimal such? Would it be simple or complicated? It would be the simplest non-linear generator, which is what we have. And there is nothing that is not contained herein. Anything more complicated would be our arbitrary imposition on God's, and on our own, freedom.
My experience with the MG and Mb leave me suspecting that there is something basic about numbers that we are missing. This something has to do with the problem of perception and anthropics. Counting is deeply imbedded in our observational and linguistic capacity. This capacity may most simply be described as labeling. Labeling brings to mind indirect perception and representationalism. This may be the point at which our epistemology has gone astray. The map becomes confused with the territory.
With mathematical physics and computers, we take numbers to be the the substratum of reality, with language and mind being epiphenomenal. The Platonic forms become divorced from our lived world, and the Cartesian dualism of matter and mind, quantity and quality raises its specter.
Yes, I am attempting to regress from quantity to quality, and, of course, this will take me uncomfortably close to the hazards of numerology. We have been there before. We are acquainted with numerical coincidences and sacred geometry. This is why the archetype of Pi figures prominently in the AZO/X/QRP(i). I am suggesting that the relational qualities of Pi are ontologically prior to its quantity. The irony is that we depend on the mechanism of the computer to demonstrate the organicity of the Mandelbrot.
Pi has an ouroboric quality, especially in the context of e^i*pi. The ouroboros has a lot to do with observancy. This quality of the ouroboros and the Mb is captured in the observance of the reflections of multiple mirrors and in paintings of paintings. It has to do with Godelian self-reference. We should not have been surprised by the Godelian construction. Is there evidence for any of this that can be found in the multiplication table? How is it imported into the Mb? How is the spark of life imported into the chaos of the primordial soup? An immaterialist does not have to play that game, but we do have to play the Mandelbrot game. How can the multiplication table be viewed as a microcosm, and not as a pure artifact? Perhaps we should be looking at the dialectic embedded in the imaginary i = sqrt(-1). Perhaps there is more to the iota than mere quantity. Can the iota sustain such an ontological burden? Perhaps only in its natural (sic) triune context. The Mandelbrot is the imago dei, especially in the triune form of the latter. Does this quasi explanation of the Mb smack of circularity? Well, welcome to the real ouroboric world! Mathematicians, for all their jadedness, have not quite outgrown the magic of the iota. And where would any of us be without Iona? They just neglect to stop and smell the flowers. The iota merely adumbrates the (observancy?) magic inherent in numbers. It is the salt in our primordial soup.
The iota is the magic mirror that we can hold up to the numbers to bring out their self-referential quality. The Godelian self-referential construct has a similar effect, but it is much more cumbersome. It should be no surprise that the iota is an essential ingredient for quantum physics, where it appears necessarily in the all-important commutation relations between complementary variables like position and momentum.
Our basic ontological dynamic is MDX(/Z), which is reminiscent of e^i*pi, also of the mother, spirit and son, if you are a reformed traditionalist. The iota here is something of the shape-shifting Trickster. It is the cosmic wild card. It mediates between mother and son, and this role captures its Dialectic quality. It is the basic mechanism of the bootstrap. The Zodiac, as a psychic circuit, bootstraps itself out of the Matrix. The X, with the help of the Trickster, sacrifices itself to break the circuit to form Creation between the Alpha and Omega. Thus the cardiacal cleavage in the Matrix, with the Zodiacal procession emanating from and returning to the nearly cleaved Matrix. Pardon me while I free-associate on the Imago Dei.
The dialectic is our biggest mystery. It is the primal generator of form. If the iota can shed any light on it, then more power to the iota. The sqrt (-1) is not just imaginary, it is impossible. Yet, it is easily the most powerful agent in mathematics. The iota provides an extra dimension to the real numbers, making visible their hidden structures, as in the Riemann Hypothesis relative to the distribution of the primes. The iota elicits hidden structure. The iota is to the reals as the dialectic is to the matrix. Is it fair to say that the functionality of the iota is dependent on the participation of an observer? It is an observational tool or operator or artifact, not unlike the projection operator in quantum physics.
Recall that the dialectic juxtaposes a thesis with its antithesis to produce a higher order synthesis. It is all about transcending the box. That juxtaposition implies an external agent. Pi bootstraps itself out of 'e' using the iota. The Mb recapitulates this process, somehow. e^i*pi is the generator of the numerals, somewhat as the primary bulb in the Mb seems to generate the lesser ones. The same bulb also seems to generate the prime minibot on the negative real axial filament. That creature is the Adam Kadmon of Creation. Like the Mb, it is apparently hermaphroditic, being in the Imago Dei. The cleaving of the cardioid/female component of the Mb was aboriginal, as in the zim-zum. (BTW, the Mb should have reminded me of the polyandrous cosmic model that appeared on my first website. The Mb is more monotheistic.)
Another point needing clarification is the relation between the logos and the dia-logos. The latter seems to be a conflation of D & X. In e^i*pi, it is the iota that bends the inflating 'e' into something cyclical. The Pi is the measure of those cycles. It projects the cyclical onto the lineal. It is the iota that may be responsible for the cleaving of the cardioid and the emergence of the first bulb; however, that point is censored, even mathematically. It is lost in the cusp singularity at (1/4, 0i). In general, the formula for a cardioid is r = 1 - cos(theta), deriving directly from e^i*pi. The Mb cardioid is exact, as is the circularity of the primary bulb. The other bulbs depart slightly from circularity, with only a fractal pattern for those departures. And, yes, we are talking about the heart of the matter.
In the MG and the Mb, numbers seem play two very different roles: ontological and epistemological, respectively. Proper names speak to individuality. Nouns and numbers speak to commonality and identity. Individuation precedes categorization. Before that there is a shining present, and perhaps a stream of consciousness. Enumeration is founded upon the experience of space and time. Then come the Cartesian coordinates and the physics that flows therefrom. That physics turns out to be derivable mainly from symmetry, which is based on identity. The Mb is the most complex object in mathematics. The Monster Group is the most complex of all mathematical groups. We have complexity with a vengeance. Do we not see that complexity reflected in the world? The BPW puts a premium on that complexity. The implication is that what we have is the optimal complexity. Anything more or less would be suboptimal. Is it possible to have too much of a good thing? Yes, but not in the BPW.
On the other hand, I supposed the Mb to be infinitely complex. I was about to say that there could be no non-cognizable complexity. Do we now have to posit an infinitely intelligent deity? Is there no limit to the discoverable coherence in the Mb, using now a more specific definition of complexity? In this case, either the Mb cannot be a microcosm, or the world is infinitely complex. The Mb is part of the world, so its level of complexity becomes that of the world. We then need to consider the ontology of that complexity. Is it actual or merely potential? How might it figure in the eschatology. Might not this conundrum force us to separate ontology and epistemology in the usual Platonic fashion? That would push the theism back toward deism. Can we posit an objectivity for the Mb that is less than that of the MG? Can the role of one be less fundamental than the other?
Consider that there are vastly more genetic combinations than there will exist humans. Does this unrealized human potential create an ontological problem? We don't normally associate any object with that unrealized genetic pool. Perhaps the Mb has less claim to objectivity than the MG. There are also many poems that will never be written. We don't usually suppose that there is a Platonic heaven for unwritten poems. That are mathematical hypotheses that will never be decided. Riemann's could be one of them. Are there hypotheses that will not be hypothesized? That need not be an idle question. Even in the BPW, the greatest symphony might never be composed or performed.
Does the Mb fail the microcosmic test? Or is its incompletion essential to it and us? Will there be no undiscovered dinosaur fossils? Is that any more or less certain than the undiscovered minibot? The Mb forces us to wrestle with the immaterialist ontology. Is there life on other planets, other suns? Are there other planets? What actually constitutes discovery and existence? The existence of the Mb can only be relative, like all else. The reality of the Mb and its parts will finally be optimal. What coheres, lasts. The minibots are like everything else, you find them when you need them. If your presidential reprieve is lost in the mail, so be it. The celestial host are there when we need them, and they need not be from another planet.
Is the Mb infinitely complex? Potentially, yes, but actually it is optimally complex, the same as the cosmos. That optimality will be determined largely by us.
I was attempting to enlist the Mb into the BPW cause, but then it threatened to take over the cosmology by dint of its potentially infinite complexity. We had to beat it back with the stick of relativity. Where does that leave us? I have made a case for the microcosmic status of the Mandelbrot set, but the case remains open. The larger problem is the role of anthropics in mathematics. Such a role runs against our deeply ingrained Platonic view of numbers. It may be the additional role of the Mb to help disabuse us of that illusion. This may be why mathematicians are reluctant to fully engage this beast. It is just too obviously organic/holistic. On the other hand, mathematical Platonism runs up against the unreasonable effectiveness of mathematics in physics. This is especially true in regard to the MG and its kin. I have previously remarked that the more we discover about math, the more we have to appreciate its interconnectedness. This fact ought not to keep surprising us, but no one is keeping score. Platonists tread softly around the problem of relativity. We physicists had to learn these things the hard way. Mathematicians want to be the last of the Mohicans. They fail to appreciate that the BPW will be the eschatological hurrah of Ionia. Plato was just an Ionian backslider. He tried to put his cart of absolutism before the Ionian donkey. Ionian truth did not need a Platonic pedestal. Socrates knew that truth would have to be hashed out in the Agora. Cosmology would ultimately be consensual. The Mandelbrot smacks of the Agora. It is the Agora of the minibots -- too much democracy for the Philosopher King. The organicism is sua sponte. The Pythagorean harmony of numbers was subverted into a Platonic mausoleum. Plato had certainty. It will take a hundred Godels and a hundred Mandelbrots to wean us away from the comfortable lap of certainty. That, or perhaps one more Srinivasa Ramanujan.
Can we extend the minibots' democracy to their numerical cousins? Let the hidden hand have its way. How do we go about this? Will the minibots divulge their secret? What have they in common with numbers? The mini-b's wear their auras on their sleeves. The numerals are much more discrete: 'there ain't no moss on us'. The moss is hidden in the elliptics. There lie the filaments. The elliptic is the cardioid. The numerals are the nearly circular bulbs. We just can't quite see the deviations that portend the greater harmony. Harmony is seen in the syzygys. It is seen in the RH. Recall (and here) the nearly integral values of the elliptically generated Ramanujan constants of the form e^pi*sqrt(n). We suppose mathematical complexity is derived from simplicity, but that may not be the case. This is the analytic illusion. By the same token, we used to think that the perceived world was generated from sense data. Quine began the deconstruction of this illusion. Much deconstruction still lies ahead. Numbers, like atoms, must be emergent entities. The same goes for logic. We haven't quite understood the measurement problem for numbers. Physicists speculate about pre-geometry. We need to speculate about the pre-numerical. Pre-geometry is usually thought to be a logical network of discrete entities. This may be too analytical. According to Leopold Kronecker (1823-91), 'God created the integers, all else is the work of man.' We have to turn that around. Let us recall Watkins, in this regard.
What does the Mandelbrot teach us of holism? It tells us about the microcosmic and relational nature of existence. This is the logical foundation of holism. In contrast to holism, there is atomism. Holism comes naturally; it is grounded in the shining present. Atomism we have to strive for. It is the end product of our analytic skills. It is based on the making of distinctions.
The ultimate distinction is between nothing and everything, between the void and the plenum. Buddhism is the religion of non-distinction. Buddhists identify the void with the plenum. It is nirvana. All problems are solved, all distinctions are dissolved. One could do a lot worse. Could we possibly do any better? The answer is a definite 'maybe'.
I am a bigger fan of the plenum than of the void. I say, 'Give the plenum a chance.' If there is going to be a plenum, it ought to be the best possible one, and so we have the Best Possible World (BPW). Why settle for less?
I make the case for the BPW. How do we get from atoms to the plenum? We consider distinction. The primal distinction is between nothing and everything. In numerical terms, this is the distinction between the null and the infinite. They are reciprocals: 0 = 1/infinity. Infinity = 1/0. That is the mathematical proof of Buddhism. To arrive at the BPW we have to look at this distinction more carefully. We can go step by step in a temporal sequence. The logical starting point is unity. From the previous construction we see that unity is the half way point or the mediator between the null and the infinite. Unity is the numerical emblem of monotheism and the prophetic tradition. It describes the ultimate state of grace or apokatastasis/restitution wherein creator and creation are reunified: the theistic nirvana.
There is a dualism implicit in the unity. Under the operation of multiplication, unity is the dividing line between the null and the infinite. If we start with, say 1.000...0001, repeated multiplication will eventually take that number to infinity, whereas its infinitely close neighbor, 0.999...999 will be sucked into the void. The numerical unit becomes the mark of distinction between the plenum and the void. In the next breath we will be speaking of heaven and hell, but let us not go there.
We continue with the mathematical foray. It is the operation of multiplication, x' = x*x, that leaves us with three distinct elements: 0, 1 and infinity. Yes, this could be one version of the Trinity. The Trinity is the simplest way to defeat the dualism inherent in monotheism. Recall from high school algebra the parabolic function y = x*x or x^2. Its general form is y = a*x^2 + b*x + c. What can we do with that? About the only thing we can do is to simplify it by finding its two roots: y = (x - r1)*(x - r2). Recall then that r(1\2) = (-b +\- sqrt(b^2 - 4*a*c))/2*a. This notorious 'quadratic formula' confronts us at once with three earthshaking 'realities': negative, irrational and imaginary numbers. The capitalist system is based on our acquiescence to the notion of (+\-)$. Greek rationalism was wrecked upon the irrationality of sqrt(-2). Quantum uncertainty is founded on the fact that the 'commutator' of [position, momentum] = sqrt(-1)*(Planck's Constant), which simply tells us that position and momentum cannot be determined simultaneously.
But this is not all. A fourth shaking of the earth comes from the quadratic. We generalize it to z' = z^2 + C, where z = x + i*y, with i = sqrt(-1), is a 'complex' number made up of real and imaginary parts. The single unit no longer serves as the boundary, under multiplication, between the finite and the infinite. The complex values of C lying on the new boundary in the complex plane define the Mandelbrot set, the most complicated object in mathematics.
I have not yet run across an explanation of the most basic fact about the Mb: how it manages to replicate itself. Mandelbrot & self-similarity (22,600 hits). Self-similarity is a defining property of fractals, but this hardly constitutes an explanation for the case of the Mb. In this case we are dealing with quasi-self-similarity. I note that the minibots or 'mu-atoms' occur at places where the filaments appear to intersect orthogonally, as with the real and imaginary axes intersecting the main body. They never occur at the branch points of the filaments where there exists only an infinite regression. One can get a feel for this property by seeing how the Julia set becomes disconnected near the apparent junctions.
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