Is this not just additional support for a constructivist view of math and physics? Are we not unnecessarily falling victim to what Whitehead sees as our proclivity for misplaced concreteness? Are we not being frightened by our own shadow, i.e. by our own abstractions? Does not the Mb demonstrate the taming of randomness? There is ever only a pseudo-randomness, and it is ever only of our own making. The same may be said of the quantum when we factor in the observer principle.
Is not experimental math founded on construction and intuition? Gregory's use of absolutism is an ill-founded justification for construction. Kurt Godel's defeat of Hilbert's absolutist agenda was purely constructive. Now Gregory seems to be returning to absolutism via the back door. Our Platonist/absolutist proclivities die hard. It is our final idolatry.
The Mb exhibits aspects of the halting problem, relating to its bounded and unbounded orbits, given a finite cut-off.
We are still being thrown back on the question of how the vital/bootstrap/dialectic manages to infiltrate the computer logic, if that is what the Mb points to. There is here a stark contrast of mechanism and organicism. Computation cannot be an absolute. But neither are we looking for a god of the gaps. We can only settle for a holistic God. How do computation and mechanism take holism onboard? Where is the leverage?
I can only think that habituation trumps logic and idealization. The vital principle enters the system through this process. The only other consideration is numerology, and this probably amounts to the same thing. It is in the difference between 8 and 8.000.... Are we just talking ordinal vs. cardinal vs. nominal? Pi and the Mb become the de facto touchstones of computation. Without their tangibility and specificity, computation is mere abstraction.
The good news is that we evolve. The bad news is that so do numbers. The good news is that Pi and the Mb provide road maps for that mutual evolutionary path. This is how the world hangs together. It can do none other. This is the foundation of the BPW: ergo, the eschatological telos.
Yes, Gregory, Pi and the Mb are brute facts. They are the brute facts of existence and life. Any other facts are figments of our imaginations. We might just as well wonder that they can be computed at all. Small miracles in a bigger miracle, like e^i*pi = -1. If we can believe that tri-unity, we ought to be able to believe all the rest.
Teleology rules, in the depths of matter, and in the bowels of our machines, simply because it is the logical alpha and omega of all being. That is the most brute of all facts. We had best get used to it. We'll never get over or beyond it. Asking how teleology works is a bit like asking why 1 + 1 = 2. It is the only way that being can be.
Does this make the job of Y2C any easier? Pi and the Mb can lead us to the water, but they cannot make us drink.
Facts: united they stand, divided they fall.
This is my day: a fool for God!
Looking back at the original mention of Mandelbrot on these pages, I notice there was a context of functionalism. I take my functionalism in the spirit of Leibniz' PSR.
Functionalism is just relationalism from a teleological perspective. Things are functional because they are related, and they are related because they are functional. This could be the first law of holism. Numbers, logic and computation are no exception. Functionality we take to be the epitome of mundane existence, in all its slimy, greasy glory. This seems just the opposite of Plato's supra-mundane habitat of numbers and forms. But in that exclusivity, Plato was abrogating the spirit of the Pythagorean harmony of being. Descartes followed Plato's felix culpa, but the mathematical physicists are trying to bring us back to Pythagoras.
Numbers exist to function, thus the UEM, the unreasonable effectiveness of mathematics. Numbers could not exist without the Telos. They cannot and do not exist in the splendid isolation of Plato's heaven.
Being the mother of fractals, the Mb is the logical venue for numbers to most freely display their functional organicity. And do they ever! Bless their little cardioids.
One glance at the Mandelbrot ought to cure the most cold hearted of us of our reductionist, deconstructionist, absolutist proclivities. That it has not yet done so, only indicates that the Mb lacks its proper champion. Can the Y2C/X2-event fail to fill that role? I've been looking high and low. Is there a better candidate for Exhibit A? Should it not suffice? Mandelbrot & God (36,900 hits). I'm not the only fool out here today! Imagine if we ever got our act together. Let the good times roll!
The Mb, how can it be? Nay! How could it fail to be? We must allow that explanatory burden to be shifted. The organicity of the Mb is the alpha and omega of numericity. We should be teaching our kids to appreciate the Mb before teaching them to add and subtract. What surer way to set our materialism on its head? It is the irreducible building block that has been sorely neglected by modernity. Where are those tie-dyed t-shirts of the '70's?
And how does the seemingly singular, solitary perfection of Pi/X emerge out of that Pandora's box? Somehow through the operation of the cardioid. What the X-bulb points to is the holistic perfection of the of the whole organic creation, without which, Pi/X would not exist. All is in harmony. Every hair is numbered. Why are we so slow to grasp this? When we use our analytic skill to calculate Pi to billions of digits, we are short-circuiting Creation. With the Mb, Creation bites back. Everything in its proper place and time. Our most strenuous efforts to thwart creation only play into its ever loving hands. Won't it be a marvel when we stop beating our heads against all fate? We realize that God's love can know no bounds.
The Mb is a hard act to follow....
Perfection and imperfection are all relative and all in the eye of the beholder. The perfect eye can only see perfection. All our eyes can and will be perfected in the Telos. They are already perfect in their context, it is the context that will shift.
God said to the Numbers, 'Be fruitful and multiply.' And Lo, the Mandelbrot! In point of fact, it was likely the Mb that taught the numbers their multiplication tables. It is the primordial/universal multiplication table.
<-- Prev Next -->
Foreseeing the Second Coming
The Second Coming must be a touchstone for any spiritually inspired vision of the world and its history. It is unavoidable even for non-Christians.
A spiritual vision of the world must be coherent and comprehensive. It must be a theory of everything. As such, it would be an understatement to say that it would constitute a revelation of biblical proportions, because it would necessarily transcend the Bible and every other previous revelation. It would have to be the seal of the prophets. And even that is not quite enough. The vision would also have to encompass all previous knowledge: spiritual, philosophical and scientific.
Virtually every tradition has its prophets, messiahs and avatars, past, present and future. Every one of them is strongly associated with the revealing of knowledge. I believe that it is not at all unfair or improper to include science among these traditions.
The next issue is whether we might not rather anticipate a partial revelation, something that falls short of a theory of everything. All I can do is give you my thinking on this matter.
It has been a long time since there has been a world-class prophet. There is a threshold that must be passed. I am only suggesting that at this late date we are in a situation of all or nothing, with respect to prophecy. For instance, neither the bible nor the Koran lend themselves to partial revision. Any emendation to those instruments would have to be perceived to be taking place in a apocalyptic or eschatological context. Buddhism and Hinduism are more flexible in this regard since they do not have a tradition of a closed cannon.
One might contemplate a vision that would bring the prophetic, theistic tradition around to a more pantheist and mystical viewpoint. This is partly true of the vision being put forward on these pages. I further suggest, however, that there is a reason for the less flexible posture of the prophetic tradition with regard to its various cannons. The simple reason is that the prophetic, theistic tradition has always been and is necessarily eschatological. This fact is not so easily rationalized, but it is perfectly evident historically. For there to be a partial vision with a global impact, it would have to successfully deconstruct or radically immanentize or psychologize the eschaton. By doing so, however, the vision either renders itself acosmic, which effectively leaves cosmology in the hands of the scientific materialists. This is exactly what the pantheists have been doing. But this sets us back to the Cartesian and gnostic vision of world divided between spirit and matter. The pantheists' can maintain their monism only by declaring matter to be a negative illusion, i.e. something opposing spirit. The very idea of Creation and Incarnation then become an anathema. At that point, any hope for a dialog with the theists runs aground.
The vision presented here purports to surmount this barrier by taking onboard pantheism's monism, universalism and immaterialism, while, at the same time, discarding the notion of an absolute or omnipotent deity. Does that bring me too far in the direction of pantheism for the theists to be able to follow. I believe not, but that remains, perhaps, the single biggest issue for the BPW vision. Theists fear letting go of their absolutism, because all they can see is a slippery slope into pantheism. Much of the challenge here is to show how that fear can be overcome; that the slope is not as slippery as most people think.
If that challenge can be met, then the BPW vision is on its way to something beyond just biblical proportions. However, its place in the pantheon of prophecy is, I suggest, best seen as being associated with the Second Coming. The next most logical association would be with the advent of the spirit of the truth as briefly described in John 16:12ff. This latter view was my original stance, but I now see that as being something of a spiritual cop-out!
Of course, it is not terribly unusual for people to have and harbor solitary cosmic visions. I submit, however, that a solitary prophetic vision borders on the oxymoronic. If the BPW vision wishes to avoid being an oxymoron, then it must have legs. In fact, it is my recently raised estimation of the suitability of the Mandelbrot set to serve as one of these 'legs' that brings me around to this recapitulation of the prophetic gambit. Indeed, I presently see the Mb as a necessary and sufficient pedagogical segue from matter to spirit. That puts the Mandelbrot out in front. Next would come the anthropic principle, and then I propose we take a leap to Srinivasa Ramanujan. As if that were not a big enough leap, our next and final touchstone may just be the Incarnation. Permit me now to outline this sequence of pedagogical steps, as a partial test of their suitability.
The Mandelbrot set has been covered extensively on the the last two pages. In the last couple of weeks, my informal demonstration of it to two small groups that had not been previously exposed to it indicate that, when presented in a suitable context, it can be a powerful visual stimulus toward rethinking the nature of mathematics, and, more importantly, about the possibility of emergence and holism in the physical world, from a non-Darwinian perspective.
The next logical step would be to raise the issue of anthropics, which has been frequently mentioned here, and which is extensively and cogently treated in a theistic context on other websites. With some additional work on linking the Mb with anthropics, there could be a significant pedagogical synergy.
If needed, there are plenty of other matters to raise, all which cast doubt on the enterprise of scientific reductionism. These could be readily added to suit the occasion. The primary issue to be raised, in this regard, is, of course, the mind-body problem, but, in the present context, I'm thinking that Srinivasa presents us with an excellent case study to this end. At the same time, Srini maybe our best segue to the ultimate issue of incarnation. I'm thinking very pragmatically here about future 'evangelical' possibilities. I have in mind informal presentations to small lay groups. The aim would be to achieve a maximum impact in a single sitting. That limits us to about two hours, which would only provide about half an hour to each of four major topics.
The point raised by Srinivasa is the issue of genius. It may well be that Srinivasa is the greatest known exemplar of this attribute. When taken in the context of the Mb and anthropics, his genius adds very significantly to the pedagogical synergy. These points have been already been treated here. If there is an intelligence behind anthropics, Srini demonstrates the astonishing degree to which the human psyche can attune itself to that cosmic, mathematical intelligence. This evidence favors theism over pantheism with regard to the cosmic intelligence. This also provides an opportunity to introduce the real possibility of immaterialism. I need to elaborate on this latter point. This will definitely be stretching our thirty minute window. The most difficult segment remains.
Is incarnation really necessary? Yes, and for many reasons. The main point is that all of us are incarnations, and by 'us', I am referring to creatures generally, but mainly to humans. Jesus may simply be seen as the primary exemplar. That there is divinity in all of us is not controversial except for a materialist. That Jesus could have a special and astonishing genius for performing his central role in a salvation economy is made more plausible by the special case of Srinivasa.
Besides the materialists, the main objections to the special divinity of Jesus come from Islam and Buddhism.
Many religionists and non-religionists object to the participation of divinity in what is ultimately such a violent act. Such folk would prefer a more remote, dignified, impassionate deity. How is this not a reversion to human sacrifice? Have we not transcended that need? I believe that this objection has been more than adequately answered by many very articulate theologians. We need only to outline these long standing arguments. The genius of Michelangelo's Pieta provides the best single response. I appreciate Mel Gibson's genius, but I give precedence to the greater universality of the Pieta.
Islam has a special objection to the issue of idolatry. It is not clear, however, that their objection is not mainly technical, and so is shared in the Protestant convention of the empty cross. I see only a matter of degree. Among Buddhists, only the purist practitioners of Zen Buddhism can object to the nearly universal notion of the Avatar. There are matters of degree here, but not of kind.
Here it is that I put forward the least orthodox aspect of my theology. This is simply a reworking of the Trinity: mother, son, spirit. In this context the son is the creative logos, and this brings us back to the Mandelbrot. The further point is that the creative logos maximally pours itself into the Incarnation. Thus does the notion of the Death of God, take on a real significance. In the apokatastasis, or universal resurrection, Jesus becomes the first of equals as we all participate in the body of Christ, and we complete our universal participation in the entire Creation, by maximally recreating God, keeping in mind that this temporal process, can occur only in the context of eternity. That sentence was a mouthful! Can we meet the two-hour deadline, without throwing out the Bambino?
The situation does not call for perfection. If we can simply enable folks to imagine an idealization of the generic presentation, we can reawaken the possibility and potency of a cosmic Evangel. That potential is our passion, not to coin a phrase. This process will certainly be a collective effort, BUT, if it is ever to take on a global dimension, the notion of a Second Coming is too thoroughly embedded in the prophetic tradition too allow for even the semblance of coyness. Ooops! Speaking of which, I have overlooked the eschaton! The idea of a Y2C/X2-event logically implies the eschaton. It should only take a very few minutes of additional hand-waving to bring the eschaton to the fore. Most of the groundwork will have been laid.
By putting it out in front, a large expository burden is placed on the Mandelbrot. If we put so many eggs in that one basket, we'll have to watch it carefully. Debunkers will likely see it as the weakest link. I can only hope that it will become their tar-baby. Come to think of it, the Mandelbrot looks like nothing if not a tar-baby!
What is left besides some embellishment and the location of a suitable flagpole? I was sufficiently lazy to hope to dispense with the pressing of the flesh, in lieu of pushing a few buttons. Road trip, anyone?
4:42 - Arrivederci, il Papa....
Have four legs, will travel: BPW with the Mandelbrot, Anthropics, Srini and Jesus. This is not the only viable configuration, but we can hope for the best, and know that the best will suffice. We are certainly not here to impose a Second Coming, but, gosh, what better vocation can there be? The view is that the earthly Christ is an office. Is that not the meaning of Anointment? The first was meant to be an easy act to follow. Let's not make it any more difficult on ourselves than necessary. One might then wonder how the returning Christ relates to the risen Christ. The biblical statement of the Second Coming is a coming down from heaven in glory. The popular view is to take that quite literally. That, however, is hardly in keeping with the divine minimalism in all things other than Creation itself. There is still the Prime Directive of non-interference, which, in this case, is minimal interference. God is not here to hit us over the head, no matter how much we might wish to see that bestowed on our brothers and sisters. The Eschaton is about the continuity of Spirit. We can let our ouroboric nature take care of itself. It might also be noted that the Jewish concept of the Messiah was always something much more mundane. Impatience is seldom a virtue.
The Second Coming is a process. But, it is a process that will be given a human face, ultimately because it is our process. It is of the people, by the people and for the people. If you know a better way, now is the time to speak up.
It just occurs to me that we might want to adjust the sequence. What about Mb:Srini::Anthropics:JC/X2? It might flow better. The Srini genius is a logical segue from the Mb to anthropics. That underscores the Pythagorean harmony of Creation, recapitulating the Mb, and the point that the anthro in anthropics is no accident. How could we have learned to count without our fingers?! Yes, this is a definite improvement. It points toward our implicit involvement in the UEM. It is we who are the link between spirit and matter, via the UEM. Therein lies much of our co-creative role. The Mb is mind from number. Srini is number from mind. How does matter come into the picture? We now have Ouroboros, MDX/Z, AZO/X/QRP & Mb:S::An:X. There is some mnemonical/archetypal integration ahead of us.
The two foci of matter in the above are R&J. We might then wonder about the role of elliptics, and, perhaps, dialectics. What is the deep and abiding dialog between matter and spirit? How does matter finally yield to spirit? Everything speaks to this issue, as does the Mb. With the Mb there are the mu-atoms whose proliferation is suggestive. There are the space time symmetries that make matter possible. There is the 2/3/4-fold symmetry of the mu-atoms. There is the ubiquitous paradox of the iota. We have a temporary covenant with matter. Matter is a frozen logic. Let us not forget e^i*pi. Do we need an analog of the big bang? The MG is also present, along with QED. On the other hand, in a truly monistic system, the specificity of matter might emerge gradually, right along with the psyches, memory, space and time. In dealing with the sun, I spoke of heliotropism. Might it have some special association with the matrix. Keep in mind that there is no such thing as bare or unqualified matter. The question in the previous paragraph needs to be reframed. The Mb might say something about the relation between Z and R in terms of their analogs of the bulbs and mu-atoms. Z/R should have something to say about mind/body. In going from Z to the mu-atoms, we go from the plenum to the space of the atoms and egos. That space is rather stringy, we might add. The bulbs on the positive cusp may relate to both Alpha and Omega. The apparent symmetry needs to be broken in the interpretation, with the X-bulb/spear serving as the pivot of the story. One is reminded of Hamlet's Mill. What is the meaning of the singularity of the cusp? Is that our big bang?
The Mb is a cosmic Rosetta stone or mathematical fossil that will stimulate us to reconsider our temporal interpretation of the physical fossils, and, hopefully, we will begin to see them in a supra-temporal light. It may also be that the Mb provides and/or indicates a link between mind and matter. It does demonstrate how an external pattern can supervene on an otherwise closed mechanical process. If the Mb cusp is meant to be an analog of the big bang, that would help to provide additional linkage between the physics and the metaphysics, but then we'll need to grasp its metaphysical import.
Please bear with me while I try this experiment in technology: The Second Coming.
This is the bare beginning of a power-point presentation. Forgive me, Lord.
Jack Sarfatti tells me that, with his iMac, he is unable to access p-pt file in its present 'mht' format. We'll need something more compatible. Here is the 'ppt' version of the above presentation, and here is a power point viewer from Microsoft. I don't know if this will help for an iMac. I may have to convert this to Adobe 'pdf' format. Here finally, for now, is the 'rft' version, lacking the ouroboric graphic. When the presentation is actually presentable, it will be at least several dozen 'slides'.
But there is a larger problem looming, now that I'm confronted with the ouroboros in all its serpentine glory. How am I to reconcile this animistic beast to theism? Funny how I have managed to dodge this bullet up to now. Is it back to the drawing boards? It's time for some heavy-duty rationalization.
I doubt that this beast is avoidable. It is also clearly reminiscent of the Taoist yin-yang symbol. It speaks to the Alpha and Omega, but also seems to be sliding into a cyclical/reincrantional view. The serpent is the symbol of the Devil in the Bible. It is also the symbol of healing as in apokatastasis. I am told by my Sufi guru, Bob Clark, that the primary and unique role that Islam assigns to Jesus is that of world healer.
It is odd then that this primal archetype seems to refer more to Jesus than to the Matrix, particularly in its logos-like pi and circularity, which is where we find X in the Mb. And we are just scraping the surface of the ultimate mystery that must underlie even the most coherent possible system of being. X supersedes Matrix, X emerges from Matrix. This is the profound paradox of eternal origination. There is an ultra dimension 'beyond space and time' (thank you, Jack), that eludes the dimensionality of our more mundane minds. This warns us not to take too literally any particular set of archetypes, leading us only to idolatry. Forewarned is fore-armed. That is the best I can do for now, folks.
I'm still working on The Second Coming: for all us dummies: (formats: PDF, MHT, PPT, RTF). I may be working on this for some time, yet. [a] The most up to date version will usually be the PDF version.