Best Possible World: Gateway to the Millennium and Eschaton

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A pressing issue is the time scale from Alpha to Omega. The most basic fact that idealism brings to cosmology is that the cosmic scale cannot transcend the bounds of the mind. The only way to maintain the scientific measure of the cosmos would be to invoke a cosmic mind quite distinct from created mind. This logical dichotomy of Creator and Creation is the dualism which deservedly brings the verdict of irrationality upon the prophetic tradition. To restore reason is to posit just one mind of which our egos are a temporarily fragmented reflection. That nature appears to break the bounds of this mutual sentience, can only be an appearance. But by the same token, it is nature which allows God to prolong Creation by postponing her final revelation. The self-revealing God is the self-concealing God, and nature is just the instrument of the latter.
To put it quite simply: it is a given that we will eventually see through nature. The scale of Creation is measured by the opacity or apparent seamlessness of nature. That nature is seamless to us is largely due to its being projected by us. The illusory quality of nature can never be empirically demonstrated outside of specific magical episodes. The Creator comes to light generally, only by the power of empathic reflection. These pages are devoted to that end.
If we could look back toward the Alpha we would see time curling up upon itself, not unlike the curling up of the extra dimensions in the higher dimensional models of physics. We may expect a similar occurrence as we move toward the Omega.

This Omega business is not going to be easy. This is the whole tamale when it comes to an idealist cosmology. To better understand the Alpha and Omega, we need to know how they relate to the present. And what is the present?

The image of the present that is the main competitor to the religious views is existentialism. This is the image of detached egos lost in space, as if we had been thrown into the world. I can agree with this up to a point. One point of agreement is the implicit view that once we were attached to something. We have not always just been floating in space. The existentialist might contend that this attachment is simply referring to our prenatal condition. But I would suggest that, even for the existentialist, something more metaphysical is implied. After all, the theistic and atheistic versions of existentialism remain close cousins. It is hard to understand one without the other.
The idea of being 'thrown' into the world implies that our parturition from wherever was haphazard. Lately, as we know, this view has been challenged by the Anthropic Principle. We may have been ejected from something, but there had to have been some care in the process, or we surely would not have survived. It is not as if we were spawned into the abyss. The more we learn about the world, the more it appears as a receptacle. And what can we say about the nature of this receptacle?

From the point of view of teleology and eschatology we must depart from the materialist view that our receptacle is, relative to our own existence, permanent. The best we could manage with a permanent world would be an arbitrary attachment and then detachment between it and anything non-material. This is the incoherence of dualism.

Our material world then must be impermanent, and its existence must be closely correlated with the existence of mind. In order for there to be a correlation between mind and matter, there must be an 'evolution' from one to the other. One must be spun-off from the other. For the immaterialist, matter must be spun-off from the mind. This is directly contrary, I readily admit, to almost every appearance. The appearance of a material evolution is the one major obstacle to idealism. It is formidable, yes, but is it insurmountable? That depends on our motivation.
I claim that surmounting materialism is the only way to go. We have sojourned nearly as far into materialism as is logically and spiritually possible. Progress, measured in almost any conceivable manner, would grind to a halt or worse, if we do not keep exploring and pushing on the boundaries of our world. As the material aspect of our existence has taken center stage, the mental and spiritual dimensions of our world have received negligible systematic, rational attention. The only way forward now is to construct an immaterialist cosmology, as a counterweight to materialism. There is nothing else to do now intellectually in order to transcend the increasingly rigid strictures of materialism as well as the decreasing marginal returns of the collective effort we have to put into it. The sense of coming to a material dead-end may still be subliminal for most of us, but it is pervasive. We have intellectually neglected the non-material dimensions for so long that we hardly know where or how to start. We will fumble along in the dark for a while longer, but then the light will begin to shine.
It is time to focus our powers of reason on an immaterial understanding of the world. We don't have to look further than Darwin to see where our work has been cut out for us. How may we transcend Darwin? We simply have to focus on the immaterialist logic behind the materialist facade of Darwinian evolution. Why, in heavens name, would there be this apparently egregious contradiction to immaterialism? The simple answer is that I, and perhaps you as well, can think of no better design plan for this world. Any other plan would be egregiously arbitrary and incoherent. This is the greatest irony we will likely have to face. Materialism is indispensable for achieving a cosmic coherence.
Let me put this another way. It is not logically or coherently possible to have just a little bit of materialism. Clearly materialism has its benefits, just a a system of existence. For the sake of argument, let us grant that in the BPW the costs of materialism can be offset by its benefits.
And yet another way: if materialism is to be more than a sideshow, it will be virtually all-encompassing, at least from a phenomenological perspective. Another caveat of the BPW is that it be taken seriously. If it is going to entail materialism, it will have to do so in a serious fashion. The material aspect of the BPW must not be perceived as superficial or as an appendix. There must be a thoroughgoing adaptation between the material and mental aspects of the world. Certainly the phenomenology of Darwinian evolution fits this bill. Is there any other means to this end? We are probably not in a position to be able to conceive of such an alternative, and, lacking such, we must explore the norms, aesthetics and functionality of materializing the mind in an adaptive regimen under the guise of Darwinism. Anything short of this would have to be considered a feeble attempt at creation and materialization.
And that brings up another point. I guess what I am struggling to say in the above paragraphs is that creation and materialization are practically synonymous. If God is to earn her stripes as a Creator, she will have to take several pages from the book of Darwin. Exactly how she sets about doing that, remains to be understood, but I have made a few stabs hereabouts at figuring out the 'mechanics' of materialization.
But why not, then, just crib all of Darwin? Why be cute about it? Why not just let the Big Bang rip, and then sit back and enjoy the show?

The Big Bang scenario implies a dualism which puts God on the spot and correspondingly would leave the creatures in a much more passive role. Following Darwin would place the onus directly on the Creator to work out the connections between mind and matter. Evolution on each planet would have to be directed, and still there is no guarantee that there would be the necessary mutuality between the material and immaterial evolutions. Putting them together would be arbitrary and after the fact. This is the incoherence of deism.

With theistic idealism, creation is maximally participatory. A direct realism of perception is built into the more distributed and participatory Creation. Having an immaterial participatory Alpha, greatly facilitates the logistics of the Omega, which then has considerable symmetry with the Alpha.
The necessary materialization aspect of Creation is then worked out by means of the Big Six, in conjunction with the related cycles. Our task on this page is to use the built-in symmetry to get a handle on the Omega. Now we can speak of a dematerialization.
Of fundamental importance for Creation is for there to be a graceful exit. For Creation to be meaningful, there must be a purpose, a teleology, a telos. The telos must be an integral part of the complete process. Completeness and wholeness are thereby ensured. An endless Creation is incomplete. Such incoherence does not recommend itself to the concept of the BPW. In large measure, the Omega must reciprocate the Alpha.

Spinning down the world is a large part of what the Millennium is about. The cyclic processes are closely associated with our materialization of the world. We have spun up the world into its present atomistic state. This is a non-analytic notion at this point, but one that needs pursuit. To complete the cosmic cycle we need to relax on the sub-cycles. OK, there is the picture of the spinning figure skater. Our ego consciousness is like the twirling figure with her arms pressed to her sides. When she extends her arms back out the spinning is reabsorbed into the cosmic cycle or cosmic consciousness. We may assume there is an energy and information increase in this reciprocal process.

Herein lies a conundrum. The faster the microcosm spins, the more linear becomes its space-time manifold. Spin down the microcosm and the space-time frame will curl up. Does this make sense? Don't be too analytical about it: use peripheral vision.
I should be able to give examples, but I suspect that there is a lot of subtlety and even cosmic censorship in play here. If this process were too obvious we would be jumping all over it and probably throwing it off its track. We will be jumping on it only when the time is right. Nascent trends and processes have to be protected. This site would be no exception. Camouflage is in fashion as we stealthily and steadily approach the Millennium and Y2C. Its OK to rock the boat as long as you don't upset the passengers. Hiding things in plain sight is a proven tactic.
After considering the cycles, there is the Big Six and its undoing. We transcend the cycles and their common points of reference. From the perspective of the Omega we have the Big Three: Sun, atoms and reproduction. The solar cycle governs all cycles short of the cosmic one. The life cycle is the microcosm of the A&O cycle. Atoms provide a common anchor for most of these cycles.
[At this point I evidently diverge from the topic of Omega, to be continued later.]
It may be, however, that the Monster Group does play a role in the 'decycling' of the cosmos, and this accounts for some of the subtlety of the process. We may have a situation reminiscent of the ancient concern with squaring the circle. The problem now is the 'rationalization' of mathematics, a feat in which the MG is likely to play a significant role. In the process we revisit the syzygy of e & pi. It was that coincidence that lured us into cycles and then to the Big Six. Come to think of it, that coincidence, when properly understood, may turn out satisfy most of our ancient concerns about the squaring of the circle. The ancient fear of the Apeiron was, I suggest, a premonition of our fall into the incoherence of materialism. In the Millennium we struggle back to coherence. The starting point for that struggle may well be something as subtle as the rationalization of e & pi. Evidently we will need to study the j-function which is related to the 'near integers' and the Monster, which latter must, in turn, play a role in Anthropics. It is turning out to be a small world out there in Mathland. We will tame it on the way to the Omega.
What I may be struggling to say here is that the observer principle (in this context) must be extended from physics to mathematics. There is a three way reciprocity between physics, math and reason. This is a theistic version of mathematical constructivism. This also figures in the rational 'deconstruction' that we may associate with the Omega. Cosmos coheres from Chaos. Mathematics is something like the fossil record of this evolution of coherence. As we reflect upon the mathematical record of the cosmic coherence, we will achieve coherence to the Nth power. Our inner coherence will subsume the external coherence going into the Omega. Just don't ask me to draw a picture of it.


Some references for the rationalization of mathematics:
* Some Contemporary Problems with Origins in the Jugendtraum -- Robert P Langlands

* Where stands functoriality today? -- Robert P Langlands

* Langlands program -- Wikipedia

* Fermat's Last Theorem After 356 Years -- Wm. F. Hammond

* Fermat's Last Theorem -- Charles Daney

* BOOK REVIEW -- KA Ribet (Rational points on elliptic curves, by Joseph H. Silverman and John T. Tate.)

* Ideal class group -- Wikipedia

* The Hilbert problems 1900-2000 -- Jeremy Gray

* e^{pi*sqrt(163)} -- Roy Williams

* On the History of Hilbert's Twelfth Problem -- Norbert Schappacher

* The Riemann Hypothesis -- J. Brian Conrey (RH <-> Langlands Prog. p.8)

* The Riemann Hypothesis -- Matthew Watkins

* WWN notes on the Riemann Hypothesis


* John Baez's Stuff

Tony Smith's Home Web Site

* Surprising connections between prime numbers and physics -- Matthew Watkins

* P-adic numbers, Topological Geometrodynamics, TGD. -- Matti Pitkanen

And some general math bookmarks for future reference:
* Arithmetic Algebraic Geometry network

* Mathematics ArXiv

* Math World

* Number Theory Web

* AIM Workshop Website Network

* Mathematical Topics

* The Internet Mathematics Library

* The Mathematical Atlas

* American Mathematical Society

* The MacTutor History of Mathematics archive

* Clay Mathematics Institute

* Mathematics -- Open Directory Project

After reviewing the above sites, I would be hard pressed to provide persuasive evidence for the increasing coherence of mathematics. I am not sure if this is the fault of mathematics or of mathematicians. There is a natural tendency for professionals to carve out niches for themselves, and it is evident that mathematicians are no exception. Good fences make good neighbors, as a poet once said. The bulk of our Millennial task will be the removal of fences. We need only find the proper motivation.
Ferdinand Toennies (1855-1936) distinguished Gemeinschaft (community) from Gesellschaft (purposive, professional association). Owen Barfield provides a third and future category of human existence: 'final participation,' a must see. Egoism or existentialism is the incoherent compromise between materialism and idealism. This is what passes for rationalism in this dark age between the Alpha and the Omega. Our least stressful means to transcend ego consciousness would have us rely strongly on our intellectual capacity to see the wholeness of the world and our proper function as its co-creators. The spirit would then follow up and subsume the intellect.
The intellectual path to a holistic cosmology will have to include mathematics in a significant manner, and after the fashion of Plato and Pythagoras. The coherence of physics has come about through its mathematicization. We now need to rationalize mathematics, but in a theocentric rather than egocentric fashion. The existence of the Monster Group should motivate us to look beyond our puny egos to a cosmic genius.
I still seek that elusive observer principle (and here and here). Godel's self-reference program is part of that picture. His constructions remain controversial.

I'm looking at Matthew Watkins 'Prime evolution notes.' He raises the intriguing possibility that the equal spacing of the integers derives from the exact placement of the primes, popular opinion notwithstanding. There is at least a mutual evolution between primes and integers. I would like to know how this might relate to the more obviously necessary evolution of the Monster (and here, here and here). An observer principle must be at work.

Why this is the case, became one of the key puzzles and led to a number of arguments with a common gist: evolution is present already at the elementary particle level and the primes allowed by the p-adic length scale hypothesis are the fittest ones.

Savant for a Day: this story appears in this weekend's New York Times Magazine. It describes the possible temporary benefits of transcranial magnetic stimulation, featuring Allan Snyder's work. If the results hold up under continued scrutiny, it does not bode well either for Darwinism or mechanism. Being able to squeeze more performance out of the brain with such crude interference just does not fit our material conception of the world. There will hand waving attempts to make it so, but some of us will still have to chuckle.

Here is a quote from J. Brian Conrey, The Riemann Hypothesis (3/2003):
There is a growing body of evidence that there is a conspiracy among L-functions-a conspiracy which is preventing us from solving RH! The first clue that zeta- and L-functions even know about each other appears perhaps in works of Deuring and Heilbronn in their study of one of the most intriguing problems in all of mathematics: Gauss’s class number problem. [...] We begin to suspect that the battle for RH will not be won without getting to the bottom of this conspiracy.
L-functions provide a connection between FLT and RH: as described here and here.
Goldston and Yildirim's 'proof' concerning the distribution of primes as indexed on Google....

Status/hiatus report:

The re-enchantment of mathematics is the most likely trigger for the Millennium, IMO. I may not have stated it quite as succinctly, but it is a bush that I have been beating around since last year. I pick math over physics or psychology. Those would be the next most likely sources of a paradigm shift. Mathematics, however, remains the soft underbelly of materialism.
Immaterialism will have to hit materialism where it hurts and where it is vulnerable. Psychology is peripheral to fortress materialism. Psychology has never been considered scientific by 'real' scientists. They do not consider it to be their concern. Physics is the key to physicalism, obviously. The cutting edge of reductionistic physics is high energy physics, but it has been running out of money, and energy. The bastion of reductionism has thus shifted, of necessity, from the experimental atom smashers to the pencil and paper crowd of theoretical or mathematical physicists. The crunching of the Riemann Hypothesis has become of greater concern to hard core science than has the smashing of quarks, in my political/psychological estimation, at least.
Let's look at Riemann, or at least at the primes. If materialism is correct, the prime numbers are random. So take a look here (and here, here and here (here!) (explanation?), and recall this, etc.) [Ulam Spiral]. To what extent can patterns such as these be deconstructed or reduced? This may be the biggest skeleton in the materialist closet. Will such pictures trigger the Millennium? Certainly not by themselves.
The space telescope and supercomputers reveal cosmological and numerical patterns, respectively, that strain our modern credulity in reductive explanation. So does biology. But it is in the mathematical realm that our intellectual attention can be most readily concentrated and guided. We would eventually like to know if mathematics is a science or an art.

I seem to be hearing contradictory statements about the primes.

There is a general agreement that there is a deep connection between the distribution of the Riemann zeroes and the primes. It is also agreed that the distribution of the zeroes can be fully explained or modeled by the distribution of the eigenvalues of random hermitian matrices. Yet we have the phenomenon of the 'jumping champions', Odlyzko, et al, 1997. The 'explanation' for this jumping phenomenon turns out to be heuristics based on a conjecture.
Quoting from Odlyzko:
Conjecture 1. The jumping champions are 4 and the primorials 2, 6, 30, 210, 2310,....
[...] There seems to be little hope of making any progress towards a proof of Conjecture 1 without assuming at least a quantitative form of the k-tuple conjecture. However, as we will show, even assuming the strongest form of that conjecture that seems reasonable in view of our knowledge of prime numbers, we are still left with formidable obstacles that prevent us from obtaining a complete proof of Conjecture 1.
We have certainly come a long way, thanks to Godel et al., from Hilbert's strictures on decidibility at the turn of the last century! But my issue here is the compatibility of the Odlyzko conjecture and the alleged randomness of the primes. I have yet to locate a discussion of this question.
Check out Lehmer's Phenomenon, and then: An improved bound for the de Bruijn-Newman constant, A. M. Odlyzko, Numerical Algorithms, 25 (2000). Andy is hot on the trail of something, and this is just his hobby:
The lower bounds support the conjecture of Newman that L >= 0. This conjecture says that if the Riemann Hypothesis is true, it is barely true, in that even small perturbations to the zeta function lead to counterexamples.
[7/22 -- here is another reference.]
Thoughts on the Riemann Hypothesis -- Gregory J. Chaitin, IBM Research (2003).
Of the authors of the above four books on the RH, the one who takes Gödel most seriously is du Sautoy, who has an entire chapter on Gödel and Turing in his book. In that chapter on p. 181, du Sautoy raises the issue of whether the RH might require new axioms. On p. 182 he quotes Gödel,* who specifically mentions that this might be the case for the RH. And on p. 202 of that chapter du Sautoy points out that if the RH is undecidable this implies that it's true, because if the RH were false it would be easy to confirm that a particular zero of the zeta function is in the wrong place.
[...] The traditional view held by most mathematicians is that these two assertions, P /= NP and the RH, cannot be taken as new axioms, and cannot require new axioms, we simply must work much harder to prove them. According to the received view, we're not clever enough, we haven't come up with the right approach yet. This is very much the current consensus. However this majority view completely ignores* the incompleteness phenomenon discovered by Gödel, by Turing, and extended by my own work on information-theoretic incompleteness. What if there is no proof?
I am certainly not a randomness freak like Gregory, but I do agree that the public attention being focused on the RH will force mathematicians to depart from their business as usual and deal with the more foundational and philosophical issues raised by the uncanny precariousness of the RH. It has the character of a syzygy. What does this mathematical fragility say to us? Is this another manifestation of an 'invisible hand' at work? What is the nature of the conspiracy that is present? Perhaps the new thinking is already out there: we need only locate it. If not we must anticipate it.

What is the significance of the RH? So what if it fails?

The RH is not just about the randomness of the primes. Clearly they are not. The Ulam spiral and the de Bruijn constant testify to structure that is hidden between zeta and the primes.
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