None of these many aspects of the iota seem to speak directly to the observer principle, beyond what is contained in the uncertainty principle. It may ultimately come back to the label of 'imaginary' that was fortuitously placed on the iota. A Pythagorean may well ague that this designation was serendipitous. When, in 1572, Rafael Bombelli introduced complex numbers (not to mention the minus sign as well!) to the world, mathematics crossed its Rubicon. That single leap from the real to the 'imaginary' on the part of an entire profession remains historically unprecedented. One may argue that real numbers are an MIR, mind independent reality, but the sqrt (1)? Yet, does not the above quantum anticommutator place the iota squarely back into the MIR? Are not atoms an MIR? Well, not according to the 'wonderful' folks of Copenhagen. The essential role of the iota in the atom, underscores the 'mystical' Copenhagen Interpretation of the quantum. Most physicists quickly become jaded on the wonder of the quantum. Theirs is not to reason why!
I would argue with the Pythagoreans that the imaginary numbers ought really to convince us that all of mathematics must exist in a Platonic realm. The Platonists, however, were dualists concerning the corruption of the mundane world. Not so the true Pythagoreans and myself. We are monistically inclined toward the singular BPW. Those same Pythagoreans, as we have seen, were reluctant to embrace the irrational, imaginary and transcendental within 'modern' mathematics. These latter artifacts imply a personal touch. Finding them, however, fully embedded in mundane physics should instead provoke us to the realization that great minds think alike. The cosmic mind and the human mind must be mutually reflective, and this does not apply just to Srinivasa I & II. All of us are invited to bask in the greater glory. Furthermore, the BPW does not end with mathematics, fantastic and transcendental though it is. That is just the beginning of the story. That is just our aperitif.
Did God and we merely discover the imaginary iota? I suggest not. It was the dynamic resonance of life and creation that spun off e, i & pi. With the materialization of e, i & pi in the observer based physical resonance of creation, the fate of the Monster was sealed. The Monster Group is indeed the tailend of the Big Six. In this case, it is the five that wag the sixth, and not the other way. There would be no monster without the vital syzygys or resonances of e, i & pi. There would be no e, i & pi outside of the cosmic creative intelligence. We are simply taking mathematical constructivism or intuitionism to its logical cosmic end. It is there that these many philosophies converge. Let us not tarry in the hinterland. The Alpha and Omega beckon.
[9/16]
Dan struggles. See Dan struggle.
Don't we all love the constant juxtaposition of idiocy and sapience in our lives. Its all a part of the aesthetics.
One might think that, like Scheherazade, I filibuster the eschaton. That may be, but it is not my conscious intent.
What I struggle with is the juxtaposition of stark simplicity and utter complexity, in math as everywhere. In this holographic world, math is a microcosm. We might think that with math, we are beginning to see the limits of complexity. That, at least, is one of my hypotheses.
Is complexity limited in the BPW? Here are some reasons. Complexity is not an end in itself. In the BPW, everything serves the greatest good which is love. Love is the one thing of which there might never be enough. For everything else there is an optimum degree. Complexity is no exception. Creation cannot be more complex than what can ultimately be comprehended by the creatures. Every creature must be able to find its way back to the Creator. This is what coherence is about. The salvational economy hinges, of course, upon us sinners. Salvation is mainly our show. We set the pace for nature. Coherence and love are our only guides. Srinivasa II or Y2C are about our recall of coherence.
In our sojourn into complexity, we have forgotten about the coherence. We just need to remind ourselves that coherence is possible, that complexity is necessarily limited by the salvation economy. We can only sojourn half way into these woods. After that we are on our way home.
With e, i & pi we see the juxtaposition of simplicity and complexity. Like three children, separately they are little angels, but together they can create untold mischief, up to and including the Monster. Their various syzygys or couplings are the path to the monster, but they are also our clues to its taming, to recasting its complexity into the service of love.
Unlike for e, there are a plethora of formulas for pi. This probably has to do with its greater complexity or irrationality measure. Yes, perhaps, I misspoke. Pi has been able to stir up a potload of trouble just on its own. e & i are responsible for recruiting pi back into the service of the simple cycle, as in e^i*pi = 1. It is almost a right of passage into the mathematics club to come up with a new and clever formula for pi. New discoveries in math frequently lead to more such possibilities. e is easily the most ubiquitous, utilitarian constant, but it is relatively forthright in its appearances. Pi tends to rely more on stealth and cleverness in its frequent cameos. e is definitely blue collar, pi is strictly tophat. But put them together and add just an iota, it is a whole new ballgame. The jfunction and its modular cousins are quickly recruited to the cause.
The Monster Group, by its definition, defines the limits of quantitative or 'classical' mathematical complexity. With the syzygys we are looking ahead to a qualitative, organic, entangled or quantumlike complexity. In a similar fashion, the genome defines the limits of quantitative biological complexity. The proteome looks ahead to a qualitative complexity. This shift from quantitative to qualitative complexity portends our shift from a materialist to an immaterialist understanding of the world. It signals our return to coherence. Coherence is how we finally tame complexity. In order to resolve the Riemann Hypothesis, I believe that we will have to come to grips with this qualitative side of math.
What will the Pythagoreans make of this shift from quantitative to qualitative complexity? Will they still be able to say that God is a mathematician? We may have to redefine what constitutes mathematics. In the last century, mathematics paralleled philosophy in its shift from the analytical to the holistic. As far back as 1931, Godel's incompleteness theorem dashed the hopes for a purely axiomatic or algorithmic program for math, even before the computer came on the scene. Mathematician could not be synonymous with computer. But now, with this new understanding of the qualitative nature of complexity, mathematics is being removed from its pedestal or intellectual compartment. The role of conjecture and intuition will have to expand to be more in line with that of other disciplines. What this indicates is that mathematical intelligence cannot exist apart from a general or natural intelligence. For instance, the aesthetic correspondences between music and math will have to be taken more seriously.
What I am pointing to is that, whatever else cosmic intelligence might be, it cannot be considered to be strictly impersonal. We will have to take more seriously the alleged correspondences between cosmic and microcosmic intelligence. To be more specific, the shift to qualitative, coherent complexity is a shift not just to immaterialism, but also toward personalism rather than to the impersonalism of the mystics and materialists. In other words, the coherence of the BPW is necessarily of, by and for persons.
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Topical Index
8/8/03
Symmetry
[...]
What immortal hand or eye
Could frame thy fearful symmetry?
 Wm Blake (late 1700s)
In my initial foray into immaterialism I postulated a chaotic primordial state: everything that could happen, would happen without benefit of time or place. Of late, I have turned more toward a primal symmetry.
The symmetry is totipotent. Actuality is realized in the breaking of the symmetry. The breaking could be spontaneous; however, an observable coherence would more likely be selfsustaining, and thus be the dominant process. That this coherence would include an 'aesthetic' dimension would only enhance its observability and so its selfperpetuation. That perception/conception is proactive in all processes has to be a given for any fully relational system.
And why couldn't we have left wellenough (Nirvana?) alone  end of story? Only a fool would be so naive as to feel tempted by such a question, so just give me time.
It is, of course, impossible for us to conceive of pretemporal or multitemporal 'processes,' but, hey, what's a body to do? And, besides, I just work here.
'Early on,' numbers are entrained in the symmetry breaking. Numbers are a significant product of the process. The prime break might be abstracted as {0,1}, with all else contained in the [0,1] interval. Is this not the A & O? Conceivability implies a prime persona, even manifesting as a 'prime mover.' The splitting persona (my poor head!) arrays itself into various configurations, and the resultant relational networks (in terms of small and not so small group dynamics) are the source of all logically subsequent mathematical physics. Such cosmic numerology is the force underlying our Pythagorean world. And if primal symmetry breaking is a ripoff of the Big Bang, well, our hats off to our physical cosmology colleagues. Cosmogony makes for strange bedfellows. Or was it the other way around?
[9/24]
'Originally', psychology, math and physics are virtually indistinguishable. We are now witness to their separate appearing niches, although our continued probing into their foundations provides ample evidence for their primal unity.
Primal symmetry breaking may be viewed as asymmetric cloning or partial mirroring. I can't really define the 'mirror' beyond a general selfreflexiveness of the prime unity, tantamount to mentation. The symmetry breaking must be selfgenerated, there being no externality to begin with. We are not talking dialectics here, either. At best, this process might be seen as a reverse dialectic. Does this imply that the Omega would be a forward dialectic? Well, OK, if that would keep our Marxist colleagues pacified.
Clonings can give rise to cyclical network dynamics. There is a reproduction cycle, which may be short on metabolism. Perhaps numbers could serve as protoatoms in a primal metabolic scheme. Atoms, cells and numbers might be indistinguishable in our primordial alphabet soup. They would provide a common currency. More accurately, they would be the necessary product of a relational, circulational network that requires lowest common denominations. Does this imply an economy? Heaven forbid? Problems of conservation and memory arise, but from physics we know that conservation and symmetry go handinhand. There must be countervailing trends of increasing and decreasing symmetry. The '1' of the primal unity is somehow replaced by the '0' or symmetric void of the spacetime background. This is surely a trick: like pulling a hat out of a rabbit. Projective geometry and spinnets might come into play, not to mention holography. Does anyone else feel like there are a few too many balls in the air at this point? A lot is up for grabs in our brave new world.
While all of this is going on, we must not neglect the A/O split, giving rise to our experience of a linear history. It is the sum over relational paths leading from the A to O. Each person represents a partial trajectory. Together we manage to optimize, with quantumlike constructive and destructive interference, the possibilities of our collective trajectory. Interpersonal dream work could be a significant part of this dynamic.
You may have noticed that while carrying on about Creation, I have had little to say about the Creator. My hunch is that our BPW Creator, while being a maximalist wrt Creation, is a selfminimizer. Besides, we are the resurrection of the primal unified persona. No point in getting in our way or unnecessarily interfering in what is a fairly 'natural' salvation economy. It happens even, or especially, while we sleep.
What I seem to be struggling for now is a sense of the creative logos. Yes, we may wish to know, how did the word become flesh. The new testament speaks of a preexistent logos, sometimes identified with sophia or the christ. The logos mediates creation. This is an odd theistic admission, one might think, but still commensurate with a trinitarian scheme. Am I then to surmise that our friendly Monster was indeed coexistent with the creator, and later to be identified with Jesus? I'm not real sure we want to go there. That is just what I have been trying to avoid.
Rather, the logos must refer to a 'protologic' where word and number could be identified. Notice that with words we are still in the realm of indivisibility. Atoms, or literally particles, are logical remnants of the primordial unity. As such do they carry their essential holographic charge. By such do they participate in the telos. The logos mediates both the alpha and the omega. It would indeed carry a salvific charge and so be identifiable with the charism. How then could we distinguish the second and third members: charism (christ?) and spirit? This may have something to do with the bios, specially linked to #2. Quantum entanglement is just the very most superficial aspect of the teleological or even eschatological charism. The quantum mystics have a point, but they have neither the logos nor the eschaton.
Does any of this help us to pin down the logos? The logos may be the closest we come to an external irritant provoking the primal break: the seed for the pearl that is creation. It is the key to the A&O. It would be the essence of cosmic mystery, partaking of the mystery of the cross. Speaking of crosses, we shift to syzygys and the mysterious couplings of eπ all part of the warp and woof of creation.
There are some in the wisdom tradition who identify the logos or creative spark with the overflow of God's love, leading to creation. In such manner we may avoid externality, but how far can we get with the logic of love?
[9/25]
Words are the prototypical exemplars of the logos. I wish to extend that designation to various other significant entities. In the interest of continuity it would be worthwhile to identify the logos as the source of the Big Six. More generally it is the source of the differentiation of the totality. In that sense it may be identified with Spencer Brown's 'mark of distinction.' Note that I have previously identified the logos with the Zimzum and the syzygy. The logos is rapidly accumulating baggage. We'll have to sort things out a bit.
Of most immediate concern is how mathematical physics may have emerged out of the operation of the logos. This, of course, is the primary point of contact between the logos and the physical or material world: the Pythagorean imperative. The important point is that the operation of the logos must be reversible. The symmetry breaking can be restored, but only after the logos has taken us to the limit of atomization and analysis. The ultimate reversal probably also invokes the third member of the trinity. I am tempted now to identify the third person with the charism of philoSophia. Philosophy was intended to be the flipside of analysis. That philosophy became identified with analysis in the previous century is one of the profound ironies of history. The dramatic turn by which philosophy regains its true identity would signal the advent noted in John 16:12&ff. It is part of the Aquarium protocol that this first advent be identified with the second, sometimes designated here as Y2C. This would be our own little syzygy: logos meets sophia.
The logos is not a dead letter. It is not mere logic chopping. It is the proactive, vital process of creative distinction. It is the only way in which the totality may circulate, recycle itself through a total reflexivity. We are the pivots of that reflection, not the passive mirrors. Astronomers now deploy activearray mirrors: that's us when you add in quantumlike observer effects.
It is a point of fact that mathematics' primary purchase on the physical is mediated at the quantum level. This is where symmetry is given a free reign. The governing structure here is just the e^i*pi = 1 coincidence, or perhaps the numerical mother or seed of all (physical) a/symmetries. When we carve out e&pi, we are carving out a very significant part of the logos. This is a probe into its operation. This little syzygy, as previously noted, captures (or even generates) much of the mathematical corpus through its various ramifications. It is also implicated as a logical source of the observer effect.
Clearly e&pi is no accident. Its reflexivities are crucial to the whole shebang. If e & pi didn't already exist, God would have had to create them, or did she? Therein lies the secret of the logos, or even of the trinity, for heaven's sake.
Am I being too farfetched here? Yes and no, but I'm not finished. One does not have to be a mystic to see some analogies. Pi stands for the totality or matrix, 'e' for the ramifying logos, and 'i' for the charism of the elusive spirit that ties everything back together. Is this 'analogos' purely fortuitous? Or is it the necessary projection of the trinity onto the realm of pure quantity? But it is just our numerological contention that there is no such thing as pure quantity. Quantity and quality are ultimately inseparable. We are trying to see how to realign and reunite them, as a significant part of the new philoSophia. This is also along the line of taming the Monster.
Quality conceives its own reflection in quantity. This is just the Pythagorean mystique. This is mathematical intuitionism raised to a new level. Quantity must be born out of quality, and we are beginning to see how. The numerical syzygys are the fossils of this birthing or evolutionary process, pace Darwin.
Let's go back a third time to the apparent jumpingoff point for this present excursion: this time for the OM, completing the cycle, as it were. In the primal potency all things exist in a virtual state. The primal syzygy is the circulating resonance, often manifested as the OM. If we project this resonance into the virtual realm of quantity, the static duality of e & pi are set into motion by the essential ambiguity of the iota that now connects them. Which came first: the OM or the e^i*pi? The point, rather, is that they are symbiotic. Reification in this case is a bootstrap. The OM is the quality of motion 'before' the quantity of time. The OM is the seed of the Alpha & Omega 'cycle' whose asymmetry manifests the historical linear time of our Metanarrative. This logos is the logical source of physics. The 'numerological' or Pythagorean aspect of it was primal.
[9/26]
I need to be patient here. If this e&pi business has any merit we will need to extract as much information from it as possible. It could be our best handle on a very obscure dynamics.
The above distinction between quality and quantity is facile. It is just that distinction that I am trying to understand. I am trying to understand or justify Matthew Watkins notion of an evolving number system. An organic, evolving numerical system may actually not be antiPythagorean, but it is very unPlatonic. That numbers constitute a mind independent reality (MIR) is deeply ingrained, but it becomes a primary obstacle for monism.
There is not, then, simply a projection from quality onto quantity. It should be more like an extrusion of quantity from quality. This extrusion has something to do with symmetry, and it must go far beyond mere enumeration.
Two candidates for the ursymmetry are the reflective and the cyclic. The former provides a basis only for enumeration. It is the cyclic symmetry that requires attention. Given a relational network of virtual mutually reflective psyches, there will be many possible circuits.... Sorry, but this still is not getting to the crux of the problem. The observer principle must be included explicitly. Now the observer is only implicit as in providing the (mental) basis of the relational network.
In quantum theory the observer is covered by the projection postulate, or by the collapse of the wave function. Looking back again, note the role of the octonions. Hold on while I take another look.
With reflective symmetry, I was using the mirror as a simile for consciousness, but, in fact, mirrors imply the prior existence of Euclidean space, an assumption which hardly conforms with immaterialism. Closer to our needs and assumptions is projective space. It probably is still too closely related to Euclid, but it is a step in the right direction.
[9/27]
It's time to toss a few more ideas into the pot, stirring vigorously. The strategy seems to be to work both ends, quantity v. quality, against coherence in the middle.
An 'early' state of creation is a growing, neurally networked, psychic pantheon. It needs to be shaped into a lattice and then into Newtonian space, along with bodies and their reproductive cycles, a la A&O.
We need a sequential circuit of psyches, a la the zodiac. This latter is just the metanarrative of the A&O written in the sky. This is the original reproducing cycle, somehow resonating and entraining the rest of the neural net. This is the big Om. In 2D it would likely start with the circle of six, going to the 12 'pack' in 3D.
In going from the finite lattice to infinite space we progress through the 17 quasiexceptional space groups up to the final jumpoff point at the sporadic monster. In the process we set up, evolve, the primes and integers by fixing 'e' and pi out of fractional dimensions of space and time(s). Transcendental pi determines translational space. Minimally transcendental 'e' determines directional time. Also, in passing from phi (1.618...) (Fibonacci's rabbit sequence) to 'e' (2.718...) we pass from lattice time to continuous time. (e/phi = 1.67999005... (= 2*3*7/5*5) for what it's worth.)
There is your basic dog's dinner, all I need now is an industrial strength blender. Where are Black&Decker when we need them? Just about a halfmile up Goucher Blvd, if they haven't moved to Bermuda.
OK. phi : e = x : pi > x = 1.870006... (= 11*17/(2*5)^2). In other words: 3*7*11*17/2*5^4 = 3.1416. Then what? Somebody wants to square the circle via Fibonacci. A strange game here.
9/28
If any meaning may be attached to this further coincidence relating pi to 'e' and phi, it indicates a deeper connection between circles and exponentials. We should have already known this from our 'mother' of syzygys: e^i*pi = 1; a fact which we have yet to understand, but of which there are many reminders. We found this reflected in the 'Ramanujan' constant, e^pi*sqrt163, which pointed to a connection between the largest finite group, MG, and the largest uniquely factorizable algebraic discriminant, 163, via the jfunction, based on the elliptic generalizations of the e^i*pi circular function, i.e. the functions of quantum angular momentum. The jfunction was discovered in the process of factoring the quintic equation. As the cubic is solved by the trisection of angles, so is the quintic, by a fivesection. Phi, of course, is the pentagonal number. Pentagonal crystals are quasiperiodic, reminiscent of various other objects of mathematical interest.
In the deck of numbers, the fivespot is more than a bit on the wild side. The power of the decimal system may be one result. Otherwise we would have been duodecimalists, following the Solar cultists. This goes back to our metric related syzygy of 2*31*127^2 = 999998, and why the inch is exactly 2*1.27 cm . And note that pi^2 ~= 10, and pi^3 = 31.006..., and while you have your calculator handy, try the windows' one with the 'scientific' view, 2*31*127^2 = 9.999996666663888885...^6. Do we think we understand exactly what is going on with these decimals, or are they just playing around? And how could we forget that e^pi  pi = 19.99909998...? I wondered about that pattern of 9s, didn't you? It turns out, after some experimenting motivated by the previous pattern, that 99.982^1/2 = 9.99909996.... Exploiting this fact gives us a recursive formula for pi = ln (pi + 10 + (100  .018)^1/2). Starting with, say, pi = 3, this formula rapidly converges on pi ~= 3.1415926527.... Pi = 3.1415926535.... The closest memorable competitor is 113\355 = 3.14159292.... You are invited to comparison shop at Math World. This is the simplest, least arbitrary of the bunch. Furthermore, it seems to beg of a functional meaning, as well as underscoring the decimal essence of pi.
