Nice job on presenting one, or of resurrecting your complicated abstract math echo of nested structural coding. It doesn't seem naive to me and I hope you can remember it. For abstract math aficionados who presently think backwards and inside-out (from the analog math perspective) such a translation may be of considerable significance, helping to catch some of those men in the net.

The so-called 1D - 3D characterizations and numbers of degrees of freedom and topological constraints (relating to properties), though, are just a rather old-world way way of thinking about, pointing at and attempting to simplify our actual reality of nested fields within nested fields. Interactions occur within containments -- ~many ~body interactions... Ditto, old-world (but very, very helpful) for the various named abstract math features such as Riemann zeta function, braids, knots and eigenstates.

Prime knots of ‘subjective accompaniments of complex energy eigenstates’ is still a rather lofty and, I think, disconnected obfuscation of attraction and repulsion in stacks and sequences of the underlying, and in one view, the 6^n, 10^20 per second internal analog math. Might you be trying to point at knots of 'prime feelings'?

There are knots on many levels. Glibly, these may be seen in the respirational water layer, bound water-protein matrices, xRNA, genetics and epi-genetics, perhaps in the synaptics and up through protein-folding into the tenuous standing waves in our functional and dysfunctional inter-personal and group dynamics, whether archetypally influenced or not.

You say eigenstate; I say nested structural coding in the analog math. The equivalences at the interface are pretty intriguing and I do hope you have very good success in communicating your expression to the rather small number of highly creative, very capable people who find themselves within, what I view as, the secondary abstract mathematical only cul-de-sac.

Pardon my analog math arrogance and insecurity-based attempted cover-up of my woefully impotent abstract math abilities. However, weak as my abstract math abilities are, the internal analog math is still primary and the origin of all abstract math expressions and repetitions. I keep thinking it is important to emphasize that fact.

I had to look the terms up to remember, but my only vague connection and partial understanding -- passing exposure, really -- of Reimann zeta function came to me, again, in analog math, in studying colloid coagulation in water and waste water treatment many years ago. From my wet chemistry technician's perspective, I'd take a wild guess that the sum of many finely divided collections (referring to sums of fractional parts in the math expressions) relate and might be visualized as in precipitation of, say, zinc hydroxide from a dissolved state in electroplating waste water. pH Adjustment encourages a 'cloud' of colloidal particles (stabilized repulsively with bound water and a so-called zeta potential), which then are encouraged to destabilize, precipitate and grow into settleable (or filterable) 'solids'. The sums of the more finely divided fractions, I expect might relate with equilibria occurring within nested fields within nested fields at various levels of organization -- the quantum level, the dissolved level, the micelle/colloid level, the charge dispersal level, the particle growth level, etc. ...nucleation, various structural coding -- knotting at the primes or at the zeroes -- to manifest as 'shift in phase -- dissolved (wavilinear) to settleable solid -- particulate.

Similarly, then, one might think of the respiration reaction where water and carbon dioxide are formed from glucose and oxygen while stripping out energy. It might be a stretch and against several rules, but one might also think of formation of water molecules and collections of available energy packets from atomic collections in glucose and the oxygen as some type of ~co-precipitation -- as yet another complex phase shift of one set of knots or eigenstatesat one or more levels of organization, into other (rather prime) sets of knots and/or eigenstates, aka, nested stacks and sequences of mostly hydrogen bonding, unfurling to influence related energetically and structurally useful sets and sequences of protein-folding (expression).

In the analog math there is just the one rather gangling, complex nested, structurally coded ~equation. In the abstract math there are apparently many, many very good container/artifact representations, Reimann's being, apparently one of the very good approximations.

Interestingly (to me) I suspect that constructions in the complex numbers (a +ib) struggle to reflect nested structural energetics. That is, the fundamentals ARE structure and energy, containment and response, related levels of organization -- and surely NOT the apparent initial estimates as mass, length and time, etc.

As for "possible connections (translations???) here with your [my] picture", that would be an intriguing development to actually experience, wouldn't it? As I said, I wish you good success in your more academically familiar and acceptable expressions whether connection forms or not. Vaguely, sometimes I do appreciate that like body and soul, abstract and analog math expressions are also unified. However, the storyline I advocate and emphasize in the tactile magnetic tetrahedral analog math is more engaged in conveying feeling -- experience -- than just a visual image. It's perhaps a bit non-verbal, yet that's one of the beauties of this analog math. It delivers low level physical intuition directly.

That is, the visual aspects of http://magtet.com/images/1model.jpg do not convey the *feel* of attractions with 1/2 spin, states and nested states, orbitals (the grounded and repulsed), damped anharmonic motion, collapse, charge (if using an added wire loop), uncertainty of position and momentum, many body interactions, and other low level features (as listed at http://magnetictetrahedra.com/ ) inherent in just doing very basic, very simple operations with such "hard numbers". Extended through the similar 6^n, 10^20 per second structural coding in the respiration reaction and condensing out within protein-folding we do arrive at all our various and sundry expressions.

I'll have to read more, and/or you and other mathematically inclined people may already know that Reimann's math expressions or relationships are applicable in many or all of these physically expressive and relevant transitions. From within the prior paradigm, we might then still ponder 'Why the ~uncanny connection between physical reality and abstract mathematics?" Reducing both to instances of ~structured~duality (or whatever the term...), in the emerging paradigm that anomaly dissipates. Taciturn, but not too much of a mystery: the abstract math arises from the primary internal, structural coding analog math.

I might encourage you to also think of prime knots and eigenstates at some of the other levels of organization and structural coding besides just instantiations in the brain... synapses, neural networks. Plus, I think if you go heavy on the abstract math route, your model will likely get into it's own tangle because you will just have an instance of structural coding rather than the structural coding naturally giving rise to instances of structural coding. That is, the structural coding in the analog math comes first -- is primary.

Intriguing, great! Pick a structure: prime knots... in the nested fields within nested fields.

Intriguing. Your ‘physical braids or complex orientable surfaces in the brain equivalent to prime knots’ strikes a somewhat resonant chord with the 6^n, 10^20 per second structural coding in the ordered water forming within our respiration sites and working outward through our expressive protein-folding.

Good luck with it.

Best regards,

Ralph Frost

http://frostscientific.com

With joy you will draw water

from the wells of salvation. Isaiah 12:3

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---In jcs-online@yahoogroups.com,

Dear Ralph,

As you say classical space is probably a secondary, maybe Machian, phenomenon but the number of degrees of freedom attributable to the vector dynamics of any particular system may be more fundamental when it comes to accounting for topological constraints on the properties of the system.

As you might expect from a psychiatrist, my original motivation for an interest in prime knots came from Carl Jung’s comment that his ‘archetypes’ have a lot in common ontologically with the natural numbers. Qualia in turn share commonalities with archetypal representations. So it seemed natural to wonder whether differences between qualia might be analogous in some sense to differences between natural numbers. Knots too are like numbers in that there are primes which are inherently different from one another and from which all knots can be generated. Knots are equivalent to braids (and to Seifert surfaces), which manifest in a range of instantiations in the brain. It was a way-out speculation whose main merit was that it is testable in principle at least. So my initial answer to your question (i.e. ‘prime knots of WHAT?) would have been: ‘physical braids or complex orientable surfaces in the brain equivalent to prime knots’ – it was probably all a bit naive and I forgot about it for a long time.

However, it turns out that energy eigenstates relate to zeros of the Riemann zeta function which are also conjectured to relate to both prime numbers and prime knots. There are, in other words, a series of hard-to-understand isomorphisms between these apparently very different concepts. This rang a bell with me because of my recent speculation (JCS 20, 9-10, pp. 77-89) that ‘consciousness’ may occur along with energy eigenstate manifestation. It looked as if it might be possible to use the old ‘knot’ idea to extend the latter speculation to account also for qualia differentiation. So my current, highly tentative, answer to your question is: ‘subjective accompaniments of complex energy eigenstates’. I think there may be possible connections (translations???) here with your picture. It would be nice if so.

best

Chris

Chris,

Prime knots of WHAT, though?

In a system of nested fields within nested fields, the notions of 1D and 3D dimensionality as giving accurate characterization of fundamentals or as accounts of the actual origin of constraints are a bit misleading, a bit inside out, overly classical, out-dated. Our familiar old-world idealized map may be helpful in many areas, but it is even more so NOT the territory today.

As for patterns of prime knots yielding the alleged and elusive qualia, can you be more specific on prime knots of WHAT? It seems to me that if one considers a clump of iron oxide and a clump of copper oxide, one may be reddish and the other greenish but the differences between iron and copper atoms in the two molecules, as characterized on the periodic chart of elements, is just in the numeric collections or aggregates of their constituent parts -- and perhaps how the the parts are structured.

Similarly with quartz and rock salt. The salt has a markedly different taste, but again the differences are just in numbers and patterns of the electrons, protons and neutrons in the collections.

These hundred-odd collections and their combinations appear to be one category of prime knots. Yet, the differences in properties (qualities) in this entire category relate strictly to the counts and structure of the constituent parts.

Similarly, in the 6^n, 10^20 per second stacks and sequences of water molecules forming during respiration, or in the structural coding in genetic and epi-genetic responses. Different associations relate to counts and patterns of the constituent parts at a certain level of organization.

Thus with these categories, we already have different qualities relating just to differences in the nested structural coding.

What is different or the same with the prime knots and/or qualia you envision in your pet or developing trial theory? Can you flesh those differences out? Prime knots of WHAT?

Best regards,

Ralph Frost

http://frostscientific.com

With joy you will draw water

from the wells of salvation. Isaiah 12:3

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