Quantization isn't fundamental

[Twodogs]

If by 'an integrative level of description' you mean 'emergent from underlying mechanics', then the answer is yes.

Thank you for wading through my questions. Regarding your answer above, where would I find a description of the ‘underlying mechanics’ from which quantum fields are ‘emergent?’ Do you mean their mathematical description or something 'deeper'?

 

[Auto-Didact]

I have been giving the bifurcation aspect of this model a bit more thought: locally, period doubling bifurcations are supercritical pitchfork bifurcations, with the visual aspect of the 'pitchfork' clear upon inspection of the bifurcation diagram; this implies that there is some symmetry in the governing equation behind the dynamics of this vacuum polarization. What on Earth is this symmetry, physically speaking?

Thank you for wading through my questions. Regarding your answer above, where would I find a description of the ‘underlying mechanics’ from which quantum fields are ‘emergent?’ Do you mean their mathematical description or something 'deeper'?

I mean something deeper: a mathematical description of some more fundamental dynamics of vacuum fluctuations which reduces in some particular limit to the equations of QFT. As far as I know, no one has ever succeeded in doing such a thing yet.

In other words, I am explicitly saying that this is an outstanding open problem in mathematical physics: identify through (trial-and-error) construction a unique nonlinear generalization of QFT which fully and non-perturbatively describes the dynamics of vacuum fluctuations as a dissipative process and at the same time has standard QFT as a well-defined limit.

 

[Auto-Didact]

Ok, thanks very much for the interesting response, Auto-Didact.

Due to my contemplations in the previous post, I just reread the paper and now see that I missed something crucial in my answer to you: in section V, Figure 8d (pg. 8) the author shows that the simplest version of the model implies the existence of a spin-2 particle i.e. possibly the graviton, but he doesn't speculate any further. Moreover, the author explicitly states in the end of section VI that the model is a space-time independent framework.

 

[*now*]

Due to my contemplations in the previous post, I just reread the paper and now see that I missed something crucial in my answer to you: in section V, Figure 8d (pg. 8) the author shows that the simplest version of the model implies the existence of a spin-2 particle i.e. possibly the graviton, but he doesn't speculate any further. Moreover, the author explicitly states in the end of section VI that the model is a space-time independent framework.

Your observations do seem crucial and more interesting, thanks Auto-Didact.

 

[Twodogs]

I mean something deeper: a mathematical description of some more fundamental dynamics of vacuum fluctuations which reduces in some particular limit to the equations of QFT. As far as I know, no one has ever succeeded in doing such a thing yet.

In other words, I am explicitly saying that this is an outstanding open problem in mathematical physics: identify through (trial-and-error) construction a unique nonlinear generalization of QFT which fully and non-perturbatively describes the dynamics of vacuum fluctuations as a dissipative process and at the same time has standard QFT as a well-defined limit.

A few, perhaps erroneous, observations:

1) The notion of particles being dissipative dynamical structures as opposed to some sort of steady state systems is a major shift of paradigm. I will have to read more to understand the mechanism for that dissipation.

2) Philip Anderson’s emergence in a nut-shell: “This, then, is the fundamental philosophical insight of twentieth century science: everything we observe emerges from a more primitive substrate, in the precise meaning of the term “emergent”, which is to say obedient to the laws of the more primitive level, but not conceptually consequent from that level”. “More is Different” – Anderson (1995, p. 2020)

3) It would seem that identifying the equations that describe ‘a unique nonlinear generalization of QFT’ would first require a characterization of the ‘more primitive substrate’ within which their dynamics would arise and sustain. In other words, the soil must suit the seed. Is that the case?

4) Upon the emergence of phenomenologically new dynamics, those of the ‘more primitive substrate’ continue to serve as their dynamical foundation.

5) I am curious to know if there is an axiomatic approach to characterizing the dynamical substrate in which self-organizing, dissipative systems could arise.

Thanks.

 

[Auto-Didact]

Agree with 1) and 2).

3) It would seem that identifying the equations that describe ‘a unique nonlinear generalization of QFT’ would first require a characterization of the ‘more primitive substrate’ within which their dynamics would arise and sustain. In other words, the soil must suit the seed. Is that the case?

4) Upon the emergence of phenomenologically new dynamics, those of the ‘more primitive substrate’ continue to serve as their dynamical foundation.

3) Yes, the substrate would have to be identified; this is certainly possible and actually there are already many existing sub-particle theories (such as strings or loops) which can readily be tried.

The really nice thing however is that a macroscopic formulation, based on a purely statistical or continuum (e.g. hydrodynamic) treatment, may lend itself through the utilization of theorems and techniques to a (physically) completely generic but mathematically essentially correct microscopic formulation.

4) Yes. Moreover, the author, Manasson, has in fact offered a tentative toy model of the proposed dynamical substrate for the vacuum field himself in his 2017 paper (see here a few posts back).

In his toy model, Manasson proposes that the vacuum consists of dust particles, themselves either essentially infinitesimal (a la Cantor dust) or roughly Planck length sized. On the characteristic scale in question - i.e. the scale of particle physics - these dust particles form a fluid: the vacuum.

This vacuum fluid has self-aggregational and self-diffusive properties, which means that 'temperature' or heat differences will spontaneously lead to the formation of convective vortex cells; vortex cells with a higher than average dust influx are positively charged, higher than average dust efflux negatively charged and zero average dust flux neutrally charged.

Using a network theoretic formulation, Manasson then demonstrates how the collective dynamics of such discrete charged vortex cells is capable of essentially reproducing all of quantum statistics, perhaps without entanglement, at least not explicitly. In particular, he effortlessly goes on to derive both Fermi-Dirac and Bose-Einstein statistics, as well as all all known Standard Model interactions directly from this toy model.

5) I am curious to know if there is an axiomatic approach to characterizing the dynamical substrate in which self-organizing, dissipative systems could arise.

5) If by axiomatic approach you mean purely formally i.e. giving proofs based on axioms, then I urge you to read this.

On the other hand, if you just meant a purely mathematical general characterization, then yes, of course. This has been achieved for thermodynamics, condensed matter theory and fluid mechanics and is still active research in countless other fields, from chemistry, to biology, to economics; it is one of the main research directions in nonlinear dynamics, non-equilibrium statistical mechanics and complexity theory.

 

[Twodogs]

Very much appreciate your taking time to reply. Will reflect...

 

[Twodogs]

The phase i am currently in is abstractions that are like interacting information processing agents and dna of law can be thought of as the computational code that determines the dices that are used to play. But each dice is fundamentally hidden to other agents whose collective ignorance supports acting as if they did not exist so that is does not quailfy as a hidden variable model. Agents also has intertia associated to the codes. This is how volatile codes can easily mutate but inertial ones not.

Here the notion of a game space resonates for me. Once one sees something it is difficult to un-see it. And so, despite the incredible breadth and cognitive density of current physical theory, I am left with a very improbable proposition.

Improbable Proposition:

There is a foundational principle implicit in our physical theory that is not fully recognized as such because it is formulaically treated in a myriad of case-by-case instances rather than seen as a general, overarching principle. It would both simplify and deepen our understanding of the universe’s foundational game-space were we to identify this principle and recognize its implications.

As slender props of this notion we note that Neils Bohr placed the yin/yang symbol on his coat of arms with the Latin motto, “Contraria Sunt Complementa," – opposites are complementary". Edward Teller wrote: "Bohr was the incarnation of complementarity, the insistence that every important issue has an opposite side that appears as mutually exclusive with the other. The understanding of the question becomes possible only if the existence of both sides is recognized".

And from David Bohm, we have a characterization of views: The universe is an "undivided wholeness" with everything in a state of process or becoming, a "universal flux" which is not static, but rather a dynamic interconnected process. There is no ultimate set of separately existent entities, out of which all is supposed to be constituted. Rather, unbroken and undivided movement is the primary notion. Movement gives shape to all forms and structure gives order to movement, and a deeper a more extensive inner movement creates, maintains, and ultimately dissolves structure".

So, here’s the question. In a very coarse-grain, cartoon sketch of our physics, leaving out 99% of the detail we would see energy as the principal player. For the sake of narrative interest, to make it more of a game, can we identify energy’s ‘counterpoise’, what’s on the other side of the net, its ‘opposable thumb?’

I would appreciate your thoughts on this.

 

[Twodogs]

And from David Bohm, we have a characterization of views: The universe is an "undivided wholeness" with everything in a state of process or becoming, a "universal flux" which is not static, but rather a dynamic interconnected process. There is no ultimate set of separately existent entities, out of which all is supposed to be constituted. Rather, unbroken and undivided movement is the primary notion. Movement gives shape to all forms and structure gives order to movement, and a deeper a more extensive inner movement creates, maintains, and ultimately dissolves structure".

Correction:
And from David Bohm, we have a characterization of his views: "The universe is an "undivided wholeness" with everything in a state of process or becoming, a "universal flux" which is not static, but rather a dynamic interconnected process. There is no ultimate set of separately existent entities, out of which all is supposed to be constituted. Rather, unbroken and undivided movement is the primary notion. Movement gives shape to all forms and structure gives order to movement, and a deeper a more extensive inner movement creates, maintains, and ultimately dissolves structure". (emphasis mine)

 

[Fra]

...
So, here’s the question. In a very coarse-grain, cartoon sketch of our physics, leaving out 99% of the detail we would see energy as the principal player. For the sake of narrative interest, to make it more of a game, can we identify energy’s ‘counterpoise’, what’s on the other side of the net, its ‘opposable thumb?’

I would appreciate your thoughts on this.

Your question and the matter is naturally fuzzy and easy to misinterpret, but given that disclaimer i can make sense of what you write, and the answer to your question from my perspective is loosely this:

As we learned from relativity, mass, inertia and energy are related in that mass is simlply a form of confined / trapped / bound energy, where the confinement usually refers to the 3D space.

Further in my views I associate structures in conditional bayesian information and probabilities with "energy" and "inertia". In information perspectives, inertia is simlpy the "amount" of evidence pointing in a certain direction, this is "confined" to the observers "subsystem", and in my view are bound to someone relted to inertia and mass. Temperatuire here is simply a kind of information divergence. You can with toy models play around with this, and notice mathematical similarities with stat mech models and heat dissipation, and models for information disspiation. But once you combine systems of non-commutative information processing systems, you have lots of opportunity to map this into the structure of physics and its laws.

So in this perspect i would say energy loosely related to "amount of evidence", which is dependent on a structure able to encode it and the opposite is this "lack of evidence", or lack of complexions. This is why i think self organisation also is related to the origin on mass and energy. So energy is not a "thing", is somehow a measure of "relational" information storage. This is a conceptual fuzzy answer.

The precise mathematical answer requires nothing less that actually completing this research program.

Edit: forgot a point. In the new perspective i paint above, the confinement does not refer to 3D space as space does not yet exist in this level of the vision. Instead spacetime and the dimensionality must be emergent as evolved self-organised relations between the interacting encoding structures. So before that happens, the confinement i more tinkg of as existing in an abstract space indexed by the observers identity. Where two observers that have the SAME information with same confidence, by definition ARE the same (indistinguishable). So "distance" and space emerges from disagreement, and along with disagreement follows "interactions" to counter them, and in all this the laws of interactions are encoded - or so goes the idea.

/Fredrik

 

[Twodogs]

Your question and the matter is naturally fuzzy and easy to misinterpret, but given that disclaimer i can make sense of what you write, and the answer to your question from my perspective is loosely this:

I am grateful for your tentative reply. I was about ready to post an apology for my question thinking it was inappropriate due to lack of clarity, excessive speculation or simple naivete. Perhaps it was a bit of all these things. In any case, your reply gives me perspectives to consider.

 

[Andrea Panza]

Hi,
My understanding of physics it is probably not deep enough to fully appreciate all this thread, but I think the link below of 'cell emergence' from a simple rule might be relevant for the discussion.



This is the link to the Nature paper:

https://www.nature.com/articles/srep37969

Regards

 

[Twodogs]

the confinement does not refer to 3D space as space does not yet exist in this level of the vision. Instead spacetime and the dimensionality must be emergent as evolved self-organised relations between the interacting encoding structures.

This seems to be a relevant insight.

 

[KipIngram]

Suffice to say, this paper is a must-read. Many thanks to @mitchell porter for linking it and to Sir Michael Atiyah for reigniting the entire discussion in the first place.

Wow - that is a pretty interesting paper. I want to find some of the counter-arguments to it as well, but thanks for bringing this one to my attention. Surely there must be some testable things here that can be checked...

 

[mitchell porter]

I have been wanting to make a comment or two about the prospects for Manasson's proposal... Consider figure 1a in his 2008 paper. That's a binary tree with sixteen leaves, the leaves being the 16 fixed points of a limit cycle in some unknown dynamical system, which are also supposed to be 16 particle states from the first generation of the standard model.

There are other ways you might want to assign particle states to the fixed points of the bifurcation diagram. For example, he doesn't include quark color, which would multiply the number of quark states by three. But that would just bring the total number of states per generation to 32, which is the number of fixed points after the next bifurcation.

Also, he implicitly treats these particles as 4-state Dirac fermions, whereas we now understand the phenomenological Dirac fermions to arise from a Higgs mechanism that pairs up two 2-state Weyl fermions. Again, this is just a change in the details, it doesn't inherently affect the viability of the concept.

But however you make the assignment, ultimately you want to mimic the standard model. We know the lagrangian of the standard model, it contains many interaction terms that involve these fermionic states. So given a particular assignment of states to the tree, you can directly translate the lagrangian into the dynamical systems language.

The lagrangian will contain terms like "electron couples to charged weak boson and becomes neutrino", or "left-handed fermion couples to right-handed fermion via Higgs". These should translate directly to statements like "third fixed point on level 4 couples to charged weak boson and becomes seventh fixed point on level 4", etc.

Recall that, on the dynamical-systems side of this correspondence, the 16 states correspond to fixed points of a limit cycle in an iterated dynamical system. So the seventh fixed point is what you get after applying some mapping four times to the third fixed point.

There is another way to get there, and that is to change levels within the tree, rather than move along the same level. But either way, once you make a specific assignment of fermion states to the tree, this implies a large number of highly specific claims about how the bosons of the standard model (whatever they are) interact with the different states of the fundamental self-organizing system described by the bifurcation diagram.

So I want to propose a rather concrete way to explore the difficulties of implementing Manasson's vision. It's partly inspired by quantum computing, where there are concepts of a "physical qubit" and a "logical qubit". A physical qubit is a concrete quantum system - a nuclear spin, an electron spin, whatever. A logical qubit is a qubit at the level of quantum algorithms. A logical qubit is typically made of some number of physical qubits with an error correction scheme applied.

Anyway, what Manasson has done is to take a type of universal dynamical behavior, and propose that some version of it underlies particle physics. To judge the viability of this idea, we need a way to explore it in generality, or at least without already knowing the details of the fundamental self-organizing system. But we also need something concrete enough that we can try to make it work, and learn from the difficulties.

I think a quantum version of the logistic map can provide a concrete starting point. The logistic map, maps one value of x to another value of x, and has a parameter r. So the first step that I suggest, is to think of these as quantum states... |x>. There can be technical problems with having a continuum of quantum states, but they are familiar from ordinary quantum mechanics and we can use ordinary methods should they prove necessary.

So then the logistic map is actually an operator on a Hilbert space, or rather a family of operators parametrized by r. These states are then analogous to the states of the "physical qubit". Then, for specific values of r, there are fixed points and basins of attraction. These are analogous to the "logical qubit" states. Note that if a particular range of x-values belong to the basin of attraction for a single fixed point, there will be a subspace of the overall Hilbert space, whose basis vectors are the |x>s in that range.

So now we have a kind of concrete model for the fundamental self-organizing system. When we say "left-handed electron is third fixed point on level 4", that refers to a particular subspace of our Hilbert space. And this also gives a new concreteness to the propositions like "third fixed point on level 4 couples to charged weak boson and becomes seventh fixed point on level 4"; that is now a statement about how certain quantum systems interact.

I know that Manasson (and also @Auto-Didact) hope to derive quantum mechanics itself from something more fundamental, but whatever the foundations, the standard model is quantum-mechanical and e.g. obeys the principle of superposition, so some version of the scheme has to make sense as a quantum theory.

Nonetheless, for those seeking something beneath quantum mechanics, I would point out a recent paper by Tejinder Singh, which takes as its subquantum theory a version of Stephen Adler's trace dynamics. It's a relatively sophisticated approach.

 

[arivero]

. Consider figure 1a in his 2008 paper.

Hey, he cites P. Cvitanovic's "Universality in chaos", a nice book. He is, I think, the same person who calculated the g-2 parameter at sixth order. Then he started to notice patterns in the calculations and went to explore other, er, branchs of physics. Before transitioning to chaos, he did some articles on "Parton Branching", this sounds as a good candidate to the "unknown dynamical system". But if Cvitanovic failed to find such system, I doubt it exists.

 

[Twodogs]

5) If by axiomatic approach you mean purely formally i.e. giving proofs based on axioms, then I urge you to read this.

I don’t know if it is interesting or fruitful, but here are two foundational axioms to consider.

Axiom One: The universe of one piece, an undivided whole.


Axiom Two: The universe is divided, one part distinct from another, and etc.

If we accept that both are still true, I am curious as to know what would follow.

 

[Auto-Didact]

I don’t know if it is interesting or fruitful, but here are two foundational axioms to consider.

Axiom One: The universe of one piece, an undivided whole.


Axiom Two: The universe is divided, one part distinct from another, and etc.

If we accept that both are still true, I am curious as to know what would follow.

The problem with axioms is that they usually are pretty shallow ideas from a fundamental exploratory perspective i.e. a careful analysis doesn't lead to any deeper understanding, only to logically possible reductionist explanations of higher level concepts. Moreover, axioms also often end up being intrinsically somewhat vague and therefore often unfalsifiable as well; if the vagueness can be removed, the deduced consequences on the basis of the axioms have the risk of changing completely.

One can often tell the difference between an axiom and a principle by how they were first comstructed, namely axioms are a priori interpretations i.e. usually non-empirical definitions tied up in some particular conventions, while principles are a posteriori descriptions i.e. hypotheses that have managed to survive repeated attempts at falsification, and so eventually end up exposing some core concept. This just shows that axioms and principles have fundamentally different aims, i.e. empirical versus rational explanation; e.g. a complete logical proof can only be based on axioms, yet the axioms may turn out to be incorrect, directly rendering some proof irrelevant and the conclusions based on it obsolete.

For example, contrast the axioms you stated with known principles, such as the principle that being at rest is a form of motion, the principle that everything the animals do result from the motion of atoms or the principle that all life springs from a common mechanism. In each of these cases, the principles are so broad that they tend to naturally apply far beyond what they were specifically aiming to describe; this is where unification comes from in the practice of physics.

In other words, far more comes out of the idea than what is originally put in, not merely in an empirical sense but also conceptually, often directly leading to novel purely mathematical constructions; Feynman liked to say 'the idea turns out to actually be simpler than it was before'. This openness of the applicability domain of a principle is the hallmark of a good principle. On the other hand, the hallmark of a good axiom is that it has a precisely delineated boundary, making long range deductions possible.

 

[Twodogs]

We are discussing the foundational substrate within which self-organized dissipative dynamics would arise as a natural consequence. Your cautionary comments on the pitfalls of axiomatic arguments are mostly understood – here my limitation rather than your lack of clarity. Granted, a hard-won, empirical principle would weigh more heavily than an axiomatic premise made for purpose of discussion.

The problem with axioms is that they usually are pretty shallow ideas from a fundamental exploratory perspective i.e. a careful analysis doesn't lead to any deeper understanding,

Moreover, axioms also often end up being intrinsically somewhat vague and therefore often unfalsifiable as well; if the vagueness can be removed, the deduced consequences on the basis of the axioms have the risk of changing completely.

Clear enough. I don’t wish to waste your time, but moving from general case to particular example, may we consider the two given axioms with the understanding that are propositions for sake of argument. The first proposition, “The universe is of one piece, an undivided whole,” is not readily apparent. It is far from, “that which commends itself as evident.” However, it was David Bohm’s often stated view and the conclusion of at least a couple of spiritual disciplines. Neither of which makes it true, but it does make it proposition worthy. It may not be sufficiently explicit, but it is a briefly stated proposition of fundamental continuity.

The second proposition, “The universe is divided, one part distinct from another, and etc.,” is readily evident, actually hard of avoid. The advance of science has regularly occurred through lifting the veil of unnecessary detail and finding beneath the unifying principle. This is the proposition of discreteness.

Considering both of these antithetical propositions as true would reflect Niels Bohr’s proclivity as outlined by Edward Teller, “…every important issue has an opposite side that appears as mutually exclusive with the other. The understanding of the question becomes possible only if the existence of both sides is recognized.”

Be that as it may, the goal of such a process is your “deeper understanding” and here I see at least one significant consequence: If we accept both propositions as valid, then all distinctions are fundamentally topological in nature.

Is that the case? Is it useful?

And once again, I appreciate your willingness to engage here. Given the subject matter, such opportunities don’t often occur.

 

[Auto-Didact]

Be that as it may, the goal of such a process is your “deeper understanding” and here I see at least one significant consequence: If we accept both propositions as valid, then all distinctions are fundamentally topological in nature.

Please elaborate.

 

[arivero]

If we accept that both are still true, I am curious as to know what would follow.

Connes's tangent groupoid.

You have separate states, but also arrows joining them, with an algebra associated to describe the topology, and an operator to describe the notion of distance.

 

[Twodogs]

Please elaborate.

The notion that all distinctions are fundamentally topological arises from the perhaps naive assumption that, if the universe is both one and two, then the two must be topological transforms of the one. This is perhaps a narrow view of the possibilities.

I believe it to be true, but I come to it via a general systems world view governed more by metaphor, analogy and rules-of-thumb than a disciplined mathematical framework. Within this world view I find that a very useful and perhaps overarching rule-of-thumb is the observation that:

Path is emergent between the traveler and the terrain.

It is emergent because its pattern is not solely determined by either traveler or terrain, but rather by their mutual dynamical interface. This is an empirically useful description on the macro level and likely to have translatable relevance on the micro level. If our complexity metric reflects long range correlation, then complexity of path is directly related to and arises from the complexity of both traveler and terrain and is maximal within some intrinsic energy regimen.

I have come to suspect that it is useful to consider that the universe is a construct of traveler and terrain dynamics ‘all the way down.’ Here we are piloted by a systems view first expressed by da Vinci and paraphrased by David Bohm: “Movement gives shape to all forms and structure gives order to movement, and a deeper a more extensive inner movement creates, maintains, and ultimately dissolves structure". This notion is sketched out here in seven-hundred words and one ‘equation.’

First, probing deeper we find a striking affinity between traveler and terrain. They are both hybrids – composite, dynamical constructs arising as sustained paths between their own intrinsic ‘travelers’ and ‘terrains.’ We find the traveler is always part terrain, the terrain is always part traveler and both share elements of a larger whole.

With a leap of soft logic, we can further devolve this pattern of nested dynamics, step by step, to a foundational level. Here, as an imprecise, qualitative ansatz and with the expectation that there is a more precise underlying, mathematical description, we will characterize traveler and terrain by two qualitative, verbal placeholders using ‘change’ for traveler and ‘constraint’ for terrain.

The benefit of this exercise is a very rudimentary equation governing the fitting together of these two antithetical qualities:

Change + Constraint = O

Wherein “O” represents any of the species of cyclical or wavelike dynamics and the properties of both addends are conserved in the sum. That is, cyclical, wavelike dynamics arise as a means of integrating these two antithetical properties into a path in which change is ongoing and yet constrained to a certain dynamical regimen. Here we note that cyclical and wavelike dynamics are ubiquitous in the universe over spatiotemporal scales varying by many orders of magnitude and, though they manifest in a myriad of distinct mechanisms, they may be similarly driven at a foundational level.

Further, on this level of first things, it is expected that:

1) “O” is the first element of time volume and the first stele in a space geometry. It is the dynamical knot that binds phenomena into being, “gives to airy nothing a local habitation and a name.”

2) ‘Change’ and ‘constraint’ represent two orthogonally opposed transforms of a single topology and may be mathematically described and developed inductively from complementarity relations and conserved properties.

3) The physical universe is the path emergent between these two topologies.

4) The “orthogonally opposed transforms” are both proto-physical and trans-physical, that is, both genesis and sustainer of the physical universe and are “present at any moment” (as in Bohm’s characterization of the implicate order). Their mutual effect is evident in the exacting dynamic translations between kinetic and potential energies. They manifest only in relation to each other and are endlessly complected (PIE root "to plait, braid") into dynamical structures.

5) The existence of “orthogonally opposed transforms” may be confirmed by measurement of the angle formed at the intersection a mason’s plum line and his(her) spirit level. It is simply a matter of interpretation. ;>)

6) This foundational schema would serve as a substrate for the emergence of iterative, self-organizing dissipative systems.

I have no idea if this will have any traction with you. Be that as it may, several years ago sonar engineers discovered that adding a little noise to a source might push its weak signal over the threshold of detection. Nice when that happens. Thanks.

 

[Auto-Didact]

The notion that all distinctions are fundamentally topological arises from the perhaps naive assumption that, if the universe is both one and two, then the two must be topological transforms of the one. This is perhaps a narrow view of the possibilities.

I believe it to be true, but I come to it via a general systems world view governed more by metaphor, analogy and rules-of-thumb than a disciplined mathematical framework. Within this world view I find that a very useful and perhaps overarching rule-of-thumb is the observation that:

Path is emergent between the traveler and the terrain.

It is emergent because its pattern is not solely determined by either traveler or terrain, but rather by their mutual dynamical interface. This is an empirically useful description on the macro level and likely to have translatable relevance on the micro level. If our complexity metric reflects long range correlation, then complexity of path is directly related to and arises from the complexity of both traveler and terrain and is maximal within some intrinsic energy regimen.

I have come to suspect that it is useful to consider that the universe is a construct of traveler and terrain dynamics ‘all the way down.’ Here we are piloted by a systems view first expressed by da Vinci and paraphrased by David Bohm: “Movement gives shape to all forms and structure gives order to movement, and a deeper a more extensive inner movement creates, maintains, and ultimately dissolves structure". This notion is sketched out here in seven-hundred words and one ‘equation.’

First, probing deeper we find a striking affinity between traveler and terrain. They are both hybrids – composite, dynamical constructs arising as sustained paths between their own intrinsic ‘travelers’ and ‘terrains.’ We find the traveler is always part terrain, the terrain is always part traveler and both share elements of a larger whole.

With a leap of soft logic, we can further devolve this pattern of nested dynamics, step by step, to a foundational level. Here, as an imprecise, qualitative ansatz and with the expectation that there is a more precise underlying, mathematical description, we will characterize traveler and terrain by two qualitative, verbal placeholders using ‘change’ for traveler and ‘constraint’ for terrain.

The benefit of this exercise is a very rudimentary equation governing the fitting together of these two antithetical qualities:

Change + Constraint = O

Wherein “O” represents any of the species of cyclical or wavelike dynamics and the properties of both addends are conserved in the sum. That is, cyclical, wavelike dynamics arise as a means of integrating these two antithetical properties into a path in which change is ongoing and yet constrained to a certain dynamical regimen. Here we note that cyclical and wavelike dynamics are ubiquitous in the universe over spatiotemporal scales varying by many orders of magnitude and, though they manifest in a myriad of distinct mechanisms, they may be similarly driven at a foundational level.

Further, on this level of first things, it is expected that:

1) “O” is the first element of time volume and the first stele in a space geometry. It is the dynamical knot that binds phenomena into being, “gives to airy nothing a local habitation and a name.”

2) ‘Change’ and ‘constraint’ represent two orthogonally opposed transforms of a single topology and may be mathematically described and developed inductively from complementarity relations and conserved properties.

3) The physical universe is the path emergent between these two topologies.

4) The “orthogonally opposed transforms” are both proto-physical and trans-physical, that is, both genesis and sustainer of the physical universe and are “present at any moment” (as in Bohm’s characterization of the implicate order). Their mutual effect is evident in the exacting dynamic translations between kinetic and potential energies. They manifest only in relation to each other and are endlessly complected (PIE root "to plait, braid") into dynamical structures.

5) The existence of “orthogonally opposed transforms” may be confirmed by measurement of the angle formed at the intersection a mason’s plum line and his(her) spirit level. It is simply a matter of interpretation. ;>)

6) This foundational schema would serve as a substrate for the emergence of iterative, self-organizing dissipative systems.

I have no idea if this will have any traction with you. Be that as it may, several years ago sonar engineers discovered that adding a little noise to a source might push its weak signal over the threshold of detection. Nice when that happens. Thanks.

I can partially see what you are trying to say, but I would like to see it worked out mathematically, before passing judgment. If you have trouble doing so yourself, I would suggest collaborating with a mathematician or programmer/computer scientist with the relevant conceptual background.

 

[Twodogs]

I appreciate your looking it over. I realize it is a bit of a popsicle stick construct and would certainly like to dialogue with someone who felt an interest in at least clarifying the ideas. It seems like it would be a real challenge to turn it into an effective mathematical statement and someone would have to want to take it on out of personal curiosity. Regards