The electron is on that scale still point like. — Haglund

Is it actually a point or also a region of excitation?

And either way, that gets us into the issue of how you can pack three degrees of freedom into such a small space and not arrive at a triad of 200 GeV particles due to momentum uncertainty.

Preon theory looks to be all epicycles to me at the moment. But I’m interested if you can offer more motivation.

The muon g2 result is explained by considering the muon a triplet of three massless Weyl particles. Each with charge -1/3. — Haglund

How does that explain the muon discrepancy? An electron would also have the same structure by your account. So why does the electron conform to Standard Model expectations but the muon hint at other BSM particle contributions?

Don't know what you mean by electrons mixing with anti-positrons. — Haglund

https://www.quantumdiaries.org/2011/06/19/helicity-chirality-mass-and-the-higgs/

The non broken gauge state has never been observed. It's a fantasy to fit the facts, like the value of the VEV, of which the origin is unknown, which is because it's just posited on purpose. — Haglund

If you call the mainstream trend of thought a fantasy, then they are right to treat you like a crackpot.

If you made a well motivated case for why it is a blind alley, that would be a different matter.

And it explains muon g2. — Haglund

OK. How?

Everyone fears to say they don't believe in the standard. Their careers... — Haglund

Sure. They are all roped together like nervous mountaineers on an unclimbed summit. You think the prize belongs to the solo athlete with grit and flair.

But if you are going to sell preons, I would expect to see a better motivation being offered. Gauge and topological order have been working for particle physics for 60 years. You sound as if you are happy to take on K2 in your bare feet and no tent.

All elementary particles are composite in some sense even in the Standard Model view. Quarks mix like neutrinos. Photons are effective mixes of Bs and W3s. The electron mixes with the anti-positron. We are back to Chew’s S-matrix bootstrap as far as I can see.

So I don’t think preons are the answer. Or at least understood as a new deeper level of concrete particles - rather than gauge degrees of freedom - would be just to recreate the old atomistic paradox of why there would be any fundamental grain of matter at all.

But there does seem to be now broad acceptance in particle physics that all fundamental particles are composite in the fashion of a soliton or other examples of topological order in condensed matter physics.

Even I sort of agree with you on preons. :grin:

I think it's pretty obvious that the basis particles are not basic at all. I asked the question about preons on several physics forums and even a philosophy part of a forum. — Haglund

There’ve been a string of past members enthusiastic about rishons and preons here. @Prishon, @MatterGauge, @EugeneW, probably many more. In fact they exactly share almost all your enthusiasms. Shame you can’t catch up with them somewhere.
.

the idea of physical necessity such that given exactly the same causal conditions, exactly the same result must always reliably follow, no matter how well attested we might think it to be by science, does not equate to logical necessity. — Janus

But isn’t that what we would say about the running of a computer program?

So it is the other way around. The problem is the need to amend the usual notion of material cause so that it ain’t so robotically determined.

If such a physical necessity does rule, which is questionable given quantum indeterminacy, then it would follow logically that given exactly the same causal conditions, then exactly the same effects must follow. — Janus

Bear in mind that the Cosmos exists to serve the second law and thus its aim is to maximise entropy. So even without the inherent quantum uncertainty, the Cosmos is committed to the production of uncertainty at every turn.

Apokrisis is claiming that flat and curved are two limits, so that all real shapes are somewhere between, being to some degree flat, and to some degree curved. — Metaphysician Undercover

Or did I say the larger picture sees flatness as poised between the opposing extremes of hyperbolic and hyperspheric curvature? And that is why the value of pi might vary between 2 and infinity, with 3.14… being the special case where the Gaussian world would intersect the Euclidean one? :chin:

Sorry, but when one's goal is to dispel illusion, — Metaphysician Undercover

:lol:

I think I see what you're saying, but that seems like an odd use of the term "a priori." — T Clark

Or maybe it's not a great term. I see Kant as very cumbersome here.

This is what Peirce fixed with his pragmatic theory of truth. He showed how reasoning involved this feedback loop of abduction, deduction and inductive confirmation.

So the choice is either to rehash the confusions of Kant endlessly, or move on to the cleaner answer.

I've nothing against Kant as he took the next step in the conversation. But he didn't resolve things in a satisfactory way.

Babies have to build their own worlds. — T Clark

This is far truer of humans than other creatures. In what may have been a happy accident, we first became bipedal apes, but that new pelvis restricted the ultimate size of the birth canal. For hominids to keep increasing their brain size, our recent ancestors had to start giving birth to kids with the same sized skull who then had an extra massive burst of brain growth immediately after being born.

That is why human babies are so helpless for so long. A newborn is producing a ridiculous number of new synapses - so many that its cortex, its higher grey matter, is essentially not connected up. The circuits aren't even created at that level.

So newborn humans are vastly more plastic. That makes them helpless, which means humans have to be far more socially organised for parenting. And that works well for the highly plastic newborns as they then have the unstructured capacity to soak up the culture and language that underpins that kind of ultra-organised sociality.

It all makes a nice feedback loop that transformed Homo erectus into Homo sapiens over the course of a million years or so.

Being useless at birth is a neural investment in being useful as a socialised adult.

Homo erectus doesn't even seem to have had an adolescent phase as we know it. Only humans have a teenage stage where the highest parts of the cortex - the impulse regulating and socially calculating frontal lobes - don't become fully myelinated, or insulated and thus fixed in place, until 20 or so.

Being risk taking and error prone is part of the Darwinian plan. It takes time to learn how to be fully adapted human. Nine months gestation doesn't get a baby much past the lower brain instinctual stage. It takes some months for a child to realise it has hands, or even to begin sorting the visual world into colours, shapes and movements with any crisp organisation.

My preference would be that we focus on the general question of what can we know without empirical knowledge rather than spending all our time on arguing the definitions of particular words. — T Clark

One quick point. How much does your question change when it is placed in time rather than regarded as an essentially timeless issue?

So speaking of "knowledge", or "truth", or "facts", has this unfortunate tendency to push it all into some Platonic realm of surety quite separate from the uncertain world. The truth "exists" in some eternal present. And yet knowledge is pragmatically a matter of experience. We develop habits of future expectation based on a history of past events.

Actual useable knowledge is thus tensed. There is the history that constrains what is to be believed or expected in terms of what in future could be the likely case.

Sure, it is useful also to take this kind of deductive approach to knowledge/truth/facts. We can abduct to make some general guess about what could be the past, and thus possibly be the future. From this hypothesis, we can then deduce the observable consequences.

That is, we can deduce the counterfactuals. We can figure out what we ought to see in the future if our guess is indeed right ... and thus also discover if what we guessed instead seems more like a wrong hypothesis.

The last bit - the checking of the predictions to confirm/deny the deductive argument - is the inductive confirmation. The more times the theory works, the more justified becomes our belief that it must be true.

This rational structure - abduction => deduction => induction - is simply the scientific method. And the deduction bit is the formal step, the application of a logical syntax or calculus - which allows us humans to step outside of our immediate experience and indeed formulate guess-based theories that have measurably-defined consequences.

Again, if you focus all your attention of the deductive apparatus, you tend to view "knowledge", "truth", and "facts", as Platonic entities - the inhabitants of some eternal present.

But if you step back to see how we came to add this formal step to our usual "experience based" habits of future forecasting, then you can see how there is a larger temporal arc at work.

Deduction - as abstract syntax - works when firmly anchored in the pragmatism of learning from the world so as to be able to live in that world. But knowledge, truth and facts aren't literally the objects of some other world.

Matt is great. But not had time to catch up on that one yet.

There's method to the madness. — Metaphysician Undercover

Not really if you simply confirm what I argue while denying you confirm what I argue.

We just need to know the proper techniques of application, to apply straight measurement principles to a curved world, and how to compensate if a real world measurement instrument, turns out to be not as straight as it was thought to be. — Metaphysician Undercover

Yes. That’s fine up until the point where you fail to deal with how we measure the measuring device.

That is where it all comes back to defining a reciprocal relation between bounding extremes.

The example I suggested you look at was hyperbolic geometry where the dichotomy of angle-line is replaced by the more general non-Euclidean dichotomy of spread-quandrance.

You have to go up a level of abstraction or idealisation to see a world in which line and curve are fixed in mutually relative terms.

We are no longer talking about just this line vs that curve in a flat metric. We are talking about the flatness vs curvature of the embedding metric itself.

This takes us beyond Galilean relativity to General relativity. Beyond first degree idealisation to a higher level of ideality.

So quit digging and start climbing. The view is better.

I'll dig as deep as necessary, until you recognize your mistakes. And from my experience, that will be very deep. — Metaphysician Undercover

Sounds like a plan. :clap:

And if indeed physical causation and logical necessity operate for the most part in separate domains then this is an argument against neural reductionism. After all, neural reductionists, of whom there are always plenty on this forum, will always claim that thinking is reducible to or caused by the brain, as if this is a strong argument for physicalism. But if logical necessity is separable from physical causation, then this claim can't be maintained. — Wayfarer

Well stated. The key here is that logical necessity is about rule-following or syntax. And that puts it in a tricky place regarding semantics. It leaves the business of interpretation in limbo.

And then physical causation might be modelled by us in terms of laws - the syntax of differential equations - yet what we really mean by those laws is that the world is structured by sets of constraints.

Constraints are quite different from rules. A constraint is a limit on uncertainty and hence only a relative thing. It is not a prohibition on uncertainty - which is what logical necessity would want to claim.

So if you are imagining the world as organised by constraints rather than rules, it is easy to see why indeterminism or local degrees of freedom might exist - indeed, must exist. If possibility is merely limited, then anything which is not being restricted is left free to happen. And that is why the Cosmos contains both structure and accident. If someone frames some "rules" then now everyone else knows "how to break them".

Thus there is a mirror confusion created by having these two notions of logical syntax and material constraint.

The logicist begs the question of how rules are interpreted - how the electron knows to follow the Maxwell equation. As an ontology, logical necessity seems to demand a faux agent. And this is where artificial intelligence gets itself in trouble. It is indeed why machines wouldn't seem capable of consciousness.

But material constraint then needs to be reduced to the simpler description that differential equations and the mechanical conception of nature offers.

The cosmos is a material structure that had to evolve its habits through some self-stabilising history of dissipation. It became "lawful" as the result of a complex and holistic process of development. To model such a world, we must break it down into some simple epistemic system of rules and measurements - differential equations that we "bring alive" by plugging in variables.

The world is reduced to a computation. And that is useful. It is the most efficient view - the one which discards the most information by simply ignoring all the messy historical development that made the Cosmos what it is.

So you do have this clash of ontologies - the logicist push rules, the materialist pushing constraints.

And then when you get to talking about organisms - creatures with life and mind - then you have the further thing of them being in fact world modelling systems. They exist by applying a mechanical approach to the holism of a physico-chemical realm that operates purely by material constraints.

Thus the two stories combine in the organism. We get the actual semiosis of a material system being organised by its concept of logical rule following. We get physical systems that interact with their worlds by using syntactic mechanism - codes like genes, neurons, words, numbers - and indeed gaining agency as that semiotic interaction is, holistically, a state of interpretance.

Oh lordy! Once you get set to digging yourself a hole, you never give up on the project, do you? :up:

I'd measure in the same way that curvature is normally measured, classically, relative to a central point. — Metaphysician Undercover

Sure, that will work if you live in a flat world. But the flatness of the world itself is what we want to check here.

:lol:

A flat thing has zero curvature. And anything which is not flat has some degree of curvature. — Metaphysician Undercover

And how are you measuring that degree of curvature exactly? What is your non-arbitrary yardstick? :rofl:

So all degrees are degrees of curvature, and flatness has no degrees, flat is zero degrees of curvature — Metaphysician Undercover

Let me check. So to be flat is to lack curve. And to be curved is to lack flat?

Thus we agree? :up:

All that remains is for you to explain how you measure the difference in some non-arbitrary metric basis.

I await the next bout of bluster and rant. You are never actually going to check out the primers I provide you.

Is your appeal to authority supposed to impress me? — Metaphysician Undercover

It is meant to inform you.

Can you justify your claim that space is the type of thing which can be both curved and not curved at the same time? Will you resolve this contradiction? — Metaphysician Undercover

What contradiction? Even in ordinary language, flat and curved would be a pair of dichotomously opposed limits - two extremes of the one spectrum. Something would be flat to the degree it wasn't curved, and curved to the degree it wasn't flat.

The question for maths is how to go about measuring the relative curvature of a smooth manifold once you have got past the naive Euclidean view that space is some kind of absolutely flat backdrop.

You might rant and rave in defence of this antique view. But geometry has just got on with developing the means for modelling spaces where perfect flatness only means an extreme constraint on any intrinsic curvature.

It would help to learn more about this subject before mouthing off further. For this purpose, I would suggest Wildberger's lectures on hyperbolic geometry.

The pertinent bit is how he shows that the Euclidean yardsticks developed for measuring spaces without curvature - distance and angle - must be replaced by the new dichotomy of quadrance and spread when dealing with hyperbolic "flatness".

So there is nothing arbitrary going on as it is all motivate by the rigorousness of dialectical argument.

And Appollonius had already worked out the basics for this approach back in 200 BC.

So even if your knowledge of maths is still rooted in distant antiquity, you ought to know better.

See Wildberger's lecture series - https://youtu.be/EvP8VtyhzXs

This again is incoherent. A 2d surface is a flat plane. To give that plane any type of curvature requires a third dimension. — Metaphysician Undercover

You are disputing about the most significant step forward in modern geometrical thought. Drop the hysteria.

The Gaussian radius of curvature is the reciprocal of Κ. For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature zero everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus.

Gaussian curvature is an intrinsic measure of curvature, depending only on distances that are measured on the surface, not on the way it is isometrically embedded in Euclidean space.

https://en.wikipedia.org/wiki/Gaussian_curvature

There's no such thing as parallel lines if space is curved. — Metaphysician Undercover

Crikey. And yet two lines - as x = 1 and x = 2 - can start off as points in parallel.

So your reference, parallel lines, has no place here in a curved space. — Metaphysician Undercover

Cripes. You mean non-Euclidean geometry is legit?

And your supposed concrete differences are just a product of contradictory premises. — Metaphysician Undercover

Jeepers. You mean that one of Euclid's axioms just got violated? And hence all straight lines are really just an especially constrained instance of a curve?

I suggest that you look at the differences you allude to, as the difference between internal and external, but the boundary between the two cannot be a straight line. — Metaphysician Undercover

I suggest you read up on intrinsic curvature and stop making a fool of yourself.

The relation between positive and negative curvature is not about a contradiction but our old friend, the dichotomy - the reciprocal relation, the (inverse) unity of opposites.

Right, but "positive" and "negative" curvature is an arbitrary convention of measurement, — Metaphysician Undercover

What’s arbitrary about it? Parallel lines converge in the one and diverge in the other. An ant traversing a sphere sees a different world from an ant exploring a hyperbolic space. There are concrete differences.

Right, so to actually be at that limit, as in having zero curvature, would be contradictory to having any degree of curvature at all. — Metaphysician Undercover

You have talked right past the point in your usual fashion. The uncurved line is what neatly separates the lines with positive curvature from those with negative curvature. Kind of like how zero separates the positive and negative integers.

So what is important is that it lacks curvature of both kinds.

Right, and to have zero curvature is to have no curvature at all, which is a direct contradiction of having curvature, being curved. — Metaphysician Undercover

It is the bounding limit on curvature.

And my point was, that the numbering system, by which the degrees are measured, is completely arbitrary. — Metaphysician Undercover

That point was dealt with.

the fact that I can interpret the words incorrectly, is clear evidence — Metaphysician Undercover

True that.

No science can explain me! — Haglund

How original.

I don't take anything seriously — Haglund

Yep. You spend all day posting and yet there is an aimless feel about these actions.

Of course they are bound. To copy heaven and life in it, they had to come up with and create particles and space in such a way that if the were let free all god creatures in heaven showed up in the universe. — Haglund

Is this your honest argument? The first cause is a copy of that which already existed? You are surely smart enough to see how that makes no sense and fails to end the infinite regress?

If you can’t make a serious case, don’t expect to be taken seriously.

However, to say that space is both flat and curved is contradictory. — Metaphysician Undercover

To be flat is simply to have zero curvature.

Or do you know a way to distinguish between some space which is flat, and some space which is curved? — Metaphysician Undercover

That’s where we started. Draw a triangle and see if it indeed adds up to 180 degrees.

Cosmic microwave background (CMB) researchers using data from the Wilkinson Microwave Anisotropy Probe (WMAP) have measured the angles of the longest triangle you can imagine. One corner is on Earth, and the other two are so far away that light has traveled about 13.3 billion years to reach us. Scientists found the angles of this triangle add up to 180°, to within small measurement uncertainties.

https://www.astronomy.com/magazine/ask-astro/2006/10/what-is-meant-by-the-term-flat-universe-how-is-this-flatness-supported-by-measurements-of-the-cosmic-microwave-background

This is inconsistent with language as we know it. — Metaphysician Undercover

Are you using the royal “we”?

Plainly language evolved to switch behaviours on and off in a social setting. That is what communication boils down to. Getting folk to act in coordinated fashion.

So the problems with Pattee's proposal are numerous. — Metaphysician Undercover

The problem is that you failed to interpret the words correctly. That shows how human language indeed creates ample scope for ambiguity, disagreement, personal freedom, along with clarity, agreement and communal wisdom.

You can’t be right unless you could have been wrong. And lucky for you, when you are so persistently misunderstanding what is said, the only way is up from here. :up:

It doesn't fail to account. — Haglund

Great. So step two. Could your divine creating intelligences have chosen the maths of symmetry to have been different? Could they have arranged things so that there were six or seven Platonic solids rather than five?

If you think a creator is not bound by some general principle of holistic self consistency - the principle that explains the emergence of invariances - then let’s hear how that might work.

SU(3) accounts for the strong force. It's the question if S(2)×U(1) accounts for an electroweak force. But apart from this, where did the interacting particles that made us invent these symmetries come from? — Haglund

In what way did we invent the symmetry? That’s like saying we invented circles.

SU(3) wasn’t constructed to fit the strong force. The structure of the strong force was found to be explained by the logic of this permutation symmetry.

So again, how does the symmetry fail to account for the structure of the interactions?

Are you wanting to claim that the two structures just happen to look alike rather than that a mathematical argument about a necessary regularity was found to shape an actually observed regularity?

That doesn't explain the very existence of particles, spacetime, or the invariances in them. — Haglund

In what way does SU(3) fail to account for the structure of the strong force? Let’s start you on an easy one.

Pattee says there’s no need for an ‘ontological dualism’. — Wayfarer

Sure. He is a physicalist just like me.

They needed to create the right stuff. Particles and space to interact in. Can this stuff, evolving into intelligent life across the universe, create itself? — Haglund

So perfect intelligence creates imperfect dumbness in order to create … some kind of half-arsed intelligence that exists to entropify. You’re really selling this one.

Doesn't Gödel's incompleteness theorem apply here to the laws of physics, rendering it impossible to explain the laws by making use of the laws? — Haglund

We can “explain” any law by appeal to the fact it survives the test of existing. There must be something about it that works, in the largest sense.

That something is usually a symmetry or invariance. Which makes sense. An invariance is something you just can’t seem to get rid of no matter how much you twist and turn.

So if you presume anything might be the case, you also know from the patterns of symmetry that not everything can in fact be the case.

This is not using a law to explain a law. It is reasoning about how a “law” - or unavoidable regularity - could even come to be.

That's the whole point of the closure. Eternal intelligence need not be created. Only the non-intelligent stuff of the universe. — Haglund

So perfect intelligence creates imperfect dumbness? Seems legit. :chin:

You mean, it provokes the discharge of endorphins? — Wayfarer

:grin:

Do you think it is sound to attribute agency to biology? — Wayfarer

You complaining that I gave you the tl;dr?

:chin: — Wayfarer

Pattee's clarity on these gritty matters always makes my soul sing. It also helps that we talked about them most days for five or six years. :grin:

There is a real conceptual roadblock here. In our normal everyday use of languages the very concept of a "physics of symbols" is completely foreign. We have come to think of symbol systems as having no relation to physical laws. This apparent independence of symbols and physical laws is a characteristic of all highly evolved languages, whether natural or formal. They have evolved so far from the origin of life and the genetic symbol systems that the practice and study of semiotics does not appear to have any necessary relation whatsoever to physical laws.

As Hoffmeyer and Emmeche (1991) emphasize, it is generally accepted that, "No natural law restricts the possibility-space of a written (or spoken) text.," or in Kull's (1998) words: "Semiotic interactions do not take place of physical necessity." Adding to this illusion of strict autonomy of symbolic expression is the modern acceptance of abstract symbols in science as the "hard core of objectivity" mentioned by Weyl. This isolation of symbols is what Rosen (1987) has called a "syntacticalization" of our models of the world, and also an example of what Emmeche (1994) has described as a cultural trend of "postmodern science" in which material forms have undergone a "derealization".

Another excellent example is our most popular artificial assembly of non-integrable constraints, the programmable computer. A memory-stored programmable computer is an extreme case of total symbolic control by explicit non-integrable hardware (reading, writing, and switching constraints) such that its computational trajectory determined by the program is unambiguous, and at the same time independent of physical laws (except laws maintaining the forces of normal structural constraints that do not enter the dynamics, a non-specific energy potential to drive the computer from one constrained state to another, and a thermal sink).

For the user, the computer function can be operationally described as a physics-free machine, or alternatively as a symbolically controlled, rule-based (syntactic) machine. Its behavior is usually interpreted as manipulating meaningful symbols, but that is another issue. The computer is a prime example of how the apparently physics-free function or manipulation of memory-based discrete symbol systems can easily give the illusion of strict isolation from physical dynamics.

This illusion of isolation of symbols from matter can also arise from the apparent arbitrariness of the epistemic cut. It is the essential function of a symbol to "stand for" something - its referent - that is, by definition, on the other side of the cut. This necessary distinction that appears to isolate symbol systems from the physical laws governing matter and energy allows us to imagine geometric and mathematical structures, as well as physical structures and even life itself, as abstract relations and Platonic forms. I believe, this is the conceptual basis of Cartesian mind-matter dualism.

This apparent isolation of symbolic expression from physics is born of an epistemic necessity, but ontologically it is still an illusion. In other words, making a clear distinction is not the same as isolation from all relations. We clearly separate the genotype from the phenotype, but we certainly do not think of them as isolated or independent of each other. These necessary non-integrable equations of constraint that bridge the epistemic cut and thereby allow for memory, measurement, and control are on the same formal footing as the physical equations of motion. They are called non-integrable precisely because they cannot be solved or integrated independently of the law-based dynamics.

Consequently, the idea that we could usefully study life without regard to the natural physical requirements that allow effective symbolic control is to miss the essential problem of life: how symbolic structures control dynamics.

Concluding...

Is it not plausible that life was first distinguished from non-living matter, not by some modification of physics, some intricate nonlinear dynamics, or some universal laws of complexity, but by local and unique heteropolymer constraints that exhibit detailed behavior unlike the behavior of any other known forms of matter in the universe?

In other words, biology invented the molecular switch. Suddenly physics could be turned on and off "at will". Nothing like this had ever been seen before in nature. A whole new biosemiotic game had been invented.

I can't see that in what I've been reading of him. — Wayfarer

Pattee, H.H.. [2001]. "The Physics of Symbols: Bridging the Epistemic Cut". Biosystems. Vol. 60

In more common terminology, this type of constraint is a structure that we say controls a dynamics. To control a dynamical systems implies that there are control variables that are separate from the dynamical system variables, yet they must be described in conjunction with the dynamical variables. These control variables must provide additional degrees of freedom or flexibility for the system dynamics. At the same time, typical control systems do not remove degrees of freedom from the dynamical system, although they alter the rates or ranges of system variables. Many artificial machines depend on such control constraints in the form of linkages, escapements, switches and governors. In living systems the enzymes and other allosteric macromolecules perform such control functions. The characteristic property of all these non-holonomic structures is that they cannot be usefully separated from the dynamical system they control. They are essentially nonlinear in the sense that neither the dynamics nor the control constraints can be treated separately.

This type of constraint, that I prefer to call non-integrable, solves two problems. First, it answers Lucretius' question. These flexible constraints literally cause "atoms to swerve and originate new movement" within the descriptive framework of an otherwise deterministic dynamics (this is still a long way from free will). They also account for the reading of a quiescent, rate-independent memory so as to control a rate-dependent dynamics, thereby bridging the epistemic cut between the controller and the controlled. Since law-based dynamics are based on energy, in addition to non-integrable memory reading, memory storage requires alternative states of the same energy (energy degeneracy). These flexible, allosteric, or configuration-changing structures are not integrable because their motions are not fully determined until they couple an explicit memory structure with rate-dependent laws (removal of degeneracy).

The crucial condition here is that the constraint acts on the dynamic trajectories without removing alternative configurations. Thus, the number of coordinates necessary to specify the configuration of the constrained system is always greater than the number of dynamic degrees of freedom, leaving some configurational alternatives available to "read" memory structures. This in turn requires that the forces of constraint are not all rigid, i.e., there must be some degeneracy to allow flexibility. Thus, the internal forces and shapes of non-integrable structures must change in time partly because of the memory structures and partly as a result of the dynamics they control. In other words, the equations of the constraint cannot be solved separately because they are on the same formal footing as the laws themselves, and the orbits of the system depend irreducibly on both (Whittaker, 1944; Sommerfeld, 1956; Goldstein, 1953; Neimark and Fufaev, 1972).

What is historically amazing is that this common type of constraint was not formally recognized by physicists until the end of the last century (Hertz, 1894). Such structures occur at many levels. They bridge all epistemic cuts between the controller and the controlled, the classifier and the classified, the observer and the observed. There are innumerable types of non-integrable constraints found in all mechanical devices in the forms of latches, and escapements, in electrical devices in the form of gates and switches, and in many biological allosteric macromolecules like enzymes, membrane channel proteins, and ciliary and muscle proteins. They function as the coding and decoding structures in all symbol manipulating systems.

https://homes.luddy.indiana.edu/rocha/publications/pattee/pattee.html