Limitations of Physics | Seeking Feedback on Ideas

[apeiron]

The HUP doesn't make a dichotomy of anything; it merely makes a precise, quantitative statement about quantum states.

One could try and reinterpret that statement as a dichotomy, but point it becomes far more useful to learn from what it actually says rather than trying to shoehorn it into one's a priori vague^* philosophical notions.
* see below[/size]

Note that the HUP isn't even a statement about measurement or observation -- quantum states inherently have some amount of localization in both position and momentum, and the HUP is merely a constraint on just how localized they can be.

There is a useful duality between position and momentum -- the Fourier transform swaps the two (up to a sign) -- but that doesn't have any resemblance to a dichotomy.

Despite your every attempt to wiggle around the issue, there is still the basic fact of position~momentum as mutually excluding measurements.

You and Georg are confusing yourselves by attempts to maintain a classical picture of reality where things just exist. I am talking about the detail of a process metaphysics where reality is formed by self-organising constraints.

This is kinda what metaphysics is, ancient or modern. If you don't want to be part of that discussion, it's fine by me.

 

[Hurkyl]

If your accuracy is bad, then you don't really know.

The fact that most quantum states have inherently inaccurate position doesn't prevent us from doing precise, accurate position measurements on them. It's just that if we repeat the experiment with identical states, we will see a wide distribution of positions.

(How do we know the measurement is accurate? We can check it by feeding in a known well-localized position states)

The fact that most quantum states have inherently inaccurate momentum doesn't prevent us from doing precise, accurate momentum measurements on them. It's just that if we repeat the experiment with identical states, we will see a wide distribution of momentums.

(How do we know the measurement is accurate? We can check it by feeding in a known well-localized momentum states)

The HUP says there do not exist states that are both well-localized in both momentum and position. That doesn't stop us from precisely and accurately measuring both. It's just that if we repeat the experiment with identical states, we will see a wide distribution of results.

I am talking about the detail of a process metaphysics where reality is formed by self-organising constraints.

I thought pure reason was discredited centuries ago?

 

[apeiron]

The fact that most quantum states have inherently inaccurate position doesn't prevent us from doing precise, accurate position measurements on them. It's just that if we repeat the experiment with identical states, we will see a wide distribution of positions.

(How do we know the measurement is accurate? We can check it by feeding in a known well-localized position states)

The fact that most quantum states have inherently inaccurate momentum doesn't prevent us from doing precise, accurate momentum measurements on them. It's just that if we repeat the experiment with identical states, we will see a wide distribution of momentums.

(How do we know the measurement is accurate? We can check it by feeding in a known well-localized momentum states)

The HUP says there do not exist states that are both well-localized in both momentum and position. That doesn't stop us from precisely and accurately measuring both. It's just that if we repeat the experiment with identical states, we will see a wide distribution of results.

Err, you are still dealing with a basic duality. The observations you can make divide neatly into two mutually exclusive categories - that is the meaning of orthogonal.

This is actually very important for a constraints based approach to modelling reality. For some reason, constraining a quantum potential so as to reduce its local degrees of freedom is dichotomous. Successfully reducing the degrees of freedom in one direction (say location), increases the degrees of freeom in the other (momentum).

If you are concerned with maintaining a mechanical, classical, view of reality, you will go to any lengths to avoid confronting these kinds of issues face on. I understand that.

I thought pure reason was discredited centuries ago?

And your point is?

 

[Hurkyl]

The observations you can make divide neatly into two mutually exclusive categories

A position measurement is not a momentum measurement. But that's not what you had been saying -- you had been saying a position measurement precludes you from also making a momentum measurement.

(And you forgot about all the other kinds of measurements that aren't functions of position or functions of momentum)

that is the meaning of orthogonal.

No, orthogonal means having inner product (or similar) equal to zero. In common parlance, refers to aspects that are independent of one another.

Classically, position and momentum are orthogonal in the latter sense. They most certainly are not orthogonal in quantum mechanics.

 

[apeiron]

A position measurement is not a momentum measurement. But that's not what you had been saying -- you had been saying a position measurement precludes you from also making a momentum measurement.

(And you forgot about all the other kinds of measurements that aren't functions of position or functions of momentum)

No, I've been saying one excludes the other. Complete information completely excludes information about the other...and partial information partially excludes information about the other.

And what other kinds of measurements do you want to talk about? And how would that alter things for the most fundamental kind of measurement we seem interested in?

Energy~time is also treated as a dichotomous or complementary pairing, but there are reasons why it is not as "pure" a case as position~momentum.

No, orthogonal means having inner product (or similar) equal to zero. In common parlance, refers to aspects that are independent of one another.

Classically, position and momentum are orthogonal in the latter sense. They most certainly are not orthogonal in quantum mechanics.

Yes, and what was I saying? Classical mechanics presumes position and momentum to be orthogonal, independent, measurements. There is no need for a further constraint to make this so. This is just the way reality is. It is a fact that simply exists. Why would we even see them related by some particular relation? You would just have position as a physical fact, momentum as another physical fact...and why stop at two? Why not a whole succession of further unrelated physical facts.

But QM showed instead that these two aspects of reality are in fact related in a very definite fashion (the HUP, the Planck scale, etc). And they are a duality. They are orthogonal. And furthermore, they are asymmetric (opposed in scale).

So QM introduces the necessity of a relationship. Position and momentum are all mixed up as a state of indeterminancy. And then further constraints have to be imposed to decohere this mixed state. (Or vague state would be more metaphysically accurate).

Classical mechanics claims position and momentum are unrelated, actually independent. QM shows they are deeply related and orthogonally organised. Constraints are needed to turn possibilities into certainties. But in a "conservation of indeterminancy" type closed system principle, increased certainty in one direction of measurement decrease certainty in its complementary direction.

 

[Pythagorean]

apeiron, how are position and momentum dichotomistic? Specifically, how are they:

a) jointly exhaustive
b) mutually exclusive

I can see how you might carefully select language to make b work, but a) doesn't make any sense to me.

 

[Hurkyl]

I can't think of any meaningful dualities or dichotomies between them.

I should add that for those who advocate categories as mathematical foundation, the main^* philosophical point actually has little to do with category theory itself -- it's that set theory unduly emphasizes the identity of mathematical objects over the interactions between mathematical objects. Category theory just happens to be a rather effective tool for describing such things.

*: Some may have other points. This is the one I'm mainly familiar with.

 

[Pythagorean]

I should add that for those who advocate categories as mathematical foundation, the main^* philosophical point actually has little to do with category theory itself -- it's that set theory unduly emphasizes the identity of mathematical objects over the interactions between mathematical objects. Category theory just happens to be a rather effective tool for describing such things.

*: Some may have other points. This is the one I'm mainly familiar with.

http://en.wikipedia.org/wiki/Abstract_nonsense

 

[apeiron]

apeiron, how are position and momentum dichotomistic? Specifically, how are they:

a) jointly exhaustive
b) mutually exclusive

I can see how you might carefully select language to make b work, but a) doesn't make any sense to me.

Metaphysics arrived at a variety of dichotomies that appeared exhaustive. That is, you had two terms, each of which was defined as having nothing of the other, but which also together then covered all possibilities.

So for instance, stasis~flux. You had a separation into that which was defined by its lack of change, and its antithesis which was defined by its lack of fixity. It was agreed - because no one could come up with anything to contradict it - that these two terms defined the landscape of what was possible.

Now modern physics uses a number of dichotomies that are rooted in stasis~flux, such as space~time (the set of locations, the space of possible transformations), and position~momentum (again what is fixed vs what moves).

What is so hard to understand about any of this?

 

[tom.stoer]

@apeiron:

For some time I had the feeling that I understand what you are saying in into which direction this discussion will go. I saw no problem in referring to pre-socratic philosophy as most intersting problems in metaphysics have already been spelled out then and have been discussed but solved since.

In the meantime I have ot say that the discussion has somehow went astray. One insists on "dichotomies" and "dualities" which are just words and which are used to explain wave-particle-xxx whereas wave-particle-xxx is used as an example for the above mentioned words.
Orthogonal has a very precise mathematical meaning (not so for duality) but is is used for position and momentum; just to remind you: orthogonal means nothing else but qp=. I am sure it's definately NOT what you want to say.
Then you use wave-particle- and position-momentum-"duality"; but these two "dualities" are something very different. Bohr called the first one "complementary" and never mixed it up with position-momentum-xxx afaik.

I still read this thread but I do no longer know how I should respond.

 

[Pythagorean]

What is so hard to understand about any of this?

Because you're kind of making it up, or at least discussing a particular aspect of position and momentum that is unclear. The position and momentum of a particle aren't jointly exhaustive properties of the particle (and you haven't showed how they are in your responses to me; you've only given more vague implications).

Head and Tails are a textbook dichotomy. The coin can only land on heads or tails (in the probability model; not reality where it can, with some probability, land on it's edge) so they're jointly exhaustive; the coin can't be both heads and tails at the same time, so they're mutually exclusive.

A particle can have a momentum and a velocity at the same time (they're not mutually exclusive properties of the particle) and momentum and velocity aren't the only two properties a particle can have (they're not jointly exhaustive properties of the particle).

So you must be talking about something specific. The HUP isn't dichotomistic: there is some bit of mutually exclusive (if you want to talk about the "crispness" of position and momentum, as you would call it)... but still, you can sacrifice a little from each and have both a momentum and a position that are both equally vague/crisp. It's not fixed to where you must measure one with high accuracy and one with low accuracy. You can compromise... that seems to fail the test for mutual exclusivity.

I can see how HUP might be jointly exhaustive (the HUP, after all, only has two variables in it), but you're still talking about a false dichotomy if only 1/2 conditions are satisfied.

 

[apeiron]

For some time I had the feeling that I understand what you are saying in into which direction this discussion will go. I saw no problem in referring to pre-socratic philosophy as most intersting problems in metaphysics have already been spelled out then and have been discussed but solved since.

It might to help to know where I am coming from on this. My own background is in mind science, and the evolution of the human mind in particular (four books, reviewed in Nature and American Scientist, columnist for Lancet Neurology, etc).

So I was dealing then with the problem of how to model complex adaptive systems. Which eventually led me to ask about the general principles of systems. I found that the people who talked the most sense about this were concentrated in theoretical biology - hierarchy theorists and other mathematical biologists like Howard Pattee (student of von Neumann), Stan Salthe, Robert Rosen, Robert Ulanowicz.

That led in turn to the next level down of open system or far from equilbrium thermodynamics - dissipative structure theorists, maximum entropy principle, condensed matter physics.

At the same time I - like many in theoretical biology - was struck by how "organic" early greek philosophy was. Enlightenment philosophy was irrelevant as it was largely a confused debate between the Christian church and Newtonian physics. And then there has also been a rediscovery of Peirce over the past 15 years. He has become very important in theoretical biology because semiosis is a logic of complex systems.

So you can see in all this that I have followed a logical path from mind science to the general modelling of systems. But I claim no professional expertise in physics or math. I am just interested in the philosophy of physics and maths because it is necessary to understand exactly what the mainstream presumes (and so how the systems approach differs, or where it connects).

In the meantime I have ot say that the discussion has somehow went astray. One insists on "dichotomies" and "dualities" which are just words and which are used to explain wave-particle-xxx whereas wave-particle-xxx is used as an example for the above mentioned words.
Orthogonal has a very precise mathematical meaning (not so for duality) but is is used for position and momentum; just to remind you: orthogonal means nothing else but qp=. I am sure it's definately NOT what you want to say.
Then you use wave-particle- and position-momentum-"duality"; but these two "dualities" are something very different. Bohr called the first one "complementary" and never mixed it up with position-momentum-xxx afaik.

Yeah, you try to talk to some people in a general way and they want to drag you into the small areas of knowledge where they feel they can comfortably have a go at you. You try not to get bogged them down with jargon, and they will use that against you as well.

So for example orthogonal. This has a clear general meaning that is useful. It is simple to see how two axis as right angles are completely excluded by definition from each other's space. It should be a powerful visual image. But Hurkly wants to turn it into a discussion of a particular formalism, Hilbert's space (I am presuming - he never spells things out). In Hilbert's space, it is the rays representing either an infinity of momentum vectors or position vectors that are orthogonal, not the momentum vectors and the position vectors. I get that. And it is not what I was talking about.

Same now with using the terms duality or complementary. You are quite right. I use dichotomy with a very specific technical meaning. But hey, who here has studied hierarchy theory and system science? I'm starting from scratch with most of these guys. And I don't get the impression they are the slightest interested.

Anyway, for me, duality is not dichotomy. A duality is where things are broken apart, no causal connection (like the Christian/Cartesian dualism of mind and matter). A dichotomy is not a breaking but instead a separation. And what gets separated can still mix. Which is where the connection with hierarchy theory and semiotics lies. From the separation of two things you then get arising the third thing of their mixing. This is what makes it a system - separation AND interaction. Differentiation AND integration. There is much more from hierarchy theory such as the claim that the emergence of higher levels acts back to constrain the degrees of freedom of the lower level. Duality is not actually a model of anything. The dichotomy is derived from the specifics of hiearchy theory. Though very much a work in progress.

Complementary is also not a term I would normally use - but Bohr did, picking it up from Taoist and Buddhist traditions (which in turn have ancient connections to the organic turn in Greek philosophy - ask Arivero who wrote a couple of nice papers on this; and while you are at it, remember Rovelli has just published a book on Anaximander).

The problem with complementary is that it is a single scale concept. You have a broken symmetry, but as with yin-yang, the two halves are the same size as each other.

The dichotomy, as I am defining it based on hierarchy theory arguments, is instead an asymmetrical breaking of symmetry. The form it takes is always, canonically, local~global. Furthermore, and here I go further than usual, it is a fundamentally dynamical story. It presumes a gradient (as required by far-from-equilbrium modelling) and so always expands.

So it is a technical idea with features that take a lot of explaining unless you are active in current theoretical biology/dissipative structure circles.

Now does this fundamental attempt at modelling "systems" apply to QM and cosmology? To me it seems to. I hear people grappling with the same issues such as "what is emergence", "how do we constrain our landscapes", "doesn't condensed matter physics seem like a good analogy".

And with QM, it just seems to be staring you in the face that mechanicalism no longer works. There is this squirrely two-ness going on that is fundamental.

If people aren't interested in asking why this might be so, and where two-ness - as a symmetry breaking across scale, a local~global two-ness - has popped up in other areas of scientific modelling and metaphysics, then that is their narrow minded choice.

But actually, in this thread I am not interested in defending any basic ideas. I was keen to focus on the quite specific issue of how global (ie: holonomic) contraints can organise landscapes of possibility...until the usual crowd derailed the discussions.

 

[apeiron]

Head and Tails are a textbook dichotomy.

No its not. It is a simple symmetry resulting in two things of the same scale. Which is trivial not deep. There is no reason why you can't have as many faces as you like. A dice has six. There are no natural constraints in this example, just artificial ones - arbitary choices about how many microstates you want your probablistic device to have.

A dichotomy is instead an asymmetry. It is a breaking across scale. And such breakings reduce to a canonical two-ness of local and global, the smallest vs the largest.

So when it comes to coin tossing, it is chance~necessity that is the relevant dichotomy. What you are trying to design is a system that maximises randomness by excluding the forces of determinism. One aspect is being made as large as possible by constraining the other, so making it as small as possible.

And these seem to be mutually exhaustive. The fall of the coin is either described by the chance, or by necessity. Unless of course we toss the coin in a somewhat slow, semi-deliberate fashion. Then we might be in that QM mixed state of being vaguely somewhere in between. We can't rightfully say which category ruled that particular toss.

A particle can have a momentum and a velocity at the same time (they're not mutually exclusive properties of the particle) and momentum and velocity aren't the only two properties a particle can have (they're not jointly exhaustive properties of the particle).

I don't think you can say that a particle has a momentum AND a velocity. If it has a momentum, then velocity is already spoken for. A particle can't have a momentum in one direction yet a velocity in a different one can it? They are not independent or orthogonal properties (whoops, I'm not supposed to say orthogonal). So we are back to position and momentum being the more exhaustive description.

 

[Pythagorean]

I meant momentum and position, I said velocity by accident.

 

[apeiron]

I meant momentum and position, I said velocity by accident.

In that case I already answered that if constraint is a dynamic, active, process, then weak measurements that only weakly constrain will give you weak information about both. But if we want to get crisp and definite - strong measurement - then information about one does exclude the other in the limit, does it not?

Where's the controversy?

In quantum mechanics, the Heisenberg uncertainty principle states by precise inequalities that certain pairs of physical properties, such as position and momentum, cannot be simultaneously known to arbitrarily high precision. That is, the more precisely one property is measured, the less precisely the other can be measured.
...Moreover, his principle is not a statement about the limitations of a researcher's ability to measure particular quantities of a system, but it is a statement about the nature of the system itself as described by the equations of quantum mechanics.
...The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength (and therefore an indefinite momentum). Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there can be no states that describe a particle with both a definite position and a definite momentum. The more precise the position, the less precise the momentum.

http://en.wikipedia.org/wiki/Uncertainty_principle

 

[DevilsAvocado]

Regarding Heisenberg uncertainty principle, is there really any doubts...

Walter Lewin MIT – The Uncertainty Principle

https://www.youtube.com/watch?v=<object width="640" height="505">
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</object>

 

[Pythagorean]

In that case I already answered that if constraint is a dynamic, active, process, then weak measurements that only weakly constrain will give you weak information about both. But if we want to get crisp and definite - strong measurement - then information about one does exclude the other in the limit, does it not?

Where's the controversy?

But one doesn't exclude the other. It's like F = ma. For a constant F, m must decrease for a to increase, but neither m nor a are ever excluded, one is just a higher value than the other (or they can be equal values, "medium" values). This is true for HUP, too. Neither is being excluded, especially if you take them to be equal.

A simple proof that this is possible:

that's the equation. There's nothing stopping us from taking:

dx = dp

so that:

h/2 <= dx*dp

-->

h/2 <= dx^2 = dp^2

which one's excluded?

 

[Hurkyl]

apeiron -- assuming for the sake of argument that you have meaningful ideas, you would probably have a much better time conveying them if you used words that mean what you are using them to mean, rather than words that don't mean what you are using them to mean.

 

[apeiron]

which one's excluded?

What is it that you don't understand about the phrase "in the limit".

 

[apeiron]

apeiron -- assuming for the sake of argument that you have meaningful ideas, you would probably have a much better time conveying them if you used words that mean what you are using them to mean, rather than words that don't mean what you are using them to mean.

Wow, thanks for this really intelligent response.

In mathematics, duality has numerous meanings, and although it is “a very pervasive and important concept in (modern) mathematics”[1] and “an important general theme that has manifestations in almost every area of mathematics”,[2] there is no single universally agreed definition that unifies all concepts of duality.

http://en.wikipedia.org/wiki/Duality_(mathematics )

 

[Pythagorean]

What is it that you don't understand about the phrase "in the limit".

Limits are defined, and there's thousands of them. Generally without more details, and in the right context, it means the classical limit of QM, but that would have nothing to do with HUP.

So what specific "limit" are you talking about?

 

[Pythagorean]

Wow, thanks for this really intelligent response.

Personally, I agree with Hurkyl's complaint; but it's about the word "dichotomy" not "duality"

In both philosophy and mathematics, "dichotomy" does have a particular definition (which we have discussed). Duality has all kinds of meanings, but that doesn't make using it any more meaningful... in fact, it makes it less meaningful and gives the user more wiggle room in discussions unless it's clearly defined.

on the coin as textbook dichotomy

No its not. It is a simple symmetry resulting in two things of the same scale. Which is trivial not deep. There is no reason why you can't have as many faces as you like. A dice has six. There are no natural constraints in this example, just artificial ones - arbitary choices about how many microstates you want your probablistic device to have.

Triviality and depth don't exclude things from the definition of dichotomy. The whole point of a trivial example is to illustrate the core mechanics of the definition. Furthermore, if you look at your greek roots, a dichotomy is about only TWO outcomes. If you want three, it's a trichotomy. Any more and it's a polychotomy.

Anyway, let's just ignore that terminology mistake. We're still looking at two independent outcomes (one happens or the other: heads or tails). What we have in HUP is a spectrum from more 'headish' to more 'tailish'. This would make it a false dichotomy.

 

[apeiron]

The whole point of a trivial example is to illustrate the core mechanics of the definition.

And I've already told you why your trivial example failed to illustrate the core mechanics.

Your example lacked scale differentiation. You might have two alternatives, but they were essentially the same thing. They were both microstates - designed to be exactly the same so as to make the coin toss fair. And there was no constraint on the number of microstates possible. You could instead of talked about a routlette wheel with 21 slots. So the two-ness of your probablistic device is just nothing to do with a dichotomy. Your obtuseness here becomes quite staggering.

A dichotomy - as I am actually defining it - involves a symmetry-breaking across scale. The emergence of an asymmetry.

So what we would have in your example is a scale based system we would describe as microstate~macrostate. You can have a system with an infinity of microstates. But the essential causal notion of what constitutes a microstate is singular. As is also obviously that of a macrostate. And 1+1 only makes 2.

I hope you get the difference. It really seems very simple.

As to false dichotomies, you will find that a way to avoid terminological confusion here would be to stick to the term "false dilemmas".

The logical fallacy of false dilemma (also called false dichotomy, the either-or fallacy) involves a situation in which only two alternatives are considered, when in fact there are other options. Closely related are failing to consider a range of options and the tendency to think in extremes, called black-and-white thinking. Strictly speaking, the prefix "di" in "dilemma" means "two". When a list of more than two choices is offered, but there are other choices not mentioned, then the fallacy is called the fallacy of false choice, or the fallacy of exhaustive hypotheses.

http://en.wikipedia.org/wiki/False_dilemma

The simple standard definition of a dichotomy is indeed "a set of two mutually exclusive, jointly exhaustive alternatives".

A system of mutual constraint that produces two choices in the limit as I said from the start.

The extra bit which would be new to most people is that to maximise a dichotomy, the separation has to happen across scale. This statement comes directly from hierarchy theory. It is a further modern development of a very old idea.

But, going back into greek metaphysics, it can be seen how the most fundamental and enduring dichotomies were the ones that indeed maximised asymmetry - a difference in scale. They took the canonical form of local~global (the dichotomy that IS hierarchy theory).

But you don't really want to know any of this...

 

[Pythagorean]

I'm fine with heirarchy theory and even duality in heirarchy theory (which is basically what you've described). It's the bastardization of the word dichotomy that is misleading, especially since it already has a formal (and useful!) meaning in philosophy.

 

[apeiron]

I'm fine with heirarchy theory and even duality in heirarchy theory (which is basically what you've described).

Citation please. Whose hierarchy theory are you talking about? I'm not familiar with any that are not dependent on scale.

 

[GeorgCantor]

Apeiron, your dichotomies surely work up to a point(it's amazing you keep missing this subtle point). They are not a fundamental constituent of the world and this is beyond doubt.

The discrete-continuous naive chatter dissolves at the Planck scale. The macro world of objects and appearances(and dichotomies!) is the last phenomenon that should be considered a framework for fundamental conclusions about reality.

If the scientifically presumed symmetry and reductionism are the right approach to truths about the reality we find ourselves in, the focus should be placed where those dichotomies cease to exist and blend into a sea of endless possibilities. This is currently one of the few limitations of physics that is certainly a serious roadblock towards further inquiry into why things happen the way they do.

Your bad example with the HUP is flawed in more ways than one, you forget that you exist in a relative reality. The momentum that YOU think you can know with precision is actually different in different referrential frames. So your "precision" is just a reflection of your position relative to the movement of other objects in space and an electron has multiple momentums and positions at the same time, depending on where and how you measure. There exist infinite "dichotomies" between position-momentum and neither of them is fundamentally right(the momentum you know with precision is WRONG and inaccurate in another FOR). There are no and there can be no fundamental dichotomies in this "world" of 4 relative, fundamental forces and their manifestations.

 

[apeiron]

Apeiron, your dichotomies surely work up to a point(it's amazing you keep missing this subtle point). They are not a fundamental constituent of the world and this is beyond doubt.

What is a "fundamental constituent"? Please define. Is a constituent an entity, a structure, a process?

In the meantime, remember that I am talking about the modelling of reality. And the three important "constituents" of this model are:

1) Vagueness - a model of how things begin.
2) Dichotomies - a model of how things develop.
3) Hierarchies - a model of how things end.

This is a modern re-working of Peirce's synechism.

 

[GeorgCantor]

What is a "fundamental constituent"? Please define.

That's difficult, but i'd put my bets on "my experience", "quantum vacuum" and "planck scale".

Is a constituent an entity, a structure, a process?

Possibly all of these plus awareness. At the same time, none of these. The deeper we delve, the harder it becomes to recognize discrete, distinct objects and structures in the blur.

In the meantime, remember that I am talking about the modelling of reality. And the three important "constituents" of this model are:

1) Vagueness - a model of how things begin.
2) Dichotomies - a model of how things develop.
3) Hierarchies - a model of how things end.

Agreed. That's very much inline with all i can think of. Dichotomies are models that belong to certain scales, where size and dimensions become meaningful constructs.

 

[Hurkyl]

That's difficult, but i'd put my bets on "my experience", "quantum vacuum" and "planck scale".

Is that a definition of the word "fundamental constituent", as you mean it?

1) Vagueness - a model of how things begin.
2) Dichotomies - a model of how things develop.
3) Hierarchies - a model of how things end.

Is that a definition of those three words, as you mean them?

 

[apeiron]

Is that a definition of those three words, as you mean them?

Definition? I was describing how systems models divide into three general components. Hopefully this makes it clear that dichotomies are only a third of the story. Even if they are central in representing the mechanism of change, of self-organising development.

So your point is? Or perhaps you don't have one...