Limitations of Physics | Seeking Feedback on Ideas

[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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[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...

 

[Pythagorean]

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

Specifically, Timothy Allen, but your must have misunderstood something I said. I made no claim about it not being dependent on scale. I'm talking about the misuse of the word dichotomy. What you're talking about seems to be "duality in heirarchy". There's no need to altar the meaning of another word (i.e. dichotomy).

Allen's essay is actually the first hit on google for "heirarchy theory" Scroll down to "dualities in heirarchy". The word dichotomy isn't needed and it just confuses the issue.

 

[apeiron]

Specifically, Timothy Allen, but your must have misunderstood something I said. I made no claim about it not being dependent on scale. I'm talking about the misuse of the word dichotomy. What you're talking about seems to be "duality in heirarchy". There's no need to altar the meaning of another word (i.e. dichotomy).

Allen's essay is actually the first hit on google for "heirarchy theory" Scroll down to "dualities in heirarchy". The word dichotomy isn't needed and it just confuses the issue.

Hah, you bluffer. You googled hierarchy theory (perhaps you even spelt it correctly) and that was the first time you had ever heard of Allen.

If this is not the case, then I'm sure you can tell me where you first came across Allen's work and how you feel it differs from other hierarchy theory approaches - why you would choose it "specifically", rather than say Stan Salthe or Howard Pattee.

But anyway, you want to turn this into some kind of debate over which words I'm allowed to use based on your attempts to position yourself as an "expert" in the field of hierarchy theory. Well, my distinctions between these various terms - dual, complementary, dichotomy - actually arose from many years of discussion with actual hierarchy theory experts like Salthe and Pattee. So if they didn't mind, perhaps you could afford to be a little more relaxed as well.

So scroll down to duality and read on...

"The dualism in hierarchies appears to come from a set of complementarities that line up with: observer-observed, process-structure, rate-dependent versus rate-independent, and part-whole."

Part~whole, or local~global, is in fact the key one here (or speaking as someone au fait with hierarchy theory, are you suggesting something else is more central?).

Also worth noting - simply in the vain hope that we might get this thread back on track - is what Allen then says about the dichotomy of construction~constraint. The complementary actions of local and global scale.

Constraints come from above, while the limits as to what is possible come from below. The concept of hierarchy becomes confused unless one makes the distinction between limits from below and limits from above. The distinction between mechanisms below and purposes above turn on the issue of constraint versus possibility.

This is what it is all about. (Though Allen does not express the idea too clearly.)

Global scale acts downwards with constraint to restrict local degrees of freedom. But in turn, those freely expressed degrees must act bottom up to construct the global constraints. The parts have to (re)construct the whole that is forming them as parts in the first place. This is the logic of hierarchical self-organisation - a dynamic process view of systems. And the necessary causal connection between what is separated (the local from the global) is why we would call it also complementary.

Applied to QM, this model would suggest that the universe arises as a system of measurement (of global, holonomic, constraint) because it is able to restrict (decohere) what would otherwise be an infinity of degrees of freedom (indeterminacy, vagueness). And the decohered grain of material events in turn is exactly that which is sufficient to (re)build the universe as the decohering global device.

But why am I explaining the basics of hierarchy theory to you when you are already an expert and are probably penning a wiki page as we speak?

 

[Pythagorean]

Wow, that whole post was basically a personal attack.

I never claimed authority on hierarchy theory, I never said I didn't google it. I just said I don't have a problem with it (having read another source besides you). Yes, it was a google hit, but being the first hit wasn't as important as it being from a scientist. I also google scholar'd it and skimmed other authors to make sure it was consistent subject matter (and it was).

Coincidentally, the research I do falls within the domains of hierarchy theory, so a lot of the technicalities aren't difficult to grasp for me.

Anyway, the whole point is that you're wasting your time trying prove that hierarchy theory is legit or tell me about it or what the mechanics are. My problem was with you making up your own definitions, and I'm quite over it by now.

 

[apeiron]

Anyway, the whole point is that you're wasting your time trying prove that hierarchy theory is legit or tell me about it or what the mechanics are. My problem was with you making up your own definitions, and I'm quite over it by now.

I quite agree that you have been wasting my time here. You have demonstrated that you have no real knowledge on which to base any opinion about my choice of definition. To pretend otherwise was dishonest.

 

[Pythagorean]

Read my language, I used words like "seems like" and even mentioned the googe hit. How do you confuse this for authority?

Anyway, like I said, it's all very similar to the research I do (complex systems, bifurcations, chaos, spatiotemporal dynamics, etc.), It just has a name now is all.

Here's something I came across pertaining directly to our discussion though, albeit in another case besides HUP:

A single-level, scale-insensitivec oncept of patches has
led to the misleading dichotomy between "fine-grained"
and "coarse-grained" organisms( MacArthura nd Levins
1964, Pianka 1983). These terms have been used to
imply that organisms may either respond to the patch
structure( coarse-grained) or perceive the environment
as homogeneous( fine-grained).A given mosaicm ay be
used in a coarse-grainedm annerb y one organism( e.g.
a barnacle settling on an intertidal rock) and a finegrained
fashion by another (e.g. a shorebird foraging
over a large area of rocky intertidal). The distinction is
useful in calling attention to such species differences in
responses to environmental patchiness, but it fails to
consider the effects of scale or levels in patch hierarchies.
Thus, an organism that does not respond to
patchiness at one scale (fine-grained) may be sensitive
to patch differences( coarse-grained)a t other scales of
heterogeneity (Morris 1987). The shorebird that ignores
small-scale patchiness within a rocky intertidal may differentiate
strongly between a patch of rocky intertidal
habitat and patches of sandy beach or exposed dunes at
a broader scale. Whether or not an organism is fine- or
coarse-grainedi s scale dependent, yet these terms are
usually applied in a scale-insensitive manner.

from JSTOR: Oikos, Vol. 59, Nov. 2

Multiple Scales of Patchiness and Patch Structure: A Hierarchical Framework for the Study of Heterogeneity.

 

[GeorgCantor]

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?

Examples of what i consider to be the building blocks(and possibly source) of reality.


What are the unchanging, non-relative, non-contextual building blocks of the universe in your opinion?(suppose for a moment there do exist such fundamental blocks that explain the existence of relative space, matter and time)


The common opinion among physicists would probably center around the idea of supersymmetry that if you keep drilling down to find out what the smallest things are made of, you would eventually find just one thing that everything is made of, guided by some sort of universal rules of physics. It feels right, but doesn't explain the emergence of 3D space and especially the passage of time, the origin of the universal rules of physics, personal experience and free-will. At the deepest levels of inquiry, it becomes hard to make a distinction between the organizing universal rules and what one may choose to call 'the Mind of God'.

 

[apeiron]

Anyway, like I said, it's all very similar to the research I do (complex systems, bifurcations, chaos, spatiotemporal dynamics, etc.), It just has a name now is all.

That is an impressive range of areas that you do research in. Out of interest, how many papers have you published so far?

Here's something I came across pertaining directly to our discussion though, albeit in another case besides HUP.

Now how does this actually pertain to our discussion? I am baffled so please spell out what you mean.

I hope you didn't just get excited by the juxtaposition of the words "misleading" and "dichotomy" because of course you will have understood that the misleading bit (according to the authors) lies in applying the dichotomy of coarse~fine (ie: discrete~continuous) to the animals when really it should be applied to the environment the animal perceives.

So the passage is straightforward enough and indeed demonstrates the use of the term "dichotomy" in precisely the same "division by scale asymmetry" sense that I have been using it.

But I can't believe your intent here was to support my position!

 

[Pythagorean]

That is an impressive range of areas that you do research in. Out of interest, how many papers have you published so far?

Actually, it's not a wide range by any means. It's all one paper: when you look for chaos in complex systems, your largest contributing tools are spatiotemporal and bifuraction analysis. One of the more important tests is the Lyapunov exponent (which can actually be framed as a scaling problem).

You can learn all of this in one book:
Nonlinear Dynamics and Chaos
Steven Strogatz

As for papers published, I've contributed to two (maybe three soon) papers, but that doesn't really matter. Being able to understand the journal papers that are already written is more important. You have to actually climb up giants to stand on their shoulders.

Now how does this actually pertain to our discussion? I am baffled so please spell out what you mean.

I hope you didn't just get excited by the juxtaposition of the words "misleading" and "dichotomy" because of course you will have understood that the misleading bit (according to the authors) lies in applying the dichotomy of coarse~fine (ie: discrete~continuous) to the animals when really it should be applied to the environment the animal perceives.

So the passage is straightforward enough and indeed demonstrates the use of the term "dichotomy" in precisely the same "division by scale asymmetry" sense that I have been using it.

But I can't believe your intent here was to support my position!

Actually, the whole point is that there is no dichotomy. That the properties are not mutually exclusive (like momentum and position).

We'll look at it closer:

mutually exclusive (either or statement)

These terms have been used to
imply that organisms may either respond to the patch
structure( coarse-grained) or perceive the environment
as homogeneous( fine-grained).

(emphasis added)

and to elaborate, he says:

The distinction is
useful in calling attention to such species differences in
responses to environmental patchiness, but it fails to
consider the effects of scale or levels in patch hierarchies.
Thus, an organism that does not respond to
patchiness at one scale (fine-grained) may be sensitive
to patch differences( coarse-grained)a t other scales of
heterogeneity (Morris 1987).

In other words, the linear thinking fails to account for every possible observation of the system. The mutually exclusive case is a special case (an exception, not a rule) and it's misleading to carry it as such. The scale variance can (not must) affect the grain sensitivity, further complicating the system (obviously, if it's one or the other, it simplifies the system).

 

[GeorgCantor]

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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That's remarkable. This is actually the 'border' between the classical and quantum domain, in action. He states the opening is 1/100th of an inch wide, or 0.25 mm when the HUP becomes noticeable(and quantum effects kick in). Pretty damn impressive! It's always great to learn something new.

 

[apeiron]

As for papers published, I've contributed to two (maybe three soon) papers, but that doesn't really matter.

What does contributed mean? You are a co-author?

Actually, the whole point is that there is no dichotomy. That the properties are not mutually exclusive (like momentum and position).

I feeling further confused. So you are saying now momentum and position are mutually exclusive? You seemed to say something different in post 71 - "A particle can have a momentum and a velocity [sic] at the same time (they're not mutually exclusive properties of the particle)".

And you also want to say that coarse and fine are not mutually exclusive terms? That coarse is not defined by its lack of fineness, fineness by its lack of coarseness?

In other words, the linear thinking fails to account for every possible observation of the system. The mutually exclusive case is a special case (an exception, not a rule) and it's misleading to carry it as such. The scale variance can (not must) affect the grain sensitivity, further complicating the system (obviously, if it's one or the other, it simplifies the system).

Your attempt at explanation is far less clear than the passage you quote. In fact it makes no sense.

Quite clearly, the dichotomy of patchy and homogenous is anchored in "must" fashion to the scale of the observer. And this in fact is a statement straight out of hierarchy theory - particularly Stan Salthe's book on scalar hierarchies, Evolving Hierarchical Systems.

The shoreline will look patchy - inhomogenous - to the bird on its scale of perceptual interest. So it will distinguish between the rocks and the beach. But patchiness at a fine grain, such as between different coloured grains of its sand under its feet, will blur into a continuous indifference. Equally, patchiness at a scale much greater than its perceptual interest, such as perhaps the patchiness of tectonic plates, will also disappear from sight, but for precisely the opposite reason. The bird will not be able to see to the boundaries of the patch it happens to exist in.

So yes this is hierarchy theory. Yes this is also a story of upper and lower bounds of scale, it is also about an asymmetric dichotomy, following my definition. There are two bounding constraints (or event horizons) on perception - when the grain of perceptual interest becomes either too fine, or too coarse. And note, just two constraints, not three, four or some other arbitrary number.

So you say your research experience in chaos and nonlinear systems gives you an ability to understand technical papers in hierarchy theory. Well, I await evidence of that claim.

 

[apeiron]

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.

This statement troubled me. It seems accepted by others that position~momentum are complementary in just the same way.

They are what Bohr calls complementary descriptions: "[the quantum of action]...forces us to adopt a new mode of description designated as complementary in the sense that any given application of classical concepts precludes the simultaneous use of other classical concepts which in a different connection are equally necessary for the elucidation of the phenomena. (Bohr, 1929, p. 10)"
The most important example of complementary descriptions is provided by the measurements of the position and momentum of an object.

http://plato.stanford.edu/entries/qt-uncertainty/#WavParDuaCom

In addition to complementary descriptions Bohr also talks about complementary phenomena and complementary quantities. Position and momentum, as well as time and energy, are complementary quantities.

(Note, that while Bohr started from the duality between the particle and wave pictures, which are mutually exclusive also in classical physics, he later considered as complementary two descriptions which in the classical theory are united.)

And oh no, what's this?...

Instead, Bohr always stressed that the uncertainty relations are first and foremost an expression of complementarity. This may seem odd since complementarity is a dichotomic relation between two types of description whereas the uncertainty relations allow for intermediate situations between two extremes. They "express" the dichotomy in the sense that if we take the energy and momentum to be perfectly well-defined, symbolically ΔE = Δp = 0, the postion and time variables are completely undefined, Δx = Δt = ∞, and vice versa. But they also allow intermediate situations in which the mentioned uncertainties are all non-zero and finite.

 

[Pythagorean]

I feeling further confused. So you are saying now momentum and position are mutually exclusive? You seemed to say something different in post 71 - "A particle can have a momentum and a velocity [sic] at the same time (they're not mutually exclusive properties of the particle)".

And you also want to say that coarse and fine are not mutually exclusive terms? That coarse is not defined by its lack of fineness, fineness by its lack of coarseness?

No they're not mutually exclusive. I reiterated that in the previous post, you just misread it. They are NOT mutually exclusive (like position/momentum are NOT mutually exclusive).

So yes this is hierarchy theory. Yes this is also a story of upper and lower bounds of scale, it is also about an asymmetric dichotomy, following my definition.

Ok, as long as you're admitting it's your definition. You kept going back and forth. At the one point you wanted to prove that it matched the conditions of the canonical, well-known definition of "dichotomy", but then you go and try to justify using another definition. You would seem to wiggle around less if you chose one or the other. If you're using your own definition, then as I've already said, there's no argument here. It's kind of funny, since so far, it's classically called a "false dichotomy" (i.e. the discussion on mutual exclusivity)

The whole point is that you confuse people who are new to the subject (i.e. me) by using words in a way people outside the field aren't familiar with, so I don't need authority here to tell you you're not being clear and your being confusing. The idea of hierarchy theory is not lost on me though, we naturally do much analysis in the sciences with hierarchy considerations (to group and classify things in the most objective manner you can is important). More importantly, massive qualitative changes in the behavior of a system as a function of scale sizes is important to complex systems (this is bifurcation, in a nut shell). We don't discuss hierarchy theory as an observer looking from the outside, we practice it out of necessity.

So you say your research experience in chaos and nonlinear systems gives you an ability to understand technical papers in hierarchy theory. Well, I await evidence of that claim.[

Of course your being stubborn and willfully misreading my posts as to confuse yourself, so you shouldn't expect to get any clarity out of your anticipatory approach.

Maybe if you close your eyes, take a breath, and we'll try again:

The misleading dichotomy (i.e., the assumption of mutual exclusivity):
"These terms have been used to imply that organisms may either respond to the patch structure( coarse-grained) or perceive the environment is homogeneous( fine-grained)."

Ok, you see how this is an either/or statement which is necessarily mutually exclusive? And the author is talking about how this is an implication, not a truth. Then he sets the record straight:

"The distinction is useful in calling attention to such species differences in responses to environmental patchiness, but it fails to consider the effects of scale or levels in patch hierarchies. Thus, an organism that does not respond to patchiness at one scale (fine-grained) may be sensitive to patch differences (coarse-grained)a t other scales of heterogeneity (Morris 1987)."

"It fails to consider the effect of scale or levels in patch hierarchies". Now we're talking about a complex system... a nonlinear system. Ideally, the hierarchy of a complex system can be defined by the bifuractions that classify the different behaviors of the system, and this can all be measured quantitatively and in a uniform fashion (since the whole system is contained in one set of equations).

Polychotomies are necessarily linear (you have an axis, and you go from one side of the axis to the other, and the dependent variable is linear with respect to the scale. It's a polychotomy because each point on the scale is a separate outcome and you can only be at one point at time.

The author is demonstrating the nonlinearity of the scaling and grain issue. There isn't only one solution for each point on the axis, there are more dependent variables now. Mutual exclusivity fails.

This is similar to the problem with classifying the sex of organisms. Biologists have long since known that organisms aren't bound to being just male or female. They are not mutually exclusive, and there's several different ways in which they aren't. There's hermaphrodites on the one hand, or strictly genetic anomalies (like Jamie Lee Curtis) on the other, then there's also behavior to consider (sexuality for instance). Obviously, there's no clear dichotomy between male and female, since the properties of being male or female are not mutually exclusive.

 

[apeiron]

Ok, as long as you're admitting it's your definition. You kept going back and forth. At the one point you wanted to prove that it matched the conditions of the canonical, well-known definition of "dichotomy", but then you go and try to justify using another definition.

Not so. I was taking classic examples of metaphysical dichotomies (or dualities, or complementaries, or antimonies) and showing how there is a fundamental, usually unrecognised, feature to them all - the feature that actually makes them seem fundamental in a maximally divided way. And that feature is asymmetry - a dichotomisation or breaking across scale. The local~global dichotomy which then is what connects a dichotomy directly with hierarchy theory, the fully developed systems view.

It probably has skipped your notice, but I have often used the term "asymmetric dichotomy" for that reason. Again, classical metaphysics arrived at dichotomies that seemed fundamental to them. I am saying the reason for this was that they are all asymmetries. They conform to the template of local~global. Which in turn connects them directly to hierarchy theory. So this is a package of ideas that indeed sharpens the definition of the terms.

If there is any back and forth, it only reflects your confusion, or over eagerness to shout me down.

You would seem to wiggle around less if you chose one or the other. If you're using your own definition, then as I've already said, there's no argument here. It's kind of funny, since so far, it's classically called a "false dichotomy" (i.e. the discussion on mutual exclusivity)

That is so bone-headed. False dichotomies, as I have already explained, are ones where you have made arbitrary divisions - just like your coin-tossing example. The choice of how many faces a thrown object might have is as large as you like. It is a free choice, unconstrained. So chosing just two is arbitrary.

However a true dichotomy is, again as I have explained repeatedly, characterised by the fact you are constrained to just two mutually-definitional choices. And this only happens when you break a symmetry along an axis of scale. When you go local~global, as in microstate~macrostate.

A dichotomy was never called classically "a false dichotomy". That only came later as fools who did not really understand how to argue these things did indeed often come up with false dichotomies. And it is always helpful to have a term to describe what not to do.

The whole point is that you confuse people who are new to the subject (i.e. me) by using words in a way people outside the field aren't familiar with, so I don't need authority here to tell you you're not being clear and your being confusing. The idea of hierarchy theory is not lost on me though, we naturally do much analysis in the sciences with hierarchy considerations (to group and classify things in the most objective manner you can is important). More importantly, massive qualitative changes in the behavior of a system as a function of scale sizes is important to complex systems (this is bifurcation, in a nut shell). We don't discuss hierarchy theory as an observer looking from the outside, we practice it out of necessity.

Well boo hoo. People who are new to a subject should admit that rather than continually pose as quasi-experts. As you are doing all over again in saying your "research in bifurcation" makes you already someone on which the subtleties are not lost, when patently, over and over, they are.

So who is this royal "we" you keep talking about. Are you part of some group of sh** hot dynamicists who all think the same way? What are the names of the people who are the leading figures in "your group". I frequently mention the people I consider part of "my group" - Salthe, Pattee, Rosen, Friston, Grossberg, Kelso, Peirce, etc. Who else is privileged to be part of the tight intellectual circle you are implying here?

Maybe if you close your eyes, take a breath, and we'll try again:

The misleading dichotomy (i.e., the assumption of mutual exclusivity):
"These terms have been used to imply that organisms may either respond to the patch structure( coarse-grained) or perceive the environment is homogeneous( fine-grained)."

Ok, you see how this is an either/or statement which is necessarily mutually exclusive? And the author is talking about how this is an implication, not a truth. Then he sets the record straight:

Err, this is setting up a doubt about the dichotomy being a fixed perceptual response. And animal is either set in one mode or the other. Instead, the dichotomy IS the perceptual response, it is an active and task-dependent choice. Which is basic psychophysics 101.

Of courses the senses have to make the choice whether to lump or split. Ever heard of gestalt psychology, phi illusions, change blindness, all that standard stuff?

So there is no denial of a dichotomy of fine~coarse, just the very valid point that it is an active choice that brains make. By a process of top-down constraint (yes, anticipatory processing/forward modelling), the brain will seek to lump or split, so avoiding a vague representation of reality and instead arriving at a crisply divided and bounded one.

You just get everything so confused right from the first sentence again. So maybe the problem really is yours. Ever considered that?

The rest of your post is so hopelessly lost that it really is time to say game over. Sorry.

 

[Hurkyl]

Okay, you've had enough rope apeiron, thread closed.