Limitations of Physics | Seeking Feedback on Ideas

[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.