Thursday, 27 March 2008

Building up a list of 'quantum chaos' links.

Connections to these thoughts

- Abstractions and their significance.
- Quantum Chaos, Martin Gutzwiller, Scientific American, January 1992

A case brought forward about quantum chaos

"At about the time of Poincare's seminal work on classical chaos, Max Planck started another revolution, which would lead to the modern theory of quantum mechanics. The simple systems that Newton had studied were investigated again, but this time on the atomic scale. The quantum analogue of the humble pendulum is the laser; the flying cannonballs of the atomic world consist of beams of protons or electrons, and the rotating wheel is the spinning electron (the basis of magnetic tapes). Even the solar system itself is mirrored in each of the atoms found in the periodic table of the elements. Perhaps the single most outstanding feature of the quantum world is its smooth and wavelike nature. This feature leads to the question of how chaos makes itself felt when moving from the classical world to the quantum world. How can the extremely irregular character of classical chaos be reconciled with the smooth and wavelike nature of phenomena on the atomic scale? Does chaos exist in the quantum world'? Preliminary work seems to show that it does. Chaos is found in the distribution of energy levels of certain atomic systems; it even appears to sneak into the wave patterns associated with those levels. Chaos is also found when electrons scatter from small molecules. I must emphasize, however, that the term 'quantum chaos' serves more to describe a conundrum than to define a well-posed problem. "

No solid base? Quantum chaos not been irrevocably confirmed or in a milder version surely footed? The term only used to describe a conundrum faced up with, a curiosity but not the processes, quantum processes, themselves?

"Considering the following interpretation of the bigger picture may be helpful in coming to grips with quantum chaos. All our theoretical discussions of mechanics can be somewhat artificially divided into three compartments [see illustration] although nature recognizes none of these divisions. Elementary classical mechanics falls in the first compartment. This box contains all the nice, clean systems exhibiting simple and regular behavior, and so I shall call it R, for regular.
Also contained in R is an elaborate mathematical tool called perturbation theory which is used to calculate the effects of small interactions and extraneous disturbances, such as the influence of the sun on the moon's motion around the earth. With the help of perturbation theory, a large part of physics is understood nowadays as making relatively mild modifications of regular systems. Reality though, is much more complicated; chaotic systems lie outside the range of perturbation theory and they constitute the second compartment. Since the first detailed analyses of the systems of the second compartment were done by Poincare, I shall name this box P in his honor. It is stuffed with the chaotic dynamic systems that are the bread and butter of science. Among these systems are all the fundamental problems of mechanics, starting with three, rather than only two bodies interacting with one another, such as the earth, moon and sun, or the three atoms in the water molecule, or the three quarks in the proton. Quantum mechanics, as it has been practiced for about 90 years, belongs in the third compartment, called Q.

Mechanics, stretching that notion wider, to include anything that is described by, and, as systems such as social, mental, psychological and therefore social, mental, psychological mechanics? Attempting such an act based broadly on chaos self-similarity principle, and even further, by its virtue to go ahead and look at social, mental, psychological mechanics in novel ways?

And what about that elaborate mathematical tool called perturbation theory, which is used to calculate the effects of small interactions and extraneous disturbances to regular systems? Could it be of any use in social, mental, psychological systems? Or should we take stalk of what Henri Poincare surmised, as it is mentioned in the same website.

"So thereafter, the great French mathematician-astronomer-physicist Henri Poincare surmised that the moon's motion is only mild case of a congenital disease affecting nearly everything. In the long run Poincare realized, most dynamic systems show no discernible regularity or repetitive pattern. The behavior of even a simple system can depend so sensitively on its initial conditions that the final outcome is uncertain."

That there is no discernible regularity or repetitive pattern, in most dynamic systems. That the behaviour of even a simple system can depend so sensitively on its initial conditions, that the final outcome is uncertain. Even a simple system? What is simple, but a construct, our minds devise, by removing all information contained in a system, or object, apart from what our minds deem as necessary? And being doing it, in individual or collective level alike? An abstraction that help us gain knowledge? The necessary information that our minds can handle, but in reality systems possess a lot more information that we actually see (likened to a tip of the iceberg?), observe and by virtue of that, no system is simple as it looks, and therefore, it can not be predicted, as Henri Poincare surmised.

Is that a blessing or a curse? It is certainly a blessing.

So perturbation theory, dealing with the minute differences, in initial conditions. A precursor of that feature of chaos? I remember reading about mathematical calculations of hard problems, riddled with infinities, which perturbation theory have been removing. Does these menacing infinities have anything to do with the dynamics of chaotic states? In a way, describing the pull or push to the path of an unfolding trajectory? That is pulled towards infinity?

And what could we make out of the statement

"With the help of perturbation theory, a large part of physics is understood nowadays as making relatively mild modifications of regular systems."

or even

"The main connection between R and P is the Kolmogorov-Arnold-Moser (KAM) theorem. The KAM theorem provides a powerful tool for calculating how much of the structure of a regular system survives when a small perturbation is introduced, and the theorem can thus identify perturbations that cause a regular system to undergo chaotic behaviour."

How much can a system take? When a small perturbation is introduced? A small change of rule, or norm or a habit? Referring to the quality of the perturbation. Its overall effect in a regular system or just a system. Taken in to account that from all the perturbations possible, it is bound to be, that only a few would actually have a profound effect on the structure of a regular system, the state of a system, the stable state attractor. Most of the perturbations would have a negligent effect.

Why did I think about conservative values? The attractors, which we will not want to change? Content with the status-quo? We do not want changes.

Sunday, 23 March 2008

Perverse legislation and City Councils

There must be a connection between the constrained generating procedures that John Holland professes and the procedures imposed by organisations such as the City Councils when dealing in its affairs, specifically the administration of the Council Tax.

Since I could see these imposed procedures generated under the constrains determined by past practices, the underlying principles should be the same and they would permeate almost any business it is involved in and further than the Council the same procedures should hold for organisations beyond Councils, which operate within the same framework of the British society at large.

An element of all these organisations is their adherence to the past. Their structure and organisation has been inherited from past organisational frameworks where they were prevalent and the whole legislative structure of the past societal models were build around them.

As this form of legislation was build to protect the business of the powerful figures amidst them, their property and well being, and strengthen further their power it was not appropriate to care for the needs of the many. In fact the many were the pawns in this framework and they were forced to abide to the rules no matter whether this meant their practical extinction, physically and figuratively.

This was a perversion of the whole system where masses of people were subjected ruthlessly in an artificial manner to the will of the most powerful figures amidst them. Only by gradually the stranglehold of the laws at certain points in history becoming unbearable to such a point to produce social unrests that the stranglehold loosened that the legislation became more representative of the society members.

But still the remnants of this legacy linger on, and is expressed in the practices of City Councils and Ross and Liddells institutions, using the courts and sheriffs to impose their will. But while in the past a visit or the involvement of sheriffs and of Majesty's courts was dreaded now however they are toothless beasts and with very little power, naturally aging as the years go by.

We should soon witness their extinction throes as they are a scourge to society a reminder of the horrid past as well as of all the legislation that accompany them and with it the outdated practices of Councils and the likes.

Concepts and retrieval. Features, tags and handles.

Trying to find a point, an edge or to use a word more modern, a tag to unravel the thoughts connected. It is what I have come across while I was reading about cognitive arrangements. Cognition describing the organization of knowledge structures in our minds. The concepts, ideas and thoughts that we have amassed and how we make use of them. I must have written something about them. All of these knowledge structures tangled up, chaotic arrangements I dare say, (I am still struggling to trace the word I am looking for), and by pulling on a specific feature you drag along the concept or concepts attached. All the concepts dragged they have specific or nonspecific connections with the feature that dragged them.

It is obvious from the above that once a concept is brought into our attention, specifically or non-specifically, it is scrutinized by our rational mechanisms for all its associated features and the feature responsible for dragging it. As a result, the concept is adapted to accommodate the new feature. A new arrangement is achieved, a new configuration depicting a new state of the world. That increases the arsenal of concepts held in storage in our brains and improves our capacity to assess the states the world daily presents to us, by being able to discern even more subtle differences between the states presented.

Oh fuck, I got the word I was looking for. Handle. Handles to grab on and drag along the whole concept. Handle being one of the features associated with any particular concept. Any feature in a concept, thought, notion or idea can act like a handle. Taking it further, it could even bring forth feelings, sensations, fears and body responses since all these are organised in the same manner with features tagging along chains of associated responses and can act as handles. So, similarly they are dragged along in our conscious mind whenever a specific or non-specific handle is grabbed on.

Now I come across, that very same mechanism of a handle in that website. The tags, like handles, drag along a host of websites that share this particular feature, the tag. The chain of websites dragged, specifically or non-specifically connected with the tag-feature, are presented in chaotic arrangements. And, in a similar manner, as it happens in our minds, we would expect that the feature-tag that dragged along all these new websites will bring out new arrangements, new configurations, re-modeling the world states we store in our minds, adapted into new knowledge structures, hopefully improved.

Thursday, 20 March 2008

Hints for imperfect minds?

From comment #20 — June 4, 2007 @ 00:05AM — Zedd, in article 'Cold War: Mistaken Conflations and Ambiguous Concepts', written by Graham McKnight and published June 02, 2007

"I personally am not that impressed with human beings and tend to believe that we are fudging it most of the time, hoping that what we endeavor to do actually works. Revisionist history often leaves out the goofs and unintended nature of the results, simply recording the framers or leaders of that time as larger than life, having great foresight and understanding. I tend to not revere the "great" ideologies which we are so attached to. While respecting the evolution of how human beings organize themselves, I believe in a practical solution for every situation. I believe in continuous change to accommodate the changes in societies."

A quote from Zedd, which agrees with the imperfect consciousness approach and that human individuals put too much faith on the rational side of their mind, and further agrees with the Godel's incompleteness theorem.

Tuesday, 11 March 2008

Building intuitions. Informed approach.

On page 44, of "Chaos, Dynamics and Fractals, an algorithmic approach to deterministic chaos", by J. L. McCauley, I read:

"Geometrically, strange attractors are made up of a continuum of points in a way that is qualitatively and nontrivially different from smooth curves and tori: they have a fragmented structure that can be like that of a Cantor set(Chapter 4), and the motion on the Cantor-like set is either completely unstable in the sense that nearby initial conditions yield orbits that develop very unsimilar spatial patterns as a function of time (Chapter 4), or else it is only marginally stable at a boundary of chaos (Chapters 5 and 6)."

Strange attractors, a continuum of points substantially different from smooth curves and tori, the classical attractors. They are more like Cantor sets, dusts, points scattered seemingly haphazardly, which makes the motion unstable as nearby initial conditions produce orbits, tracked by the motion of the phase point developing unsimilar spatial patterns, (the strange attractors?) as the time progresses to infinity. It can be seen as well as being stable marginally on the verge of chaos.

Stability is the essence? There is stability, despite being marginal even when the system develops strange attractors?

In page 41, of "Chaos, Dynamics and Fractals, an algorithmic approach to deterministic chaos", by J. L. McCauley, I read:

"We begin with the way that deterministic chaos was discovered numerically in a system of three coupled nonlinear differential equations by the meteorologist E. Lorenz, in an attempt to integrate the model on a computer. In addition, Lorenz showed analytically that orbits are attracted to enter a certain phase space volume from which escape is impossible, but which contains no stable classical attractors (equilibria, limit cycles, and tori). Consequently, he discovered numerically that nearby initial conditions yielded trajectories with entirely different spatial patterns."

Chaotic orbits, defined by the system of the three nonlinear equations, are attracted to enter a certain phase space volume from which escape is impossible. Phase space volume from which escape is impossible, trapped as time goes by, even to infinity. How that abstract phase space can be visualised in its real form? The model built by the three nonlinear equations, is a replica, it simulates events taking place in the real world. No matter how stripped down, the model is, still depicts a real situation. Weather development and orbits forever trapped in, within the boundaries of a particular phase space. Since it can not escape, confers by it, stability. Within the limits of the phase space, the sum or set of particular states, happen again and again. As the same states are repeated over and over, therefore stability , stable states.

States that, their role is to represent or are directly related to states of the world. The points plotted, swirling around within the boundaries of the phase space, the leading phase point represent the numerical values of variables of the real world. Be that temperature, moisture, wind velocity all closely intertwined, influenced by one another, constantly changing affecting world states and as their numerical counterpart reveals, being trapped within the confines of attractors, the world states that bring about are determined by the range of values permitted by the confining attractors. So there would either be rain, snow or even sunshine. The attractors provide the measure of states of the world they model about. And as the particular attractors, or subsets of attractors, or phase space patterns developed, sensitively depend on the initial conditions of the system, the small fluctuations exponentially amplified, brings about the constantly changing face of the world.


Saturday, 1 March 2008

Futile endeavours?

Gross generalisations, that is what the un-mathematical human mind can do, in view of the sheer complexity of approaching chaos manifestations mathematically. Can these be of any use? Could these assist someone in establishing a framework upon which to base action acts, understanding the workings of mind, nature, life? Is it a matter of proximity? Analysing chaos mathematically, is as if you are close to each individual trajectory, hot in its trail, its minutest detail, the tinier shift away or towards attractors. You are only capable to watch the unraveling from afar. A close scrutiny for the untrained mind is prohibitive. Is that a blessing or a curse?

Could an untrained mind draw useful conclusions? Could any conclusions drawn, in any way affect one's life, in a meaningful fulfilling way? What could drawn conclusions be compared against? Against a state of no conclusions, lack or absence of?

Extracting the general from the specific. Equipped to view the larger picture. Generalisations are easily transferred from system to system. Views are multiplied . Develop a keen eye. Fresh looks of age-old problems, all kinds of problems.