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(kā`ōs), in Greek religion and mythology, vacant, unfathomable space. From it arose all things, earthly and divine. There are various legends explaining it. In one version, EurynomeEurynome
, in Greek mythology, daughter of Oceanus and Tethys and mother, by Zeus, of the Graces. In the mythology of the Pelasgians, an aboriginal non-Greek people living in Greece before the Mycenaean period, she rose alone out of chaos and separated the earth from the sky.
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 rose out of Chaos and created all things. In another, Gaea sprang from Chaos and was the mother of all things. Eventually the word chaos came to mean a great confusion of matter out of which a supreme being created all life.


System behavior that depends so sensitively on the system's precise initial conditions that it is, in effect, unpredictable and cannot be distinguished from a random process, even though it is deterministic in a mathematical sense.

Throughout history, sequentially using magic, religion, and science, people have sought to perceive order and meaning in a seemingly chaotic and meaningless world. This quest for order reached its ultimate goal in the seventeenth century when newtonian dynamics provided an ordered, deterministic view of the entire universe epitomized in P. S. de Laplace's statement, “We ought then to regard the present state of the universe as the effect of its preceding state and as the cause of its succeeding state.”

But if the determinism of Laplace and Newton is totally accepted, it is difficult to explain the unpredictability of a gambling game or, more generally, the unpredictably random behavior observed in many newtonian systems. Commonplace examples of such behavior include smoke that first rises in a smooth, streamlined column from a cigarette, only to abruptly burst into wildly erratic turbulent flow (see illustration); and the unpredictable phenomena of the weather. See Fluid flow, Turbulent flow

Transition from order to chaos (turbulence) in a rising column of cigarette smokeenlarge picture
Transition from order to chaos (turbulence) in a rising column of cigarette smoke

At a more technical level, flaws in the newtonian view had become apparent by about 1900. The problem is that many newtonian systems exhibit behavior which is so exquisitely sensitive to the precise initial state or to even the slightest outside perturbation that, humanly speaking, determinism becomes a physically meaningless though mathematically valid concept. But even more is true. Many deterministic newtonian-system orbits are so erratic that they cannot be distinguished from a random process even though they are strictly determinate, mathematically speaking. Indeed, in the totality of newtonian-system orbits, erratic unpredictable randomness is overwhelmingly the most common behavior. See Classical mechanics, Determinism

One example of chaos is the evolution of life on Earth. Were this evolution deterministic, the governing laws of evolution would have had built into them anticipation of every natural crisis which has occurred over the centuries plus anticipation of every possible ecological niche throughout all time. Nature, however, economizes and uses the richness of opportunity available through chaos. Random mutations provide choices sufficient to meet almost any crisis, and natural selection chooses the proper one.

Another example concerns the problem that the human body faces in defending against all possible invaders. Again, nature appears to choose chaos as the most economical solution. Loosely speaking, when a hostile bacterium or virus enters the body, defense strategies are generated at random until a feedback loop indicates that the correct strategy has been found. A great challenge is to mimic nature and to find new and useful ways to harness chaos.

Another matter for consideration is the problem of predicting the weather or the world economy. Both these systems are chaotic and can be predicted more or less precisely only on a very short time scale. Nonetheless, by recognizing the chaotic nature of the weather and the economy, it may eventually be possible to accurately determine the probability distribution of allowed events in the future given the present. At that point it may be asserted with mathematical precision that, for example, there is a 90% chance of rain 2 months from today. Much work in chaos theory seeks to determine the relevant probability distributions for chaotic systems.

Finally, many physical systems exhibit a transition from order to chaos, as exhibited in the illustration, and much work studies the various routes to chaos. Examples include fibrillation of the heart and attacks of epilepsy, manic-depression, and schizophrenia. Physiologists are striving to understand chaos in these systems sufficiently well that these human maladies can be eliminated. See Period doubling

Reduced to basics, chaos and noise are essentially the same thing. Chaos is randomness in an isolated system; noise is randomness entering this previously isolated system from the outside. If the noise source is included to form a composite isolated system, there is again only chaos.


(kay -os) Broken terrain. The word is used in the approved name of such a surface feature on a planet or satellite.




the disordered formless matter supposed to have existed before the ordered universe


A property of some non-linear dynamic systems which exhibit sensitive dependence on initial conditions. This means that there are initial states which evolve within some finite time to states whose separation in one or more dimensions of state space depends, in an average sense, exponentially on their initial separation.

Such systems may still be completely deterministic in that any future state of the system depends only on the initial conditions and the equations describing the change of the system with time. It may, however, require arbitrarily high precision to actually calculate a future state to within some finite precision.

["On defining chaos", R. Glynn Holt <> and D. Lynn Holt <>.]

Fixed precision floating-point arithmetic, as used by most computers, may actually introduce chaotic dependence on initial conditions due to the accumulation of rounding errors (which constitutes a non-linear system).


The science that deals with the underlying order of the seemingly random nature of the universe. See fractals.
References in periodicals archive ?
Our enemy is disorganized chaos, which leads to poorly managed risks.
Disorganized attachment is a key risk factor in the development of psychopathology and later coping difficulties (Carlson, 1998; Lyons-Ruth, 1996; van Uzendoorn, Schuengel, & Bakermans-Kranenburg, 1999).
School professionals and parents are the intended audience for this book, in which contributors discuss young people, identified as "disorganized children," whose symptoms are mild enough to elude formal diagnosis but who may benefit from treatments applied to ADHD, Tourette and Asperger syndromes, dyslexia, epilepsy, OCD and other neurological conditions.
In short, if your offices look messy, disorganized or just plain tired, that glimpse can turn into a lasting image of your company that is very hard to change.
But the stark truth of Northern municipalities is they are without a game plan: disorganized. To become a cohesive progressive thinking body, key people need to be encouraged to, for example, travel to Asia and learn how to find future markets.
The agency developed organized and disorganized typologies as a result of these interviews, primarily as a means to assess the level of an offender's criminal sophistication.
When she becomes famous for her disorganized room, in defiance to what her mother feels is best, it sets the stage for a difficult conflict and some soul-searching questions.
I have far too many recipe books and a disorganized recipe collection.
Sample items for the SIAS include "I am not bothered by statisticians speaking too quickly" and "I get upset when research findings contain too much statistical terminology." Sample items for the SPAS include, "I do not worry when I hear new or unfamiliar statistical terminology, I am confident that I can understand it" and I feel anxious if a statistics class seems disorganized. Finally, sample items for the SOAS include, "I may know the proper statistical terminology expression but when I am nervous it just won't come out" and "I get upset when I know how to analyze statistical data but I just cannot interpret them."
A child with disorganized attachment may stay very close to his caregiver and be very distressed when she leaves.
If they were given the six different flavors separated, they ate about 12, and if the jelly beans were disorganized, they ate 23--almost twice as much.
Disorganized attachment in children also is highly correlated with unresolved issues of loss or trauma in parents, and with serious marital discord, partner violence, and some forms of mental illness.