In the metaphysical or conceptual sense, balance is used to mean a point between two opposite forces that is desirable over purely one state or the other, such as a balance between the metaphysical Law and Chaos – law by itself being overly controlling, chaos being overly unmanageable, balance being the point that minimizes the negatives of both.

More recently, the term balance has come to refer to a balance of power between multiple opposing forces. Lack of balance is generally considered to cause aggression by stronger forces towards weaker forces less capable of defending themselves. In the real world, unbalanced stronger forces tend to portray themselves as balanced, and use media controls to downplay this, as well as prevent weaker forces from coming together to achieve a new balance of power.

In constructed worlds, such as in video gaming, where nearly all-powerful corporate interests strive to maintain a balance of power among players, players tend to be extremely vocal about what they see as unbalanced mechanics, providing the unbalance negatively affects them. And though the strong and unbalanced or overpowered players are commonly vigorous in denial of any lack of balance, the comparative media equality among all player brings change quickly, to further a sense of balance.

The twentieth century saw the development of both law and chaos in art to the point that the end product became unintelligible at an instinctive or emotional level. Many composers saw one or other of these controlling trends as superior to the other. The truth may lie in a fundamental acceptance of balance as the controlling force in art. In time, we may even come to accept balance between structural and emotional as the essence of beauty.

The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a dynamic system may produce large variations in its long term behavior. This is sometimes presented as esoteric behavior, but can be exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position.

The phrase refers to the idea that a butterfly’s wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in a certain location. The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale alterations of events. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different. While the butterfly does not cause the tornado, the flap of its wings is an essential part of the initial conditions resulting in a tornado.

Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely.

Recurrence, the approximate return of a system towards its initial conditions, together with sensitive dependence on initial conditions are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range, since it is impossible to measure the starting atmospheric conditions completely accurately.

The term “butterfly effect” itself is related to the work of Edward Lorenz, an American mathematician and meteorologist, and is based in Chaos Theory and sensitive dependence on initial conditions. It was first described in literature by the  French mathematician Jacques Hadamard in 1890, and popularized in Pierre Duhem’s 1906 book La théorie physique son objet et sa structure (The physical theory, its purpose and structure).

The idea that one butterfly could eventually have a far-reaching ripple effect on subsequent historic events seems first to have appeared in a 1952 short story by the cience fiction author Ray Bradbury, although Lorenz made the term popular. In 1961, Lorenz was using a numerical computer model to rerun a weather prediction, when, as a shortcut on a number in the sequence, he entered the decimal .506 instead of entering the full .506127 the computer would hold.

The result was a completely different weather scenario. Lorenz published his findings in a 1963 paper for the New York Academy of Sciences noting that “One meteorologist remarked that if the theory were correct, one flap of a seagull’s wings could change the course of weather forever.” Later speeches and papers by Lorenz used the more poetic butterfly. According to Lorenz, upon failing to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” as a title.

Benoît B. Mandelbrot is a mathematician, best known as the father of fractal geometry. He was born in Warsaw, Poland. His family moved to France when he was a child, and he was educated in France. He is a dual French and American citizen. Mandelbrot now lives and works in the United States.

From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory, economics, and fluid dynamics. He became convinced that two key themes, fat tails and self similar structure, ran through a multitude of problems encountered in those fields. Mandelbrot found that price changes in financial markets did not follow a Gaussian distribution, but rather stable distributions having theoretically infinite variance. He found, for example, that cotton prices followed a Levy stable distribution with parameter equal to 1.7 rather than 2 as in a Gaussian distribution.

He also put his ideas to work in cosmology. In 1974 he offered a new explanation of Olbers’ Paradox (the “dark night sky” riddle), which states that in an infinite universe, the night sky should blaze with the light of the stars that lie in all directions, even those far away. Mandelbrot postulated that if the stars in the universe were fractally distributed, it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.

Although Mandelbrot coined the term fractal, some of the mathematical objects he presented had been described by other mathematicians. Before Mandelbrot, they had been regarded as isolated curiosities with unnatural and non intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools to extend the scope of science to non smooth objects in the real world. He highlighted their common properties, such as self similarity and scale variance.

He also emphasized the use of fractals as realistic and useful models of many rough phenomena in the real world. Natural fractals include the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies. Fractals are found in human pursuits, such as music, painting, architecture, and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry.

Mandelbrot has been called a visionary. His informal and passionate style of writing and his emphasis on visual and geometric intuition made his publication The Fractal Geometry of Nature accessible to non specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.

Discordianism is a modern religion centered on the idea that chaos is as important as order. It was founded in 1959 with the publication of its principal text, the Principia Discordia. There is some division as to whether it should be regarded as a parody religion, and if so to what degree. It has been called Zen for roundeyes, based on similarities with absurdist interpretations of the Rinzai school.

Discordianism recognizes chaos, discord, and dissent as valid and desirable qualities, in contrast with most religions which idealize harmony and order. Eris, the Greek mythological goddess of discord, has become the matron deity of the religion.

It is difficult to estimate the number of followers and correctly identify Discordian groups. There is an encouragement to form schisms and cabals. Additionally, few adherents hold Discordianism as their only or primary faith.

Many practicing Discordians believe that humanity suffers from the curse of taking itself too seriously and thus needs to be saved from this grave outlook on life. Thus the Discordians seek to reverse the curse by teaching people to laugh at themselves and their problems and lives. This, the Discordians believe, would solve most of the problems of the world.

The Principia Discordia often hints that Discordianism was founded as a dialectic antithesis to more popular religions based on order, although the rhetoric throughout the book describes chaos as a much more underlying impulse of the universe. This may have been done with the intention of merely balancing out the creative forces of order and disorder, but the focus is certainly on the more disorderly aspects of the world. At times the forces of order are even vilified.

The very idea of a Discordian organization is something of a paradox. Nevertheless, some structure is indicated in Principia Discordia. The most general group, presumably including all Discordians and potentially others, is The Discordian Society, whose definition has no meaning. Within the society are sects of Discordianism, each under the direction of an Episkopos, translated as overseer from Greek, and source of the English bishop and episcopal.

Discordians who do not form their own sects, whether they belong to someone else’s sect or not, make up the Legion of Dynamic Discord, and may be referred to as Legionnaires. Would be Discordians are told in the Principia Discordia that it is hard to describe Discordianism as a religion because Discordians do not have any specific beliefs or dogma that would set them apart from the practitioners of other religions.

The Principia Discordia was written by Malaclypse The Younger, an alias of Greg Hill. This book contains many references to an earlier source, The Honest Book of Truth. From the quotations, it seems to be arranged like the Bible, consisting of verses grouped into chapters grouped into books grouped into the Honest Book of Truth itself.

The Principia Discordia includes a large portion of a chapter of The Book of Explanations which recounts how the Honest Book of Truth was revealed to Lord Omar Khayyam Ravenhurst. It may be worth noting that the tale of the discovery of the Honest Book of Truth contains many similarities to the tale of the discovery of the Book of Mormon, and that Thornley had been a Mormon. It also includes part of the next chapter, telling how the Honest Book of Truth was acquired by a garbage collector, who refused to return it.

In April 2006, the first edition of the Principia Discordia was recovered from the John F. Kennedy archives. This contains Malaclypse the Younger’s long sought for Myth of Ichabod, more commonly known as The Myth of Starbuck. According to the first edition, this originally appeared in Summa Universalia.

While Discordianism is separate from modern neopaganism, a number of neopagans have incorporated elements of Discordianism into their beliefs. In addition, Neopagan author Margot Adler discussed Discordianism in her book, Drawing Down the Moon, while religious authority J. Gordon Melton lists Discordianism among various Neopagan groups in his Encyclopedia Of American Religions. Melton claims to have excommunicated all other Discordians, based on the fact that he is a Discordian Pope. Since every man, woman and child is considered a Discordian Pope, they then de-excommunicated themselves and each other.