Declaration For Greater Independence

Pythagoreanism

(Pythagoreanism was a) philosophical school and religious brotherhood, believed to have been founded by Pythagoras of Samos, who settled in Croton in southern Italy about 525 BCE.

General features of Pythagoreanism

The character of the original Pythagoreanism is controversial, and the conglomeration of disparate features that it displayed is intrinsically confusing. Its fame rests, however, on some very influential ideas, not always correctly understood, that have been ascribed to it since antiquity. These ideas include those of (1) the metaphysic of number and the conception that reality, including music and astronomy, is, at its deepest level, mathematical in nature; (2) the use of philosophy as a means of spiritual purification; (3) the heavenly destiny of the soul and the possibility of its rising to union with the divine; (4) the appeal to certain symbols, sometimes mystical, such as the tetraktys, the golden section, and the harmony of the spheres; (5) the Pythagorean theorem; and (6) the demand that members of the order shall observe a strict loyalty and secrecy.

By laying stress on certain inner experiences and intuitive truths revealed only to the initiated, Pythagoreanism seems to have represented a soul-directed subjectivism alien to the mainstream of pre-Socratic Greek thought centering on the Ionian coast of Asia Minor, which was preoccupied with determining what the basic cosmic substance is.

In contrast with such Ionian naturalism, Pythagoreanism was akin to trends seen in mystery religions and emotional movements, such as Orphism, which often claimed to achieve through intoxication a spiritual insight into the divine origin and nature of the soul. Yet there are also aspects of it that appear to have owed much to the more sober, "Homeric" philosophy of the Ionians. The Pythagoreans, for example, displayed an interest in metaphysics, as did their naturalistic predecessors, though they claimed to find its key in mathematical form rather than in any substance. They accepted the essentially Ionian doctrines that the world is composed of opposites (wet-dry, hot-cold, and so on) and generated from something unlimited; but they added the idea of the imposition of limit upon the unlimited and the sense of a musical harmony in the universe. Again, like the Ionians, they devoted themselves to astronomical and geometrical speculation. Combining, as it does, a rationalistic theory of number with a mystic numerology and a speculative cosmology with a theory of the deeper, more enigmatic reaches of the soul, Pythagoreanism interweaves rationalism and irrationalism more inseparably than does any other movement in ancient Greek thought.

Metaphysics and number theory

According to Aristotle, number speculation is the most characteristic feature of Pythagoreanism. Things "are" number, or "resemble" number. To many Pythagoreans this concept meant that things are measurable and commensurable or proportional in terms of number—an idea of considerable significance for Western civilization. But there were also attempts to arrange a certain minimum number of pebbles so as to represent the shape of a thing—as, for instance, stars in a constellation that seem to represent an animal. For the Pythagoreans even abstracted things "have" their number: "justice" is associated with the number four and with a square, "marriage" with the number five, and so on. The psychological associations at work here have not been clarified.

The harmony of the cosmos

The sacred decad (the sum of the first four numbers) in particular has a cosmic significance in Pythagoreanism: its mystical name, tetraktys (meaning approximately "fourness"), implies 1 + 2 + 3 + 4 = 10; but it can also be thought of as a "perfect triangle."

Speculation on number and proportion led to an intuitive feeling of the harmonia ("fitting together") of the kosmos ("order of things"); and the application of the tetraktys to the theory of music revealed a hidden order in the range of sound. Pythagoras may have referred, vaguely, to the "music of the heavens," which he alone seemed able to hear; and later Pythagoreans seem to have assumed that the distances of the heavenly bodies from the earth somehow correspond to musical intervals—a theory that, under the influence of Platonic conceptions, resulted in the famous idea of the "harmony of the spheres." Though number to the early Pythagoreans was still a kind of cosmic matter, like the water or air proposed by the Ionians, their stress upon numerical proportions, harmony, and order constituted a decisive step toward a metaphysic in which form is the basic reality.

The doctrine of opposites

From the Ionians, the Pythagoreans adopted the idea of cosmic opposites, which they—perhaps secondarily—applied to their number speculation. The principal pair of opposites is the limit and the unlimited; the limit (or limiting), represented by the odd (3,5,7,...), is an active force effecting order, harmony, and "cosmos" in the unlimited, represented by the even. All kinds of opposites somehow "fit together" within the cosmos, as they do, microcosmically, in an individual person and in the Pythagorean society. There was also a Pythagorean "table of ten opposites," to which Aristotle has referred:

• limit-unlimited
• odd-even
• one-many
• right-left
• male-female
• rest-motion
• straight-curved
• light-darkness
• good-evil
• square-oblong

The arrangement of this table reflects a dualistic conception, which was apparently not original with the school, however, or accepted by all of its members.

The Pythagorean number metaphysic was also reflected in its cosmology. The unit (1), being the starting point of the number series and its principle of construction, is not itself strictly a number; for, to be a number is to be even or odd, whereas, in the Pythagorean view, "one" is seen as both even and odd. This ambivalence applies, similarly, to the total universe, conceived as the One. There was also a cosmogonical theory (a theory of the origins of the cosmos) that explained the generation of numbers and number-things from the limiting-odd and the unlimited-even— a theory that, by stages unknown to scholars, was ultimately incorporated into Plato's philosophy in his doctrine of the derivation of sensed realities from mathematical principles.

Music

The achievements of the early Pythagoreans in musical theory are somewhat less controversial. The scientific approach to music, in which musical intervals are expressed as numerical proportions, originated with them, as did also the more specific idea of harmonic "means." At an early date they discovered empirically that the basic intervals of Greek music include the elements of the tetraktys, since they have the proportions 1:2 (octave), 3:2 (fifth), and 4:3 (fourth). The discovery could have been made, for instance, in pipes or flutes or stringed instruments: the tone of a plucked string held at its middle is an octave higher than that of the whole string; the tone of a string held at the 2/3 point is a fifth higher; and that of one held at the 3/4 point is a fourth higher. Moreover, they noticed that the subtraction of intervals is accomplished by dividing these ratios by one another. In the course of the 5th century they calculated the intervals for the usual diatonic scale, the tone being represented by 9:8 (fifth minus fourth); i.e., 3/2 ÷ 4/3, and the semitone by 256:243 (fourth minus two tones); i.e., 4/3 ÷ (9/8 x 9/8). Archytas made some modification to this doctrine and also worked out the relationships of the notes in the chromatic (12-tone) scale and the enharmonic scale (involving such minute differences as that between A flat and G sharp, which on a piano are played by the same key).

Symbiosis

(Symbiosis refers to) any of several living arrangements between members of two different species, including mutualism, commensalism, and parasitism (qq.v.). Both positive (beneficial) and negative (unfavourable to harmful) associations are therefore included, and the members are called symbionts.

Any association between two species populations that live together is symbiotic, whether the species benefit, harm, or have no effect on one another.

Mutualism

(Mutualism refers to the) association between organisms of two different species in which each is benefited. Mutualistic arrangements are most likely to develop between organisms with widely differing living requirements. The partnership between nitrogen-fixing bacteria and leguminous plants is an example, as is the association between cows and rumen bacteria (the bacteria live in the digestive tract and help digest the plants eaten by the cow). The associations between tree roots and certain fungi are often mutualistic.

Intestinal flagellated protozoans and termites exhibit obligative mutualism, a strict interdependency, in which the protozoans digest the wood ingested by the termites; neither partner can survive under natural conditions without the other.

Acacia ants (Pseudomyrmex ferruginea) inhabit the bull-horn acacia (Acacia cornigera), upon which they obtain food and shelter; the acacia depends on the ants for protection from browsing animals, which the ants drive away. Neither member can survive successfully without the other, also exemplifying obligative mutualism.

The yucca moth is dependent on the yucca plant and vice versa: the moth acts as pollinator at the same time that she lays her eggs in the seed pods of the yucca; the larvae hatch and feed on some but not all the seeds. Both organisms benefit: the plant is pollinated, and the moth has a source of food for its larvae.

Commenalism

In biology, (Commenalsim refers to) a relation between individuals of two species in which one species obtains food or other benefits from the other without either harming or benefiting the latter. (This kind of relation can be contrasted with mutualism, in which both species benefit.) The commensal (the species that benefits from the association) may obtain nutrients, shelter, support, or locomotion from the host species, which is substantially unaffected. The commensal relation is often between a larger host and a smaller commensal; the host organism is unmodified, whereas the commensal species may show great structural adaptation consonant with its habits, as in the remoras that ride attached to sharks and other fishes. Both remoras and pilot fishes feed on the leftovers of their hosts' meals. A commensal relation based on shelter is seen in clown fishes (Amphiprion percula), which live unharmed among the stinging tentacles of sea anemones, where they are protected from predators. Numerous birds feed on the insects turned up by grazing mammals, while other birds obtain soil organisms stirred up by the plow. Various biting lice, fleas, and louse flies are commensals in that they feed harmlessly on the feathers of birds and on sloughed-off flakes of skin from mammals.

Parasitism

(Parasitism refers to the) relationship between two species of plants or animals in which one benefits at the expense of the other, sometimes without killing it. Parasitism is differentiated from parasitoidism, a relationship in which the host is always killed by the parasite; parasitoidism occurs in some Hymenoptera (ants, wasps, and bees), Diptera (flies), and a few Lepidoptera (butterflies and moths): the female lays her eggs in or on the host, upon which the larvae feed on hatching.

Parasites may be characterized as ectoparasites—including ticks, fleas, leeches, and lice—which live on the body surface of the host and do not themselves commonly cause disease in the host; or endoparasites, which may be either intercellular (inhabiting spaces in the host's body) or intracellular (inhabiting cells in the host's body). Intracellular parasites—such as bacteria or viruses—often rely on a third organism, known as the carrier, or vector, to transmit them to the host. Malaria, which is caused by a protozoan of the genus Plasmodium transmitted to humans by the bite of an anopheline mosquito, is an example of this type of interaction. The plant disease known as Dutch elm disease (caused by the fungus Ceratocystis ulmi) can be spread by the European elm bark beetle.

A form of parasitism called brood parasitism is practiced by the cuckoo and the cowbird, which do not build nests of their own but deposit their eggs in the nests of other species and abandon them there. Though the cowbird's parasitism does not necessarily harm its host's brood, the cuckoo may remove one or more host eggs to avoid detection, and the young cuckoo may heave the host's eggs and nestlings from the nest.

Another form of parasitism, such as that practiced by some ants on ants of other species, is known as social parasitism. Parasites may also become parasitized; such a relationship, known as hyperparasitism, may be exemplified by a protozoan (the hyperparasite) living in the digestive tract of a flea living on a dog.

Cannibalism (Animal Behavior)

(Cannibalism) in zoology, (is) the eating of any animal by another member of the same species. Cannibalism frequently serves as a mechanism to control population or to ensure the genetic contribution of an individual. In certain ants, injured immatures are regularly consumed. When food is lacking, the colony turns to the remaining healthy immatures. This practice allows the adults to survive the food shortage and live to breed again. In lions, males taking over a pride may kill and eat the existing young; the mothers who lose their cubs will then more rapidly become impregnated by the new dominant males. Aquarium guppies will regulate their population size by eating most of their young. When confined to cages, many animals, among them the popular golden hamster, may devour their young if disturbed.

Cannibalism (Human Behaviour)

Also called anthropophagy

(Cannibalism refers to the) eating of human flesh by humans. The term is derived from the Spanish name (Caríbales, or Caníbales) for the Carib, a West Indies tribe well known for its practice of cannibalism. A widespread custom going back into early human history, cannibalism has been found among peoples on most continents.

Though many early accounts of cannibalism probably were exaggerated or in error, the practice prevailed until modern times in parts of West and Central Africa, Melanesia (especially Fiji), New Guinea, Australia, among the Maoris of New Zealand, in some of the islands of Polynesia, among tribes of Sumatra, and in various tribes of North and South America.

In some regions human flesh was looked upon as a form of food, sometimes equated with animal food, as is indicated in the Melanesian pidgin term long pig. Victorious Maoris often cut up the bodies of the dead after a battle and feasted on the flesh, and the Batak of Sumatra were reported to have sold human flesh in the markets before they came under full control by the Dutch.

In other cases the consumption of particular portions or organs was a ritual means by which certain qualities of the person eaten might be obtained or by which powers of witchcraft or sorcery might be employed. Ritual murder and cannibalism in Africa were often related to sorcery. Headhunters and others often consumed bits of the bodies or heads of deceased enemies as a means of absorbing their vitality or other qualities and reducing their powers of revenge). The Aztecs apparently practiced cannibalism on a large scale as part of the ritual religious sacrifice of war captives and other victims.

In some cases, the body of a dead person was ritually eaten by his relatives, a form called endo-cannibalism. Some Aboriginal Australians performed such practices as acts of respect. In other cases, ritual cannibalism occurred as a part of the drama of secret societies.

There is no one satisfactory and all-inclusive explanation for cannibalism. Different peoples have practiced it for different reasons, and a group may practice cannibalism in one context and view it with horror in another. In any case, the spread of modernization usually results in the prohibition of such practices. In modern society cannibalism does occasionally occur as the result of extreme physical necessity in isolated surroundings.

Catabolism

(Catabolism refers to) the sequences of enzyme-catalyzed reactions by which relatively large molecules in living cells are broken down, or degraded. Part of the chemical energy released during catabolic processes is conserved in the form of energy-rich compounds (e.g., adenosine triphosphate [ATP]).

Energy is released in three phases. In the first, such large molecules as those of proteins, polysaccharides, and lipids are broken down; small amounts of energy are released in the form of heat in these processes. In the second phase, the small molecules are oxidized, liberating chemical energy to form ATP as well as heat energy, to form one of the three compounds: acetate, oxaloacetate, or α-oxoglutarate. These are oxidized to carbon dioxide during the third phase, a cyclic reaction sequence called the tricarboxylic acid (or Krebs) cycle. Hydrogen atoms or electrons from the intermediate compounds formed during the cycle are transferred (through a succession of carrier molecules) ultimately to oxygen, forming water. These events, the most important means for generating ATP in cells, are known as terminal respiration and oxidative phosphorylation.

Anabolism

Also called biosynthesis.

(Anabolism refers to) the sequences of enzyme-catalyzed reactions by which relatively complex molecules are formed in living cells from nutrients with relatively simple structures. Anabolic processes, which include the synthesis of such cell components as carbohydrates, proteins, and lipids, require energy in the form of energy-rich compounds (e.g., adenosine triphosphate) that are produced during breakdown processes. In growing cells, anabolic processes dominate over catabolic ones; in nongrowing cells, a balance exists between the two.