I differentiate Kaos from chaos to emphasize a different aspect of kaotic energies, that of pure creativity. In a sense, discordance isn't an bad definition, but it's from the wrong perspective. The creative forces are manic. They focus in as many places as possible, in as many aspects as possible. A good example is the animal world. Mutations are the rule, species that don't change, eventually die out. Dinosaurs, for example, survived, but in radically different form from their ancestors. We see them everyday, as birds. They mutated and persevered. The diversity of the animal speies has led to the continuation of life on Earth. Diversity does, unfortunently, often lead to competition and conflict. The more creativity at work, the greater the eventual discordance. The Kaos forces don't work for discord though, it's the byproduct of a vital living and growing system.
I first heard of the creative aspect of chaos from Michael Moorcocks books. In his "Eternal Champion" universe there are two primary sets of God/desses, those of Law and those of Chaos. The Law god/desses get very little attention in the novels, Moorcocks conception of them is of beings who basically keep to themselves. The Chaos deities, on the other hand, are vital and active forces. They are continually interfering with the affairs of mortals. In fact, they created the older races, Elfin, and as we later find out, the younger races, Humans, as well. It's interesting to note that We aren't told why. The older races feel that the Chaos God/desses have betrayed them by creating new races. This is the nature of Chaos, it has no morality or immorality. The Chaos deities have no specific plans. The reader is left with the impression that they aren't working for any particular goals. What is displayed in Moorcocks books are the pan-fecund powers of pure Chaos, they change form constantly and the lands they inhabit are in continual flux; fields of flowers erupting into myriad flames, fantastic castles continually shifting dimensions.
The one time Moorcock deals with pure Law we are faced with a lone inhabitant of a grey featureless plane. By the force of his Will this being had reduced his home to virtual non-existence. The Eternal Champion kills the being, and the realm returns to normal. This is somewhat different from the usual conception of Chaos and Law, I found it very appealing.
Kaos is creative. I use the "K" both to differentiate it from simple chaos, and to emphasize the Magickal aspects. "K" is the eleventh letter in most alphabets, and in Qabalah it means "palm". The palm is one of the channelers of the Current, in ancient works; neolithic, Celtic, we see the Horned God sitting with one hand down and one up. He is conducting the Earth energies upward and the celestial energies downward. This is similar to the Tantric practice of raising Kundalini up from the Muladhara Chakra, the Earth center, to the Sahasra Chakra, the Celestial center. In Tantra though, the energies are internalized, they are raised in the spinal column and brought back down. In the Shamanic practice the energies are channeled through the body, but they don't stay in the body. In Kaos Magick these are both important Magickal works.
The eleventh letter stands for Daath on the tree of life. This is "knowledge", and the gateway to the City ov the Pyramids. The Kabbalists considered this to be a cursed number. They were working for the old God, Yahweh, who would prefer humanity remain in slavery. Crowley entered thee City and recounts it in Liber 418. It was there that he heard one of his true names, Nemo. While there Crowley was told "The eye is called seventy, and the triple Aleph whereby thou perceivest it, divided into the number of the terrible world that is the key of thee Abyss". The triple seventy adds up to 210, the triple eyes of Ayin, or Set, the Devil card in the Tarot. It Represents the unification of opposites in Tantra, the two being -1 and 1, -1+1=0. It is symbolized in the Ankh, the lower line being the world of plurality, the bar being the barrier to the greater consciousness or Metamind, and the circle representing the enlightened being.
The eleventh letter, K, also is important for it's emphasis on combining the female and male energies. This is part of the creative process of Universe. Eleven is six and five, the Elevenstar that Crowley created. Five is the female, Babalon, the five petalled lotus, the downward pointing pentagram in the book of Thoth. It moves from the stable foundation of the four, Earth, to the stable hexagram. It is a dynamic energy. In Tantra this is Kali, the creative aspect of Universe, at least as the Alchemists understood it to be.
The Six and Five unite in the Eleven. The pure creative energies of Kali crystallizes in the forms of the elements. Combined, they are the Elevenstar Magicks. As Magickians, one of our goals is to discern the mysteries and through Gnosis and Will become creative beings.
The next letter in Kaos is "A", Alpha. The beginning, the Aces in the Tarot. This is the first step after channeling the creative energies, to start the magickal Work, and the goal of the neophyte, to achieve the Great Work, to find the Grail and through it, remanifest. Omega is thee third letter, the end. Within Kaos is the beginning, Arche, and the end, Telos. Kaos is complete in itself, seeded by it's own will. In the very ancient Goddess creation myths we often see this parthenogenic process. The Goddess arises from the Chaos waters and from herself creates the divine consort, the Serpent. This is the last letter, "S". It is the Logos, the transmitter of the divine Gnosis. It is Hermes, Thoth, and Legba. The opener of the way. In the garden humankind was like the beast. The Serpent, sent as thee divine messenger gave humanity the Gnosis, or the knowledge to transform ourselves. This Gnosis is the knowledge of thee creative process, Magick, and with it we became more than beasts. We left the garden of our own accord.
In Physics matter is considered to be in particular energy states. Take away a certain amount ov energy, and it falls to a less active, but stable energy state, put energy in and it moves to a higher specific energy state. Kaos is the energy, Order is the stable state. From the pure Kaos, the waters ov Nuit, coums the four God/desses ov Order and Chaos. Using thee Egyptian cosmos, Set is the ordered Kaos God, Nepthys the Kaotic Kaos Goddess, Osiris thee Ordered God ov Order, and Isis the Kaotic Goddess ov Order.
Nepthys is the energy Neter for the creative power. In pure form her forces is continually reforming, never stable. This is the raging force of Universe expanding. Through the Dark Goddess Kaos manifests into thee Matrix formed by Set. Set creates thee matrix for transformative order, the dynamic state ov balance always working for a higher state ov being. Isis is thee patterned Kaos force, the energy ov nature, the creation ov mutating form. Osiris is thee force ov inertia. His power is thee tendency for all matter and energy to resist change.
Thee Priest/esses of Set/Nepthys are those intrepid and creative people who thrive on new ideas. They are thee rebels and thee inovators. From them coum thee heretics ov science and religion, those who seek change for it's own sake. Thee people who recognize that humanity thrives on diversity. Thee Priest/esses ov Isis are thee ones seeking Gnosis ov thee existing Universe. They work on what iz known, give us a deeper knowledge ov what thee heretics have discovered. Thee Priest/esses ov Osiris are thee conservatives. They wish for no change, work only for greater enslavement. They create thee rules and regulations that keep humanity from moving forward. In thee middle ages they were very powerful, in thee New Aeon they have no place. Inertia is fine for keeping creation at a steady pace, but no more than that.
Magickians are those few who seek to understand Universe and work with it. We recognize thee Kaos forces as thee true source ov Gnosis and through Will we becoum Priest/esses ov thee Dark Deities who offer them. As we progress from thee Neophyte to thee Maga/Magus we face thee oppressive forces ov thee Old Aeon with knowledge, strength, and creativity. Through these the Kaos forces manifest. Kali, Arcana, Oshun, Sophia. In Light, Life, Love and Liberty.