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One of the cornerstones of elemental magic is an observation that the disparate elements “seek balance” and “prefer symmetry”. In brief: elements work well alone, but only work together when they offset each other equally. This observation was first documented in a treatise written by the little-known, yet oft-quoted Melf.

Part of the Second Age's “Awakening” period of magical research, Melf is known to have authored only two works that survive to this day: A simple, yet effective spell for striking a target with acid, and a theory on the fundamental properties of elemental energies that serves as a foundation to almost all modern elemental magical theory.

This latter document has been translated and annotated innumerable times over the centuries and routinely sparks debate within the decennial Council of Wizards research seminars.

The basic premise of Melf's Guidance of Symmetry (or simply “The Guidance”) states that equal parts of opposing elements can be used to invoke a magical power level over and above the level that can be obtained with a single element alone. However, if the elements are out of balance, the effect is diluted, and the power level will be markedly lower.

In the simplest case, two opposing elements (such as Fire and Water) can be brought forth in equal quantities to produce an effect that contains more than double the equivalent energy of each element.

However, the Guidance also allows for combinations of three or more elements in non-obvious ways. One example is 1 part each of Smoke and Magma plus 1.4 parts of Water. Since Smoke is the junction of Air and Fire, while Magma is the junction of Fire and Earth, it follows that 1 parts each of Smoke and Magma would be equivalent to 1/2 part each of Air and Earth, along with 1 full part Fire. However, Melf's tables show that the elements do not add in this forthright fashion. In fact, the Smoke and Magma add up to roughly 0.7 part Air and Earth, along with 1.4 parts Fire. Thus, the Air and Earth are already in balance, and to bring the entire system into symmetry requires 1.4 parts Water.

That 0.7 and 0.7 add up to 1 is oftentimes referred to as “Melf's Paradox”. However, the effects can be easily diagrammed on any flat surface.

Rather than learn Melf's arcane notation (which he refers to as “vector addition”), most Wizards memorize the “combination tables” contained in Melf's document. However, as these tables cover several pages, such memorization is a non-trivial task.

The Guidance becomes trickier when the spiritual elements are taken into account. For non-aligned magic, a simple flat diagram can be used to determine balance. However, when any portion of positive or negative energy is invoked, a three-dimensional model is needed to see what effect those energies will have on the system's symmetry.

A convenient shorthand is to treat the physical elements as if they were part of one system, while the spiritual elements form a second system. This notation, however, fails in the all-too-often case when the amount of spiritual energy is difficult to measure. (The most common explanation for this is when an incantation relies in part on the inherent “goodness” or “evilness” of the caster).

Any discussion of Melf's Guidance would be incomplete if it did not mention the numerous observations made over the centuries that defy it. Some Wizards insist that Melf had it all wrong and that far more complex rules govern the behavior of the elemental energies. However, even the critics will agree that Melf's Guidance is a useful rule for common, lower powered magics.

One side-effect of The Guidance is the creation of shadow. This quasi-elemental energy is not mentioned directly by Melf (although one obscure reference to “waste energy” is often cited as proof that Melf was at least aware of this phenomenon).

Specifically, when two elements oppose each other, a vacuum is created by their separation. This vacuum is filled by a swirling mixture of energy which contains equal parts of the opposing elements. If all six elements are brought into balance, this “opposition vacuum” will be filled with pure shadow. Until this year, such energy has always been considered (as Melf himself called it) “waste energy”. However, now every wizard interested in his future is doing research on this substance.

excerpts from “Treatise on Elements and Ethicants” by Bigby:

…where Melf fell short was in not considering the degree of free will in actions and power. Where Good and Evil are weak human manifestations of positive and negative energy, he neglects the orthogonal Ethicants, Axiomatic and Stochastic (others will use 'anarchic' as the chaos descriptor, but I find this an excessively sociological, rather than logical, term)

Like the concepts of Good and Evil, the precepts of Law and Chaos drive description of human behavior. So, in the same way that Melf considered the extension into positive and negative energy, I will consider the extension into Axiomatic and Stochastic behavior. The important result to note is that it takes a combination of these to create Free Will. A purely Stochastic creature will behave in a wholly unpredictable manner; in the same way, an Axiomatic creature will be created with a specific purpose or action, and will not be able to deviate from this purpose. Ergo, neither has free will. Thus, in the same way that humanoids are not capable of the purity of evil or good as Outsiders (making the concepts of corruption and redemption possible), they are also not capable of true Law of Chaos.

Magical energies are generally composed of both positive and negative energy (the power of the Fireball comes from positive energy focusing Fire; the destruction that it causes represents negative. (personal note: It would be interesting to conduct experiments on fireballs into empty areas, to see if they actually do generate power, as they lead to no destruction) In the same way, Axiomatic and Stocastic ethicants are present in the fireball. There is no uniformity of density or result in a fireball, representing the chaotic nature of the spell itself, not that of fire. To counter this, the fireball takes a very precise diameter…precise enough to allow the skilled mage to avoid harming a complatriot who is adjacent to an enemy.

Increasing the Axiomatic or Stochastic ethicants of a spell would be useful; note the means by which Vincent and Kesi managed to totally avoid being harmed by a fireball…were this a fully axiomatic spell, there would be no quiescent areas for them to dodge into; if stochastic, there would be no prediction possible.

The presense of Axiomatic or Stochastic creatures is, at this time, purely speculative (Slaad and Modrons, although known agents of 'Law' and 'Chaos', posess enough intelligence and/or will that they cannot be pure creatures)

As such, I am preparing an experiment. Having studied Flint and his summoning of Elementals, I believe I can do the same for Axiomatic and Stochastic creatures. As these are not, at my current level of experience, separable Ethicants, I will simultaneously summon one of each. Although I believe this experiment to be safe, I will enlist the aid of my compatriots in case unforseen circumstances occur (especially those involving Shadow)

In whole, this experiment (the first of several I have outlined elsewhere) will expand the theory of Magical Chromodynamics beyond Melf's crude theories of balance, into the element/antielement/ethicant/antiethicant conformal map.

Editor's Note: During his adventuring career, Bigby was infected with an epic level of Chaos – and is considered insane (even by wizard standards).

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