I know I'm saying the same thing over and over but what are "right words, symbols, formulae"?
I can see that arcane magic is like a science, and that you are directly accessing the power of the universe, but why would a special word or symbol help you in this? Why does gesture A + word B make a fireball (or whatever)?
And I know that its a game and all you need to say is "hey its magic!"
I just got to thinking if magic did really work, how would it work?
Well maybe I'm wrong here for taking it into an Anime/Manga example; but in Full Metal Alchemist everything they
do with Circles to most common people LOOKS like magic, but they repeatedly remind lay people that it is a science. (Even though it basically is
Functional Magic.)
Whether using Alchemy or Alkehesty in the setting, it involves channeling energy and shaping or directing from the earth or from a source and using the circle to (a symbol) that can be simply drawn in chalk, blood, or written on the body in tattoo or even carved/scratched into material and using that to change something. Activating the circle involves clapping your hands once, and then making physical contact with it. The EXACT details of how a circle works or what elements of the design do what is never actually discussed, but some symbology such as specifc symbols for the sun, god, and other things have ocassionally come up.
Still, it obeys laws of conservation/mass densisty unless you use human souls which lets you appear to make something 'out of nothing' or transmute any material into ANY other material, not just similar ones. Those who have performef the hubris of human transmutation have seen "Truth" -and though they lose a part of their body in the process, they gain an almost "Arcane" or intrinsic, unexpressable secret knowledge that lets them perform Alchemy without a circle simply by clapping their hands and using their force of will. Some circles have specific purposes, but many transmutations can be performed with just one so it seems to me that some "mental" effort is still involved.
In Naruto the source of power for "ninja magic" or "jutsu" is personal, bodily and spiritual "chakra". The hand seals/signs they use shape and concentrate that energy in a specific way to result in a specific effect. Also in Naruto are Blood Seals which are tattooed on the body or written on Scrolls, and then marked with blood, and activated with further hand seals.
Basically in similar fashion, this is why I think in fantasy settings, why symbols and gestures function in magic, it involves drawing energy into your body or into drawings and shaping/directing it with either on or both. IIRC in Complete Arcane there is a chapter whose opening pictures show some arcane somatic components, and they make me think of Naruto's hand seals.
EDIT:
My bad, its in Spell Compendium; Spell Lists (Part 2). My table biched at me once when I was playing my sorc and randomly did a fast string of Naruto Seals (I'm a nerd) -
but THATS what they look like to me! Albeit to be fair, somatic gestures probably involve a fair amount of arm waving since armor gets in the way. But the fact you can IDENTIFY a spell by its somatic compants obviously means that each spell has its own which MAY be TOTALLY UNIQUE to that spell, or else as in Naruto, there is a "set" gestures, used in varying combinations.
On a side note for those of you who watch Last Airbender series, all their martial arts moves in reguards to "bending" elements are basically full body somatic gestures.
It should also be NOTED that Arcane Verbal Components (its mentioned SOMEWHERE; IDR) that they are NOT and are NEVER mistaken for intelligble speech. These sounds essentially do the same thing as somatic components (In contrast, at least IMC divine spells may invoke prayers in various languages). I will also call attention to various mythology where god or gods "spoke" the universe into existence. In this case I would look at the universe as a kind of computer perhaps, in which case a special word or command might exist (although simply knowlede of the word/sound is probably not enough by itself, there's probably a great deal of mental effort involved, and high ability scores that normal Farmer Joe doesnt have).
Focus components aid in focusing and channeling arcane power, while material components are consumed and aid in materializing the effect.