What is magic? No, not card tricks or sleight of hand: real magic. To understand that you'll have to suspend your disbelief for a moment and entertain a theory.
There is no one reality, consensual or otherwise. If the everyone on earth suddenly believed that the moon was made of green cheese and the sun revolved around the Earth, really truly believed, nothing would change, not really. There is no one reality. Each of us is a reality of one. We have our own belief about how things work, our own set of preconceptions about how the world should be, and our own doubts about just how much we believe. We have to coexist in one universe, continuum, correspondence point, whatever, and so our realities overlap. Where we agree is what makes what is seen as reality. Even animals believe things, but they tend to believe what they see or smell and not overanalyze things. Day follows night, gravity holds us down, and people can't wave their hands and say a few words to make a ball of fire.
What if I told you I could do that? What if I waved my hands and said a few words and claimed to have summoned a ball of flame? At best you'd think I was making a joke. If I persisted, showed that I really believed that I could do that, you'd think I was insane. Even if I saw the ball of flame arc between my fingers and make a pretty pattern, you wouldn't. Neither would your friends. They have places where people like that won't hurt themselves. Where people like that can be talked into seeing reality how it really is, or at least how the majority of people around them think it really is.
Now, what if I was a mage? What if I was one in a million, someone whose beliefs in what was real were stronger than anyone else's belief in what was impossible? If I said a few words and made a fireball, you'd see it, because my belief would be stronger than your disbelief. You probably wouldn't believe it was magic. You'd probably expect that it was smoke and mirrors or a trick of the light. If the magic ended soon enough or you got away, you might even escape with your sense of reality intact.
Everyone does that. Even if your disbelief isn't as strong as my belief you can make it harder for me. And you could punish me for upsetting you. That's paradox; when something happens that, according to all logic, does not make sense. The collective beliefs of billions create a wall that, when pierced by an outside force, comes tumbling down on the heretic. In a universe where the status quo is to be maintained, paradox hits hard those who disrupt it.
But wait, what about technology? That would be a good question to ask. What if someone left a gun or a CD player laying around for some Amazon primative to find? One of those few people that haven't heard of technology, that wouldn't believe in anything more advanced than the atl-atl? Would the gun still fire or the CD still play, even if nobody there believed in it? It would. Any good shaman will tell you that every inanimate object has a spirit. Unlike the people around it, it doesn't doubt. Ever. It just knows what it's supposed to do and that it will do it for eternity or until it wears out or breaks. It might suffer some in the hands of an unbelieving individual, might not shoot as far, might not last as long, but it manages to slip in under the radar of belief.
That's why the Technocracy is winning. Not because science is inherently more believable than magic. Not because they won the war of Ascension. It's because of the inanimate. Enlightened Science believes that the intuition and will are just the guides on inanimate objects and principles. Gunpowder explodes when ignited, people react a certain way to music, and solar radiation makes skin cells cancerous. While a Technocratic plasma caster may work on principles that the world doesn't believe in, yet, and while it will work better in the hands of a Technocrat, the plasma cannon has a belief of its own. It knows that it was made to throw plasma, reliably and repeatably, and will do so until it wears out or breaks.
It's really a matter of permanence, which, incidentally, explains vampires, werewolves, ghosts, and assorted other nasties. Back when that kind of thing was commonplace, when people wouldn't even be the least surprised about meeting a dead man on a dark road, they were created. They've only grown in strength since then, and they've moved from our conscious belief to our unconscious. You may say that you don't believe in ghosts, that you know they're logically impossible, but can you tell me truthfully that you don't imagine translucent figures in the dark of a country road, that you would simply ignore such a thing if you saw one because it didn't exist? You might be able to rationalize it in the morning, blame it on a bad dream or a trick of the light, but right then it would be just as believable as day following night. We've been telling stories about vampires, werewolves, and ghosts for all of human history, in some form or another, and that gives them just enough of an in to our minds to continue to exist in our conception of reality.
Aha, but in that case, haven't we always told stories about mages too? About King Solomon and Merlin, about Hercules and Dr. Strange? Those were ordinary men who did the impossible, and they have just as much tradition as vampires or ghosts. You'd be right about that. There are thousands of individuals that can do the impossible every day with magic that you'd never be able to disbelieve. A man can say a proper incantation and summon a fireball. But that's not a mage. That magic works exactly the same way as the powers of vampires and ghosts. In short, it follows reliable, repeatable rules. Just like science, such sorcery has it's own spiritual permanency, its own conceptual truth that has lodged in the collective unconscious over aeons of use and is damned hard to work out. It is being worked out, though, as magic across the world becomes harder and harder over time, as magic becomes more and more unbelievable.
Then a mage isn't just a guy that can make a fireball? No, he's not. Like I said earlier, a mage is someone that can overcome your belief with his own. He doesn't use ancient hedge pathways of the unconcious. He may do something similar, following those mythic threads, and therefore less Vulgar and upsetting, but it doesn't follow any rules that you and he agree on, at least subconsciously. If he believed that he could make a fireball by just squinting his eyes the right way, even though your unconsious said that doing that requires a great deal of time and mystical words, he could do it. His act of magic is unacceptable, obscene even, and challenges your perceptions right down to the core. Even if he does such a thing unobserved, his surroundings will almost always punish him. The walls of his house probably believe, undoubtingly, that he can't do that the same way they believe that they can support the roof against gravity.
Those are two reasons why mages have paradigms. Permanence and Focus. As I mentioned, there are mythic threads. If you're forcing your beliefs on others, it only makes sense to do it in a fashion that is more unconsciously believable than others. The mage traditions are just that, traditional. They teach things that worked in the past and which are not entirely out of the universal mind. The same lessons, taught to less innovative, less strongwilled individuals can become hedge magic that works nearly anywhere. That's why the Traditions are the most powerful force against the Technocrats, because they use mythic threads that are much more firmly settled into the unconscious than those employed by the various crafts and dead sects around the world. A craft mage is much more limited in what he can do, having to take much greater steps to activate pathways and slip by collective disbelief than a traditionalist who can use weakening but still viable pathways.
But I also mentioned focus. That's really the key. Why do mages believe that they have to have runes and chants and magic wands to do something when it would be much easier to believe that just wishing is enough? Because of human nature, mostly. If you tell someone that he can change the world by following and improvising on some basic theories and rules he can do it. His powers come from his belief in their workings, but he doesn't necessarily know that. If you just told him that all he had to do was believe and it would happen, you've just screwed him up. How do you tell someone how to drive themselves insane just for the asking? If you show someone how to make a fireball by waving his hands and saying a few words, that's much more believable than showing someone how to make a fireball just by wanting it. Would it be easier for you to believe that just wanting it is easier to do than a spell? Many mages are, indeed, told the secret of what they do, but it doesn't really matter, because it's much easier to believe in something rather than nothing.
Yet that's the point. That's the prize of Ascension that everyone is fighting over. It's a shocking moment or gradual process of clarity, where you learn not only how to manipulate reality, but how to manipulate reality just by wanting it. The greatest mages are great because they've learned how to believe in nothing, how to generate belief of what they need when they need it, and then allow that belief to fade into the ether when it's no longer necessary. Once you reach this stage of enlightnment, when desire translates to belief translates to reality, it's only one more step to ultimate power or ultimate revelation. That's why mages struggle to Ascend, and that's why so few of them ever achieve it.
Would you believe that just by waving my hands and saying a few words I can make a ball of fire? I thought you might.