When you take Newtons's Calculus at the end of High School, you learn formulas for sifting out the answers to gnarly questions. But, when you integrate the quantities, you have to plug them back into the equation to see if they satisfy it because sometimes, the answers will be extraneous.
Real magic is actually very scientific. A real wizard doesn't continue to believe something that experience has shown him to be false. But, he keeps an open mind when looking for ways to cause desirable effects. Still, every shaman still needs a tradition in which to immerse him/herself. Social magic is sometimes known as white, and antisocial magic is sometimes known as black.
So, pay attention to which deities may be calling you to the Path. Eventually, a witch needs friends and spiritual siblings in order to help solve daily and arcane problems, just like a mathematician, medical researcher, or military strategist. Essentially, though, witches and wizards are healers who use natural and supernatural medicine to heal and shield their allies. Some formulas are secret, so there seems a blurring of the distinctions between doctrine and doctoring.