Since the Fool is numbered zero, the Magician is numbered one. One is the identity element for multiplication. In math, an identity element is the number that doesn’t change other numbers (when multiplied, in this case). This is why it is called the identity element: other numbers keep their identity, their same value, when multiplied by one. Their nature remains unchanged by the operation. So what is it that one is doing when it interacts with other numbers?
At the same time, every number keeps coming back to the identity element. In multiplication, every number except zero has a counterpart, and when you multiply a number times its counterpart (also called its multiplicative inverse) you get 1. So you can always come back to this identity element. In some sense, it contains the seeds of all the other numbers, or the potential to take on the identity of any other number multiplied by it.
I think there’s a resonance between the nature of the identity element and the symbolism of the Magician card. The Magician works with the natural forces represented by the tools shown in the card, but she doesn’t fundamentally change those forces; she uses them as tools to accomplish her own goals. She doesn’t change the nature of Air or Water, or restrict the burning passion of the flame she lights, but by working with them she creates change around herself. Or perhaps she creates the change within herself…
And so we are brought back to the paradoxical heart of magic. We create change by starting that change within ourselves. And yet, somehow, we retain a coherent identity. In fact, for many of us, the kinds of change that we create are a lynchpin of our identities. Think about it this way: our skills and abilities are one of the major components of our identities. What are those skills and abilities besides the ability to create change in particular ways? I go to work, and I change the world. It’s only a tiny bit, but I think it matters. Tomorrow I’ll do it again. The changes we make are something we depend on for our very sense of self.
In this sense the Magician is very much about identity because the Magician is one who makes change possible and thus creates identity, and who really has an independent identity, as opposed to the kind of blank canvas that the Fool represents. The Magician has her tools to hand: she is holding all the aces of the Tarot deck, the potential power of each suit, and beginning to use them to create something new, something that could be almost anything.
At the same time, she must balance the opposites within herself, both the opposites contained in the different qualities of the suits and natural powers and the contrasts between what is and what might be. These inverses keep looping back to her, as the infinity symbol on her card keeps crossing through its own center. Out of that central point, out of her identity as an element of change, comes a realm of nearly infinite possibility, with the potential for so many different outcomes that points to the rest of the deck as an unfolding exploration.
NB: For those who are interested, zero is the additive identity – and zero also “breaks” multiplication by not having a multiplicative inverse. In many ways everything I say here about one is also true about zero under addition, but with much stranger overtones because of the way it behaves under multiplication. I chose to emphasize the properties of the numbers this way because I think it teaches more about the meanings of the cards.