In Chapter 5, we noticed this constraint: The exploration of pristine experience has to be iterative. As we turn the screw ever more securely into the notion of faithfully apprehending experience, it's time to return to that constraint, which I think is of fundamental but largely overlooked importance to consciousness science. We could not have discovered the fragmented multiplicity of bulimia (Chapter 2) without an iterative method; we could not have made the slow-forming images or black-and-white images speculations (Chapter 9) without an iterative method. This chapter explains why.

I use iterative in the same way a mathematician uses it: a series of successive approximations leading to a satisfactorily close approximate solution. Suppose a mathematician uses an iterative method to determine the value of x when f(x) = F. She guesses an initial value x1 and determines f(x1). If f(x1) is satisfactorily close to F, then she's done: x1 is the desired solution. Otherwise, she uses this new information (f(x1)) to make a second (better) guess x2 and then determines f(x2). If f(x2) is satisfactorily close to F, then she's done: x2 is the desired solution. Otherwise she uses this new information (f(x2)) to make a third (even better) guess x3.