The purpose of this book is to construct a scientific framework of the process by which the brain responds to stimuli and integrates sensory data and, further, how it synthesizes perceptions and ideas. Because the brain puts pieces of information together in stages, classical mathematics and scientific thinking, which usually employ a single formula to sweep from minus infinity to plus infinity, are not directly applicable. The mathematical thinking needed to describe how the brain works must weight and combine small bits of information into larger pieces, do the same for the result, and repeat this operation several tomes to obtain the whole picture. The result of this study will be a representation of neural firing that yields organized information that can be observed and validated by reproducing visual images and auditory sounds. A fundamental hypothesis of this book is that all knowledge, sensing, and feeling, every idea, every fleeting thought, and every emotions arise from the firing of our neurons. And if all our awareness and sensing and knowledge are due to neural firing, then it should be possible to show how our theories of philosophy, science, mathematics, art, and humor also arise from such firings.