To understand the Electrocardiogram, one must understand both the origin of the waves (PQRST) and intervals between them (PQRST to PQRST or R-R). The waves are intrinsically generated within the heart, with some regulation by the cardiac nerves, but the intervals are extrinsically controlled primarily by the brain, through projections to both the auricular pacemakers and the ventricular tissues. That is, the intervals are regulated by the brain, as mediated through the autonomic effectors. To understand the R-R interval variations, one must understand the neural mechanism(s) that underlie changes in the T to P segments, which are lengthened and shortened in time to create the R-R variation. The Society for Neuroscience does not pay substantive attention to Cardiology, and the various societies of Cardiology do not pay much attention to Neuroscience. This two-way neglect has forced the formation of a new society devoted to both fields of inquiry. The Society for Heart-Brain Medicine was formed in 2007, and the plenary talks that established the field on its own foundation included two by the current authors (Skinner, 2007a;2007b). A paradigm is a way of thinking, and a new one is a way of "thinking outside the box." Two new paradigms were presented by us at the first SHBM Meeting and each was based on pivotal new discoveries. First, we showed that only nonlinear algorithms are appropriate for analysis of physiological data, because the data themselves are nonlinear---a nonlinear algorithm is thus a more sensitive measure of the heartbeat dynamics (e.g., of R-R variability) than all previous stochastic measures, such as the, mean, standard deviation, power spectrum, and so on. Secondly, small proteins and peptides are known to regulate physiology in parallel with the nervous system---that is, the "state" (behavioral / neural) determines the outputs of these two types of physiological effectors. Hibernation, for example, in which the cold eventually shuts off the nervous system, continues to be regulated by neuroendocrine molecules, some of which were indicated in a similar state (REM sleep) to have salutary effects on the ischemic heart (suppression of arrhythmogenesis in the electrocardiogram). This analogy between the similar states enabled conventional proteomics to be used in the other state (e.g., in hibernation) and thus formed the basis for a new way to discover drugs, "state-dependent proteomics." With the method a new (antiinfarction) drug candidate was actually discovered (Skinner, 2007a). The realization that the heartbeat intervals in the electrocardiogram are primarily regulated by the brain provides us with an entirely new way to look at the electrocardiogram -the intervals are not intrinsically regulated by currents and pacemakers within the heart, as are the waves, but rather are under extrinsic control by the brain, mediated of course through the autonomic www.intechopen.com Advances in Electrocardiograms -Methods and Analysis