Foreword

The field of extraplanar topography has recieved much attention in recent years. This is hardly surprising, when we consider the rich theoretical yields coming from the adjoining discipline of extraplanar topology (which first proved that most basic equivalence between the completeness of any given spatio-temporal description of matter and the existence of alternate planes of reality only a few decades ago) and the spectacular observational results from recent collaborations like IHRLab and BOSECAT. Since the latter's historic release of the first-ever continuous image of our own universe's local neighborhood (see Figure 1), our species has been almost singularly focused on the practical implementation of methods for observing (and one day maybe even traversing!) the multiverse we now know to exist all around us.

Figure 1: "Rainbow Sea," the famous false-color image of the local Boundary captured through contour-interferometry by twelve satellites orbiting four different stars. Our own universe is the bottom-most singularity, visible at the tip of the branch-cut. Seventeen other singularities can be seen, including the famed "quadrupole sun" which appears brighter than the rest due to residue artifacting. Image credit: BOSECAT collaboration.

Do all of these local singularities actually contain true universes inside of them? Can these hypothetical universes support the existence of stable matter? Of life? How many more exist beyond the boundary of the image? Why do most of the visible singularities (including our own!) seem to come in pairs? Is it unusual for a world to be located at the tip of a branch-cut?

This book cannot promise to provide directly the answers to any of these questions; the answers are simply not known. But the discoveries that prompted these questions in the first place were built on the shoulders of scientific and mathematical giants: the ancient titan of Complex Analysis and the young but ferocious behemoth of Tensor Polarimetry. Together these bodies of work enable the analysis and observation of the extraplanar through the use of contour techniques and abstract imaging. This book promises to equip the attentive reader with the essential tools-of-the-trade from each of these, so that they may be ready to climb those very same shoulders and build their own science atop the summit.

This text will not be laid out like traditional books on the subject. Rather than bore the reader with the axiomatic development neccessary to derive the equivalencies that underpin extraplanar boundary mechanics, we dive right into the equivalencies themselves, and build on a pedagogy of real-world examples. The justification for this is tripartite:

The first reason is historical. The reader is invited to note that without the proginating study of complex numbers in the ancient realms, there would be no life on earth as we know it today. The most thrilling result in the field was of course (and I do state this claim with complete objectivity) Cauchy's discovery of the equivalence between contour integration and complex differentiation at the outset of Century of Loathing. As such it should hardly come as a surprise that the development of analogical methods for probing higher realities rely on the very same techniques, and are best synthesized in terms of similar equivalencies.

The second reason is somewhat circular in nature; ie, the book will be laid out this way simply because it is. Nobody is allowed to tell the author what to do. He secured the contract to write this book and can write it however he damn well pleases. If the publishers don't like his "untested pedagogical approach", that's tough titties. We're testing it right now. The stuffshirts over at Interhume would do well to remember that the author has a science prize[1], a conceptual hierarchy[2], and a locus-polarimetry technique[3] named after him. I built this field with my own sweat and blood, and I'm not about to let it be turned into some math-department proofshow.

The author makes no claims as to what the third reason is.

The final (and most extreme) non-traditional aspect of this text will be its emphasis on historical examples--and one example in particular with which we shall become intimately familiar. This emphasis is so sharp that at times it may seem to the reader more of an accounting than a guide. But fear not, dear reader: you will see in time that the journey through this example is so spectacular that it inevitably serves as a better guide to the exploration and understanding of the Numinum Boundary than any fabricated set of problems or examples could ever hope to be.

It is an exciting time to be an observational numinologist. Our list of unanswered questions in the field has exploded, and the means to tackle them lie within our reach. If you are reading this textbook, then the means very literally lie within your reach! The author hopes this text can serve as a guide to the next generation of young scientists who seek to undertake this historic work. Join me, as we lead our species forth to traverse this broad topic—and one day perhaps the Numinum itself.

Bessel J.