Shock-Induced Formation of Timelike Manifolds; Conceptual Similarity to "N-dimensional" Magnetic Reconnection and Issues in Mathematics

In this mp3, I talk a little about the notion that one can divide a region of space into infinitely many subregions, and, in my opinion, one cannot do that in the way that most people think about the process of "division."

[The download url is this: (http://www.divshare.com/download/13170940-b8b)]



This is actually really interesting and covers some important issues [Sattig, 2003: (http://www.artsci.wustl.edu/~tsattig/Research_files/TP-final.pdf)], but the author makes a distinction between time and space. As a human would perceive events to be in the past or future of his or her life, those past or future events are, in any concept of spacetime that is consistent with reality, in my opinion, at least partially intact, physically, in regions of spacetime that are not completely "contained" within one's sensory "sphere" of perception. I don't know precisely what a human's perceptual region should be defined as being, but one way to think about it is to say that sheets of spacetime extend out of the brain and form a kind of thin and dynamic "coating" of one's immediate surroundings but that one experiences memories, in part, as a result of the spacetime manifolds, connecting one's mind to other regions of spacetime that one perceived in the past, becoming unstable or not as robustly-maintained as they might be. But to say that one can divide a region into infinitely many sub-regions [some of the problems with this assumption are hinted at by Morriston, 2002: (http://spot.colorado.edu/~morristo/kalam-not.html#_edn)] is, essentially, to say that one can keep going farther and farther inward, into a region that is smaller and smaller, and that one can keep "entering" this region, zooming in and zooming in, for an infinitely-long interval of "perceptual time." If this were the case, then one would, basically, be saying that this infinitely-small region is, in fact, infinitely large and that the supposedly-infinitely-small subregion has "broken out" of the region whose boundaries one initially defined as being finite. It's possible to illustrate this concept by looking at graphs in Gaussian coordinate systems. I think this image was used in a wikimedia commons article on antialiasing in computer graphics. It shows the way in which the division of a region into vast numbers of smaller regions could give the region so much depth as to cause the sub-regions to become "distant" or to "be" distant (in the sense that it requires the sub-regions, as their numbers increase without boundary, to become distant and to roll away, out of the scope of visible perception):


(This photo is in the public domain and is from Wikimedia Commons: (http://commons.wikimedia.org/wiki/File:Reconstruction-Gaussian-Zone.png)]

This point is actually very important in the context of extradimensional or non-Euclidean spacetime geometry and physics, and it's important for understanding the formation of shock-induced "break-out" manifolds (similarly, one can envision open magnetic field lines, formed by the type of magnetic reconnection in which magnetic flux lines "break out" of an existing flux loop or current loop and reconnect at sites that may be very distant from the site at which the breaking out occurred, as being timelike magnetic field lines, for example) [see Somov, 2009, p. 18, Figure 10, discussed on pp.17-18: (http://arxiv.org/pdf/0901.4697)] at sites of nuclear detonations or, as discussed in the mp3, at the sites of shock-induced particle accelerations in pulsar-wind nebulas, etc.