Human potential: via mysterious coupling of extremes?

Local Reality of Overcrowding -- Global Unreality of Overpopulation (Part #8)

It is useful to consider the possibility that any relation between local and global may indeed be more complex than is readily assumed -- if only, or especially, in cognitive terms. The challenge has been evident in the late acceptance of the Earth as a sphere moving in relation to the Sun. It is even more explicit in the attempts to reconcile the dynamics of local and global sociopolitical preoccupations. How are the many local perspectives to be understood as "moving" in relation to a global frame of reference? The insights offered by the inverse cube law, and its subtleties, help to frame exploration of requisite complexity.

Light? A good starting point is in the response to why the inverse square law -- the more obviously comprehensible pattern locally -- is not sufficient in regard to global frameworks. The relevant distinctions can be made with respect to electromagnetism of which light is perhaps the most valuable example -- especially given its metaphorical associations with comprehension.

A light wave composed of both an electric field and a magnetic field. Both are governed by the fact that the magnetic and electric field intensities drops as 1/r, where r is the distance away from the source. What diminishes as 1/r² -- according to the inverse square law -- is the power of the light. The power of the light is related to the electric field intensity times the magnetic field intensity. Because both diminish as 1/r, this results in (1/r) x (1/r) = 1/r².

The cubic behavior of fields depends on the source of the field. A radio wave, just like light, usually gets launched by an antenna. Far away from the antenna the field behaves as expected with the power of the radio wave diminishing as 1/r² -- termed "far field" behaviour. Near the antenna, the fields behave in a much more complex manner (called the "near field" behavior). Some of the fields will "cling" close to the antenna and not radiate. These are not evident in the far field, and thus it is then reasonable to use the inverse square law. Near the antenna, the field behavior, both electric and magnetic, can have inverse cubic behaviour as 1/r³.

Magnetism? Magnetic structures are different. Unlike positive or negative charged particles, a North pole or South pole does not exist by itself. They must necessarily come in pairs as magnetic dipoles, namely two opposite charges of equal magnitude fairly close together. No magnetic monopoles have yet been found. In this case the field drops off rapidly away from the magnet, so that it is the near field conditions which call for particular consideration. The far field conditions can be understood as following the inverse square law (1/r²), whereas the near field conditions are best understood in terms of the inverse cube law (1/r³). The magnetic dipole moment of an object is readily defined in terms of the torque that object experiences in a given magnetic field (André Michaud, On The Magnetostatic Inverse Cube Law and Magnetic Monopoles, International Journal of Engineering Research and Development 7, 2013, 5).

Magnetic dipole	Inverse square vs Inverse cube

Interrelating sphere and cube: The intensity of the Earth's magnetic field follows the inverse square law, but only to a degree. At high altitudes above the poles it is indeed, to a first approximation, an inverse square relationship. However, as a law it only applies to point sources, whereas close to the surface the situation is more complex, varying with latitude and longitude.

Developing the argument above for the contrasting role of the senses in terms of proximity, the relevance of the following depiction might then be explored. This endeavours to show (speculatively) how the senses associated with greatest proximity (taste and touch) are governed by the inverse cube law, in contrast to the senses operating over greater distances (hearing, sight) governed primarily by the inverse square law.

As presented, the depiction is reflected between a "local" condition of greater direct physical familiarity (left-most portion) and a "global" (distant) condition (right-most portion). The prevailing role of the inverse cube law in the later case is usefully exemplified by proximity to a "black hole", whether imagined in astrophysical terms or experienced metaphorically with respect to a financial black hole (with which the former is so often compared). The well-known power of attraction in the physical case is effectively projected (to some degree) onto the remote attractor -- an experience thereby imaginatively reframed.

Interrelating comprehension of "local" and "global" as a cognitive dipole (tentative)
"local" compactification experienced as globally encompassing	"distance" between local and global in terms of comprehension	"global" compactification described by local metaphors