Shinichi and the Dimensional Paradox

In relation to the succinct observation below:

J. Smithy Another Possible (Fundamental) Formalization of “An Inquiry into the Nature and Causes of the Wealth of Nations”

 …on a plane/surface, such as our planet and in relation to the “nature and causes” of “wealthy nations”, there is necessitated a minimum of 4 main distinct “resources” (food, shelter, fresh water, “money”) needed to create a Nash equilibrium for stability. For example (or in other words), if there was only 3 main resources there would always then be a competitor to offer at least one of the same resources as one of the other civilizations. If 5 or greater main resources were required it might not necessarily then be a Nash Equilibrium since such a market/trade equilibrium might “evolve” to only needing 4 (thus destabilizing it).

We might understand the significance by looking at Nick Szabo’s formalization of Adam Smith’s Treatise “An Inquiry Into the Nature and Causes of the Wealth of Nations”:

From Nick Szabo, Transportation, divergence, and the industrial revolution:

Metcalfe’s Law states that a value of a network is proportional to the square of the number of its nodes.  In an area where good soils, mines, and forests are randomly distributed, the number of nodes valuable to an industrial economy is proportional to the area encompassed.  The number of such nodes that can be economically accessed is an inverse square of the cost per mile of transportation.  Combine this  with Metcalfe’s Law and we reach a dramatic but solid mathematical conclusion: the potential value of a land transportation network is the inverse fourth power of the cost of that transportation.

This might prove interesting in relation to (seemingly) otherwise irre-levant observations by Dr. Nash on the differences between a “2-D” type of production such as agriculture versus that of a “3-D” type like mining:

John Nash Ideal Money:

 …the inherent nature of mining and mining technology makes it possible for the prices of certain commodities that are produced as a result of the devotion of labor and capital to the effort of mining to increase less (or decrease more) than might be expected.  There is a “dimension paradox”: Agricultural products are produced by using the two-dimensional resource of the earth surface, so the “disappearing frontier” creates a limitation. In contrast, some mining, particularly for elemental metals, can essentially be done in three dimensions, although, of course, there are increasing costs for deep digging.

Then naturally we might begin to extend and project our understanding:

John Nash Ideal Money (2)

It is also notable that there has been an overall sense of always increasing human per capita wealth, globally, as technological advances continue to modify the nature of the global economy. But consider the effect of measuring wealth purely in terms of square miles owned per capita of the earth’s land surface. If each Hopi tribesman owns x by this measure and each Navaho tribesman owns y by the measure then, with global population steadily increasing, should they feel happy or sad?
Perhaps humanity will REALLY arrive at increased wealth if we can successfully colonize lands beyond Terra, like the surfaces of Mars,the Moon, and some asteroids. (But of course we could not illogically claim ALREADY to own the whole Solar System at least, so it is clear that psychological alternatives enter here also with regard to the issue of the “true” evaluation of per capita wealth.)
Possibly the full psychological effect of human “ownership” of the surface of Mars would not be realized until that area had been divided into plots regarded as the private property of specific corporate or personal owners!

What is notable is the obvious psychological re-levance, and furthermore we could explore this content in relation to different maths that might represent different (and/or partial) dimensions and possibly even that of the inter-universal kind.


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