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. A reduction in transportation costs in a trade network by a factor of two increases the potential value of that network by a factor of sixteen. While a power of exactly 4.0 will usually be too high, due to redundancies, this does show how the cost of transportation can have a radical nonlinear impact on the value of the trade networks it enables. This formalizes Adam Smith's observations: the division of labor (and thus value of an economy) increases with the extent of the market, and the extent of the market is heavily influenced by transportation costs (as he extensively discussed in his Wealth of Nations).

I learned that and more from this post on how critical horses were to the industrial revolution. Because Europe had horses to move natural resources while China relied on human porters, the 1800's saw Europe surge past China. Later, non-European countries like Japan just skipped the horses and went to steam engines to play another round of leapfrog.

We continue to see leapfrogging all over the world with a variety of technologies, like cellular technology (skipping landlines) and near field payments (hopping past credit cards). To take a more recent example, it would not surprise me if we first saw widespread deployment of drone delivery technology in countries other than the U.S., where regulations and solid alternatives exist. It's not surprising to hear that Amazon is looking to test drone delivery in India first.