Explaining Technology
47 Pages Posted: 1 Jun 2021
Date Written: May 30, 2021
Abstract
We propose a mathematical model of the combinatorial evolution of technology (“TAP”), which
explains three radically and unexplained different data sets. First, global GDP per capita
increased at a glacial pace from the beginning of the common era about 2000 years ago to about
1800, when it exploded upward increasing global and per capita wealth. TAP explains this
“hockey stick of economic growth” as due mostly to the combinatorial explosion in the variety
of good produced. Second, the diversity of goods from simple to complex has also exploded in
the past 2000 years. TAP may also explain this characteristic pattern in technological evolution.
Third, we consider US patent citations from 1835-2010. These data exhibit a power law in the
distribution of direct and indirect descendants. One patent is a direct descendant of another if it
incorporates the first patent’s technology. Indirect descendants are the “children” and
“grandchildren” and so on of direct descendants. Power laws fitted by earlier researchers
consider only direct descendants and ignore indirect descendants. The same TAP process
predicts such a power law. The same simple TAP theory of cumulative combinatorial invention
can explain three very different sets of data covering different segments of time and space. This
“tri-data result” is strong evidence for both the general combinatorial approach we share with
many other researchers and our unique mathematical model of it.
Keywords: adjacent possible,growth,combinatorial explosion,history
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