Here we imagine a thought experiment in which the human understanding of number in physics and mathematics was completely different - where we could easily and clearly think in precise mathematical terms about systems and emergent properties, but had almost no ability to count and manipulate the things we currently apply numbers to.
In this world we would instantly know how trust-worthy someone was, of how selfless they were (to one hundred decimal places), but not how many legs they had. We could tell how happy a group of people or a city was, but not how many people there were.
Would it not be the case that our "money" and systems of power and reputation would be completely different?
Since my early 20's I've been thinking and struggling to create irrational numbers in this sense - that is systems of democracy or currency (token exchange games0 that capture richer and deeper human values.
# See also * Irrational Number