Re:The Epic Collapse of Deutsche Bank
by majewsky on Sunday July 10, 2016 @12:23PM
(#12066099)
There are always two boundaries for exponential growth: the amount of desires that can be catered to (as you mentioned), and also the amount of resources available to us.
The second one is instructive because you can derive a nice asymptotic bound for it: If you were to conquer space and harvest all available resources on all reachable celestial bodies, your civilization could cover a growing spherical volume of space, bound by the speed of light. That gives a maximally polynomial growth of available resources, O(t^3), assuming an even distribution of resources in space (over cosmic scales). Now observe that every exponential curve (c^t for any c > 1) will outgrow this t^3 behavior eventually.
Of course, that still does not solve the question of when this outgrowing eventually happens. But I feel like resource availability (bound also by technological advances in resource mining and recycling) will be a stronger constraint on growth than our ability to sell shiny new things to people.
The second one is instructive because you can derive a nice asymptotic bound for it: If you were to conquer space and harvest all available resources on all reachable celestial bodies, your civilization could cover a growing spherical volume of space, bound by the speed of light. That gives a maximally polynomial growth of available resources, O(t^3), assuming an even distribution of resources in space (over cosmic scales). Now observe that every exponential curve (c^t for any c > 1) will outgrow this t^3 behavior eventually.
Of course, that still does not solve the question of when this outgrowing eventually happens. But I feel like resource availability (bound also by technological advances in resource mining and recycling) will be a stronger constraint on growth than our ability to sell shiny new things to people.