we have several brick walls ahead of us that are going to break the premise. the immediate future is not infinite growth. it's a millennium or more of stagnation, and quite plausibly a dark age of quantum mysticism.
....and that is, of course, if we can avoid extinction or collapse in the next century.
i might suggest that an alternate theory is more plausible: in order for a species to survive the invention of technology, it's adoption rate would have to not outstrip it's ability to adapt to it. that is, a species that innovates at an exponential rate is all but certain to destroy itself.
successful adaptation to technology presupposes linearity.
we are ourselves likely the necessary counter-example to his theory.
https://www.youtube.com/watch?v=2KK_kzrJPS8&lc=z13aejkrhvebdb3qc04cjz3beortchnb3vs0k
"the odds of life evolving are one in billions. therefore, life doesn't exist."
derrrrrrrrrp.
in fact, the probability that life might evolve given that life did evolve is one.
rare events happen.
all the time....
the error is in interpreting probability as a physical law that exists in reality, rather than merely as a purely intellectual tool of analysis that only exists in our minds.
stated differently: it is not the case that the universe somehow obeys the laws of probability theory. it is merely the case that we've invented the laws of probability theory to help us guess how the universe might work.
we have no reason at all to be surprised when the universe tells our arbitrary ratios to fuck off, and does what it pleases, anyways.