All of bertrand's Comments + Replies
The calculations for total bits in the systems is correct: 9.82*10^74 bits (earth) and 4×10^106 bits (galaxy). The bit limit grows quadratically as you expand out the radius and energy-mass content.
12,395 years of 2% growth to achieve the the upper bound of the galaxy's information content given perfect mass-energy efficiency.
Stepping back, this exercise in extrapolating 2% growth to extremes can be reduced to just the mathematical statement that any exponential growth will exceed a (constant or sub-exponentially...
The argument here by appealing to too few atoms in the galaxy as a limit to economic growth is poor physics. The fundamental limit to economic value is that of information density.
Most of the galaxy (and universe) is entirely devoid of matter. Visible matter is exceedingly rare. But not energy. And energy may be assembled into economically valuable patterns, most clearly as information. E.g. a radio transmission of an opera to listeners does not require consumption of atoms.
An upper bound for information density is given by ht...
I've never heard of the Bekenstein bound; thanks for this sharing this additional way to estimate the limits of economic efficiency.
An upper bound for information density is given by https://en.wikipedia.org/wiki/Bekenstein_bound and it is exceedingly large, so large that there isn't a fundamental limit on the time frames considered here.
This doesn't seem right. Specifically it seems like the Bekenstein bound might be larger than the limit Holden discusses in his post, but not so large as to not be reachable with Business As Usual exponential growth in...
I avoided the 'productivity' or 'economic value' to focus on something physically tangible. Markets put an objective value on those, but there's no physical laws to help here.
Generally you'd expect the marginal value of information to fall as more information is created. Aristotle's works vs another youtube video or terrabytes of system logs. The information-density-value-efficiency gets lower as you get bigger. Our own hard drive's content is a good additional example: probably <5% of the contents are high value, contrast to wh... (read more)