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 growing) limit in finite time. Yes… QED.
Solutions like expanding this future-humanity’s Boltzmann-economy at a 2% radius per year get you to faster-expansion than the speed of light quickly. Quadratic (or similar orders) is probably the best one can do in the long run.
TLDR: in bits, exponential growth at a fixed growth rate forever of an economy is impossible (ad absurdum), but something like quadratic growth forever is not impossible.
An important point that I don’t think we’ve said yet is that information density is of course not the same as economic productivity.
What would the Gross Galactic Product be of a maximally-efficient galaxy economy that had reached the 4×10^106 bit information density limit? It would necessarily be close to $10^106 or close to 10^106 times greater than the size of today’s GWP, right?
Similarly, if annual GWP increases at 2%/year, that does not necessarily mean that the economy’s information density (or perhaps more accurately, the information density of the system the economy is enclosed in) is increasing at close to 2%/year, does it?
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 when we all had much smaller storage (e.g. 2.5 inch floppy drives).
That said, this is analogous to diminishing marginal value (or returns) to scale in economic activity.
Efficiency of any economic system with respect to fundamental resource usage (information, energy) probably is almost certainly declining in scale. Friction adds up.
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 growing) limit in finite time. Yes… QED.
Solutions like expanding this future-humanity’s Boltzmann-economy at a 2% radius per year get you to faster-expansion than the speed of light quickly. Quadratic (or similar orders) is probably the best one can do in the long run.
TLDR: in bits, exponential growth at a fixed growth rate forever of an economy is impossible (ad absurdum), but something like quadratic growth forever is not impossible.
An important point that I don’t think we’ve said yet is that information density is of course not the same as economic productivity.
What would the Gross Galactic Product be of a maximally-efficient galaxy economy that had reached the 4×10^106 bit information density limit? It would necessarily be close to $10^106 or close to 10^106 times greater than the size of today’s GWP, right?
Similarly, if annual GWP increases at 2%/year, that does not necessarily mean that the economy’s information density (or perhaps more accurately, the information density of the system the economy is enclosed in) is increasing at close to 2%/year, does it?
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 when we all had much smaller storage (e.g. 2.5 inch floppy drives).
That said, this is analogous to diminishing marginal value (or returns) to scale in economic activity.
Efficiency of any economic system with respect to fundamental resource usage (information, energy) probably is almost certainly declining in scale. Friction adds up.