This reminds me. An interesting question is, assuming constant mass/person, how long until the speed of light becomes a limiting factor? I.e. given a fixed growth rate, at what total population would the colonization speed be approaching the speed of light just to keep the # humans per cubic parsec of space constant? It is clear that this will happen at some point, given the assumptions of constant birth rate and constant body mass, because the volume of colonized space only grows as time cubed, while the population grows exponentially.
Here is a back-of-the-envelope stab at it. I have not googled it beforehand, because it’s fun to do one’s own estimate.
Assume 1 habitable planet (10^10 people) per cubic light year, the total colonized number of planets ~ #years^3 after the onset of interstellar travel at near light speed. (I am not accounting for the relativistic time dilation, though the correction should be small, since only a minority of people are in-flight at any given time.) I’m ignoring the factors of the order of 1, such as 4 pi/3 for the volume of a sphere.
Assume 0.1%/year growth rate. This is about 1⁄20 of the current birth rate. Total number of occupied planets = 1.001^(#years).
The two numbers become comparable after about 30,000 years. This is less than one third of the size of the Milky Way galaxy (in light years). After that, the population growth will be limited by the known physical laws, long before other galaxies are explored.
If the economy continues to grow at roughly the present rate, using more energy as it does so, when will we be consuming the entire solar energy output each year? And if this energy growth happens on the surface of the earth and heat dissipation works in a naive way then how long till the surface of the earth is as hot as the sun? Answers: A bit less than 1400 years from now to be eating the sun, and a bit less than 1000 years from now till Earth’s surface is equally hot, respectively. Blog post citation!
The same blogger did a followup post on the possibility of economic growth that “virtualizes our values” (my terminology, not the blogger’s, he calls it “decoupling”) so that humanity gets gazillions of dollars worth of something while energy use is fixed by fiat in the model. Necessarily the “fluffy stuff” (his term) somehow takes over the economy such that things like food are negligible to economic activity. With 5% “total economy” growth and up-to-an-asymptote energy growth, by 2080 98% percent of the value of the economy is made of of “fluffy stuff” which seems to imply that real world food and real world gasoline would be less than 2% of the economy… which implies that the average paycheck would be spent on very very little food or gas and quite a lot on “fluffy stuff”.
The blogger takes this as evidence that the fluffy economy is impossible and (implicitly) that we should just accept that civilization has peaked and should turn into lowered-expectations-hippies, but to me his “ridiculous” energy scenario sounds suspiciously similar to Hanson’s em scenario. What use has an em for a real hamburger made out of real beef grown with real grass shined on by real sunshine? Very little use. It would be like having the deed to an extrasolar planet. How awesome would it be to be an em? Very much awesome :-)
The blogger takes this as evidence that the fluffy economy is impossible and (implicitly) that we should just accept that civilization has peaked and should turn into lowered-expectations-hippies
Ems or other more efficient versions of living intelligence just put off the exponential malthusian day of reckoning by 100 years or a 1000 years or 10000 years. As long as you have reproducing life, its population will tend to or “want to” grow exponentially, while with technical improvements, I can’t think of a reason in the world to expect them to be exponential.
I also wonder at what point speciation becomes inevitable or else extremely likely. Presumably in a world of ems with 10^N more ems than we now have people, and very fast em-thinking speeds restricting their “coherence length” (the distance over which they have significant communication with other ems within some unit of time meaningful to them) of perhaps 10s of km, we would it seems have something like 10^M civilizations averaging 10^(N-M) as complex as our current global civilization, with population size standing in as a rough measure of complexity. Whether ems want to compete or not, at some point you will have slightly more successful or aggressive large civilizations butting up against each other for resources.
In the long run, I think, exponentials dominate. This is the lesson on compound interest I take from Warren Buffett. Further, one of the lesson’s I take from Matt Ridley’s “Rational Optimist” is that the Malthusian limit is the rule and the last 2 centuries saw us nearly hitting it a few times, with something like the “Green Revolution” coming along in a “just in time” fashion to avoid it. Between what Hanson has to say and what Ridley has to say, and what Buffett has to say (about compound interest i.e. exponentials), it sure seems likely that in the long run Malthus is the rule and our last one or two centuries have been a transition period between Malthusian equilibria.
This reminds me. An interesting question is, assuming constant mass/person, how long until the speed of light becomes a limiting factor? I.e. given a fixed growth rate, at what total population would the colonization speed be approaching the speed of light just to keep the # humans per cubic parsec of space constant? It is clear that this will happen at some point, given the assumptions of constant birth rate and constant body mass, because the volume of colonized space only grows as time cubed, while the population grows exponentially.
Here is a back-of-the-envelope stab at it. I have not googled it beforehand, because it’s fun to do one’s own estimate.
Assume 1 habitable planet (10^10 people) per cubic light year, the total colonized number of planets ~ #years^3 after the onset of interstellar travel at near light speed. (I am not accounting for the relativistic time dilation, though the correction should be small, since only a minority of people are in-flight at any given time.) I’m ignoring the factors of the order of 1, such as 4 pi/3 for the volume of a sphere.
Assume 0.1%/year growth rate. This is about 1⁄20 of the current birth rate. Total number of occupied planets = 1.001^(#years).
The two numbers become comparable after about 30,000 years. This is less than one third of the size of the Milky Way galaxy (in light years). After that, the population growth will be limited by the known physical laws, long before other galaxies are explored.
Other physical angles:
If the economy continues to grow at roughly the present rate, using more energy as it does so, when will we be consuming the entire solar energy output each year? And if this energy growth happens on the surface of the earth and heat dissipation works in a naive way then how long till the surface of the earth is as hot as the sun? Answers: A bit less than 1400 years from now to be eating the sun, and a bit less than 1000 years from now till Earth’s surface is equally hot, respectively. Blog post citation!
The same blogger did a followup post on the possibility of economic growth that “virtualizes our values” (my terminology, not the blogger’s, he calls it “decoupling”) so that humanity gets gazillions of dollars worth of something while energy use is fixed by fiat in the model. Necessarily the “fluffy stuff” (his term) somehow takes over the economy such that things like food are negligible to economic activity. With 5% “total economy” growth and up-to-an-asymptote energy growth, by 2080 98% percent of the value of the economy is made of of “fluffy stuff” which seems to imply that real world food and real world gasoline would be less than 2% of the economy… which implies that the average paycheck would be spent on very very little food or gas and quite a lot on “fluffy stuff”.
The blogger takes this as evidence that the fluffy economy is impossible and (implicitly) that we should just accept that civilization has peaked and should turn into lowered-expectations-hippies, but to me his “ridiculous” energy scenario sounds suspiciously similar to Hanson’s em scenario. What use has an em for a real hamburger made out of real beef grown with real grass shined on by real sunshine? Very little use. It would be like having the deed to an extrasolar planet. How awesome would it be to be an em? Very much awesome :-)
See an earlier discussion for some more criticism of the blogger’s claim.
Ems or other more efficient versions of living intelligence just put off the exponential malthusian day of reckoning by 100 years or a 1000 years or 10000 years. As long as you have reproducing life, its population will tend to or “want to” grow exponentially, while with technical improvements, I can’t think of a reason in the world to expect them to be exponential.
I also wonder at what point speciation becomes inevitable or else extremely likely. Presumably in a world of ems with 10^N more ems than we now have people, and very fast em-thinking speeds restricting their “coherence length” (the distance over which they have significant communication with other ems within some unit of time meaningful to them) of perhaps 10s of km, we would it seems have something like 10^M civilizations averaging 10^(N-M) as complex as our current global civilization, with population size standing in as a rough measure of complexity. Whether ems want to compete or not, at some point you will have slightly more successful or aggressive large civilizations butting up against each other for resources.
In the long run, I think, exponentials dominate. This is the lesson on compound interest I take from Warren Buffett. Further, one of the lesson’s I take from Matt Ridley’s “Rational Optimist” is that the Malthusian limit is the rule and the last 2 centuries saw us nearly hitting it a few times, with something like the “Green Revolution” coming along in a “just in time” fashion to avoid it. Between what Hanson has to say and what Ridley has to say, and what Buffett has to say (about compound interest i.e. exponentials), it sure seems likely that in the long run Malthus is the rule and our last one or two centuries have been a transition period between Malthusian equilibria.