1. If you have no idea what that means, try my short economic growth explainer.
2. Global real growth has generally ranged from slightly negative to ~7% per year.
3. I’m skipping over 2020 here since it was unusually different from past years, due to the global pandemic and other things.
4. For the historical data, see Modeling the Human Trajectory. The projections are rough and meant to be visually suggestive rather than using the best modeling approaches.
5. This refers to real GDP growth (adjusted for inflation). 2% is lower than the current world growth figure, and using the world growth figure would make my point stronger. But I think that 2% is a decent guess for “frontier growth”—growth occurring in the already-most-developed economies—as opposed to total world growth, which includes “catchup growth” (previously poor countries growing rapidly, such as China today).
To check my 2% guess, I downloaded this US data and looked at the annualized growth rate between 2000-2020, 2010-2020, and 2015-2020 (all using July since July was the latest 2020 point). These were 2.5%, 2.2% and 2.05% respectively.
6. 2% growth over 35 years is (1 + 2%)^35 = 2x growth.
7. Wikipedia’s highest listed estimate for the Milky Way’s mass is 4.5*10^12 solar masses, each of which is about 2*10^30 kg, each of which is estimated as the equivalent of about 1.67*10^-27 hydrogen atoms. (4.5*10^12 * 2*10^30)/(1.67*10^-27) =~ 5.4*10^69.
8. Wikipedia: “In March 2019, astronomers reported that the mass of the Milky Way galaxy is 1.5 trillion solar masses within a radius of about 129,000 light-years.” I’m assuming we can’t travel more than 129,000 light-years in the next 8200 years, because this would require far-faster-than-light travel.
9. This calculation isn’t presented straightforwardly in the post. The key lines are “No matter what the technology, a sustained 2.3% energy growth rate would require us to produce as much energy as the entire sun within 1400 years” and “The Milky Way galaxy hosts about 100 billion stars. Lots of energy just spewing into space, there for the taking. Recall that each factor of ten takes us 100 years down the road. One-hundred billion is eleven factors of ten, so 1100 additional years.” 1400 + 1100 = 2500, the figure I cite. This relies on the assumption that the average star in our galaxy offers about as much energy as the sun; I don’t know whether that’s the case.
10. There is an open debate on whether Modeling the Human Trajectory is fitting the right sort of shape to past historical data. I discuss how the debate could change my conclusions here.
11. 250 doublings would be a growth factor of about 1.8*10^75, over 10,000 times the number of atoms in our galaxy.
12. 20 years would be 240 months, so if each one saw a doubling in the world economy, that would be a growth factor of about 1.8*10^72, over 100 times the number of atoms in our galaxy.
13. That’s because of the above observation that today’s growth rate can’t last for more than another 8200 years (82 centuries) or so. So the only way we could have more than 82 more centuries with growth equal to today’s is if we also have a lot of centuries with negative growth, ala the zig-zag dotted line in the “This Can’t Go On” chart.
14. This dataset assigns significance to historical figures based on how much they are covered in reference works. It has over 10x as many “Science” entries after 1500 as before; the data set starts in 800 BC. I don’t endorse the book that this data set is from, as I think it draws many unwarranted conclusions from the data; here I am simply supporting my claim that most reference works will disproportionately cover years after 1500.
15. To be fair, reference works like this may be biased toward the recent past. But I think the big-picture impression they give on this point is accurate nonetheless. Really supporting this claim would be beyond the scope of this post, but the evidence I would point to is (a) the works I’m referencing—I think if you read or skim them yourselves you’ll probably come out with a similar impression; (b) the fact that economic growth shows a similar pattern (although the explosion starts more recently; I think it makes intuitive sense that economic growth would follow scientific progress with a lag).
16. The papers cited in The Duplicator on this point specifically model an explosion in innovation as part of the dynamic driving explosive economic growth.
1.The best example I can think of, but surely not the only one.
2. The movie The Matrix gives a decent intuition for the idea with its fully-immersive virtual reality, but unlike the heroes of The Matrix, a digital person need not be connected to any physical person—they could exist as pure software.
The agents (“bad guys”) are more like digital people than the heroes are. In fact, one extensively copies himself.
3. See Age of Em Chapter 6, starting with “Regarding the computation …”