[Bartweiss]

This is the problem with real-world Malthusian predictions. There are (obviously) hard limits on growth and carrying capacity for Earth, but extrapolating from some existing metric like food growth per human is an atrocious way to find them.

A convincing Malthusian argument needs to take one of two forms: either concede that it represents doom without engineering progress, or convincingly argue that it represents a physical boundary rather than an engineering one.

[dredmorbius]

Engineering limits frequently fall below physical limits.

[eudox]

Yes, that's the point. But it's very hard to point to the effective engineering limit.

For example: the ultimate limit to computing power is Bremermann's limit, but that's only reached in the surface of a black hole. The effective limit of computation – how much you can compute in Baryonic matter – is going to be far lower. How low is a hard question to answer.

[dredmorbius]

But computing power is at best a second-order productivity factor.

If you can apply it to a network system, you've got some options for increased efficiency. If you're applying it to an energy system, the improvement is far more likely in the 5-25% range.

Example: automobiles have made increasing use of computers since the 1970s. Computer performance has improved on the order of millionsfold. Automobile fuel efficiency has less-than doubled. A small compact of the early 1970s could achieve ~30 mpg, or 7.84 l/100km, a more useful measure of efficiency. Current models are in the 40 - 50 mpg range, let's take the upper limit, giving 4.70l/100km.

That's a 40% reduction in fuel use. Even before considering countervailing offsets via the Jevons Paradox.

Google have recently similarly claimed a 15% efficiency improvement in data center energy management, again resulting from massive increases in compute efficiency. That is, the end-point energy use impacts aren't much changed.

There's more to this, and the story is complicated. But while computing has very high potential increases, the end-point impacts (worker productivity, economic efficiency, even technical capabilities) are often oddly muted.

To put another twist on this: the Apollo lunar missions had a few hundred pounds of computer assembled in a ring around one of the higher (IIRC above the 3rd stage) boosters. Swapping out that compute capacity for an equivalent mass of modern tech would have very minimal impact on the mass, range, or accuracy of the system as a whole. The main advantage is that an equivalent compute capacity -- sufficient for the mission, could be provided in vastly less mass, which is critical for Earth-based rocket launches. But the improvement then is based on the reduction in the physical requirements for providing compute capacity, not the increased performance of massively more compute capacity itself.

[Bartweiss]

Precisely, thanks. I can get an upper bound on Earth's carrying capacity with (volume of earth / volume of a human), but it's going to be way harder to calculate the number that will actually matter.

[dredmorbius]

Joel E. Cohen has done some of the more substantive, and range-based, estimates that I'm aware.

http://science.sciencemag.org/content/269/5222/341.long

(Numerous other articles and books.)