> you offered no hypothesis as to why energy needs might increase 100x in just 30 years

Right, because I was un-asking the question. There's no such thing as "energy needs", just energy conversion and dissipation, so your question is nonsensical. Up a couple of levels I linked to Marco Schulte, who's using an Arduino Nano, with maybe half a million transistors in it, to detect when his espresso machine turns on and count up the seconds of espresso brewing on Nixie tubes.

Have "transistor needs" thereby increased by half a million transistors? No, clearly this could have been done with 50 transistors or less. Or not done at all; plenty of espresso machines get by without timers protruding from the top, and plenty of people get by without coffee. There was no need, just consumption. But at this point we have something like 15 or 20 sextillion transistors in the world, so speaking of "transistor needs" is nonsense. Transistors are not rationed like covid vaccines in a backward country, where you only get to use as many as you can prove you need. They're still not free, though—though you can use half a million transistors as easily and cheaply as you can use one, a chip with sixteen billion transistors costs a little more than a chip with half a million, and a machine with a hundred billion transistors (16 GiB of RAM or Flash, for example) costs more than that and also takes up space and uses a significant amount of power. And once you're up into the trillions of transistors the cost goes up linearly with transistor count.

So, in short, Marco Schulte is using half a million transistors to detect his espresso machine turning on because transistors are cheap enough that he doesn't get any advantage he cares about by using less.

This phenomenon is not limited to transistors. Demand for just about anything will increase if it gets cheap enough. Forgive me if I point out that this assumption, that demand curves are generally downward-sloping, is fundamental to economic theory; it's not something I need to offer an argument for in a particular case, because the exceptions are few and far between.

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Of course, that doesn't tell us how much the demand will increase. The 100× ballpark comes from taking, not the 39% yearly exponential growth in installed photovoltaic capacity over the period 01993 to 02018 https://commons.wikimedia.org/wiki/File:PV_cume_semi_log_cha..., but the much slower 23% yearly exponential growth we've seen over the last few years; extrapolating it 30 years into the future; and then dividing by 5 to make the estimate "conservative." Of course it's only really conservative if we don't hit some limiting factor before that point, as we did, for example, with oil in the 01970s. That exponential growth will surely level off at some point, at which point such empirical extrapolations become nonsense.

So what's the limiting factor? I don't know.

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What will people be using abundant solar photovoltaic energy for in 30 years? Probably mostly things that are too absurd for us to imagine now, like Marco Schulte's espresso machine, whose coffee timer has roughly the computational power of the 24 AN/FSQ-7 computers that made up NORAD's missile defense system in 01965. I can come up with lots of uses for lots of energy that aren't so absurd, though they aren't likely to be the real answer:

- Mining Bitcoin. There's no limit to how much energy you can spend on that, because it's purely competitive, like soccer. It takes all the hashing you can do just to stay in the same place with respect to the other miners.

- Making more solar cells. The raw materials (except silver) are abundant, and the processing is highly automated, but it takes a lot of energy. So having a lot of solar cells sitting around producing cheap electricity makes it cheaper to make more solar cells, which in turn makes the electricity they produce even cheaper.

- Smelting aluminum. Currently 20%–40% of the cost of smelting aluminum is just the cost of the energy, but it's only that low because aluminum smelting pots are designed to be efficient and not waste too much energy. You can always trade off some efficiency for other desirable attributes of the design, like cheapness. Probably this would reduce the cost of aluminum per unit of strength below the cost of steel.

- Smelting ferrosilicon, which is used as a feedstock for, for example, magnesium. More generally all kinds of mining and smelting processes use a lot of energy, and have even energy-hungrier alternative processes that we don't use because they're more expensive than the ones we do use.

- Desalination for irrigation. The Sorek reverse-osmosis plant produces drinking water at a total cost of US$0.58/kℓ at 70 atmospheres, which is 7.1 kJ/ℓ; energy is something like a third of the cost, and as with aluminum, you can presumably make other aspects of the plant cheaper if you can afford to waste more energy. Suppose this less efficient design uses 20 kJ/ℓ. Growing rice needs about 5 feet of water (acre-feet per acre) per crop, because a rice field is basically a swamp; with 2 feet of water per year, you can get pastureland or vineyards instead of a swamp. 5 feet of water (1.5 m) per year at 20 kJ/ℓ is just under 1 W/m². So turning the Sahara (9.2 million km²) into rice fields would cost 9.2 terawatts, which is about half of total world marketed energy consumption as of 02021. At current prices, the requisite solar panels (which would themselves occupy about ½% of the Sahara) would cost US$1.4 trillion.

- Direct air capture of CO₂ to reverse global warming, which requires minimally about a gigajoule (250 kWh) per tonne on entropic grounds, and maybe 10 GJ/tonne if we can't figure out how to approach the theoretical efficiency. We need to remove about 1.29 × 10¹⁶ kg to get back to pre-industrial levels (see Derctuo for the calculation) and if we do that over 25 years at this 10%-efficient 10 GJ/tonne level, it will take 160 TW, about 9 times current world marketed energy consumption.

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Now, right now, most of these projects would be uneconomic, because energy is so expensive, so it's tempting to reject them out of hand as implausible. No doubt von Neumann would have done the same if you'd told him a prophecy of Hypercard, which shipped 30 years after his death in 01957. How much more so your ignorant USan man on the street, whose knowledge of computers in 01957 was limited to DO NOT FOLD, SPINDLE, OR MUTILATE, a UNIVAC trying to take over the world in The Invisible Boy, and breathless newspaper articles about "giant electronic brains"?

On the flip side, what would someone in the 01957 USA have thought if you told them that in 01987 all the US manufacturers of small planes would be bankrupt, leaded gasoline outlawed, and the interstate speed limits reduced to 55 mph?

The future is not only stranger than we imagine; it is stranger than we can imagine.

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So, I ask you, a third time: Can you think of any other limiting factors I don't know about? What other possible limits do you think we might encounter between here and Kardashev Type 1?