Paul_Christiano

2056Joined Aug 2014

Comments
225

How would a language model become goal-directed?

Here is my story, I'm not sure if this is what you are referring to (it sounds like it probably is).

Any prediction algorithm faces many internal tradeoffs about e.g. what to spend time thinking about and what to store in memory to reference in the future. An algorithm which makes those choices well across many different inputs will tend to do better, and in the limit I expect it to be possible to do better more robustly by making some of those choices in a consequentialist way (i.e. predicting the consequences of different possible options) rather than having all of them baked in by gradient descent or produced by simpler heuristics.

If systems with consequentialist reasoning are able to make better predictions, then gradient descent will tend to select them.

Of course all these lines are blurry. But I think that systems that are "consequentialist" in this sense  will eventually tend to exhibit the failure modes we are concerned about, including (eventually) deceptive alignment.

I think making this story more concrete would involve specifying particular examples of consequentialist cognition, describing how they are implemented in a given neural network architecture, and describing the trajectory by which gradient descent learns them on a given dataset. I think specifying these details can be quite involved both because they are likely to involve literally billions of separate pieces of machinery functioning together, and because designing such mechanisms is difficult (which is why we delegate it to SGD). But I do think we can fill them in well enough to verify that this kind of thing can happen in principle (even if we can't fill them in in a way that is realistic, given that we can't design performant trillion parameter models by hand).

How would a language model become goal-directed?

Some examples of more exotic sources of consequentialism:

  • Some consequentialist patterns emerge within a large model and deliberately acquire more control over the behavior of the model such that the overall model behaves in a consequentialist way. These could emerge randomly, or e.g. while a model is explicitly reasoning about a consequentialist (I think this latter example is discussed by Eliezer in the old days though I don't have a reference handy). They could either emerge within a forward pass, over a period of "cultural accumulation" (e.g. if language models imitate each other's outputs), or during gradient descent (see gradient hacking).
  • An attacker publishes github repositories containing traces of consequentialist behavior (e.g. optimized exploits against the repository in which they are included). They also place triggers in these repositories before the attacks, like stretches of low-temperature model outputs, such that if we train a model on github and then sample autoregressively the model may eventually begin imitating the consequentialist behavior included in these repositories (since long stretches of low-temperature model outputs occur rarely in natural github but occur just before attacks in the attacker's repositories). This is technically a special case of "#1 imitating consequentialists" but it behaves somewhat strangely since the people training the system weren't aware of the presence of the consequentialist.
  • An attacker selects an input on which existing machinery for planning or prediction within a large model is repurposed for consequentialist behavior. If we have large language models that are "safe" only because they aren't behaving as consequentialists, this could be a bad situation. (Compromised models could themselves design and deploy similar attacks to recruit still more models; so even random failures at deployment time could spread like a virus without any dedicated attacker. This bleeds into the first failure mode.)
  • A language model can in theory run into the same problem as described in what does the universal prior actually look like?,  even if it is only reasoning abstractly about how to predict the physical universe (i.e. without actually containing malign consequentialists). Technically this is also a special case of #1 imitating a consequentialist, but again it can be surprising since e.g. the consequentialist wasn't present at training time and the person deploying the system didn't realize that the system might imitate a consequentialist.

I find it interesting to think about the kind of dynamics that can occur in the limit of very large models, but I think these dynamics are radically less important than #1-#5 in my original answer (while still not being exhaustive). I think that they are more speculative, will occur later if they do occur, and will likely be solved automatically by solutions to more basic issues. I think it's conceivable some issues of this flavor will occur in security contexts, but even there I think they likely won't present an alignment risk per se (rather than just yet another vector for terrible cybersecurity problems) for a very long time.

How would a language model become goal-directed?

Here are five ways that you could get consequentialist behavior from large language models:

  1. They may imitate the behavior of a consequentialist.
  2. They may be used to predict which actions would have given consequences, decision-transformer style ("At 8 pm X happened, because at 7 pm ____").
  3. A sufficiently powerful language model is expected to engage in some consequentialist cognition in order to make better predictions, and this may generalize in unpredictable ways.
  4. You can fine-tune language models with RL to accomplish a goal, which may end up selecting and emphasizing one of the behaviors above (e.g. the consequentialism of the model is redirected from next-word prediction to reward maximization; or the model shifts into a mode of imitating a consequentialist who would get a particularly high reward). It could also create consequentialist behavior from scratch.
  5. An outer loop could use language models to predict the consequences of many different actions and then select actions based on their consequences.

In general #1 is probably the most common ways the largest language models are used right now. It clearly generates real-world consequentialist behavior, but as long as you imitate someone aligned then it doesn't pose much safety risk.

#2, #4, and #5 can also generate real-world consequentialism and pose a classic set of risks, even if the vast majority of training compute goes into language model pre-training. We fear that models might be used in this way because it is more productive than #1 alone, especially as your model becomes superhuman. (And indeed we see plenty of examples.)

We haven't seen concerning examples of #3, but we do expect them at a large enough scale. This is worrying because it could result in deceptive alignment, i.e. models which are pursuing some goal different from next word prediction which decide to continue predicting well because doing so is instrumentally valuable. I think this is significantly more speculative than #2/4/5 (or rather, we are more unsure about when it will occur relative to transformative capabilities, especially if modest precautions are taken). However it is most worrying if it occurs, since it would tend to undermine your ability to validate safety--a deceptively aligned model may also be instrumentally motivated to perform well on validation. It's also a problem even if you apply your model even to an apparently benign task like next-word prediction (and indeed I'd expect this to be a particularly plausible if you try to do only #1 and avoid #2/4/5 for safety reasons).

The list #1-#5 is not exhaustive, even of the dynamics that we are currently aware of. Moreover, a realistic situation is likely to be much messier (e.g. involving a combination of these dynamics as well as others that are not so succinctly described). But I think these capture many of the important dynamics from a safety perspective, and that it's a good list to have in mind if thinking concretely about potential risks from large language models.

On Deference and Yudkowsky's AI Risk Estimates

I'm not sure either of the quotes you cited by Eliezer require or suggest ridiculous overconfidence.

If I've seen some photos of a tiger in town, and I know a bunch of people in town who got eaten by an animal, and we've all seen some apparent tiger-prints near where people got eaten, I may well say "it's obvious there is a tiger in town eating people." If people used to think it was a bear, but that belief was formed based on priors when we didn't yet have any hard evidence about the tiger, I may be frustrated with people who haven't yet updated. I may say "The only question is how quickly people's views shift from bear to tiger. Those who haven't already shifted seem like they are systematically slow on the draw and we should learn from their mistakes." I don't think any of those statements imply I think there's a 99.9% chance that it's a tiger. It's more a statement rejecting the reasons why people think there is a bear, and disagreeing with those reasons, and expecting their views to predictably change over time. But I could say all that while still acknowledging some chance that the tiger is a hoax, that there is a new species of animal that's kind of like a tiger, that the animal we saw in photos is different from the one that's eating people, or whatever else. The exact smallness of the probability of "actually it wasn't the tiger after all" is not central to my claim that it's obvious or that people will come around.

I don't think it's central to this point, but I think 99% is a defensible estimate for many-worlds. I would probably go somewhat lower but certainly wouldn't run victory laps about that or treat it as damning of someone's character. The above is mostly a bad analogy explaining why I think it's pretty reasonable to say things like Eliezer did even if your all-things-considered confidence was 99% or even lower.

To get a sense for what Eliezer finds frustrating and intends to critique, you can read If many-worlds had come first (which I find quite obnoxious). I think to the extent that he's wrong it's generally by mischaracterizing the alternative position and being obnoxious about it (e.g. misunderstanding the extent to which collapse is proposed as ontologically fundamental rather than an expression of agnosticism or a framework for talking about experiments, and by slightly misunderstanding what "ontologically fundamental collapse" would actually mean). I don't think it has much to do with overconfidence directly, or speaks to the quality of Eliezer's reasoning about the physical world, though I think it is a bad recurring theme in Eliezer's reasoning about and relationships with other humans. And in fairness I do think there are a lot of people who probably deserve Eliezer's frustration on this point (e.g. who talk about how collapse is an important and poorly-understood phenomenon rather than most likely just being the most boring thing) though I mostly haven't talked with them and I think they are systematically more mediocre physicists.

On Deference and Yudkowsky's AI Risk Estimates

I think my views about takeoff speeds are generally similar to Robin's though neither Robin nor Eliezer got at all concrete in that discussion so I can't really say. You can read this essay from 1998 with his "outside-view" guesses, which I suspect are roughly in line with what he's imagining in the FOOM debate.

I think that doc implies significant probability on a "slow" takeoff of 8, 4, 2... year doublings (more like the industrial revolution), but a broad distribution over dynamics which also puts significant probability on e.g. a relatively fast jump to a 1 month doubling time (more like the agricultural revolution). In either case, over the next few doublings he would by default expect still further acceleration. Overall I think this is basically a sensible model.

(I agree that shorter timelines generally suggest faster takeoff, but I think either Robin or Eliezer's views about timelines would be consistent with either Robin or Eliezer's views about takeoff speed.)

On Deference and Yudkowsky's AI Risk Estimates

e.g. Paul Christiano has also said that Hanson's predictions looked particularly bad in the FOOM debate

To clarify, what I said was: 

I don't think Eliezer has an unambiguous upper hand in the FOOM debate at all

Then I listed a bunch of ways in which the world looks more like Robin's predictions, particularly regarding continuity and locality. I said Robin's predictions about AI timelines in particular looked bad. This isn't closely related to the topic of your section 3, where I mostly agree with the OP.

On Deference and Yudkowsky's AI Risk Estimates

This doesn't feel like a track record claim to me. Nothing has changed since Eliezer wrote that; it reads as reasonably now as it did then; and we have nothing objective against which to evaluate it.

I broadly agree with Eliezer that (i) collapse seems unlikely, (ii) if the world is governed by QM as we understand it, the whole state is probably as "real" as we are, (iii) there seems to be nothing to favor the alternative interpretations other than those that make fewer claims and are therefore more robust to unknown-unknowns. So if anything I'd be inclined to give him a bit of credit on this one, given that it seems to have held up fine for readers who know much more about quantum mechanics than he did when writing the sequence.

The main way the sequence felt misleading was by moderately overstating how contrarian this take was. For example, near the end of my PhD I was talking with Scott Aaronson and my advisor Umesh Vazirani, who I considered not-very-sympathetic to many worlds. When asked why, my recollection of his objection was "What are these 'worlds' that people are talking about?  There's just the state." That is, the whole issue turned on a (reasonable) semantic objection.

However, I do think Eliezer is right that in some parts of physics collapse is still taken very seriously and there are more-than-semantic disagreements. For example, I was pretty surprised by David Griffiths' discussion of collapse in the afterword of his textbook (pdf) during undergrad. I think that Eliezer is probably right that some of these are coming from a pretty confused place. I think the actual situation with respect to consensus is a bit muddled, and e.g. I would be fairly surprised if Eliezer was able to make a better prediction about the result of any possible experiment than the physics community based on his confidence in many-worlds. But I also think that a naive-Paul perspective of "no way anyone is as confused as Eliezer is saying" would have been equally-unreasonable.

I agree that Eliezer is overconfident about the existence of the part of the wavefunction we never see. If we are deeply wrong about physics, then I think this could go either way. And it still seems quite plausible that we are deeply wrong about physics in one way or another (even if not in any particular way). So I think it's wrong to compare many-worlds to heliocentrism (as Eliezer has done). Heliocentrism is extraordinarily likely even if we are completely wrong about physics---direct observation of the solar system really is a much stronger form of evidence than a priori reasoning about the existence of other worlds. Similarly, I think it's wrong to compare many-worlds to a particular arbitrary violation of conservation of energy when top quarks collide, rather than something more like "there is a subtle way in which our thinking about conservation of energy is mistaken and the concept either doesn't apply or is only approximately true." (It sounds reasonable to compare it to the claim that spinning black holes obey conservation of angular momentum, at least if you don't yet made any astronomical observations that back up that claim.)

My understanding is this is the basic substance of Eliezer's disagreement with Scott Aaronson. My vague understanding of Scott's view (from one conversation with Scott and Eliezer about this ~10 years ago) is roughly "Many worlds is a strong prediction of our existing theories which is intuitively wild and mostly-experimentally-unconfirmed. Probably true, and would be ~the most interesting physics result ever if false, but still seems good to test and you shouldn't be as confident as you are about heliocentrism."

Updating on Nuclear Power

And here's the initial post (which seems a bit less reasonable, since I'd spent less time learning about what was going on):

Given current trends in technology and policy, solar panels seem like the easiest way to make clean electricity (and soon the easiest way to make energy at all). I’m interested in thinking/learning about what a 100% solar grid would look like.

Here are my own guesses.

(I could easily imagine this being totally wrong because I’m a layperson who has only spent a little while looking into this. I’m not going to have “I think caveats” in front of *every* sentence but you should imagine them there.)

Overall I was surprised by how economical all-solar seems. Given 10-20 years and moderate progress on solar+storage I think it probably makes sense to use solar power for everything other than space heating, for which it seems like we should probably just continue to use natural gas. I was surprised by how serious and isolated a problem space heating seemed to be.

Other forms of power like nuclear or fusion might be even better, but it feels like all-solar will still be cheaper and easier than the status quo and won’t require any fossil fuels at all. Issues with storage would create big fluctuations in the price of electricity, which would change the way we use and think about electricity but would not change the basic cost-benefit analysis.

ETA: feels like the main problem is if there's variability in how dark winters are and some of them are quite dark. This is related to the heating issue, but might be a big problem even for non-heating needs.

1. Night vs day

It looks like the costs of overnight energy storage will eventually dominate the costs of solar, but still be low enough to easily beat out other power sources.

For example, the cost of a Tesla powerwall like $400/kWH; they can be cycled 5000 times under warranty. If you did that every night for 15 years it’s a total cost of $0.08/kWH stored. The cost of battery storage has fallen by a factor of 3 over the last 5 years and seems likely to continue to fall, and I expect utility-scale prices to also fall to keep up roughly with batteries.

Here are some cost projections of $400/kWH in 2020 falling to $200/kWH in 2030: https://www.nrel.gov/docs/fy20osti/75385.pdf. Here is a description of historical costs that finds them falling from $2150/kWH to $625/kWH in 2018: https://www.eia.gov/todayinenergy/detail.php?id=45596. Overall it looks to me like the $200/kWH looks pretty realistic

(ETA: I now think that forecast is probably pretty conservative and $100/kWH or less is more likely. But the rest of the post doesn't depend on such aggressive estimates, except for the part where I talk about heating.)

The efficiency of storage is 90%+ which is high enough to not matter much compared to the cost of storage, especially as solar prices fall.

Current electricity prices are around $0.10/kWH. So at $0.08/kWH solar couldn’t be quite competitive, but another factor of 2-4 could easily do it (especially if other costs of solar continue to fall to negligible levels at their current very rapid clip). I haven’t seen anyone projecting batter prices to plateau before hitting those levels.

Overall the trends on storage are worse than on panels themselves; it’s already the biggest cost of an all-solar grid and I think it would just become totally dominant. But they still seem low enough to make it work.

Storage is a lot cheaper if you are using some of your electricity directly from panels (as under the status quo) and need to store <100% of your power. You’d only need 100% in the worst case where all solar power arrives in a burst at noon, and the real world isn’t going to be quite that bad.

I could easily imagine cutting this down to only needing to store 50-75% of electricity, which cuts the cost with current technologies to $0.04-0.06/kWH. I think cutting costs in this way would be important in practice, but given that we’re only talking about a factor of 2 it’s not going to make a big difference unless battery costs plateau in the next few years.

Meaningful amounts of solar are only available for ~1/3 of a day (depending on latitude) so if you just used energy constantly and wasted nearly half of the solar power you’d need like 66% storage (depending a lot on latitude and season). Today we have a *lot* of appliances that use electricity a small fraction of their life and that you can run when electricity is cheap; and also most of our needs are when humans are awake and the sun is up. But if you switch to using electricity for more applications and if we industrialize further (as I’d expect) then this will get less possible. Amongst the things that can be shifted, you might as well put them at the peak hours around noon, which helps cut peak losses. (For things like cars and computers with batteries, you can either think of these as flexible appliances or as further reasons.)

That’s a complicated mess of considerations. 50-75% is a rough guess for how much you’d have to store but I’m not at all confident.

Eventually it will be unrealistic to amortize battery costs over 15 years. That said, 30 year interest rates are currently 1% and I think time horizons are changing pretty slowly, so I expect this trend to be much slower than changes in storage costs.

2. Winter vs summer

My impression is that solar panels give like 33% less power in winter than summer (obviously depending a ton on latitude, but that’s a typical value for populated places). Storing energy across seasons seems completely impractical.

That sounds like a lot but even in the worst case it only increases the cost of solar power by 50%, since you can just build 50% more panels. That doesn’t seem like enough overhead to make a fundamental difference.

Most importantly, this doesn’t increase the number of batteries you need. You will have enough batteries to store power in the winter, and then in the summer you will have a ton of extra production that you can't store and so use in some low-value way. So if batteries are the dominant cost, you don’t even care.

I think this is the main answer, and the rest of this section is gravy. But as in the last section, the “gravy” could still cut costs by 10% or more, so I think people will care a lot about it and it will change the way we relate to electricity. So also interesting to talk about.

Here are some guesses about what you could scale up in the summer:

* You can run some machines only during the summer, e.g. if the main cost of your computer was the cost of running it (rather than capital costs) then you might as well scale down your datacenters in the winter. Of course, you probably wanted to move that kind of machine towards the equator anyway where electricity prices would be lower.

* You could imagine literally migrating your machines to wherever the power is cheap (e.g. moving your datacenter to the other hemisphere for the winter). This sounds a bit crazy but I wouldn’t be at all surprised if it works for a non-negligible % of energy. Perhaps the simplest case would be moving vehicles and having people travel more during their summer.

* There are lots of small tweaks on the margin, e.g. using 10% more energy during the summer than you would if electricity was constant-price and using 10% less energy during the winter. You can do everything a bit slower and more efficient when it gets colder.

These things are interesting to think about—I like the image of a civilization that hums to life during the summer days—but it doesn’t seem like it changes the calculation for feasibility of solar at all. You could just totally ignore all of this and pay a small premium, from 0% (if batteries dominate anyway) to +50%. Some of these changes would happen from the most cost-conscious customers.

3. Other fluctuation and peaking power

In addition to winter/summer and night/day there is also some variability from weather day-to-day. My impression is that this is a smaller deal than the other two factors and doesn’t change the calculus much for a few reasons:

* As discussed in the last section, you probably want to have too many panels anyway and be bottlenecked by storage. In that case, variability in weather doesn’t matter much since you have too much capacity most days.

* It only really potentially matters in the winter months with already-low light, where you may fall short on total production (and not even be able to charge batteries).

* But once you are talking about a small fraction of the year, it’s pretty cheap for some people to just turn off the power (e.g. scaling down my datacenter) from time to time. If I’m doing that for 5% of the year it effectively increases capital costs by 5%, which is only really a problem if electricity costs are a tiny fraction of my net expenses. And there only have to be a few industries that can do that. So we only have a problem if the all-solar grid is serving every industry exceptionally well (in which case the absolute size of my problem is quite small).

There are also fluctuations in demand. In general having variable demand seems like it’s probably good, since by passing on costs appropriately you can shift demand to times when power is available. But big exogenous changes could cause trouble. This seems to be by far most troubling at the scale of days rather than hours (since you have a ton of batteries to handle within-day variability).

I think most people can avoid huge fluctuations in demand most of the time---there just aren’t that many things that bounce around from day to day where I have very little control over when they happen. The big exception I know about is climate control—people want to use a lot more power for AC during hot days and for heating during cold days (if we move away from natural gas for heating).

AC isn’t a problem, because it happens during hot summer days when you have tons of extra power anyway. So that brings us to...

4. Heating

Heating during cold periods seems like a big problem. As far as I can see it's the biggest single problem with an all-solar grid (with all-electric heating)

Unfortunately, I think heating is a giant use of energy (at least in the US). Right now I think it’s almost half of home energy use, mostly natural gas, and I’d guess something like 10-20% of total energy use in the US.

It's also the worst possible case for solar. It’s seasonal, which is already bad, and then there is huge variation in how cold it actually gets. And it’s really bad if you aren’t able to keep things heated during a cold snap. In practice you should just stop other uses of electricity when it gets cold. But with an all-solar grid you aren’t going to be putting many energy-intensive activities in places with cold winters, so you may have less cheap slop than you wanted and blackouts from cold could be quite expensive (even if you literally aren't having people freeze in their homes).

Here are some options:

* Use peaking power plants basically just for heating. It’s crazy to me to imagine the world where this is the *only* reason you actually need peaking power plants. I suspect you don’t want to do this.

* Use natural gas to heat homes. This is appealing because it’s what we currently do so doesn’t require big changes, it’s pretty clean, and you don’t need to maintain a bunch of peaking power plants with significant efficiency losses in transit. I think the main cost is maintaining infrastructure for delivering natural gas.

* Do something creative or develop new technologies. In some sense heating is an incredibly “easy” problem, since anything you do with electricity will generate heat. The problem is just getting it where you want to go. You could move more electricity-consuming appliances into homes/offices you want to heat, or do cogeneration with data centers, or something else crazy.

Here are some reasons the heating cost may not be so bad, so that you may be able to just eat the costs (for any of the above proposals).

* If we are doing a lot of electricity-intensive industry then space heating may be a much smaller fraction of costs. Honestly, I think this whole discussion is mostly relevant if we want to scale up electricity use quite a lot, but I don’t expect to scale up space heating in the same way. So I think it would be reasonable to keep meeting our heating needs in a primitive way while scaling up an all-solar grid for our increasing energy needs.

* You could massively improve insulation over the status quo if heating costs were actually a big deal. Right now heating is a huge fraction of energy but a much smaller fraction of costs. Under an all-solar grid the energy for heating would be by far the most expensive energy, and so incentives to save on heat would be much larger.

* We could generally move to hotter places. They get more appealing as AC gets cheaper / heating is more expensive, and I’m told global warming will make everywhere a bit hotter.

* We could probably modestly improve the energy efficiency of heating by using heat pumps Unfortunately it’s kind of hard to improve efficiency in any other way. And heat pumps are pretty scary since they don’t work when it gets really cold.

Overall my guess is that you should just leave natural gas infrastructure in place, especially in cold places, and use solar for everything else.

Updating on Nuclear Power

No, sorry. Here's a copy-paste though.

Yet another post about solar! This time about land use.

— TL;DR

Suppose that you handle low solar generation winter by just building 3-6x more panels than you need in summer and wasting all the extra power.

1. The price of the required land is about 0.1 cents per kWh (2% of current electricity prices).

2. Despite the cost being low, the absolute amounts of land used are quite large. Replacing all US energy requires 8% of our land, for Japan 30%. This seems reasonably likely to be a political obstacle.

I’m not too confident in any of these numbers, corrections welcome.

— Background

I’ve been wondering about the price of an all-solar grid without any novel storage or firm generation. In my first post I proposed having enough batteries for 1-2 days, and said that buying that many batteries seemed affordable (https://www.facebook.com/paulfchristiano/posts/10226561810329293). In the second I argued that emergency natural gas you never actually use looked like it was totally affordable (https://www.facebook.com/paulfchristiano/posts/10226568532377340).

A potential drawback of the all solar plan is that you *massively* overbuild panels so that you have enough generation in the winter months. This isn’t too expensive because most of your capital cost was storage anyway. But it does mean you use a boatload of land. I wanted to understand that better. See the TL;DR above for my conclusions.

After this post, I think the biggest unresolved question for me is how variable cloud cover is during the winter—I know that large solar installations are pretty consistent at the scale of months (and can fall back to emergency natural gas in the rare cases where they aren’t). But is it the case that e.g. there is frequently a bad 4-day stretch in January where the average solar generation across Japan is significantly reduced?

My second biggest question is about the feasibility and cost of large-scale transmission, both to smooth out that kind of short-term variability and to supply power further north.

— A note on location

The feasibility of this depends a ton on where you are. I’m going to start by talking about the largest US solar farms in the southwest. I believe the situation gets about 2x worse if you move to the US northeast or northern Europe.

If you go further north it gets even more miserable---wintertime solar is much more sensitive to latitude than summer solar. I'd guess that people in the US northeast should already be importing power from sunnier places, to say nothing of Canada. I don’t know how politically realistic that is. If you didn’t have backup natural gas it sounds insane, but if everyone is just building backup natural gas anyway I think it might be OK.

— Efficiency of solar

I looked up the Topaz solar farm (info taken from wikipedia: https://en.wikipedia.org/wiki/Topaz_Solar_Farm).

Setting aside its first year while panels were still be installed, its worst month was December of 2016 were it generated about 57 million kWh.

The “overbuild panels” plan requires us to build enough panels that we’d be OK even in the deepest winter. If we pessimistically assume that all of the excess power is completely wasted, that means you get about 684 million kWh per year.

The site area is 7.3 square miles. So in total we are getting about 94 million kWh per square mile per year. (Or 145 thousand kWh per acre).

I got almost identical numbers for McCoy solar installation.

I think you could push the numbers somewhat higher, perhaps a factor of 2, by economizing more on land (check out that picture of Topaz solar farm from space, tons of room to improve density), improving panel efficiency (once panel costs are no longer a major expense you can focus on efficiency rather than price), and focusing on winter generation. When I did this calculation on paper I got numbers 2-4 higher than the practical ones.

I’m going to just round the number up to 100 million kWh to make things simple. In reality you’d probably increase density above this but may also be pushed to use worse sites, so this seems fine for the headline figures.

— How much land is needed in the US?

In 2020 the US used about 100 quadrillion BTUs of power (mostly oil and natural gas), a bit less than 3e13 kWh: https://www.eia.gov/energyexplained/us-energy-facts.

If we pretend it was always midwinter, this would require 300,000 square miles. This is about 8% of all the land in the US.

To help understand what this means, this site gives us the total breakdown of US land. I don’t trust it totally but I think it’s roughly right. https://www.visualcapitalist.com/america-land-use/

* 842,000 square miles of forest

* 750,000 square miles of shrub

* 530,000 square miles of farmland

* 530,000 square miles of grassland (I assume this breakdown was just made up?)

* 400,000 square miles of other nature

* 63,000 square miles of cities

— How expensive is that land?

Suppose that we put solar farms on cropland. The cost of 1 acre of farmland in the US is about $3000. Renting an acre of unirrigated land is about $140/year. (https://www.nass.usda.gov/.../land-values-cash-rents.pdf)

Pasture is quite a lot cheaper than that, and you’d only have to use ~50% of the US pasture to put in all this solar. So I think $140/acre/year is pretty conservative.

Above we estimated that an acre generated 145,000 kWh per year.

So even if you are renting farmland, and *throwing away all power above the amount generated in midwinter*, the price is only a tenth of a cent per kWh. That’s about 50x lower than the current price of power. So it won’t be a large part of the price until you are dropping electricity costs by 10x or more.

— What about Japan?

Japan uses about 386 million tons of oil equivalent per year, or 4.5e12 kWh. By the same calculation that would require about 45,000 square miles. (I think Japan has fewer good solar sites than the southwest US, so they’ll be leaning more on the hope that you can squeeze more density out of installations).

The area of Japan is about 145,000 square miles. So this is about 30% of the total area. Right now in Japan I believe essentially all of this would have to come from clearing forest. The cost of clearing that land isn’t significant (and it’s not any more expensive than cropland), but I expect people would be unhappy about losing 1/3 of their forest.

— Other thoughts

These proposals involving wasting 65-85% of all the generation. If you are able to use more electricity on summer days, that helps a lot, as discussed in previous posts. The most obvious way this happens is if you can synthesize fuel, and energy costs of synthesis are dominant rather than capital costs. That would be a game-changer for the all-solar grid (as well as removing the need to electrify all your cars and planes).

I’ve ignored increasing energy usage. That seems kind of reasonable because I’ve discussed the US and Japan, two countries with relatively high energy use that has been declining in recent years. But big increases in energy use would change the picture.

In the long run it does seem like floating solar over the ocean could be quite important. But I have no idea how to think about the costs for that, and especially energy transport.

Depending on the design of your panels, putting down this many could change significantly heat the earth just by absorbing sunlight. This is on the same order of magnitude as the heat generated by running appliances (e.g. the heat generated by the engine of your car and the friction of your wheels against pavement), but if your panel is 20% efficient then I think it probably ends up about 2-3x bigger. I don’t normally think about e.g. space heaters contributing to global warming by literally heating up the house. It does seem like a consideration but I’d like to better understand how it compares.

If clearing forests or pasture, it seems important not to release all that carbon into the atmosphere. My guess would have been that most of this land would be at rough equilibrium and so this isn’t going to have a CO2 effect (assuming you don’t burn the biomass or let it rot), but I’d be interested to know, and am not sure if that’s feasible.

Updating on Nuclear Power

This does require prices going down. I think prices in many domains have gone up (a lot) over the last few years, so it doesn't seem like a lot of evidence about technological progress for solar panels. (Though some people might take it as a warning shot for long-running decay that would interfere with a wide variety of optimistic projections from the past.)

I think it's not clear whether non-technological factors get cheaper or more expensive at larger scales. Seems to me like "expected cost is below current electricity costs" is a reasonable guess, but ">75% chance of being economically feasible" is not.

My current understanding is that there are plenty of the relevant minerals (and in many cases there is a lot of flexibility about exactly what to use), and so this seems unlikely to be a major driver of cost over the very long term even if short-term supply is relatively inelastic. (Wasn't this the conclusion last time we had a thread on this?)

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