The Dumbest Thing I've Read This Week II: Space Mirrors

I'm Sorry, But You Will Have To Do Math In The Future

Mirrors in space are a dumb idea.

Put that aside for a second.

I want to talk about math, and how physicists use math. And why you need to be better at using math as part of your thought process. It's going to touch on some AI stuff, and I want to get across why you need to be more mathematically literate even with all these new tools. Because math and sciences are liberal arts, no less than writing or history or drama. They are skills you need to be able to live up to the obligations that are inherent to being a member of a democratic society. As long as humans are the ones making the decisions, we need to be able to think critically using mathematics when appropriate.*

* As an aside, it is natural at this point to say "well, people aren't going to be making the decisions for much longer" and my response is that the decision to let an LLM make your decisions is, in fact, a decision. People (and governments and corporate leaders) letting the LLM make their choices for them are trying to flip the saying "a computer can never be held responsible so a computer can never be held responsible so a computer can never make a management decision" to their own advantage. Because computers are not held responsible, if you offload the decision to the computer (which has been carefully tuned to select outcomes you already agree with) you have found a way to make the choice you wanted to make while pretending you didn't. The LLMs are acting as the modern version of hiring a consulting firm to make the unpopular decisions you already wanted to make. They are the newest iteration of the "bad boyars" who are ruining the empire behind the back of the good emperor who would fix it if only they were made aware. If only the Tsar knew.

One thing I hear a lot in the context of LLMs as learning tools (which is, by the way, a terrible idea in general) is some variation of "my teachers used to say I wouldn't have a calculator with me when I needed to do math and jokes on them because my phone has a calculator" with the implication that, I dunno, you don't need to learn things anymore because you'll have the linear algebra equivalent of a hungry ghost in a jar that you can ask for answers to literally everything.

So let's talk about calculators and math. Here's the dirty little secret of my life as a working theoretical physicist, someone who has a degree in mathematics in addition to my degrees in physics: I use a calculator all the time.

In fact, I have access to a number of extremely powerful mathematics engines for which "calculator" is only the most basic of their functionalities. And I use them all. the. time. I use them for addition and subtraction sure, but also integration, differentiation, plotting, statistics, you name it. If I need to multiply two numbers together for work, I'm going to use a calculator.

But I still need to have all that elementary school mathematics and I still use that all the time. More than I use a calculator. I still need to know how to do multiplication and division in my head. Because I need to know what the approximate answer is before I use the calculator. A lot of my job involves thinking about things far outside of my day to day experience, across scales that I can't directly envision. And before I do some super-complicated calculation, I need to be able to run some numbers through my head and estimate the answer. Doing this is part of figuring out if whatever I'm thinking about is even vaguely plausible (and often it isn't).

Space Mirrors

To do this sort of mathematical estimation, you don't need to be super accurate, but you do need to be able to do basic arithmetic. So with that in mind, let's talk about mirrors in space, or "sunlight on demand." These are -- apparently serious -- plans to launch large mirrors into orbit, and use the sunlight reflected from those mirrors to illuminate parts of the surface of the Earth. One of the companies claiming that they will do this is Reflect Orbital which claims their reflected light will be localized to within 5 km, and can be used for "Energy, Response, Industrial, and Agriculture." By energy they mean using solar panels at night, by agriculture they mean increasing plant grow by reflected light, and by "response and industrial" they mean using reflected light to make it brighter at night in small areas so that you can do search and rescue or make it easier to work outside at night.

And look. There are some incredibly obvious problems here, that go beyond basic math. Does shining a light on staple crop plants 24 hours a day make them grow better? I dunno. Maybe, but also maybe not, because plants evolved on Earth. Where it gets dark. At night. Then you have questions about the lift capacity required to put large orbital mirrors in space, how long they'll last before the mirror degrades, the dangers of Kessler syndrome when one of these gets inevitably blown to pieces by micrometeorites, or even basic questions of "how do you plan to illuminate a small patch of ground when the mirror necessarily orbits once over 80 minutes and thus will cross your horizon within a few minutes and you will have to rotate the mirror rapidly to keep it focused on a single location."

But let's put all that aside, and just talk about why this idea is so fucking stupid. In my previous rant about why "datacenters in space" are so fucking stupid, there were a couple of steps to the problem (again, ignoring things like the burn-out time for GPUs, increased radiation, impossibility of repair, and long latency):

1. Space is a vacuum, so you need radiator fins.
2. Radiator fins are heavy, as are solar panels and GPU racks.
3. It will cost an insane amount of money to launch these things in to orbit, and they'll break within a year, so you'll do this forever.

For orbital mirrors, the reason they are dumb as shit can be summarized like this:

1. The Sun is really bright. Go outside nerds, touch some grass.

We'll get some math in a second, but the basic point I want to make is that the Sun puts a lot of energy out, and that energy is what solar panels and plants collect. Orbital mirrors are not going to reflect meaningful amounts of energy, and so the light they create on the ground is going to be pathetic compared to what you get in daylight. You can fuck around all you want, but you cannot get around this.

So, here's a number you should know: the Solar insolation at the Earth's surface is (at maximum) about 1050 watts per square meter (it's 1360 W/m^2 before you factor in the atmospheric scattering). This differs by time of year and latitude and time of day (and cloud cover, obviously), but at best, for every 3 feet by 3 feet square on the ground, you can collect 1050 watts, or 1.05 kW. Let's round, and say 1 kW/m$^2$.

Is that a lot? Let's start doing some of the kind of math that I was talking about at the top. My house is fairly energy efficient for its age, and in the spring I use about 20 kW (20,000 W) over a day, that is, I use 20 kWh (kilo-Watt-hours) of energy.

20 kWh over a day is 20 kWh over 24 hours. So on average I use 20/24 kW of power. I don't want to think what that is, so I, a fully accredited physicist with advanced degrees in physics and math, say "fuck it, 20/24 is pretty close to 1." I could be more accurate, but I don't need to in order to get a sense of the problem.

So I need about 1 kW continuously to power my house, averaged over the day. That's close to the 1050 W the Sun gives at maximum, so to this level of approximation I only need about 1 square meter to power my house.

Of course, that's not quite how it works. Solar panels cannot capture 100% of the sunlight that falls on them (mine are rated for about 300 W), and of course the light falling on my panels is rarely the maximum (for one thing, you have to point your panel directly at the Sun, and my roof doesn't rotate). But order of magnitude, you need a few square meters of panel to power an ordinary home.

We can use that same sort of logic to think about electric vehicles. In the spring, when the weather is warm, my EV gets about 4 miles per kWh. Let's call the Solar insolation 1 kW/m$^2$. The roof of my car is what, like a square meter or two? Let's call it 2 square meters. Then, under ideal conditions with idealized perfect panels, I could go about 2 miles with the energy I could collect from a solar panel on the roof of the car in an hour (in reality, it will be much worse, since the panels collect far less than a kW per square meter). This might help explain why we can't easily power cars with solar panels on the roof and don't bother.

Let's think not about my house, but something that has a huge requirement of electricity. Let's pick a datacenter. Let's pick one of the fuck-off big ones: a GW (that's a billion watts, or a million kW) datacenter. OK, how many panels do we need?

Again, with our favorable 1 kW/m$^2$ rounding of the power you can get from the Sun, I need 1 million square meters of solar panel. Sounds like a lot: 1 million square meters is 1000 meters, squared, or a solar panel array 1 km on a side. That's a lot, but the world added 360 GW of solar capacity in the first six months of 2025. Solar panels are becoming cheap to manufacture, and fairly easy to install. We have lots of places we can put them, and the US is far behind other nations in doing so.

So, here's the think to keep in mind throughout every further discussion of putting solar panels in space: a modern datacenter needs (optimistically) a square kilometer of solar panels to power it. To this level of approximation doesn't matter if that panel is in space or the ground, or the light is coming from the Sun or reflected by a mirror. Unless the light is brighter than the Sun, you need a square km of panels to get a GW of power.

So, when thinking about mirrors in space, the question to ask is this: "is this cheaper and a better investment than just putting solar panels over a bunch of carparks?" Because mirrors in space can redirect light, but they can't create light. Even in some idealized case where 100% of the reflected light was picked up on Earth and turned into electricity, to power a 1 GW datacenter, you'd need a square km of mirror: because you need a square km of sunlight (in fact, you'll need a hell of a lot more, but I'm being as generous as possible to this idea).

So, fundamentally, the reason there is no reason energy-generation reason to put a mirror in space is that it will always, always, be cheaper and easier and a better investment to just put more solar panels here on Earth. End of story. Even in the science-fictional version of these mirrors, they'd have to be enormous to collect meaningful sunlight, and we can just do that here on Earth easier.

We have a lot of carparks.

The datacenters-in-space people do, in fact, run the numbers (though they assume ridiculously optimistic launch costs that are two orders of magnitude cheaper). They just rely on no one reading or thinking carefully about those numbers or the implications of them. Space is cold, the problems with datacenters is they are hot, problem solved.

The space mirror people are also not ignoring the numbers (as far as I can tell), but they are trusting you won't think carefully about the implications. Their grand idea for millions of mirrors in space sort of maths out (even with the disastrous numbers I'll talk about below), but they are trusting that their audience will say "oh wow, free energy from mirrors, I bet that solves a bunch of problems" and not just multiplying the energy you can get from the Sun by the size of the mirrors and saying "wait a minute, we could just build some more panels here on Earth. Just do that."

And that's the bottom line you should take away from this. Do some simple math, see that the energy gains we're talking about, even in the most optimistic scenarios, don't justify the insane expense (and destruction of the night sky). End of story. If you want, you can stop reading now.

It Gets Worse

But if you want, read on. Because in reality, the numbers are much worse than the optimistic ones. Which are already bad.

As I said, when the grifters are trying to sell datacenters in space, the thing they are relying on is that people are going to think "space is cold" and not think about the fact that so is the space in between the walls of your thermos and that's the problem. With mirrors in space, the bullshit they are using is saying that their mirrors are "as bright as the full Moon" and from that relying on their audience thinking that this means you can get meaningful amounts of energy from the mirrors. Because sure, the Sun is bright, but, you know, the full Moon is pretty bright, so sure you'll get something from those mirrors. Won't be as much, but it'll be something. Right? (And then they trust that Americans won't do math and see how bad even this idea is.)

But let's think this next step through.

Here's a fun fact about the way your senses work: your eyes are logarithmic detectors. You can see in broad daylight, but also (after your eyes adapt) you can see in levels of light orders of magnitude dimmer than daylight. Isn't that cool? Evolution is really amazing.

But while our eyes are logarithmic detectors, solar panels are linear. If you make something a thousand times less bright than the Sun, we'll still see in that level of light. But a solar panel would collect 1/1000 as much energy.

The full Moon is, obviously, dimmer than the Sun. But it's not a 10th as bright. Or a 100th as bright. Or a 1000th as bright. The full Moon gives you about one millionth the power as the Sun. The Sun, remember, gives us 1 kW per square meter of energy. The Moon gives less an a milliwatt (1 thousandth of a watt, or a millionth of a kW) per square meter.

You know what else gives a mW of energy per square meter? An ordinary beeswax candle. That's right, every time someone tries to sell you on a mirror in space to reflect sunlight onto solar panels at night, and brags about the panels being as bright or brighter than the Moon, ask yourself "is the money required to build this better spent just burning candles right in front of the solar panels?" Because odds are you'll get more electricity with the latter approach.

There is a really nice paper by Oliver Hainaut that goes through the details, but a 50x50 meter mirror in space will be about 2 mW/m^2 in the brightest region of it's reflected light. A candle gives something like 10 mW/m^2. We'd be far better off building 2500 m$^2$ of solar panels, or if you really insist, just buying birthday candles.

So when the space mirrors people brag about their mirrors being 4 times as bright as the Moon, sure, that's going to be really bright.

For you. Because your eyes are logarithmic detectors that adjust to the ambient light, and this will be the brightest thing at night.

It's going to annoy the shit out of you, every night. It's going to ruin astronomy.

But for a solar panel? That light is nothing. Because solar panels are linear response, not logarithmic. A cloud passing over the panels during the day will have more impact on your energy generation ability than one of these panels

And just think how bright that night sky will seem to your logarithmic-response eyes.

Just build more solar panels on Earth. The Sun is really bright. You can't build another one out of tin foil.