SpaceX’s $2 Trillion Bet Has a Physics Problem

0:00 net net effect is that the lowest cost place to put AI will be space. I think the the case it's it's a no-brainer for building AI solar powered AI data centers in space. cuz as you mentioned it's it's also very cold in space. If you're if you're if you're in the shadow then it's it's very cold in space. There's 3° Kelvin. So you just have you have solar panels facing the sun and then a radiator that's like point like pointed away from the sun. so it has no sign incidents and then it's and then it's just cooling. It's a very efficient cooling system.

0:33 >> So in order to start to make some progress on the cognitive scale we need to launch satellites to to to orbit Earth and capture solar power and that avoids the need to build massive power plants on Earth and deal with cooling cuz cooling is actually much easier in space than it is on Earth. that's Elon Musk explaining why he thinks the future of artificial intelligence is in orbit. And he isn't the only one who thinks so. A startup backed by Nvidia has already launched a data center class GPU into space and trained an AI model on it.

1:11 Google has a moonshot project exploring putting its AI chips on solar powered satellites. And SpaceX, which merged with Musk's AI company XAI earlier this year, went public in June with a pitch in which the vast majority of the market they say they're going after is AI. The argument goes something like this. AI needs two things in enormous quantities. Power and cooling. We're running short on both here on Earth. Space has sunlight around the clock and space is cold. So why not put the data centers up there? I think this idea rests on a misunderstanding of some pretty basic physics. The kind of physics you could work out on a blackboard in a high school classroom. So that's what I want to do today. I want to take the two big claims that there's more power in space and that it's easier to cool things in space and check them for ourselves. I think by the end you'll see that the first claim is only partly true and the second one is pretty much backwards.

2:06 Let me lay out the argument as it's usually made. Data centers on Earth have real problems. A lot of them use huge amounts of water for cooling. They put a big strain on local power grids. And in a lot of the US, a large new data center can wait years just to get hooked up to the grid. Over the last couple of years, the thing holding back AI construction has gone from a shortage of chips to a shortage of electricity. On paper, space gets around all that. In the right orbit, you get sunlight nearly all the time. You don't need any water. You don't have to wait in line for a grid connection, and there are no neighbors showing up to town meetings to complain about the noise. People also argue it's better for the environment here on Earth. Although getting everything up there takes a whole lot of rockets and those come with their own environmental impact. Some of what I just said is true and I'll get to which parts. But the cooling claim in particular is the kind of thing I'd be very surprised to hear from any of the thermal engineers who actually work at SpaceX. Keeping hardware from overheating is one of the hardest parts of designing a spacecraft.

3:04 And anyone who has done it for a living knows that. In fact, when SpaceX had to describe its orbital data center plans in its IPO filing, where the company is legally on the hook for what it says, the tone changed quite a bit there. They're described as involving quote significant technical complexity and unproven challenges that quote may not achieve commercial viability. That's a long way from much easier. >> Cooling is actually much easier in space. The lowest cost place to put AI will be space >> as we're going to see. And as any SpaceX engineer or first year physics undergrad will tell you, it is not easy to cool things in space at all.

3:46 Before getting into the physics, I want to mention a few practical problems that I don't think get nearly enough attention. The first is that once something is in orbit, you can't fix it. In a data center on Earth, when a part fails, someone walks down the aisle, pulls it out, and puts in a new one. and parts fail all the time. Back Blaze, a cloud storage company that publishes failure statistics on hundreds of thousands of drives, finds that a little over 1% of their hard drives die every year. Solid state drives do a bit better at just under 1%. Now, those numbers are from data centers on the ground where there's no space radiation flipping bits and slowly degrading the electronics.

4:22 GPUs are worse. When Meta trained one of its big llama models on about 16,000 GPUs, they logged over 400 unexpected interruptions in less than 2 months. And around half of those were caused by the GPUs or their memory failing. That works out to roughly one GPU related failure every 6 hours. On Earth, that's an inconvenience. But in orbit, every one of those failures is a piece of hardware you paid to launch. That's now that's just dead weight and nobody's coming to swap it out. Now, to be fair, Google has tested its AI chips in a particle beam, and they held up to the amount of radiation they'd see over roughly a 5-year mission. That's encouraging, but a chip that survives 5 years in orbit still has to be worth running for those 5 years, which brings me to the second problem. AI hardware gets better really fast. A new generation of chips comes out every year or two. But even if the hardware keeps working, it becomes less valuable as newer chips come out that do more for the same power. On Earth, you can deal with that by moving older GPUs to lighter workloads or selling them off or swapping in new ones. But in space, you can't do any of that without launching new hardware. So, in the worst case, you could end up with a constellation that's worth a fraction of what you paid for it within a couple of years before it's had the chance to pay for itself. Now, I admit these are engineering and business problems, and engineers are very good at solving engineering problems. So, for the rest of this video, I want to focus on the physics because physics is a lot harder to engineer your way around.

5:56 Let's start with power. On Earth, you have plenty of options for generating power. Gas, hydrodnamical, wind, solar, nuclear. But for the space data centers being pitched right now, you've really got only one, and that's solar. So, how much solar panel would you actually need to run an AI data center? Let's go to the blackboard and work it out. Okay, so the first question that we're going to answer is how much sunlight is there available at Earth at Earth's orbit for a solar panel to take advantage of. All right, you can imagine if you place a solar panel at the orbit of Pluto, it's going to have a lot less energy to work with and if it's at the orbit of Mercury, it's going to have a lot more.

6:34 So, how much does this kind of come into play? What energy budget are we talking about here from a solar panel placed in orbit that might feasibly power a data center? So the physical picture that we're sort of picturing here is we've got the sun and it's kicking off energy in all directions. That energy travels to roughly the earth around which the data setters will be orbiting and earth is in an orbit. That orbit has some radius. We're going to call it d for distance. We want to calculate what the power budget is available at this distance. because somewhere in orbit we've got a little solar panel that is collecting energy.

7:14 So the formula for this is quite simple. The formula reports the power as a function of how bright the object is is this wonderful luminosity relation. Luminosity is how much energy the sun is outputting per second. And then we plug that into this formula, spread it over an area, it gives us a a flux density or a a power per unit area basically. So L here is the luminosity, D is our distance. This is the quantity information, the power per square meter available to the solar panel. we'll calculate this. Now we just need to know what L and D are. Now for the sun, the luminosity of the sun, I as an astronomer, I know in URGs per second, it's 10^ the 33 URGs per second. but a more normal unit is watts and there's roughly 10^ the 7 URGs per watt. So this is actually more like 10^ the 26 watts. So that's the power output of the sun. Now it's being spread over this area which reduces the number of photons that you'll catch at this radius. Right?

8:21 Now what's this 4 pi d^2 term here? Well let's calculate that out. So 4 pi d^2. What's the distance of the sun? The distance of the sun is roughly 100 million miles. okay. So 100 million miles it's about 100 * 10 6 miles. Now a mile and a kilometer are roughly order of magnitude the same. It's about a factor of two. So it's like 200 * 10 6 km. So that's going to be something like that's going to be something like 2 * 10 8 km. Now we want it in meters. So we'll just convert from kilome to meters is another factor of 10 3. So this is going to be 2 * 10 to the 11 m. That's the distance that we're working with.

9:10 Okay. So we're going to plug that in here. 2 * 10 11 I'm just going to we're talking about 10 11 here. A factor of two. We don't care. so 10 10 11 we'll plug it in. that gives us 11 * 2 10 22. This is 10^ the 22 m^ squared. And then the 4 pi is a factor of 12. I'm going to round that to 10. So I'm going to say this factor in the bottom is roughly 10^ the 23 m^ squar. Now it's really convenient because 10 26 watts if we convert to kilowatts which is what data setters use this is about 10 23 kilow.

9:48 So if we plug everything into here we have 10^ the 23 kilow divided by 10^ the 23 m^ squared. And so that's going to give us roughly power per unit area, the flux density of the sun, which is one kilowatt per square meter. So this is kind of the number that a solar panel has to work with at roughly one earth orbit. So the second question that we're going to try to answer is how much panel do you actually need to achieve a particular power target? So essentially we took a power from the sun and divided over a big area. So, we just got to bring the area back in, spread our solar panels over some area to collect some of that power back. So, the power that a solar panel collects is essentially the flux density that the flux of the sun is outputting multiply by the area of your solar panels, your collecting area. And then we're going to multiply by an efficiency factor. Because solar panels aren't perfectly efficient, they don't convert 100% of the energy that falls on them to power. And typically ADA is like 20% for solar panels roughly. So what do we actually want? We we know ADA is square to 20%. We just calculated S right we have S is roughly one kilowatt per square meter. So now we want to get we want to ask for what power do we need a particular area. So in this case we know that the power of a rack of server of a rack of GPUs in a in a data center.

11:27 So this is our our GPU rack. It's puts out roughly 120 kilow. We just plug this in here. We want to solve this equation for the areas. So a is going to be roughly power that we want to achieve divided by the efficiency times the flux. Okay. And the power we want to achieve is roughly 120 kow. So that's going to be 120 * 10 3 watt. And now 20% of a kilowatt per square meter is going to be 200 watts.

12:03 So it's going to be 2 * 10 2 watts. So this is let's call this 100 * 10 3. So it's 10 5 / 10 2 and we're left with and remember this is a watts per meter squared. and we're left with about 10 to the three square meters. So what does that correspond to? That's roughly a basketball court in size. So in order to power one GPU rack, you need roughly a basketball court- sized area of solar panels. And that's just one rack. They don't want one rack. They want one gigawatt worth of racks. That's how roughly you know how much that's a a good scale for the data centers we have here on earth. So this is 10^ the 9 watts. So if we do 10 the 9 watts divided roughly we'll say 10 the 2 watts per meter squared that's approaching 10 the 7 square meters. So to power a gigawatt data center of solar panels, you would need roughly 2 km by 2 km worth of solar panels laid out.

13:17 Not impossible to do on Earth, pretty hard to do in space. And that's just for a gigawatt. Musk has said he wants not a gigawatt, but one terowatt of AI data centers in space. the the next step beyond Earth data centers is our our Earth orbital data centers and we'll be launching with SpaceX orbital data centers at the 100 to 200 gawatt per year level not cumulative I mean per year and ultimately we see a path to maybe launching as much as a terowatt per year of compute from earth >> we can go through the calculation this is 10 12 / 10 So that's going to be roughly 10^ the 10 square meters. That's 10 billion square meters. And that corresponds to a square not 2 km by 2 km, but about 50 km by 50 km. Now this is ridiculous. It's hard to explain how ridiculous. So I'm going to give you a scale. To power a terowatt data center, you need about 50 kilometers by 50 kilometers of solar panels. A neutron star, an astrophysical object with one of the most powerful magnetic fields in the universe. An astrophysical object, the neutron star has a diameter that is about 20 km. So you would need an array of solar panels sign like a factor of two larger than a neutron star in order to power the promised terowatts data center.

15:03 Again not impossible but very very challenger. Now there's something to the claim about power. At any given moment sunlight in orbit is only a little stronger than sunlight on the ground on a clear day. But averaged over time, orbit does a lot better because up there you don't have nights or clouds and the sun isn't sitting low on the horizon for half the day. Musk and Google both say a solar panel in space produces several times more energy than the same panel on the ground. And I think that's a fair point. What it doesn't change is that every watt you want still costs you area. The area costs you mass and all that mass has to go up on a rocket. On Earth, land is relatively cheap, and if you're short on it, you can go with nuclear power, which gets you about 20 times more power per acre than solar.

15:48 But in space, every square meter is something you have to build, launch, unfold, and protect from debris. And at the scale Musk is talking about, the sheer area starts to become a problem on its own because you're putting a huge and constantly growing target into an orbit that's already getting pretty crowded. You're so photogenic. So, on power, I'd say the claim is partly right. There is more sunlight up there, but collecting it comes at a steep price. You're very interested in this, huh? Solar power also brings up a second problem, which is that all that power has to end up somewhere.

16:27 A GPU doesn't lift anything or move anything because energy is conserved. Basically, every watt that goes into a computer comes back out as heat. So you can think of a space data center as a machine that takes in sunlight and turns it into waste heat doing some computation along the way. All of that heat has to get out of the machine somehow or the chips will overheat. That's the whole reason data centers on Earth use so much water. Now Musk says cooling is much easier in space because space is cold.

16:56 >> Cooling is actually much easier in space. It's it's a no-brainer for building AI solar powered AI data centers in space. because as you mentioned it's it's also very cold and spacey. >> So let's look at whether that holds up. It depends a lot on what you mean by cold. Here's something fun. The thin gas up where the space station orbits is actually hot. Hundreds of degrees and sometimes over a thousand° C. And yet astronauts go on spacew walks all the time without catching fire. That's because temperature tells you how energetic the particles are. It doesn't tell you how much energy they can actually move to you or away from you.

17:33 Up there, there are so few particles that their temperature hardly matters. So, when people say space is cold, what they really mean is that if you point something at the dark sky, there's almost nothing out there radiating heat back at you. So, how do things actually cool down then? Well, there are three ways: conduction, convection, and radiation. Here on Earth, we lean mostly on the first two. Air molecules bump into something warm, pick up some of its energy, and air currents carry that energy away. That's why a fan feels so good on a hot day. Water does the same thing, much better, which is why the serious data centers use liquid coolant.

18:10 But in space, there's no air and no water, so there's nothing around to bump into your hardware and carry the heat away. The only option left is radiation. Hot things glow, and they lose energy through the light they give off. At room temperature, that glow is in the infrared, so we can't see it, but it is there. At the kinds of temperatures computer chips can tolerate, radiation is one of the slowest ways there is to get rid of heat. So, the same thing that makes space cold, the fact that it's mostly empty, is also what makes it so bad at cooling things down. It's the same idea behind a thermos. Some thermoses keep your coffee hot all day by having a vacuum between the walls.

18:48 And vacuum is very good at trapping heat. In that sense, putting your data center in space is a bit like sealing it inside a giant thermos. And yet, despite this, this idea that space is cold and so it's good at cooling things has spread pretty far. While I was researching this video, I searched for why SpaceX is expected to be different from other AI companies. And this is what Google's AI summary told me. It says that because cooling servers and getting solar power is quote vastly more efficient in orbit, SpaceX could host AI at a fraction of the cost of data centers on Earth. So, the claim has made it all the way into the tools a lot of people now use to look things up, stated as if it were settled fact. So, why should you believe me over Elon Musk and Google? Let's go to the board and put some actual numbers on it.

19:42 Okay. So now I want to move on to the next sort of claim that's being used to talk about this. We've sort of looked at the first one. There is enough power up there to do this, but it's the the scale of the problem is hard really fast. But I want to talk about the second thing. Elon Musk in an interview said that it's really easy to cool things up there because space is cold. >> Cooling is actually much easier in space.

20:08 >> Is that true? To do this calculation, we're going to go back to our sun emitting photons. There's our sun. And we're once again going to sit at one Earth distance. And we're going to place a one square meter or yeah, we can scale. It doesn't really matter. One square meter piece of lac material. And we want to ask a simple question. What temperature does it is does it achieve? Right? It's radiating, which is what Elon Musk claims is cooling things super efficiently in space, radiating in vacuum. And the only energy it's getting is the same energy the solar panels are going to get, which is the energy from the sun. So you put something out in space where it's theoretically very cold and ask how hot does it get? Well, we can turn to something called the Stefan Boltzman law. So this is the Stefan Boltzman law.

21:12 And this law relates two interesting quantities. The flux coming off of something to its temperature. And in this case, the temper the flux scale is temperature to the fourth the power area because of temperature to the fourth with this scaling constant. It's a step- on Bolston constant. Now you can just solve what the step on bullsman constant is but the question we got to ask is this the we we already calculated s right s is roughly 1 kilowatt per square meter so that's you know 1 me square if it's warming a kilowatt of power and what temperature is it going to equilibrate to as a result so it needs to in order to equilibrate it has to give off the same amount of temperature that it's taking in now it's got 1 me square but it's got two sides. So, it's going to radiate on both sides. So, that's just something we want to keep in mind. But we know that whatever this is, this this side of the equation, in order for it to be at a constant temperature, the power in has to be the energy coming in has to equal the energy coming out. And so, we know that 1 kilowatt per meter squared, which is the amount of power absorbing, has to equal this essentially. Now you can just do this calculation, plug in the Stefan Bolson value, solve for T 4th, and I'll just tell you what it is. You're going to get a temperature of roughly 300 Kelvin. Now 300 Kelvin is sufficient to radiate five roughly 500 watts per square meter. Now you notice is 500 and not a kilowatt, 1,000 watts.

22:56 And that's because there's two sides. So at 300 Kelvin, both sides will radiate 500 watts per square meter each. And so that means that the this piece of material is going to be at roughly 300 Kelvin. So even though space is cold, we've place something out into the empty vacuum of space and it actually gets really hot. And this is just a a simple example to show you what we're talking about here. space is cold does not mean that space is good at cooling things down. Because if it were, this thing would be very, very cold, wouldn't it? So, let's dive into that. Now that we've separated space being cold from space being good at cooling things down, we can ask the question, how good is space at cooling things down? And so, in order, well, what we mean by cool? to cool things down is we need to carry heat away.

23:54 And this is done on Earth in a couple ways. As I mentioned in the back in the study, you know, you can do convection, conduction, and radiation. But convection and conduction only work when there's stuff around to convect and conduct. In space, there's nothing. So, you can only radiate. So you we can calculate how much something this piece of material can radiate or how much rather space allows you to radiate how much energy you're allowed to lose in space and we can compare that to some other things. So let me give you some numbers to compare to. So if we look at still air.

24:27 So this is just truly still air. No wind, no currents, nothing. Just still air. We can ask a simple question. Let's say I have some let's say I have some reservoir of heat here. It's at some temperature. I raise the temperature 1 Kelvin. How much heat, how much power does the environment allow me to shed extra per 1 Kelvin of temperature that I add? That's kind of the picture we want here.

24:58 Now, for still air, this works out to about 10 watts per square meter. So, you raise the temperature of something by 1 Kelvin, and still air will allow you to radiate roughly 10 watt per meter squared into it. If you add a fan and get the air moving, that's going to be more like 100 watts per meter squared. So, a fan is like 10 times better. That's why it feels so nice when when the when you when you cool yourself down with a fan. But if you add liquid like water, so liquid's cooling and circulation, it's more like 1,000 to 10,000 watt per square meter per Kelvin that you increase per one Kelvin that you increase the your object. So liquid cooling is much better than cooling, which is much better than still air acts at cooling things down with each with each Kelvin of temperature that you add. So let's calculate what it is for space which is only radiation based.

26:02 So we use pretty easily. We just showed up here from the Stephan Boltzman law that the flux that you can radiate is proportional to your temperature to the 4th. Now we're sitting at roughly 300 Kelvin. If we add 1 Kelvin that corresponds to about a.3% increase in the temperature. So what happens to the power that's additionally radiated when we increase the temperature by 0.03 by.3% sorry. So we essentially want to take 3% and we have to raise it to the 4th and this is going to be roughly 1%.

26:40 So we said that you could radiate roughly 500 watts per square meter at 300 Kelvin. So 1% times that is about is about five watts per square meter. Okay. So where does that live? How does space rank? Cuz we were told I was told in no uncertain terms >> cooling is actually much easier in space than it is on Earth. >> That space is way better at cooling things.

27:11 And yet what we calculate on just some basic physics is that space is way worse than almost any cooling system you can think of besides warm still air. I guess no one serious would use still air for circul for for cooling something down. And yet space is as bad or worse than still air. So even though space is very cold, yes, the temperature of outer space is roughly 3 Kelvin and that comes mostly from the cosmic microwave background, that doesn't mean it's good at cooling things down. You put something out there, it'll collect radiation and get hot and it has a really tough time cooling it down because space is at a vacuum is actually worse than still air at just cooling up. When you can only radiate, it becomes really hard to lose your energy.

28:07 We've now established that space is cold, but things still get hot in space and it is not very easy to cool them down. So, you ask a question, how big of a radiator would you need per rack of the GPUs? So, we established earlier that one GPU rack requires about 120 kilowatts of power. per rack. The size of the radiator we need depends on what temperature the chips need to operate at. Now, Nvidia says from Nvidia, their new chips, ideally they need to be operating at around 45° C or that's the temperature that the coolant needs to come back to the chips at in order for those to be optimal.

28:59 We're trying to keep things I'm trying to keep things in my head here. So, so now we know that a RA we just calculated that a radiator at 300 Kelvin will radiate about 500 watts per square meter which times two for the two sides is radiating on one side and the other is going to be 1,000 watts per square meter which is a kilowatt per square meter. So the question then becomes we have the temperature we need to operate at. The question then becomes how big of a surface area do we need to cool one rack essentially. So we can use the same formula as before. Remember the the flux here is power per unit area. So we can get our power back by taking our flux and multiplying it by the area. And we can solve for the area and just say all right the area is going to be the power divided by the flux. And our power we know is 120 kow.

29:59 And our flux that's allowed to radiate is essentially 1 kilowatt per square meters. Now just for the sake of argument I will round this. And so this works out to be about turns out you need 100 square meters of radiator to cool one rack. So one rack of a GP of a GPUs in a data center in space needs a 100 square meters to cool it down. And what's interesting is we calculated that you know you can calculate what area you need to acquire this amount of power right we said that roughly you get the the the power that you get from the sun at this earth's distance is roughly 500 to 1,000 watts per square meter. So, if you want 100 kilowatts, you're going to need roughly the area you'll need for the solar panels is going to be, you know, a thousand square meters. We're working with factors of two here, but the point is that you're going to need a lot more radiators sorry, you're going to need a lot few about within a fac order of magnitude radiator area as a solar panel area. So, whatever your estimate is for the solar panels, you can basically just multiply by two and that gives you your total area that you're going to need approximately.

31:19 that's pretty interesting though. So, in order to cool one rack, you're going to need 100 square meters of radiator. That's a lot of area for one rack. And I want to give you an idea of how much area that is. You may be familiar with the International Space Station. And this is my terrible drawing of the International Space Station. International Space Station has the same problem as our data center. It produces heat. Space is a vacuum. It has to cool it down. So the ISS has these big radiators that point away from the sun and they try to radiate as much heat out as possible. Now, the ISS was calibrated or it was built to radiate about 70 kilowatts of power. Now, you'll notice this is less than the amount required for one rack. So, we think it's a fair question. You can just round one and say they're roughly comparable. They're factor two. Astrophysicists don't care about factors of two. So, how did ISS do it? Well, they have six radiators.

32:24 They have six radiators and each of them is about 80 square meters. So they ended up having around 500 square meters of radiators to cool down the ISS. And now each of these radiators weighs about 1,000 kg. So you end up with in terms of weight just to cool down the ISS 7,000 kilograms of radiators roughly. Sorry, a little over 1,000, but roughly 7,000 kilograms of radiators for the ISS just to cool 70 watts. Now, if you talk to any engineer, they're going to tell you weight is the hardest thing to do.

33:12 Like, for every gram you want to put in orbit, it's precious. And keeping your astronauts from not overheating is important, which is why they spent 7,000 kg of the ISS on it. But this is a factor of two less than one rack in a data center. So, so let's run the numbers. For one rack, let's review. For one rack of GPUs in a data center, you need about 500 square meters of panels around 100 square meters of radiators for a total of roughly 600 m. And that's about two ISS's or roughly 14 14,000 kg roughly.

34:00 Okay. So for a gigawatt data center, which is what we have here on Earth, or we're building here on Earth, you're going to need roughly three square kilometers of solar panels. So I should probably label these. This is the thing. This is the solar panels you need, the radiators you'll need, and this is how many ISS you'll need. And roughly one kilometer squared of radiators.

34:30 And that corresponds to about 10,000 international space stations. That's about 70. It's a lot. 10,000 international space stations is is very, very, very heavy. Here's where it gets fun. For a terowatt, you're going to need about 3,000 square kilometers of solar panels with about 1,000 square kilmters of radiators. And now to cool them all, you're going to need 10 million equivalents of the International Space Station. That's so much. Now, there's two things I want to point out here. One, the International Space Station was built, you know, is from the '9s. So the radiator chology is a little out of date, but even if you multiply the slash these numbers by a factor of 10, this is a mortifying amount of things to put in space. And I think most engineers that I know would bulk at this. not to say it's necessarily impossible, but it's very very very far from a sure thing. So we've done the math on. Now let's go back to the study and close things out.

35:53 So, what did we learn? First, I want to be really clear that none of this makes it impossible. The physics allows it. If you could build perfect radiators running at exactly the right temperature, they would actually end up smaller than your solar panels according to our math. If someone tells you space data centers completely break the laws of physics, I think they're overselling it. But showing something is possible is a long way from showing it's cheaper than building it on Earth. The real radiators we've actually flown on the International Space Station perform far worse than that ideal. A single rack of modern AI hardware puts out about as much heat as the space station's entire main cooling system was designed to handle. A gigawatt data center would need thousands and thousands of space stations worth of cooling. And to hit their own targets, SpaceX's planning numbers require entire satellites, solar panels, chips, radiators, structures, all of it to be much lighter for the power they handle than the space station's radiators are by themselves.

36:51 The obvious response to all this is that the technology will get better, and I'm sure it will. But it's worth thinking about which improvements actually help where. Chips that do more computing per watt help data centers on Earth just as much as in space. Better cooling technology in general helps both too. The improvements that help space specifically are lighter radiators and cheaper launches. So the whole thing really comes down to a bet on rockets getting cheaper and radiators getting lighter. And meanwhile, the basic physics that makes cooling hard in space stays exactly the same. You can upgrade your rockets, but nobody gets to upgrade the Stefon Boltzman law. Now data centers on Earth have their own headaches. Power lines, permits, and long waits to connect the grid. Those are slow and frustrating problems and they're very real, but they're problems people can solve with paperwork and construction. Personally, I'd much rather deal with a permit office than with restrictive or possibly impossible thermodynamics.

37:46 So, why does any of this matter? When SpaceX went public in June, it was valued at close to $2 trillion, which made it one of the most valuable companies on the US stock market on its first day of trading. Within weeks, it was added to major indices like the NASDAQ 100, which means that if you have a retirement account or an index fund, there's a decent chance you own a little piece of it. In its IPO filing, the vast majority of the market the company says it's going after is AI. One analyst described the offering as quote, "An AI valuation wearing a rocket suit."

38:19 Morning Star, which is one of the few firms I could find that actually tried to put a price on space data centers specifically, attributed a substantial chunk of its valuation of SpaceX to them and described that piece is more of a long shot than a base case. Now, I'm not a financial adviser, and none of this is financial advice. I'm an astrophysicist. But I think it's worth noticing that the fact that the one of the largest companies in the world is asking people to bet on a future that depends in part on a claim about heat you can check with a blackboard and a few equations from high school physics. And when you check it, it doesn't hold up. This happens a lot with big claims about the future.

38:56 Someone very famous and very confident says something that sounds intuitive. Space is cold, so cooling must be easy up there. And it gets repeated by investors, by journalists, and now by AI summaries until it starts to feel like common knowledge. But the number of people repeating a claim or how rich the person who started it is has no bearing on whether it's correct. The only way to find out is to check against reality. And in this case, reality is a few hundred years of physics that hasn't budged just because there's suddenly a lot of money riding on it. At the end of the day, space is cold. It also just happens to be really bad at cooling things and I'd want the people asking for a few trillion dollars to know the difference. Thanks for watching and stay tuned for more videos like this from Astravea.