The following is a conversation with David Newman. She's the Apollo Program Professor at MIT and the former Deputy Administrator of NASA and has been a principal investigator on four space flight missions. Her research interests are in aerospace biomedical engineering, investigating human performance in varying gravity environments. She has designed and engineered and built some incredible space suit technology, namely the BioSuit that we talk about in this conversation. Due to some scheduling challenges on both our parts, we only had about 40 minutes together. And in true engineering style, she said, I talk fast, you pick the best questions, let's get it done. And we did. It was a fascinating conversation about space exploration and the future of spacesuits. This is the Artificial Intelligence Podcast. If you enjoy it, subscribe on YouTube, give it five stars on Apple Podcast, support it on Patreon, or simply connect with me on Twitter at Lex Friedman, spelled F R I D M A N. 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You circumnavigated the globe on boat, so let's look back in history. 500 years ago, Ferdinand Magellan's crew was first to circumnavigate the globe, but he died, which I think people don't know, like halfway through, and so did 242 of the 260 sailors that took that three year journey. What do you think it was like for that crew at that time heading out into the unknown to face probably likely death? Do you think they were filled with fear, with excitement? Probably not fear, I think in all of exploration, the challenge and the unknown, so probably wonderment. And then just when you really are sailing the world's oceans, you have extreme weather of all kinds. When we were circumnavigating, it was challenging, a new dynamic, you really appreciate Mother Earth, you appreciate the winds and the waves, so back to Magellan and his crew, since they really didn't have a three dimensional map of the globe, of the Earth when they went out, just probably looking over the horizon thinking, what's there, what's there? So I would say the challenge that had to be really important in terms of the team dynamics and that leadership had to be incredibly important, team dynamics, how do you keep people focused on the mission? So you think the psychology, that's interesting, there's probably echoes of that in the space exploration stuff we'll talk about. So the psychology of the dynamics between the human beings on the mission is important? Absolutely, for a Mars mission, it's lots of challenges, technology, but since I specialize in keeping my astronauts alive, the psychosocial issues, the psychology of psychosocial team dynamics, leadership, that's, you know, we're all people, so that's gonna be, that's always a huge impact, one of the top three, I think, of any isolated, confined environment, any mission that is really pretty extreme. So your Twitter handle is devaexplorer, so when did you first fall in love with the idea of exploration? Ah, that's a great question, you know, maybe as long as I can remember, as I grew up in Montana in the Rocky Mountains and Helena in the capital, and so literally, you know, Mount Helena was my backyard, was right up there, so exploring, being in the mountains, looking at caves, just running around, but always being in nature, so since my earliest memories, I, you know, think of myself as kind of exploring the natural beauty of the Rocky Mountains where I grew up. So exploration is not limited to any domain, it's just anything, so the natural domain of any kind, so going out to the woods into a place you haven't been, it's all exploration. I think so, yeah, I have a pretty all encompassing definition of exploration. So what about space exploration? When were you first captivated by the idea that we little humans could venture out into the space, into the great unknown of space? So it's a great year to talk about that, the 50th anniversary of Apollo 11, as I was alive during Apollo, and specifically Apollo 11, I was five years old, and I distinctly remember that, I remember that humanity, I'm sure I probably didn't know their names at the time, you know, there's Neil Armstrong, Buzz Aldrin, and never forget Michael Collins in orbit, you know, those three men, you know, doing something that just seemed impossible, seemed impossible a decade earlier, even a year earlier, but so the Apollo program really inspired me, and then I think it actually just taught me to dream, to any impossible mission could be possible with enough focus, and I'm sure you need some luck, but you definitely need the leadership, you need the focus of the mission, so since an early age, I thought, of course, people, it should be interplanetary, of course, people, we need people on Earth, and we're gonna have people exploring space as well. So that seemed obvious, even at that age, of course. It opened it up, before we saw men on the moon, it wasn't obvious to me at all, but once we understood that yes, absolutely, astronauts, that's what they do, they explore, they go into space, and they land on other planets or moons. So again, maybe a romanticized philosophical question, but when you look up at the stars, knowing that, you know, there's at least 100 billion of them in the Milky Way galaxy, right, so we're really a small speck in this giant thing that's the visible universe, how does that make you feel about our efforts here? I love the perspective, I love that perspective, I always open my public talks with a big Hubble Space Telescope image, looking out into, you mentioned just now, the solar system, the Milky Way, because I think it's really important to know that we're just a small, pale, blue dot, we're really fortunate, we're on the best planet by far, life is fantastic here. That we know of, you're confident this is the best planet. I'm pretty sure it's the best planet, the best planet that we know of. I mean, I searched my researches, you know, in mission worlds, and when will we find life? I think actually probably the next decade, we find probably past life, probably the evidence of past life on Mars, let's say. You think there was once life on Mars, or do you think there's currently? I'm more comfortable saying probably 3.5 billion years ago, feel pretty confident there was life on Mars, just because then it had an electromagnetic shield, it had an atmosphere, has wonderful gravity level, three HGs, fantastic, you know, you're all super human, we can all slam dunk a basketball, I mean, it's gonna be fun to play sports on Mars. So I think we'll find past, no, fossilized, probably the evidence of past life on Mars. Currently, that's okay, we need the next decade, but the evidence is mounting for sure. We do have the organics, we're finding organics, we have water, seasonal water on Mars. We used to just know about the ice caps, you know, North and South Pole, now we have seasonal water. We do have the building blocks for life on Mars. We really need to dig down into the soil, because everything on the top surface is radiated, but once we find down, will we see any life forms? Will we see any bugs? I leave it open as a possibility, but I feel pretty certain that past life, or fossilized life forms, we'll find. And then we have to get to all these ocean worlds, these beautiful moons of other planets, since we know they have water, and we're looking for some simple search for life, follow the water, carbon based life, that's the only life we know. There could be other life forms that we don't know about, but it's hard to search for them, because we don't know. So in our search for life in the solar system, it's definitely search, follow the water, and look for the building blocks of life. So you think in the next decade, we might see hints of past life, or even current life? I think so, that's it. Pretty optimistic. I love the optimism. I'm pretty optimistic. Do humans have to be involved, or can this be robots and rovers and? Probably teams, I mean, we've been at it, on Mars in particular, 50 years. We've been exploring Mars for 50 years, great data, right? Our images of Mars today are phenomenal. Now we know how Mars lost its atmosphere. We're starting to know, because of the lack of the electromagnetic shield. We know about the water on Mars. So we've been studying 50 years with our robots, we still haven't found it. So I think once we have a human mission there, we just accelerate things. But it's always humans and our rovers and robots together. But we just have to think that 50 years, we've been looking at Mars, and taking images, and doing the best science that we can. People need to realize Mars is really far away. It's really hard to get to. You know, this is extreme, extreme exploration. We mentioned Magellan first, or all of the wonderful explorers and sailors of the past, which kind of are lots of my inspiration for exploration. Mars is a different ball game. I mean, it's eight months to get there, year and a half to get home. I mean, it's really extreme. The harsh environment in all kinds of ways. But the kind of organisms we might be able to see hints of on Mars are kind of microorganisms perhaps. Do you think? Yeah, and remember that humans, we're kind of, you know, we're hosts, right? We're hosts to all of our bacteria and viruses, right? Do you think it's a big leap from the viruses and the bacteria to us humans? Put another way, do you think on all those moons, beautiful, wet moons that you mentioned, you think there's intelligent life out there? I hope so. I mean, that's the hope, but you know, we don't have the scientific evidence for that now. I think all the evidence we have in terms of life existing is much more compelling again, because we have the building blocks of life now. When that life turns into intelligence, that's a big unknown. If we ever meet, do you think we would be able to find a common language? I hope so. We haven't met yet. It's just so far, I mean, do physics just play a role here? Look at all these exoplanets, 6,000 exoplanets. I mean, even the couple dozen Earth like planets that are exoplanets that really look like habitable planets. These are very Earth like. They look like they have all the building blocks. I can't wait to get there. The only thing is they're 10 to 100 light years away. So scientifically, we know they're there. We know that they're habitable. They have, you know, everything going from, right? Like, you know, we call them in the Goldilocks zone, not too hot, not too cold, just perfect for habitability for life. But now the reality is if they're 10 at the best to 100 to thousands of light years away, so what's out there? But I just can't think that we're not the only ones. So absolutely life, life in the universe, probably intelligent life as well. Do you think there needs to be fundamental revolutions in how we, the tools we use to travel through space in order for us to venture outside of our solar system? Or do you think the ways, the rockets, the ideas we have now, the engineering ideas we have now will be enough to venture out? Well, that's a good question. Right now, you know, cause again, speed of light is a limit. We don't have a warp speed warp drive to explore our solar system, to get to Mars, to explore all the planets. Then we need a technology push, but technology push here is just advanced propulsion. It'd be great if I could get humans to Mars and say, you know, three to four months, not eight months. I mean, half the time, 50% reduction. That's great in terms of safety and wellness of the crew. Orbital mechanic, but physics rules, you know, orbital mechanics is still there. Physics rules, we can't defy physics. I love that. So invent a new physics. I mean, look at quantum, you know, look at quantum theory. So you never know. Exactly, I mean, we are always learning. So we definitely don't know all the physics that exist too, but we're, we still have to, it's not science fiction. You know, we still have to pay attention to physics in terms of our speed of travel for space flight. So you were the deputy administrator of NASA and during the Obama administration, there's a current Artemis program that's working on a crewed mission to the moon and then perhaps to Mars. What are you excited about there? What are your thoughts on this program? What are the biggest challenges do you think of getting to the moon, of landing to the moon once again, and then the big step to Mars? Well, I love, you know, the moon program now, Artemis. It is definitely, we've been in low earth orbit. I love low earth orbit too, but I just always look at it as three phases. So low earth orbit where we've been 40 years, so definitely time to get back to deep space, time to get to the moon. There's so much to do on the moon. I hope we don't get stuck on the moon for 50 years. I really want to get to the moon, spend the next decade, first with the lander, then humans. There's just a lot to explore, but to me it's a big technology push. It's only three days away. So the moon is definitely the right place. So we kind of buy down our technology. We invest in specifically habitats, life support systems. So we need suits. We really need to understand really how to live off planet. We've been off planet and low earth orbit, but still that's only 400 kilometers up, 250 miles, right? So we get to the moon. It really is a great proving ground for the technologies. And now we're in deep space, radiation becomes a huge issue and to keep our astronauts well and alive. And I look at all of that investment for moon exploration to the ultimate goal, the horizon goals we call it, to get people to Mars. But we just don't go to Mars tomorrow, right? We really need a decade on the moon, I think, investing in the technologies, learning, making sure the astronauts are, their health, they're safe and well, and also learning so much about in situ research utilization, ISRU, in situ resource utilization is huge when it comes to exploration for the moon and Mars. So we need a test bed. And to me, it really is a lunar test bed. And then we use those same investments to think about getting people to Mars in the 2030s. So developing sort of a platform of all the kind of research tools of all the, what's the resource utilization, can you speak to that? Yeah, so ISRU for the moon, it's, we'll go to the South Pole and it's fascinating. We have images of it. Of course, we know there's permanently shaded areas and like by Shackleton crater, and there's areas that are permanently in the sun. Well, it seems that there's a lot of water ice, water that's entrapped in ice and the lunar craters. That's the first place you go. Why? Because it's water and when you wanna try to, it could be fuel, life support systems. So you kind of, again, you go where the water is. And so when the moon is kind of for resources utilization, but to learn how to, can we make the fuels out of the resources that are on the moon? We have to think about 3D printing, right? You don't get to bring all this mass with you. You have to learn how to literally live off the land. We need a pressure shell. We need to have an atmosphere for people to live in. So all of that is kind of buying down the technology, doing the investigation, doing the science. What are the basically called lunar volatiles? What is that ice on the moon? How much of it is there? What are the resources look like? To me, that helps us, that's just the next step in getting humans to Mars. You know, it's cheaper and more effective to sort of develop some of these difficult challenges, like solve some of these challenges, practice, develop, test, and so on on the moon. Absolutely. That is on Mars. Absolutely. And people are gonna love to, you know, you get to the moon, you get to, you have a beautiful Earthrise. I mean, you have the most magnificent view of Earth being off planet. So it just makes sense. I think we're gonna have thousands, lots of people, hopefully tens of thousands in low Earth orbit, because low Earth orbit is a beautiful place to go and look down on the Earth, but people wanna return home. I think the lunar explorers will also wanna do round trips and, you know, be on the moon, three day trip, explore, do science, also because the lunar day is 14 days and lunar nights, also 14 days. So in that 28 day cycle, you know, half of it is in light, half of it's in dark. So people would probably wanna do, you know, couple of week trips, month long trips, not longer than that. What do you mean by people? People, explorers. I mean, yeah, astronauts are gonna be civilians in the future too. Not all astronauts are gonna be government astronauts. Actually, when I was at NASA, we changed, we actually got the law changed to recognize astronauts that are not only government employees, you know, NASA astronauts or European Space Agency astronauts or Russian Space Agency that astronauts, because of the big push we put on the private sector, that astronauts essentially are gonna be astronauts. You get over 100 kilometers up and think once you've done orbital flight, then you're an astronaut. So a lot of private citizens are gonna become astronauts. Do you think one day you might step foot on the moon? I think it'd be good to go to the moon. I'd give that a shot. Mars, I'm gonna, it's my life's work to get the next generation to Mars. That's you or even younger than you, you know, my students generation will be the Martian explorers. I'm just working to facilitate that, but that's not gonna be me. Hey, the moon's pretty good. And it's a lot tough. I mean, it's still a really tough mission. It's an extreme mission, exactly. It's great for exploration, but doable, but again, before Apollo, we didn't think getting humans to the moon was even possible. So we kind of made that possible, but we need to go back. We absolutely need to go back. We're investing in the heavy lift launch capabilities that we need to get there. We haven't had that, you know, since the Apollo days, since Saturn five. So now we have three options on the board. That's what's so fantastic. NASA has its space launch system. SpaceX is gonna have its heavy capability and Blue Origin is coming along too with heavy lifts. So that's pretty fantastic from where I sit. I'm the Apollo program professor. Today I have zero heavy lift launch capability. I can't wait, just in a few years, we'll have three different heavy lift launch capabilities. So that's pretty exciting. You know, your heart is perhaps with NASA, but you mentioned SpaceX and Blue Origin. What are your thoughts of SpaceX and the innovative efforts there from the sort of private company aspect? Oh, they're great. They're, remember that the investments in SpaceX is government funding. It's NASA funding, it's US Air Force funding, just as it should be, because they're betting on a company who is moving fast, has some new technology development. So I love it. So when I was at NASA, it really was under our public private partnerships. So necessarily the government needs to fund these startups. Now, SpaceX is no longer a startup, but you know, it's been at it for 10 years. It's had some accidents, learned a lot of lessons, but it's great because it's the way you move faster. And also some private industry folks, some private businesses will take a lot more risk. That's also really important for the government. What do you think about that culture of risk? I mean, sort of NASA and the government are exceptionally good at delivering sort of safe, like there's a bit more of a culture of caution and safety and sort of this kind of solid engineering. And I think SpaceX as well has the same kind of stuff. It has a little bit more of that startup feel where they take the bigger risks. Is that exciting for you to see, seeing bigger risks in this kind of space? Absolutely. And the best scenario is both of them working together because there's really important lessons learned, especially when you talk about human space flight, safety, quality assurance. These things are the utmost importance, both aviation and space, you know, when human lives are at stake. On the other hand, government agencies, NASA can be European Space Agency, you name it, they become very bureaucratic, pretty risk averse, move pretty slowly. So I think the best is when you combine the partnerships from both sides. Industry necessarily has to push the government, take some more risks. You know, they're smart risk or actually gave an award at NASA for failing smart. Failing smart, I love that. You know, so you can kind of break open the culture, say, no, look at Apollo, that was a huge risk. It was done well. So there's always a culture of safety, quality assurance, you know, engineering, you know, at its best. But on the other hand, you want to get things done and you have to also get them, you have to bring the cost down. You know, for when it comes to launch, we really have to bring the cost down and get the frequency up. And so that's what the newcomers are doing. They're really pushing that. So it's about the most exciting time that I can imagine for space flight. Again, a little bit, it really is the democratization of space flight, opening it up, not just because of the launch capability, but the science we can do on a CubeSat. What you can do now for very, those used to be, you know, student projects that we would go through, conceive, design, implement, and think about what a small satellite would be. Now they're the most, you know, these are really advanced instruments, science instruments that are flying on little teeny CubeSats that pretty much anyone can afford. So there's not a, there's every nation, you know, every place in the world can fly a CubeSat. And so that's... What's a CubeSat? Oh, CubeSat is a, this is called 1U. CubeSats we measure in terms of units. So, you know, just in terms of, I put my, both my hands together, that's one unit, two units. So little small satellites. So CubeSats are for small satellites. And we actually go by mass as well. You know, a small satellite might be a hundred kilos, 200 kilos, all well under a thousand kilos. CubeSats then are the next thing down from small sats. You know, basically, you know, kilos, tens of kilos, things like that. But kind of the building blocks, CubeSats are fantastic design, it's kind of modular design. So I can take a 1U, one unit of CubeSat and, you know, but what if I have a little bit more money and payload, I can fly three of them and just basically put a lot more instruments on it. But essentially think about something the size of a shoe box, if you will. You know, that would be a CubeSat. And how do those help empower you in terms of doing size, in terms of doing experiments? Oh, right now there's, again, back to private industry, Planet, the company, is, you know, flying CubeSats and literally looking down on Earth and orbiting Earth, taking a picture, if you will, of Earth every day, every 24 hours, covering the entire Earth. So in terms of Earth observations, in terms of climate change, in terms of our changing Earth, it's revolutionizing because they're affordable. We can put a whole bunch of them up. Telecoms, we're all, you know, on our cell phones and we have GPS, we have our telecoms, but those used to be very expensive satellites providing that service. Now we can fly a whole bunch of modular CubeSats. So it really is breakthrough in terms of modularity, as well as cost reduction. So that's one exciting set of developments. Is there something else that you've been excited about, like reusable rockets, perhaps, that you've seen in the last few years? Yeah, well, the reusability you had, and the reusability is awesome. I mean, it's just the best. Now we have to remember, the shuttle was a reusable vehicle. Yes. Which, and the shuttle is an amazing, it's narrow space engineer. You know, I mean, the shuttle is still, this is the most gorgeous, elegant, extraordinary design of a space vehicle. It was reusable, it just wasn't affordable. But the reusability of it was really critical because we flew it up, it did come back. So the notion of reusability, I think absolutely. Now what we're doing with we, you know, the Global We, but with SpaceX and Lord Jim, setting the rockets up, recovering the first stages, where if they can regain 70% cost savings, that's huge. And just seeing the control, you know, being in control and dynamic as a person, just seeing that rocket come back and land. Oh yeah, that's. It never gets old, it's exciting every single time you look at it and say, that's magic. So it's so cool. To me, the landing is where I stand up, start clapping, just the control. Yeah, just the algorithm, just the control algorithms, and hitting that landing, it's, you know, it's gymnastics for rocket ships, but to see these guys stick a landing, it's just wonderful. So every time, like I say, every time I see, you know, the reusability and the rockets coming back and landing so precisely, it's really exciting. So it is actually, that's a game changer. We are in a new era of lower costs and the higher frequency. And it's the world, not just NASA, many nations are really upping their frequency of launches. So you've done a lot of exciting research, design, engineering on spacesuits. What does the spacesuit of the future look like? Well, if I have anything to say about it, it'll be a very, it'll be a very tight fitting suit. We use mechanical counter pressure to pressurize right directly on the skin. Seems that it's technically feasible. We're still at the research and development stage. We don't have a flight system, but technically it's feasible. So we do a lot of work in the materials. You know, what materials do we need to pressurize someone? What's the patterning we need? That's what our patents are in, the patterning, kind of how we apply. This is a third of an atmosphere. Just to sort of take a little step back, you have this incredible biosuit where it's tight fitting, so it allows more mobility and so on. So maybe even to take a bigger step back, like what are the functions that a spacesuit should perform? Sure, so start from the beginning. A spacesuit is the world's smallest spacecraft. So I really, that's the best definition I can give you. Right now we fly gas pressurized suits, but think of developing and designing an entire spacecraft. So then you take all those systems and you shrink them around a person, provide them with oxygen to breathe, scrub out their carbon dioxide, you know, make sure they have pressure. They need a pressure environment to live in. So really the spacesuit is a shrunken, you know, spacecraft in its entirety, has all the same systems. Communication as well, probably. Yeah, communications, exactly. So you really, thermal control, little bit of radiation, not so much radiation protection, but thermal control, humidity, you know, oxygen debris. So all those life support systems, as well as the pressure protection. So it's an engineering marvel, you know, the spacesuits that have flown because they really are entire spacecraft, they're the small spacecraft that we have around a person, but they're very massive, but 140 kilos is the current suit, and they're not mobility suits. So since we're going back to the moon and Mars, we need a planetary suit, we need a mobility suit. So that's where we've kind of flipped the design paradigm. I study astronauts, I study humans in motion, and if we can map that motion, I want to give you full flexibility, you know, move your arms and legs. I really want you to be like a Olympic athlete, an extreme explorer. I don't want to waste any of your energy, so we take it from the human design. So I take a look at humans, we measure them, we model them, and then I say, okay, can I put a spacesuit on them that goes from the skin out? So rather than a gas pressurized shrinking that spacecraft around the person, say, here's how humans perform, can I design a spacesuit literally from the skin out? And that's what we've come up with, a mechanical counter pressure, some patterning, and that way it could be order of magnitude less in terms of the mass, and it should provide maximum mobility for moon or Mars. What's mechanical counter pressure? Like how the heck can you even begin to create something that's tight fitting and still doesn't protect you from the elements and so on and the whole, the pressure thing? That's the challenge, it's a big design challenge we've been working on it for. So you can either put someone in a balloon, that's one way to do it, that's conventional, that's the only thing we've ever formed. What's that mean? That means the balloon that you fill with gas? That's a gas pressurized suit. If you put someone in a balloon, it's only a third of an atmosphere to keep someone alive. So that's what the current system is. So depending on what units you think, in 30 kilopascals, 4.3 pounds per square inch. So much less than the pressure that's on Earth. You can still keep a human alive with 0.3 and it's alive and happy. Alive and happy. And you mix the gases. June, we're having this chat and we're at one sea level in Boston, one atmosphere. But a suit. Oxygen and nitrogen. Oxygen and nitrogen. And you put a suit, if we put someone to a third of an atmosphere, so for mechanical counter pressure now, so one way is to do it with a balloon. And that's what we currently have. Or you can apply the pressure directly to the skin. I only have to give you a third of an atmosphere. Right now, you and I are very happy in one atmosphere. So if I put that pressure, a third of an atmosphere on you, I just have to do it consistently, across all of your body and your limbs. And it'll be a gas pressurized helmet. Doesn't make sense to shrink wrap the head. See the blue mangrove, that's a great, it's a great act. But we don't need to, there's no benefits of like shrink wrapping the head. You put, you know, a gas pressurized helmet because the helmet then, the future of suits, you asked me about, the helmet just becomes your information portal. So it will have augmented reality. It'll have all the information you need. Should have, you know, the maps that I need. I'm on the moon. Okay, well, hey, smart helmet. Then show me the map, show me the topography. Hopefully it has the lab embedded too. If it has really great cameras, maybe I can see with that regolith. That's just lunar dust and dirt. What's that made out of? We talked about the water. So the helmet then really becomes this information portal is how I see kind of the IT architecture of the helmet is really allowing me to, you know, use all of my modalities of an explorer that I'd like to. So cameras, voiceover, images, if it were really good, it would kind of be, would have lab capabilities as well. Okay, so the pressure comes from the body, comes from the mechanical pressure. It's fascinating. Now, what aspect, when I look at Biosuit, just the suits you're working on, sort of from a fashion perspective, they look awesome. Is that a small part of it too? Oh, absolutely, because the teams that we work with, of course, I'm an engineer, there's engineering students, there's design students, there's architects. So it really is a very much a multidisciplinary team. So sure, colors, aesthetics, materials, all those things we pay attention to. So it's not just an engineering solution. It really is a much more holistic, it's a suit. It's a suit, you're, you know, you're dressed in a suit now. It's a warm fitting. So we really have to pay attention to all those things. And so that's the design team that we work with. And my partner, Geetraati, you know, we're partners in this in terms of, he comes from an architecture, industrial design background. So bringing those skills to bear as well. We team up with industry folks who are in, you know, athletic performance and designers. So it really is a team that brings all those skills together. So what role does this space suit play in our longterm staying in Mars, sort of exploring the, doing all the work that astronauts do, but also perhaps civilians one day, almost like taking steps towards colonization of Mars? What role does a space suit play there? So you always need life support system, pressurized habitat. And I like to say, we're not going to Mars to sit around. So you need a suit. You know, even if you land and have the lander, you're not going there to stay inside. That's for darn sure. We're going there to search for the evidence of life. That's why we're going to Mars. So you need a lot of mobility. So for me, the suit is the best way to give the human mobility. We're always still going to need rovers. We're going to need robots. So for me, exploration is always a suite of explorers. Some people are going to, some of the suite of explorers are humans, but many are going to be robots, smart systems, things like that. But I look at it as kind of all those capabilities together make the best exploration team. So let me ask, I love artificial intelligence and I've also saw that you've enjoyed the movie Space Odyssey, 2001 Space Odyssey. Let me ask the question about HAL 9000. That makes a few decisions there that prioritizes the mission over the astronauts. Do you think, from a high philosophical question, do you think HAL did the right thing of prioritizing the mission? I think our artificial intelligence will be smarter in the future. For a Mars mission, it's a great question that the reality is for a Mars mission, we need fully autonomous systems. We will get humans, but they have to be fully autonomous. And that's a really important, that's the most important concept because there's not going to be a mission control on Earth. 20 minute time lag, there's just no way you're going to control it. So fully autonomous, so people have to be fully autonomous as well, but all of our systems as well. And so that's the big design challenge. So that's why we test them out on the moon as well. When we have a, okay, a few second, three second time lag, you can test them out. We have to really get autonomous exploration down. You asked me earlier about Magellan. Magellan and his crew, they left, right? They were autonomous. You know, they were autonomous. They left and they were on their own to figure out that mission. Then when they hit land, they have resources, that's in situ resource utilization and everything else they brought with them. So we have to, I think, have that mindset for exploration. Again, back to the moon, it's more the testing ground, the proving ground with technologies. But when we get to Mars, it's so far away that we need fully autonomous systems. So I think that's where, again, AI and autonomy come in, a really robust autonomy, things that we don't have today yet. So they're on the drawing boards, but we really need to test them out because that's what we're up against. So fully autonomous meaning like self sufficient. There's still a role for the human in that picture. Do you think there'll be a time when AI systems, beyond doing fully autonomous flight control will also help or even take mission decisions like Hal did? That's interesting. It depends. I mean, they're gonna be designed by humans. I think as you mentioned, humans are always in the loop. I mean, we might be on Earth, we might be in orbit on Mars, maybe the systems of landers down on the surface of Mars. But I think we're gonna get, we are right now just on Earth based systems, AI systems that are incredibly capable and training them with all the data that we have now, petabytes of data from Earth. What I care about for the autonomy and AI right now, how we're applying it in research is to look at Earth and look at climate systems. I mean, that's the, it's not for Mars to me today. Right now AI is to eyes on Earth, all of our space data, compiling that using supercomputers because we have so much information and knowledge and we need to get that into people's hands. First, there's the educational issue with climate and our changing climate. Then we need to change human behavior. That's the biggie. So this next decade, it's urgent we take care of our own spaceship, which is spaceship Earth. So that's to me where my focus has been for AI systems, using whatever's out there, kind of imagining also what the future situation is, what's the satellite imagery of Earth of the future. If you can hold that in your hands, that's gonna be really powerful. Will that help people accelerate positive change for Earth and for us to live in balance with Earth? I hope so. And kind of start with the ocean systems. So oceans to land to air and kind of using all the space data. So it's a huge role for artificial intelligence to help us analyze, I call it curating the data, using the data. It has a lot to do with visualizations as well. Do you think in a weird, dark question, do you think human species can survive if we don't become interplanetary in the next century or a couple of centuries? Absolutely we can survive. I don't think Mars is option B actually. So I think it's all about saving spaceship Earth and humanity. I simply put, Earth doesn't need us, but we really need Earth. All of humanity needs to live in balance with Earth because Earth has been here a long time before we ever showed up and it'll be here a long time after. It's just a matter of how do we wanna live with all living beings, much more in balance because we need to take care of the Earth and right now we're not. So that's the urgency. And I think it is the next decade to try to live much more sustainably, live more in balance with Earth. I think the human species has a great long optimistic future, but we have to act. It's urgent. We have to change behavior. We have to realize that we're all in this together. It's just one blue bubble. It's for humanity. So when I think people realize that we're all astronauts, that's the great news is everyone's gonna be an astronaut. We're all astronauts of spaceship Earth. And again, this is our mission. This is our mission to take care of the planet. And yet as we explore out from our spaceship Earth here out into the space, what do you think the next 50, 100, 200 years look like for space exploration? I'm optimistic. So I think that we'll have lots of people, thousands of people, tens of thousands of people, who knows, maybe millions in low Earth orbit. That's just a place that we're gonna have people and actually some industry, manufacturing, things like that. That dream I hope we realize, getting people to the moon. So I can envision a lot of people on the moon. Again, it's a great place to go. Living or visiting? Probably visiting and living. If you want to, most people are gonna wanna come back to Earth, I think. But there'll be some people and it's not such a long, it's a good view, it's a beautiful view. So I think that we will have many people on the moon as well. I think there'll be some people, you told me, wow, hundreds of years out. So we'll have people, we'll be interplanetary for sure as a species. So I think we'll be on the moon. I think we'll be on Mars. Venus, no, it's already a runaway greenhouse gas. So not a great place for science. Jupiter, all within the solar system, great place for all of our scientific probes. I don't see so much in terms of human physical presence. We'll be exploring them. So we live in our minds there because we're exploring them and going on those journeys. But it's really our choice in terms of our decisions of how in balance we're gonna be living here on the Earth. When do you think the first woman, first person will step on Mars? Ah, step on Mars? Well, I'm gonna do everything I can to make sure it happens in the 2030s. 2030s. Say mid, 20, mid 20, 2025, 2035, we'll be on the moon. And hopefully with more people than us. But first with a few astronauts, it'll be global, international folks. But we really need those 10 years, I think, on the moon. And then so by later in the decade, in the 2030s, we'll have all the technology and know how, and we need to get that human mission to Mars done. We live in exciting times. And, Dava, thank you so much for leading the way and thank you for talking today. I really appreciate it. Thank you, my pleasure. Thanks for listening to this conversation and thank you to our presenting sponsor, Cash App. Remember to use code LexPodcast when you download Cash App from the App Store or Google Play Store. You'll get 10 bucks, $10, and $10 will go to FIRST, a STEM education nonprofit that inspires hundreds of thousands of young minds to learn and to dream of engineering our future. Thank you and hope to see you next time.

Dava Newman: Space Exploration, Space Suits, and Life on Mars | Lex Fridman Podcast #51


The following is a conversation with Gilbert Strang. He's a professor of mathematics at MIT and perhaps one of the most famous and impactful teachers of math in the world. His MIT OpenCourseWare lectures on linear algebra have been viewed millions of times. As an undergraduate student, I was one of those millions of students. There's something inspiring about the way he teaches. There's at once calm, simple, and yet full of passion for the elegance inherent to mathematics. I remember doing the exercise in his book, Introduction to Linear Algebra, and slowly realizing that the world of matrices, of vector spaces, of determinants and eigenvalues, of geometric transformations and matrix decompositions reveal a set of powerful tools in the toolbox of artificial intelligence. From signals to images, from numerical optimization to robotics, computer vision, deep learning, computer graphics, and everywhere outside AI, including, of course, a quantum mechanical study of our universe. This is the Artificial Intelligence Podcast. If you enjoy it, subscribe on YouTube, give it five stars on Apple Podcast, support on Patreon, or simply connect with me on Twitter at Lex Friedman, spelled F R I D M A N. This podcast is supported by ZipRecruiter. Hiring great people is hard, and to me is the most important element of a successful mission driven team. I've been fortunate to be a part of and to lead several great engineering teams. The hiring I've done in the past was mostly through tools that we built ourselves, but reinventing the wheel was painful. ZipRecruiter is a tool that's already available for you. It seeks to make hiring simple, fast, and smart. For example, Codable cofounder Gretchen Huebner used ZipRecruiter to find a new game artist to join her education tech company. 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Brokerage services are provided by Cash App Investing, a subsidiary of Square, and member SIPC. I'm excited to be working with Cash App to support one of my favorite organizations that many of you may know and have benefited from, called First, best known for their first robotics and Lego competitions. They educate and inspire hundreds of thousands of students in over 110 countries, and have a perfect rating on Charity Navigator, which means the donated money is used to maximum effectiveness. When you get Cash App from the App Store or Google Play, and use code LexPodcast, you get $10, and Cash App will also donate $10 to First, which again, is an organization that I've personally seen inspire girls and boys to dream of engineering a better world. And now, here's my conversation with Gilbert Strang. How does it feel to be one of the modern day rock stars of mathematics? I don't feel like a rock star. That's kind of crazy for an old math person. But it's true that the videos in linear algebra that I made way back in 2000, I think, have been watched a lot. And well, partly the importance of linear algebra, which I'm sure you'll ask me, and give me a chance to say that linear algebra as a subject has just surged in importance. But also, it was a class that I taught a bunch of times, so I kind of got it organized and enjoyed doing it. The videos were just the class. So they're on OpenCourseWare and on YouTube and translated, and it's fun. But there's something about that chalkboard and the simplicity of the way you explain the basic concepts in the beginning. To be honest, when I went to undergrad. You didn't do linear algebra, probably. Of course I didn't do linear algebra. You did. Yeah, yeah, yeah, of course. But before going through the course at my university, there was going through OpenCourseWare. You were my instructor for linear algebra. Right, yeah. And that, I mean, we're using your book. And I mean, the fact that there is thousands, hundreds of thousands, millions of people that watch that video, I think that's really powerful. So how do you think the idea of putting lectures online, what really MIT OpenCourseWare has innovated? That was a wonderful idea. I think the story that I've heard is the committee was appointed by the president, President Vest, at that time, a wonderful guy. And the idea of the committee was to figure out how MIT could be like other universities, market the work we were doing. And then they didn't see a way. And after a weekend, and they had an inspiration, came back to President Vest and said, what if we just gave it away? And he decided that was okay, good idea. So. You know, that's a crazy idea. If we think of a university as a thing that creates a product, isn't knowledge, the kind of educational knowledge, isn't the product and giving that away, are you surprised that it went through? The result that he did it, well, knowing a little bit President Vest, it was like him, I think, and it was really the right idea. MIT is a kind of, it's known for being high level, technical things, and this is the best way we can say, tell, we can show what MIT really is like, because in my case, those 1806 videos are just teaching the class. They were there in 26, 100. They're kind of fun to look at. People write to me and say, oh, you've got a sense of humor, but I don't know where that comes through. Somehow I'm friendly with the class, I like students. And then your algebra, the subject, we gotta give the subject most of the credit. It really has come forward in importance in these years. So let's talk about linear algebra a little bit, because it is such a, it's both a powerful and a beautiful subfield of mathematics. So what's your favorite specific topic in linear algebra, or even math in general to give a lecture on, to convey, to tell a story, to teach students? Okay, well, on the teaching side, so it's not deep mathematics at all, but I'm kind of proud of the idea of the four subspaces, the four fundamental subspaces, which are of course known before, long before my name for them, but. Can you go through them? Can you go through the four subspaces? Sure I can, yeah. So the first one to understand is, so the matrix is, maybe I should say the matrix is. What is a matrix? What's a matrix? Well, so we have like a rectangle of numbers. So it's got n columns, got a bunch of columns, and also got an m rows, let's say, and the relation between, so of course the columns and the rows, it's the same numbers. So there's gotta be connections there, but they're not simple. The columns might be longer than the rows, and they're all different, the numbers are mixed up. First space to think about is take the columns, so those are vectors, those are points in n dimensions. What's a vector? So a physicist would imagine a vector or might imagine a vector as a arrow in space or the point it ends at in space. For me, it's a column of numbers. You often think of, this is very interesting in terms of linear algebra, in terms of a vector, you think a little bit more abstract than how it's very commonly used, perhaps. You think this arbitrary multidimensional space. Right away, I'm in high dimensions. Dreamland. Yeah, that's right. In the lecture, I try to, so if you think of two vectors in 10 dimensions, I'll do this in class, and I'll readily admit that I have no good image in my mind of a vector of an arrow in 10 dimensional space, but whatever. You can add one bunch of 10 numbers to another bunch of 10 numbers, so you can add a vector to a vector, and you can multiply a vector by three, and that's, if you know how to do those, you've got linear algebra. 10 dimensions, there's this beautiful thing about math, if we look at string theory and all these theories, which are really fundamentally derived through math, but are very difficult to visualize. How do you think about the things, like a 10 dimensional vector, that we can't really visualize? And yet, math reveals some beauty underlying our world in that weird thing we can't visualize. How do you think about that difference? Well, probably, I'm not a very geometric person, so I'm probably thinking in three dimensions, and the beauty of linear algebra is that it goes on to 10 dimensions with no problem. I mean, that if you're just seeing what happens if you add two vectors in 3D, yeah, then you can add them in 10D. You're just adding the 10 components. So, I can't say that I have a picture, but yet I try to push the class to think of a flat surface in 10 dimensions. So a plane in 10 dimensions, and so that's one of the spaces. Take all the columns of the matrix, take all their combinations, so much of this column, so much of this one, then if you put all those together, you get some kind of a flat surface that I call a vector space, space of vectors. And my imagination is just seeing like a piece of paper in 3D, but anyway, so that's one of the spaces, that's space number one, the column space of the matrix. And then there's the row space, which is, as I said, different, but came from the same numbers. So we got the column space, all combinations of the columns, and then we've got the row space, all combinations of the rows. So those words are easy for me to say, and I can't really draw them on a blackboard, but I try with my thick chalk. Everybody likes that railroad chalk, and me too. I wouldn't use anything else now. And then the other two spaces are perpendicular to those. So like if you have a plane in 3D, just a plane is just a flat surface in 3D, then perpendicular to that plane would be a line. So that would be the null space. So we've got two, we've got a column space, a row space, and there are two perpendicular spaces. So those four fit together in a beautiful picture of a matrix, yeah, yeah. It's sort of a fundamental, it's not a difficult idea. It comes pretty early in 1806, and it's basic. Planes in these multidimensional spaces, how difficult of an idea is that to come to, do you think? If you look back in time, I think mathematically it makes sense, but I don't know if it's intuitive for us to imagine, just as we were talking about. It feels like calculus is easier to intuit. Well, I have to admit, calculus came earlier, earlier than linear algebra. So Newton and Leibniz were the great men to understand the key ideas of calculus. But linear algebra to me is like, okay, it's the starting point, because it's all about flat things. Calculus has got, all the complications of calculus come from the curves, the bending, the curved surfaces. Linear algebra, the surfaces are all flat. Nothing bends in linear algebra. So it should have come first, but it didn't. And calculus also comes first in high school classes, in college class, it'll be freshman math, it'll be calculus, and then I say, enough of it. Like, okay, get to the good stuff. And that's... Do you think linear algebra should come first? Well, it really, I'm okay with it not coming first, but it should, yeah, it should. It's simpler. Because everything is flat. Yeah, everything's flat. Well, of course, for that reason, calculus sort of sticks to one dimension, or eventually you do multivariate, but that basically means two dimensions. Linear algebra, you take off into 10 dimensions, no problem. It just feels scary and dangerous to go beyond two dimensions, that's all. If everything's flat, you can't go wrong. So what concept or theorem in linear algebra or in math you find most beautiful, that gives you pause that leaves you in awe? Well, I'll stick with linear algebra here. I hope the viewer knows that really, mathematics is amazing, amazing subject and deep, deep connections between ideas that didn't look connected, they turned out they were. But if we stick with linear algebra... So we have a matrix. That's like the basic thing, a rectangle of numbers. And it might be a rectangle of data. You're probably gonna ask me later about data science, where often data comes in a matrix. You have maybe every column corresponds to a drug and every row corresponds to a patient. And if the patient reacted favorably to the drug, then you put up some positive number in there. Anyway, rectangle of numbers, a matrix is basic. So the big problem is to understand all those numbers. You got a big, big set of numbers. And what are the patterns, what's going on? And so one of the ways to break down that matrix into simple pieces is uses something called singular values. And that's come on as fundamental in the last, certainly in my lifetime. Eigenvalues, if you have viewers who've done engineering, math, or basic linear algebra, eigenvalues were in there. But those are restricted to square matrices. And data comes in rectangular matrices. So you gotta take that next step. I'm always pushing math faculty, get on, do it, do it. Singular values. So those are a way to break, to find the important pieces of the matrix, which add up to the whole matrix. So you're breaking a matrix into simple pieces. And the first piece is the most important part of the data. The second piece is the second most important part. And then often, so a data set is a matrix. And often, so a data scientist will like, if a data scientist can find those first and second pieces, stop there, the rest of the data is probably round off, experimental error maybe. So you're looking for the important part. So what do you find beautiful about singular values? Well, yeah, I didn't give the theorem. So here's the idea of singular values. Every matrix, every matrix, rectangular, square, whatever, can be written as a product of three very simple special matrices. So that's the theorem. Every matrix can be written as a rotation times a stretch, which is just a diagonal matrix, otherwise all zeros except on the one diagonal. And then the third factor is another rotation. So rotation, stretch, rotation is the breakup of any matrix. The structure of that, the ability that you can do that, what do you find appealing? What do you find beautiful about it? Well, geometrically, as I freely admit, the action of a matrix is not so easy to visualize, but everybody can visualize a rotation. Take two dimensional space and just turn it around the center. Take three dimensional space. So a pilot has to know about, well, what are the three, the yaw is one of them. I've forgotten all the three turns that a pilot makes. Up to 10 dimensions, you've got 10 ways to turn, but you can visualize a rotation. Take the space and turn it. And you can visualize a stretch. So to break a matrix with all those numbers in it into something you can visualize, rotate, stretch, rotate is pretty neat. It's pretty neat. That's pretty powerful. On YouTube, just consuming a bunch of videos and just watching what people connect with and what they really enjoy and are inspired by, math seems to come up again and again. I'm trying to understand why that is. Perhaps you can help give me clues. So it's not just the kinds of lectures that you give, but it's also just other folks like with Numberphile, there's a channel where they just chat about things that are extremely complicated, actually. People nevertheless connect with them. What do you think that is? It's wonderful, isn't it? I mean, I wasn't really aware of it. We're conditioned to think math is hard, math is abstract, math is just for a few people, but it isn't that way. A lot of people quite like math and they liked it. I get messages from people saying, now I'm retired, I'm gonna learn some more math. I get a lot of those. It's really encouraging. And I think what people like is that there's some order, a lot of order and things are not obvious, but they're true. So it's really cheering to think that so many people really wanna learn more about math. Yeah. And in terms of truth, again, sorry to slide into philosophy at times, but math does reveal pretty strongly what things are true. I mean, that's the whole point of proving things. It is, yeah. And yet, sort of our real world is messy and complicated. It is. What do you think about the nature of truth that math reveals? Oh, wow. Because it is a source of comfort like you've mentioned. Yeah, that's right. Well, I have to say, I'm not much of a philosopher. I just like numbers. As a kid, this was before you had to go in, when you had a filly in your teeth, you had to kind of just take it. So what I did was think about math, like take powers of two, two, four, eight, 16, up until the time the tooth stopped hurting and the dentist said you're through. Or counting. Yeah. So that was a source of just, source of peace almost. Yeah. What is it about math do you think that brings that? Yeah. What is that? Well, you know where you are. Yeah, it's symmetry, it's certainty. The fact that, you know, if you multiply two by itself 10 times, you get 1,024 period. Everybody's gonna get that. Do you see math as a powerful tool or as an art form? So it's both. That's really one of the neat things. You can be an artist and like math, you can be an engineer and use math. Which are you? Which am I? What did you connect with most? Yeah, I'm somewhere between. I'm certainly not a artist type, philosopher type person. Might sound that way this morning, but I'm not. Yeah, I really enjoy teaching engineers because they go for an answer. And yeah, so probably within the MIT math department, most people enjoy teaching people, teaching students who get the abstract idea. I'm okay with, I'm good with engineers who are looking for a way to find answers. Yeah. Actually, that's an interesting question. Do you think for teaching and in general, thinking about new concepts, do you think it's better to plug in the numbers or to think more abstractly? So looking at theorems and proving the theorems or actually building up a basic intuition of the theorem or the method, the approach, and then just plugging in numbers and seeing it work. Yeah, well, certainly many of us like to see examples. First, we understand, it might be a pretty abstract sounding example, like a three dimensional rotation. How are you gonna understand a rotation in 3D? Or in 10D? And then some of us like to keep going with it to the point where you got numbers, where you got 10 angles, 10 axes, 10 angles. But the best, the great mathematicians probably, I don't know if they do that, because for them, an example would be a highly abstract thing to the rest of it. Right, but nevertheless, working in the space of examples. Yeah, examples. It seems to. Examples of structure. Our brains seem to connect with that. Yeah, yeah. So I'm not sure if you're familiar with him, but Andrew Yang is a presidential candidate currently running with math in all capital letters and his hats as a slogan. I see. Stands for Make America Think Hard. Okay, I'll vote for him. So, and his name rhymes with yours, Yang, Strang. But he also loves math and he comes from that world of, but he also, looking at it, makes me realize that math, science, and engineering are not really part of our politics, political discourse, about political government in general. Why do you think that is? Well. What are your thoughts on that in general? Well, certainly somewhere in the system, we need people who are comfortable with numbers, comfortable with quantities. You know, if you say this leads to that, they see it and it's undeniable. But isn't that strange to you that we have almost no, I mean, I'm pretty sure we have no elected officials in Congress or obviously the president that either has an engineering degree or a math degree. Yeah, well, that's too bad. A few could, a few who could make the connection. Yeah, it would have to be people who understand engineering or science and at the same time can make speeches and lead, yeah. Yeah, inspire people. Yeah, inspire, yeah. You were, speaking of inspiration, the president of the Society for Industrial and Applied Mathematics. Oh, yes. It's a major organization in math, applied math. What do you see as a role of that society, you know, in our public discourse? Right. In public. Yeah, so, well, it was fun to be president at the time. A couple years, a few years. Two years, around 2000. I just hope that's president of a pretty small society. But nevertheless, it was a time when math was getting some more attention in Washington. But yeah, I got to give a little 10 minutes to a committee of the House of Representatives talking about who I met. And then, actually, it was fun because one of the members of the House had been a student, had been in my class. What do you think of that? Yeah, as you say, pretty rare, most members of the House have had a different training, different background. But there was one from New Hampshire who was my friend, really, by being in the class. Yeah, so those years were good. Then, of course, other things take over in importance in Washington, and math just, at this point, is not so visible. But for a little moment, it was. There's some excitement, some concern about artificial intelligence in Washington now. Yes, sure. About the future. Yeah. And I think at the core of that is math. Well, it is, yeah. Maybe it's hidden. Maybe it's wearing a different hat. Well, artificial intelligence, and particularly, can I use the words deep learning? Deep learning is a particular approach to understanding data. Again, you've got a big, whole lot of data where data is just swamping the computers of the world. And to understand it, out of all those numbers, to find what's important in climate, in everything. And artificial intelligence is two words for one approach to data. Deep learning is a specific approach there, which uses a lot of linear algebra. So I got into it. I thought, okay, I've gotta learn about this. So maybe from your perspective, let me ask the most basic question. How do you think of a neural network? What is a neural network? Yeah, okay. So can I start with the idea about deep learning? What does that mean? What is deep learning? What is deep learning, yeah. So we're trying to learn, from all this data, we're trying to learn what's important. What's it telling us? So you've got data, you've got some inputs for which you know the right outputs. The question is, can you see the pattern there? Can you figure out a way for a new input, which we haven't seen, to understand what the output will be from that new input? So we've got a million inputs with their outputs. So we're trying to create some pattern, some rule that'll take those inputs, those million training inputs, which we know about, to the correct million outputs. And this idea of a neural net is part of the structure of our new way to create a rule. We're looking for a rule that will take these training inputs to the known outputs. And then we're gonna use that rule on new inputs that we don't know the output and see what comes. Linear algebra is a big part of finding that rule. That's right, linear algebra is a big part. Not all the part. People were leaning on matrices, that's good, still do. Linear is something special. It's all about straight lines and flat planes. And data isn't quite like that. It's more complicated. So you gotta introduce some complication. So you have to have some function that's not a straight line. And it turned out, nonlinear, nonlinear, not linear. And it turned out that it was enough to use the function that's one straight line and then a different one. Halfway, so piecewise linear. One piece has one slope, one piece, the other piece has the second slope. And so that, getting that nonlinear, simple nonlinearity in blew the problem open. That little piece makes it sufficiently complicated to make things interesting. Because you're gonna use that piece over and over a million times. So it has a fold in the graph, the graph, two pieces. But when you fold something a million times, you've got a pretty complicated function that's pretty realistic. So that's the thing about neural networks is they have a lot of these. A lot of these, that's right. So why do you think neural networks, by using sort of formulating an objective function, very not a plain function of the folds, lots of folds of the inputs, the outputs, why do you think they work to be able to find a rule that we don't know is optimal, but it just seems to be pretty good in a lot of cases? What's your intuition? Is it surprising to you as it is to many people? Do you have an intuition of why this works at all? Well, I'm beginning to have a better intuition. This idea of things that are piecewise linear, flat pieces but with folds between them. Like think of a roof of a complicated, infinitely complicated house or something. That curve, it almost curved, but every piece is flat. That's been used by engineers, that idea has been used by engineers, is used by engineers, big time. Something called the finite element method. If you want to design a bridge, design a building, design an airplane, you're using this idea of piecewise flat as a good, simple, computable approximation. But you have a sense that there's a lot of expressive power in this kind of piecewise linear. Yeah, you used the right word. If you measure the expressivity, how complicated a thing can this piecewise flat guys express? The answer is very complicated, yeah. What do you think are the limits of such piecewise linear or just of neural networks? The expressivity of neural networks. Well, you would have said a while ago that they're just computational limits. It's a problem beyond a certain size. A supercomputer isn't gonna do it. But those keep getting more powerful. So that limit has been moved to allow more and more complicated surfaces. So in terms of just mapping from inputs to outputs, looking at data, what do you think of, in the context of neural networks in general, data is just tensor, vectors, matrices, tensors. Right. How do you think about learning from data? How much of our world can be expressed in this way? How useful is this process? I guess that's another way to ask you, what are the limits of this approach? Well, that's a good question, yeah. So I guess the whole idea of deep learning is that there's something there to learn. If the data is totally random, just produced by random number generators, then we're not gonna find a useful rule because there isn't one. So the extreme of having a rule is like knowing Newton's law. If you hit a ball, it moves. So that's where you had laws of physics. Newton and Einstein and other great, great people have found those laws and laws of the distribution of oil in an underground thing. I mean, so engineers, petroleum engineers understand how oil will sit in an underground basin. So there were rules. Now, the new idea of artificial intelligence is learn the rules instead of figuring out the rules with help from Newton or Einstein. The computer is looking for the rules. So that's another step. But if there are no rules at all that the computer could find, if it's totally random data, well, you've got nothing. You've got no science to discover. It's an automated search for the underlying rules. Yeah, search for the rules. Yeah, exactly. And there will be a lot of random parts. A lot of, I mean, I'm not knocking random because that's there. There's a lot of randomness built in, but there's gotta be some basic. It's almost always signal, right? In most things. There's gotta be some signal, yeah. If it's all noise, then you're not gonna get anywhere. Well, this world around us does seem to be, does seem to always have a signal of some kind. Yeah, yeah, that's right. To be discovered. Right, that's it. So what excites you more? We just talked about a little bit of application. What excites you more, theory or the application of mathematics? Well, for myself, I'm probably a theory person. I'm not, I'm speaking here pretty freely about applications, but I'm not the person who really, I'm not a physicist or a chemist or a neuroscientist. So for myself, I like the structure and the flat subspaces and the relation of matrices, columns to rows. That's my part in the spectrum. So really, science is a big spectrum of people from asking practical questions and answering them using some math, then some math guys like myself who are in the middle of it and then the geniuses of math and physics and chemistry who are finding fundamental rules and then doing the really understanding nature. That's incredible. At its lowest, simplest level, maybe just a quick in broad strokes from your perspective, where does linear algebra sit as a subfield of mathematics? What are the various subfields that you think about in relation to linear algebra? So the big fields of math are algebra as a whole and problems like calculus and differential equations. So that's a second, quite different field. Then maybe geometry deserves to be thought of as a different field to understand the geometry of high dimensional surfaces. So I think, am I allowed to say this here? I think this is where personal view comes in. I think math, we're thinking about undergraduate math, what millions of students study. I think we overdo the calculus at the cost of the algebra, at the cost of linear. So you have this talk titled Calculus Versus Linear Algebra. That's right, that's right. And you say that linear algebra wins. So can you dig into that a little bit? Why does linear algebra win? Right, well, okay, the viewer is gonna think this guy is biased. Not true, I'm just telling the truth as it is. Yeah, so I feel linear algebra is just a nice part of math that people can get the idea of. They can understand something that's a little bit abstract because once you get to 10 or 100 dimensions and very, very, very useful, that's what's happened in my lifetime is the importance of data, which does come in matrix form. So it's really set up for algebra. It's not set up for differential equation. And let me fairly add probability, the ideas of probability and statistics have become very, very important, have also jumped forward. So, and that's different from linear algebra, quite different. So now we really have three major areas to me, calculus, linear algebra, matrices, and probability statistics. And they all deserve an important place. And calculus has traditionally had a lion's share of the time. A disproportionate share. It is, thank you, disproportionate, that's a good word. Of the love and attention from the excited young minds. Yeah. I know it's hard to pick favorites, but what is your favorite matrix? What's my favorite matrix? Okay, so my favorite matrix is square, I admit it. It's a square bunch of numbers and it has twos running down the main diagonal. And on the next diagonal, so think of top left to bottom right, twos down the middle of the matrix and minus ones just above those twos and minus ones just below those twos and otherwise all zeros. So mostly zeros, just three nonzero diagonals coming down. What is interesting about it? Well, all the different ways it comes up. You see it in engineering, you see it as analogous in calculus to second derivative. So calculus learns about taking the derivative, the figuring out how much, how fast something's changing. But second derivative, now that's also important. That's how fast the change is changing, how fast the graph is bending, how fast it's curving. And Einstein showed that that's fundamental to understand space. So second derivatives should have a bigger place in calculus. Second, my matrices, which are like the linear algebra version of second derivatives are neat in linear algebra. Yeah, just everything comes out right with those guys. Beautiful. What did you learn about the process of learning by having taught so many students math over the years? Ooh, that is hard. I'll have to admit here that I'm not really a good teacher because I don't get into the exam part. The exam is the part of my life that I don't like and grading them and giving the students A or B or whatever. I do it because I'm supposed to do it, but I tell the class at the beginning, I don't know if they believe me. Probably they don't. I tell the class, I'm here to teach you. I'm here to teach you math and not to grade you. But they're thinking, okay, this guy is gonna, when is he gonna give me an A minus? Is he gonna give me a B plus? What? What have you learned about the process of learning? Of learning. Yeah, well, maybe to give you a legitimate answer about learning, I should have paid more attention to the assessment, the evaluation part at the end. But I like the teaching part at the start. That's the sexy part. To tell somebody for the first time about a matrix, wow. Is there, are there moments, so you are teaching a concept, are there moments of learning that you just see in the student's eyes? You don't need to look at the grades. But you see in their eyes that you hook them, that you connect with them in a way where, you know what, they fall in love with this beautiful world of math. They see that it's got some beauty there. Or conversely, that they give up at that point is the opposite. The dark could say that math, I'm just not good at math. I don't wanna walk away. Yeah, yeah, yeah. Maybe because of the approach in the past, they were discouraged, but don't be discouraged. It's too good to miss. Yeah, well, if I'm teaching a big class, do I know when, I think maybe I do. Sort of, I mentioned at the very start, the four fundamental subspaces and the structure of the fundamental theorem of linear algebra. The fundamental theorem of linear algebra. That is the relation of those four subspaces, those four spaces. Yeah, so I think that, I feel that the class gets it. At length. Yeah. What advice do you have to a student just starting their journey in mathematics today? How do they get started? Oh, yeah, that's hard. Well, I hope you have a teacher, professor, who is still enjoying what he's doing, what he's teaching. They're still looking for new ways to teach and to understand math. Cause that's the pleasure, the moment when you see, oh yeah, that works. So it's less about the material you study, it's more about the source of the teacher being full of passion. Yeah, more about the fun. Yeah, the moment of getting it. But in terms of topics, linear algebra? Well, that's my topic, but oh, there's beautiful things in geometry to understand. What's wonderful is that in the end, there's a pattern, there are rules that are followed in biology as there are in every field. You describe the life of a mathematician as 100% wonderful. No. Except for the grade stuff. Yeah. And the grades. Except for grades. Yeah, when you look back at your life, what memories bring you the most joy and pride? Well, that's a good question. I certainly feel good when I, maybe I'm giving a class in 1806, that's MIT's linear algebra course that I started. So sort of, there's a good feeling that, okay, I started this course, a lot of students take it, quite a few like it. Yeah, so I'm sort of happy when I feel I'm helping make a connection between ideas and students, between theory and the reader. Yeah, it's, I get a lot of very nice messages from people who've watched the videos and it's inspiring. I just, I'll maybe take this chance to say thank you. Well, there's millions of students who you've taught and I am grateful to be one of them. So Gilbert, thank you so much, it's been an honor. Thank you for talking today. It was a pleasure, thanks. Thank you for listening to this conversation with Gilbert Strang. And thank you to our presenting sponsor, Cash App. Download it, use code LexPodcast, you'll get $10 and $10 will go to FIRST, a STEM education nonprofit that inspires hundreds of thousands of young minds to learn and to dream of engineering our future. If you enjoy this podcast, subscribe on YouTube. We have five stars in Apple Podcast, support on Patreon or connect with me on Twitter. Finally, some closing words of advice from the great Richard Feynman. Study hard what interests you the most in the most undisciplined, irreverent and original manner possible. Thank you for listening and hope to see you next time.

Gilbert Strang: Linear Algebra, Teaching, and MIT OpenCourseWare | Lex Fridman Podcast #52