What was the big deal about Chandrasekhar’s discovery? Why did he meet so much resistance? How is his work tied to everything from supernovae to black holes? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPT (AUTO-GENERATED)

1.4. I want you to remember that number even long after this episode. It's rare that the universe just hands us a number that's so important, so critical to explaining and understanding how it all works. And we have a few. Pi, 4, 1 over 137. And today we'll be talking about another one. 1.4. But more important than the number. It's the person behind it, the man who discovered this number, or rather the importance of this number, and it was Indian physicist Subramanian Chandrasekhar. And since we named an X-ray telescope in his honor but shortened it to Chandra, I feel fully justified in giving him a nickname of my own, one that speaks to his critical, but sometimes overlooked, contributions to fundamental physics and astronomy. Ladies and gentlemen, today's episode is a look into the life and work of Big Chandra. And there are three words to describe the career of Big Chandra. Triumph, humiliation, and vindication. Let's start with triumph. Big Chandra was born in 1910 in Lahore, although at the time he was still only a little Chandra.

Chandra, by the way, means moon or luminous in Sanskrit, which is lovely and appropriate. His uncle was C.V. Rahman. who would later win the 1930 Nobel Prize in Physics for the discovery of the Raman effect. He didn't name it the Raman, and I've told that joke a bunch of times, kind of worn it out. So no pressure at home to succeed in life or anything like that, although the story goes that while working in his uncle's lab, he once broke a critical piece of equipment and realized then that the life of the experimentalist was not for him. His father wanted him in the Indian Civil Service, a safe and prestigious path in life. Chandra wanted mathematics. His mother took his side, saying something along the lines of, that a person does best the thing he most loves to do. So there was a compromise in the household. The compromise was a physics honors degree, and his father largely relented because old Uncle Rahman's fame had made his science career look respectable. So thanks, Uncle. Anyway, Big Chandra has had a big brain, and he was super smart, and he was working years ahead of his peers.

He attended Presidency College, and while there, the great Arnold Sommerfeld, one of the literal architects of quantum theory, swung by on a lecture tour. Most students attended the lecture and comprehended a small portion of it. Big Chandra had already read and mastered Sommerfeld's textbook on atomic structure and spectral lines. And guess what Sommerfeld told him during that 1928 visit? That textbook that Chandra had mastered was now out of date. It was based on the old Bohr model of the atom, not the new quantum theory of Schrödinger, Heisenberg, and Dirac. Sommerfeld doesn't just punch him in the gut, however, and leave him hanging. He hands Chandra a galley proof of a brand new paper where he applied the brand new fancy-pants mathematical techniques known as Fermi-Dirac statistics to understanding how electrons worked inside of metals. Chandra would call this... one of the most consequential moments of his life. We have this kid, this teenager in India, who is now in possession of advanced physics that not even most Europeans know about yet.

And what does Chandra do? Well, he reads it, he understands it, and months later writes his own paper based on the same mathematics. But how does a kid get a paper published? Big Chandra needed someone eminent to communicate his paper to the proceedings of the Royal Society. So he sent it to Ralph Fowler in Cambridge. Now, why Fowler? Because Fowler was the one man who could instantly understand it. In 1926, Fowler had written the landmark paper that used those same Fermi direct statistics to explain white dwarf stars. And here is Chandra applying Fermi direct statistics... to a new problem. Fowler was impressed because how could you not be, and he gets the paper published. Two years later, Chandra wins a scholarship to attend Trinity College in Cambridge, with Fowler working behind the scenes to make it happen. So Big Chandra loads up on a boat for a two and a half week voyage to England, and he's got a few things to occupy his time. One, the brand new mystery of white dwarf stars, which is something like the mass of the sun compressed into the volume of the earth.

which are blistering hot and obviously radiating away energy and cooling off, but somehow not collapsing as they do. This was the hot new topic in astronomy. We had recently uncovered them and discovered them. These are the objects that Sir Arthur Eddington, who will make much more of an appearance later in this story, remarked something along the lines of, you know, nature showed us this ridiculous object and our reaction as scientists and humans was to tell nature to shut up. because it was so insane. Right now, I mean, in modern times, we're used to white dwarfs and neutron stars and black holes and weird exotic objects. A hundred years ago, this was brand new stuff. White dwarfs made no sense, and the most confusing thing about them was how they stayed, how they existed. Because if you're giving off energy, and you're not creating new sources of energy that then you should cool off and shrink. That's what hot stuff in the universe does, and white dwarfs were not doing that. Something had to hold up the white dwarf stars.

So there's this hot new mystery, and then there's Fowler's hot new paper on the subject, which it's actually four years old at this point, but at the time it's still hot and new. Things moved a little bit slower back then. Fowler's paper says, applied what are called Fermi Dirac statistics to explain, potentially explain, what holds a white dwarf star up. And Fermi Dirac statistics is a quantum mechanical view of how matter arranges itself. So not looking at any individual particle, but a whole collection of particles, like in a gas or in a solid, and using quantum mechanics to describe how how that whole object, that big ball of gas, or this solid object, or this white dwarf star, should behave. And the key part of Fermi-Dirac statistics, named after Enrico Fermi and Paul Dirac, worked it out, is that a lot of the particles that we are familiar with, particles like electrons, can only pack themselves down so tightly. That's it. We call this degeneracy pressure because the quantum mechanical states become degenerate.

It's not the greatest name. But the way I like to look at it, the analogy I like to turn to is if you imagine putting a bee in a box. And if you have a large box, that bee, which is our electron in this analogy, by the way, just buzzes around, lands on a surface, walks upside down for a little bit, then buzzes back. It's no big deal. But then you shrink the box. You shrink the allowable volume that this particle can occupy. And the bee starts to get a little agitated. It wants to fly freely and go look for pollen or whatever bees do. But it can't. So it knocks against the walls of the box. And then you make the box even smaller. Now the bee is really agitated. It's trying to go somewhere. But it keeps pump, pump, pump, pump, hitting the sides of the box. And then you squeeze it down all the way. to just barely contain the bee. And now the bee, its wings are vibrating, its legs are going, it's pushing against the box. A particle pushing against a box is what we call pressure. And when you try to squeeze electrons down, you try to squeeze a whole bunch of bees together in tiny little boxes, the electrons don't like that.

There's only so much space they can occupy. and they can't get any smaller, so they resist compression, and that shows up as a pressure. Now, this degeneracy pressure that we call it is everywhere. It's in metals, it's in materials, and it's in white dwarf stars. Fowler is looking at white dwarf stars, seeing how they don't cool off, or seeing how they are cooling off, they're radiating heat, yet they're not getting smaller, and there's no new sources of fusion. So what is holding up a white dwarf star? Fowler says, I think it's degeneracy pressure. I think electrons can only be crammed into so small of a volume. Now, this was a controversial idea. It was one idea of many, but it was one that Chandra found himself really attracted to on this boat ride to England. So he's got white dwarf stars. He's got Fowler's potential solution to explaining how white dwarf stars stay up. And then he's got all the mathematics of Fermi direct statistics bouncing around in his head. On this voyage, Big Chandra spots an opening.

And that opening is relativity. You see, Fowler's work stops short of the full calculations. They were just too complex to be done at the time. Relativity is our language of objects moving really, really fast. And if your box around the bees is large enough, then the bees are moving normally. But if you squeeze it down so tightly... And the bees start being really agitated and moving around really, really quickly. Eventually, their speeds approach the speed of light, which means your assumption that, hey, I don't need to incorporate relativity. The math is really hard. I can just use plain old Newtonian mechanics and plain old quantum mechanics to describe how these electrons behave inside of a white dwarf star. That assumption breaks down because the electrons start moving too quickly. And so you need a new mathematics. You need to bring in additional tools. You need to do the hard work, which is really, really not fun to do because incorporating relativity into quantum mechanics is a real beast.

But we got big Chandra over here, don't we? Big Chandra with nothing to do for two whole weeks. So he folds in relativity into the calculations. He sees what happens when these electrons get really, really squeezed as you start adding more mass to the white dwarf star, which increases the gravitational weight, which squeezes the electrons down to even smaller volumes, which pushes their little buzzing velocities to even greater speeds. And he finds that there's a limit. That the bees, the electrons in a white dwarf star, their quantum degeneracy pressure, can support a star. You can have a white dwarf star living basically forever, as long as it's below a certain mass. And that mass is 1.4 times the mass of the sun. If you add more weight to it, if you put another cup of white dwarf stuff, another kilogram of white dwarf stuff on top of the star and make across that threshold, then the gravity gets stronger, pulls inward, squeezes those electrons a little bit more. And in the classical picture and Fowler's picture, you could just keep doing this.

You can have white dwarf stars of 10 solar masses, a hundred solar masses. It didn't matter. But with the proper relativistic treatment, there's a breakdown because the electrons can't go faster than the speed of light. You can squeeze and squeeze and squeeze and they can go faster and faster and faster, but they can't go faster than the speed of light. So that puts a limit on how tightly you can squeeze them. And that limit is 1.4 solar masses. Now on the boat ride, he estimated it was like 0.9 solar masses because the actual number depends on various assumptions about stellar properties and densities and all that. Eventually, he arrived at 1.4, and that is very close to the modern-day answer. This answer he got was through a marriage of quantum mechanics and special relativity, a very difficult, tricky thing to do, something few people at the time were capable of doing. This was brand-new stuff. Not a lot of people knew how to apply special relativity to the rules of the subatomic world.

Big Chandra was one of them. As to what happens to a white dwarf star, If it crosses over that threshold, if it has more than 1.4 solar masses, well, Chandra couldn't say exactly what. It looked like catastrophic collapse because here we have a dead star, run out of fuel, not fusing for energy anymore, relying on quantum degeneracy pressure to support itself against gravity. But then if you add too much gravity and there's nothing to fight against it, what happens? I mean, there were some ideas floating around, like maybe they turned into black holes, but I don't know. No one knew. Chandra even didn't know. He's like, all I know is that something bad happens. So we've got this 19-year-old kid who just made a major breakthrough, but he doesn't feel like he belongs anywhere. He does the calculation on the way to England. He shows up in England. But his application got bungled and he was almost sent back before Fowler intervened. And the sources say intervened aggressively. I imagine it involved a lot of yelling and creative use of swear words.

Big Chandra wanted to do mathematics, but felt like he got pulled into physics as the only viable option. And then he ended up solving a problem in astrophysics, which he was only barely familiar with as a field of study. And he would later remark that he never really felt at home in that field. And the hardest part is he's a kid, a bright kid, smart kid, but a kid. And a bright kid showing up in an unfamiliar country and an unfamiliar institution is useful and interesting and novel to all the established people at that new institution in this new country when he's working on problems they like and producing results they agree with. It's not so great when you've got a bright kid like the Doogie Howser of physics here proposing a new result that suggests that maybe stars can die and never recover. Which brings us to the second phase of his career, humiliation. It's January 11th, 1935, Burlington House, London. It's a Friday. The Royal Astronomical Society is set to meet. Big Chandra secures an invitation to speak from none other than Sir Arthur Eddington, perhaps the most preeminent, the preeminent of preeminent astronomers in the world at the time.

Eddington was one of the people who led investigations into white dwarf stars and relativity and how stars work. He unlocked like nuclear fusion is what powered stars. Like Eddington is Eddington. And Eddington was curious about Chandra's work and had spoken to him many times, encouraged him to share his strange and unexpected results that white dwarf stars might have a limit once you properly include relativity into your quantum mechanics calculations and wanted to share them with the world. So Chandra gets up to speak, presents his arguments. It's flawless and impeccable as always. There's applause, questions, curious audience. The usual. Chandra sits down. And then Eddington gets up to speak. And when Eddington speaks, he spends his entire lecture time giving a prepared presentation, absolutely tearing down everything that Chandra just said. He rejects Chandra's math, his results, his conclusions, argues that there is no way that a star could just implode like that, says, quote, various accidents may intervene to save a star, but I want more protection than that.

I think there should be a law of nature to prevent a star from behaving in this absurd way. Eddington didn't stop that night. Later, during a talk at Harvard, he called Chandra's mass limit stellar buffoonery and laid out a case against Chandra as a reductio ad absurdum, saying, sure, Chandra may be brilliant at math and understands both relativity and quantum mechanics like few people do, But he's not an astronomer, and his conclusion that stars can collapse catastrophically is so ridiculous that we can throw the whole thing out on that alone, and that the real work is finding the little technical details that render Big Chandra's argument absurd. He argued that Chandra had illegitimately married relativity to quantum theory, that he did it wrong, and that Eddington would not, quote, regard the offspring of such a union as as born in lawful wedlock. Eddington had his own ideas of how to unite quantum mechanics and relativity, thought Chandra's math was wrong and his was right, and didn't like the result that Chandra got.

To this day, we don't know why Eddington went on the attack like this, and why he kept at it for years. Did he not like Chandra? Was he upset that a kid came up with this stunning result of mathematical mastery and physical insight? Was he upset that it was an Indian kid that came up with it? Or was it the result itself? Maybe, just maybe, it was because he didn't contribute to Patreon. That's patreon.com slash pmsutter. That's P-M-S-U-T-T-E-R. It's how you can keep this show going, and I truly do appreciate it. We do know one thing. Eddington liked to stick to his guns, especially when it came to white dwarf stars. Chandra once said this of Eddington. Quote, Despite this man's incredible physical insight, he has always operated with preconceived ideas. This is Eddington just looking at Chandra's result and saying, no, I don't like this. Stars shouldn't collapse. We're not going to entertain the thought of things like black holes or the deaths of stars. White dwarfs are weird enough, but that is where it stops.

This is Eddington's line of argument, and he comes into the argument this discussion with chandra with this belief that stars can't collapse and here's big chandra saying i think they can but chandra's just a kid eddington does have a history of disparaging results he doesn't like remember chandra's got his model of how white dwarf stars work eddington has his own model other people are proposing their own ideas there's this one guy milne That proposed his own idea of how white dwarf stars work. Here's what Eddington had to say of Milne. Milne wrote a paper and someone said, Hey, Eddington, have you read Milne's paper about white dwarf stars? What do you think of that? Here's Eddington's response. Quote, It is difficult to discuss this paper. Professor Milne did not enter into detail as to why he arrives at results so wildly different from my own. And my interest in the rest of the paper is dimmed because it would be absurd to pretend that I think there's the remotest chance of his being right.

So Eddington's kind of got a shtick here, and he's going to stick to it. He doesn't like disagreement, especially when it comes from kids. Here's the thing. Privately, everybody knew that Eddington was wrong. Bohr, Pauli, even Dirac. You know, the Dirac of Fermi, Dirac statistics. The one possible human on the planet that could judge if someone knew how to marry. Quantum mechanics and relativity. would privately tell Chandra that they knew he was right, that his mathematics were on point, that his mathematics were impeccable, and that his conclusions were right. And they knew that Eddington's were wrong. His arguments were wrong. His physics were incorrect. He did not get quantum mechanics and relativity the right way, the way that Dirac and Chandra did. But Eddington was also famous and powerful. And famous and powerful in his domain, astronomy and astrophysics. Bohr, Pauli, Dirac, they were physicists. So in a sense, they lacked standing to go after, at least not publicly. Because if they said, like, look, Eddington, I think you're wrong.

I think you're getting the physics wrong. Eddington will say, well, that's cute. You understand, you know, quantum systems in a laboratory. I'm out here dealing with white dwarf stars in the universe. So step off. Get way off my back, man. You all know how this dynamic works. Here's a quote from William H. McCree, who was in that room in 1935 when Eddington tore down Chandra. He said, quote, my instincts seem to tell me that Eddington might be right. His arguments were superficially satisfying to me. And since they satisfied Eddington, I confess that I was content to let it go like that. When someone big and powerful says, look, this kid is wrong and I'm right. And Eddington's been right before. He had a whole career of being right. What are you going to do? Here's another incident. Later that year, Eddington gave a talk in Paris. And here's what Chandra said of that incident. He attended this lecture because they're all moving in the same circles, giving their talks. Chandra said, quote, Eddington gave an hour's talk, criticizing my work extensively and making it into a joke.

I sent a note to Henry Norris Russell, who is presiding, telling him I would wish to reply. Russell sent back a note saying, I prefer that you didn't. And so I had no chance even to reply and accept the pitiful glances of the audience. This is how powerful and influential Eddington was. Chandra couldn't even get a word in edgewise in any public forum. There was one incident where Eddington had to hear the truth. In July 1939, at dinner at the High Table of Cambridge, Chandra Sekhar, Eddington Dirac, and a young physicist named Maurice Price were seated together And here is Chandra Sekhar's description of events. Price expressed surprise at seeing me and asked me whether I would join them in discussion with Eddington after Hall on the matter of relativistic degeneracy. After Hall, we adjourned to Price's room in Neville's court. The discussion began with Price trying to tell Eddington his version of Eddington's arguments against relativistic degeneracy, that is, Chandra's work, so that Eddington Eddington could be satisfied that he, Price, understood Eddington's argument.

So Price is sitting here, like, recapturing Eddington's arguments. Like, saying, is this what you think? Am I getting it right? Is this what you're saying? Do I understand your arguments right here, Eddington? After Price had completed his narration, Eddington remarked that Price's account was entirely fair and accurate. And asked... What was the argument about? Hey, okay, why are you doing this? Why are you repeating my own arguments? Yeah, you understand it. You get it right. What's the big deal? Price turned to Dirac and asked him, did you agree with any of the things I've said? Dirac said, no. Which is classic Dirac. You're not a big talker, that guy. Dirac said, no. Price added, I do not either. Eddington became very angry. In fact, it was the only occasion when I saw him really angry. He got up from his chair, walked back forth, and said, This matter is not for joking. He went on finding fault with Price's argument, even though he had agreed with it a moment earlier. And for the next hour or so, it was Eddington's monologue.

Next day, after all, Eddington came up to me and said that he was very disappointed that Dirac did not seem to understand the implications of his own relativity theory of the electrons. So here's Eddington being corrected by Dirac. Dirac saying, Eddington, you're wrong. And Eddington's like, I'm sorry you don't understand your own theory? So now Eddington is confronting Chandra, who didn't even set this up. He didn't even want to be in the room when this happened. Chandra said, I did not assent or dissent with Eddington's remark, but asked instead, how much... of your fundamental theory depends on your ideas on relativistic degeneracy. He replied, why all of it? So Chandra's saying, well, okay, you're saying Dirac doesn't understand his own theory. And so Chandra's like, okay, how much of your idea about how white dwarf stars work, which says that they don't collapse, how much depends on your own work, your own understanding of relativity and quantum degeneracy? And he's just like, all of it.

Chandra continues, since I did not react to that remark, he asked me why I had asked the question. My response was, I am only sorry. Not a polite remark to have made, but by that time, I was really enraged with Eddington's supreme confidence in himself and his own ideas. Yeah, I mean, the restraint that Chandra is showing. This whole affair almost drove Chandra from physics altogether. Here he is coming up with, he's just exploring his curiosity, doing math. making insights. And yeah, you expect debate and discussion and pushback. That's part of scientific culture. That's how we make progress, is by disagreeing with each other and not believing each other automatically. But then here's Eddington turning it into a personal crusade and being wrong about it. Wrong in a way that everyone who understands the math is saying you're wrong and Eddington not buying it, but no one being able to do this publicly. And Chandra keeps his composure so well that the most he says to Eddington is, basically, I'm sorry you're a moron.

Not in those words. Do not put those words in Chandra's mouth. Those are my words. Chandra realized that he could not stay in Europe under Eddington's shadow, so he moves to the United States. But even there it haunted him. Chandra carried anger and hurt about this for decades and returned to that day again and again. Here's a quote from a biography of Chandra. A.L. Miller's Empire of the Stars, quote, even though science deals with abstractions and grand cosmic issues that dwarf our small human lives, those who carry out scientific research and spend their lives absorbed in calculations and theories are human beings. They may be driven by irrational impulses, as was Eddington when he refused to believe a result which did not square with his view of the universe. And as they go about their intensely solitary work, They may be haunted by passions, jealousies, fears, ambitions, and disappointments. Chandra Sekhar's eternal quest for personal peace could never be fulfilled. I mean, that's gotta hurt.

That's gotta hurt. Especially at such a young age. In the end, Big Chandra actually pities Eddington. Chandra knew he was right and that Eddington had missed a huge opportunity. After all, Eddington had been thinking about white dwarf stars for years, decades, before Chandra even got on the boat to England. So Chandra later wrote, quote, He, Eddington, would have found that there was no reductio ad absurdum, no stellar buffoonery. If Eddington had done that, he would stand today as the greatest theoretical astronomer of this century. In other words, if Eddington had simply done the work and paid attention to the math, And trusted where the math led instead of where his instincts and preconceived notions led. He might have been even bigger. He might have been huge. Eddington, yeah, he goes down in history. But not in a way he could have. But Big Chandra's no slouch. And he's no sulker. He moves beyond white dwarfs. He leaves it behind. He develops a practice of becoming interested in any subject.

obtaining complete mastery of it, making enormous progress, then turning around to write the definitive book on the subject, and then abandoning that subject and becoming a beginner all over again. He repeats this cycle again and again throughout his life. Here's how he approached science in a quote. It's a lengthy quote, but it's a good one. In my entire scientific life, extending over 45 years, the most shattering experience is has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe. Pausing his quote here, the Kerr solution to relativity described rotating black holes, which is actual black holes in the physical description not of an idealized object but something that nature actually produces this was revolutionary this is chandra appreciating someone else's work and he continues quote this shuddering before the beautiful this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in nature persuades me to say that beauty is that to which the human mind responds at its deepest and most profound.

Chandra is interested in beauty and mathematics and uses that as a lens to discover truth. That's what he did on that boat on his way to England. That's what upset Eddington. Chandra was just approaching this with no preconceived notions about how the universe ought to work, just following beauty in physics to see where it led. And he saw a mirror of that in Kerr's solution. Kerr wasn't opening telescopes to look for black holes. He was just following mathematics and looking for beauty. And he found a solution that appeared in nature. And so Chandra's insight is that by chasing beauty, we're discovering something about reality. He later wrote a book called Truth and Beauty, a collection of essays. In that book, he said, quote, it is indeed an incredible fact That what the human mind at its deepest and most profound perceives as beautiful finds its realization in external nature. What is intelligible is also beautiful. I can't think of a more pure expression of physics. It is a search for meaning in the universe.

And here is Big Chandra finding meaning in the beauty of mathematics and physical theory and then not being surprised that it mirrors reality. Chandra becomes a professor at the University of Chicago, a resident at Yerkes Observatory. He becomes known for his uncommon command of subjects and his graceful yet rigorous teaching style. In the winter of 1948, for example, he drove the long haul from Yerkes to the Chicago campus every week, something like 90 minutes one way, to teach an advanced course to just a handful of students. Two of the students in that room, Sung Dao Lee and Chen Ning Yang, would win the Nobel Prize in 1957, and Rico Fermi, who already had his prize, sat in on the class. When asked why he bothered for so few, he reportedly just said they were good students. He also became the editor of the Astrophysical Journal from 1952 to 1971. When he started, it was a low-stakes journal that barely anyone published in. But through his stewardship, it became the premier flagship journal for astrophysics in the United States.

Heck over half my papers are published there and it's viewed as a prestigious journal because of his work of guiding the editorial standards of that journal. His lifelong conviction was that correct physics is beautiful. He drew insights from Shakespeare, from Beethoven, from an aesthetic tradition that when you find a beauty, you're finding truth. That the universe is under no obligation to be beautiful and yet it is. And that beauty is a guide towards the truth. And his entire life is the argument. The beautiful result was the true one. And the powerful man who called it ugly was simply wrong. And then there were the black holes. In 1936, he was mocked by Eddington for even gesturing towards the possible existence of black holes by pointing out that white dwarf stars can collapse. And even after the field accepted his physics, they had no other choice because he was right. They invented various exotic scenarios like mass loss to prevent white dwarfs from turning into black holes. By the 1960s, the concept of black holes went from mathematical curiosity to nearly certain reality.

Big Chandra, in his usual style, became the master of the subject, writing in 1983 the ultimate treatise on the subject, The Mathematical Theory of Black Holes. In 1983, roughly half a century after the boy got off the boat, the 72-year-old Big Chandra was awarded his Nobel Prize. But ironically, he was actually upset about it, cited his older work on white dwarf stars, which took him all of a few weeks to work out and not his near decade spent developing the theory of black holes. Oh, and Eddington? He never got a Nobel Prize. Big Chandra did accept the award and the vindication that came with it. He said, quote, I am grateful for the award. since it is possible that it may provide a measure of encouragement to those who, like myself, have been motivated in their scientific pursuits principally for achieving personal perspectives while wandering mostly in the lonely byways of science. Thank you to Matthew Z, Roy Snowey, Neil P., and at Callan Richards for the questions that led to today's episode.

Thank you for all my supporters. That's patreon.com slash pmsutter. That's how you can keep the show going. Thank you for all of your wonderful reviews on your favorite podcasting platform that help the show visibility. And most importantly, thank you for all your questions. You can keep sending me questions at askaspaceman at gmail.com or the website askaspaceman.com. Before I go, I'd like to thank my top Patreon contributors this month. It's not all of them. but I am truly grateful for each and every one of you. Thank you to Justin G, Chris L, Alberto M, Duncan M, Corey D, Michael P, Nyla, Sam R, Joshua, Scott M, Rob H, Scott M, Lewis M, John W, Alexis, Gilbert M, Rob W, Jessica M, Jules R, Jim L, David S, Scott R, Heather, Mike S, Pete H, Steve S, Lisa R, Kevin B, Eileen G, Deb A, Michael J, Philip L, and Stephen B. That's patreon.com slash pmsetter, and I will see you next time for more Complete Knowledge of Time and Space.

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