IRA FLATOW: This is Science Friday. I’m Ira Flatow. When famed physicist Stephen Hawking passed away this spring, the world took note, certainly. He was interred at Westminster Abbey with Charles Darwin and Isaac Newton. Actor Benedict Cumberbatch spoke at his funeral, while his frequent collaborator Sir Roger Penrose wrote his obituary for The Guardian. And here at Science Friday, we said, what could we do to commemorate his life?

And we realized that a lot of people, a lot of our staff, hadn’t read this most famous work, the general audience book about the big questions of the universe. Of course you remember that. It’s A Brief History of Time. So we read it, and we invited you to read it. And we’re here one last time to talk about it.

Did you finish the book? What did you think? Is it different from the first time? Remember, the edition we’re reading is actually a different edition than the original edition. It might have extra stuff in it that you didn’t read the first time. We want to know what you thought. 844-724-8255. That’s 844-SCI-TALK. You can also tweet us @scifri.

With me is SciFri book maven Christie Taylor, who’s been shepherding this reading. Welcome.

CHRISTIE TAYLOR: Hi, Ira.

IRA FLATOW: Good to have you back.

CHRISTIE TAYLOR: Glad to be here.

IRA FLATOW: OK. That’s the thing we’re here to talk about, right? Fall is in the air. People are starting to go back to school. It’s hard to believe we’re at the other end of a SciFri Book Club. It’s come and gone.

CHRISTIE TAYLOR: Yeah, but we really packed a lot into this brief piece of time. Sorry about that. We did a lot with this book club. We had artists create original Hawking-inspired pieces of art. We had a cocktail party last week to sort of bring together physicists and interested members of the public to do some hands-on demos and stuff. We read a whole book. And we answered as many questions as we possibly could for our listeners on Twitter, in our newsletter, and on the air. So we’ve really done a lot, I think, Ira.

IRA FLATOW: You know, I was like most listeners. I remember when the book came out, I opened it for a little bit. I read a little bit of it. Then I put it on my coffee table, where everybody else had put their books. So this really is the first time that I read the book straight through. How about you?

CHRISTIE TAYLOR: It was my first time even trying, and I will say it was not brief. It took me some time. I had some chapters that stumped me that I had to reread. I will say quantum gravity is not an easy concept or just the unification of physics.

So I’m glad that we’re going to have some friends on here today to help us talk through some of the things here. You may remember them from our kickoff. We have Priya Natarajan, our professor of astronomy and physics at Yale in New Haven, Connecticut, and then Clifford Johnson, a professor of astronomy and physics at the University of Southern California. And he’s joining us from NPR West in Culver City. So hi, friends.

PRIYA NATARAJAN: Hi.

CLIFFORD JOHNSON: Hi. Good to be back.

CHRISTIE TAYLOR: I want to start just with talking about the language in the book because, again, one of the things that we remember Hawking for is working to make physics more approachable. I had a lot of favorite passages. He talks about trying to visualize the shape of the universe, if it curves in certain ways. He talks about this idea of traveling through such a universe. He talks about the expansion of space and time after the Big Bang. Ira, do you have any favorite descriptions that Hawking gave us?

IRA FLATOW: Yeah. He had a description of how to visualize light. He created a little visual for a light that was sort of like an egg timer shape. And you looked at it, and I said, you know, I have seen this before in other physics books written since then. I didn’t realize how far back it went all the way through Stephen Hawking’s original book here. But it was hard to look at the visual because it’s not your typical x-y diagram, and you have to actually study it. That image has stayed with me through the whole book.

CHRISTIE TAYLOR: Yeah, I like that too. Priya, when you look at some of the descriptions that Hawking gave us in this book, do you have any that really stand out to you as a physicist?

PRIYA NATARAJAN: You mean as a physicist, or for the kind of explanatory power, sort of, I know? I liked a lot of the artistic impressions that he had because I think they were right on in terms of physics concepts, and yet they conveyed sort of– so for example, in chapter 6, he has this really nice kind of artist’s impression of how a black hole would be feeding from a nearby star– this would be a stellar-mass black hole– and what we would end up seeing.

So to me, for example, that artistic impression, because it packs a lot of physics in correctly– is one of the ones that I really like a lot.

CHRISTIE TAYLOR: And Clifford, what about you? For explanatory power or physics concepts, either one.

CLIFFORD JOHNSON: Well, I think the light cone example that Ira brought up is actually great because it shows that this is a tool that we actually use as physicists. If you sit in on a seminar on some technical aspect of quantum gravity or something, you will see someone actually draw a light cone. And so it’s actually great to see that some of the tools we use to visualize things can also be used, and quite accessible, with a good writer. And it also tells people that we rely on little cartoons to figure stuff out, as well. It’s not dumbed down. It’s really the real thing.

IRA FLATOW: And if you want to comment, our number is 844-724-8255. And you can also tweet us @scifri. Those graphics were great. Yeah.

CHRISTIE TAYLOR: Yeah. And I wanted to say, so Priya, when you joined us for the kickoff of this book club back in July, we kind of hinted that we’ve learned a lot since Hawking wrote this book back in 1988. But also Hawking himself contributed a lot to our understanding of especially black holes. So looking back at this book that was written back in 1988, what was the most groundbreaking thing that it introduced to us at that time?

PRIYA NATARAJAN: I actually did reread the book, although I had the old edition, so I was able to compare notes mentally to what we know now. So I think where we’ve made a lot of major leaps are in the real, deeper understanding of astrophysical black holes that he kind of set up at the time. So the data was just starting to come in.

But in this book, he already started to speculate how we might detect black holes, how they might grow. And now we know a lot more about how black holes actually form, how they actually grow, because we’ve had data in multiple wavelengths looking at black holes. The Chandra telescope has shown us how gas actually feeds into black holes and the presence of supermassive black holes in nearby bright galaxies. Effects have been detected by Hubble Space Telescope data.

So he foregrounded– he kind of anticipated– all these developments that were kind of along the pike at the time. And of course, the most exciting thing that he was looking forward to, both in the book and later, was the detection of gravitational waves, the first detection from colliding black holes, which LIGO reported a couple of years ago. So I think he anticipated in this book a lot of the observational verification we would have for astrophysical black holes.

And I keep making that distinction because Hawking works a lot on the mathematical model of black holes, a mathematical solution, but I think he could see that they were becoming quite real in a major way in the sense that there would be an explosion of understanding and information about the properties of black holes– the details of how they would feed and so on and so forth. And to say nothing of– also, this was before we got very detailed maps of the cosmic microwave background radiation.

So the detection had already happened in the ’60s, but the details– the detailed anisotropies, the pockmarks in this radiation relic map from the early universe that the WMAP satellite and the Planck satellites have brought us have really ratified the standard model of structure formation that Stephen sort of laid out in this book and brought to the public. At the time, it was at the frontier of our understanding, and now we have a really embellished picture, although there are still lots of things we don’t know. We still don’t know what dark matter is and what dark energy is.

CHRISTIE TAYLOR: Yeah. And Clifford, Hawking also tries to tell us about this crazy thing called string theory. Was that a weird idea at that time?

CLIFFORD JOHNSON: It was a weird idea at that time, and it remains weird, but weird and wonderful because it really helped expand on and answer a number of questions that he was laying out in the book. He was one of the people responsible for doing some of the first major steps in our understanding of quantum gravity, which is what happens when you have this thing which comes from classical Einstein general relativity– and by classical, I mean there’s no quantum stuff from Einstein’s equations– this thing called the black hole. And then he thinks about what would happen if you sprinkle some quantum mechanics in there, as we have to because the universe is quantum mechanical. And he discovers the thing that bears his name, Hawking radiation.

And in the following years, with a number of collaborators, he actually developed this wonderful framework of what’s called semi-classical quantum gravity. And he actually explains some of it in the book. So all of that stuff to do with imaginary time and so on and so forth, that’s the toolbox. And he lays out some of it there.

But because it’s an incomplete theory of quantum gravity, he’s struggling to tell you what the end of the story is. He explains that string theory is one of the approaches and tells you a little bit about string theory as it was understood at the time.

What’s happened since then is amazing. String theory has a lot of shortcomings, but one of the things it’s extremely good at, we’ve come to realize, is understanding quantum aspects of gravity in certain regimes. And it turns out that, once we started understanding string theory well enough to study black holes, we were able to answer a lot of the questions that Hawking had asked about the quantum nature of black holes. In fact, there was a big battle between him and the string theory field because he was actually resistant to some of our results for a long time. But some of the results turned out to be so beautiful and so compelling he eventually changed his mind.

IRA FLATOW: We have a really interesting tweet here from Mark, who actually teaches philosophy class. Political science, he says. “I’ll admit I didn’t read along with the book club, but I assigned the intro and conclusion in my political science classes at NC State.” And here’s the interesting reason. He says, “Because it does a masterful job of laying out the basic logic and process of science and the creation and accumulation of knowledge.”

CHRISTIE TAYLOR: I really like that. Ira, I was going to ask you, because you’re someone who thinks about science probably more than most people who aren’t scientists, but you still have things that you get hung up on when we talk about these concepts, right?

IRA FLATOW: Yeah.

CHRISTIE TAYLOR: It’s not just easy as pie, even though you keep reading and reading about it.

IRA FLATOW: I’ve read it [? for ?] years, trying to get some– the hardest thing, I think, for the public to think about is to come to terms with the concept of infinity. When he talks about the Big Bang, there was an infinite amount of heat. How can you have an infinite amount of heat in zero time? People– well, can’t there be more heat? Can’t there be more space? That kind of thing. And he, throughout the book, tries his best to try to bring that to the public. It’s a hard thing to understand. Do you agree, Clifford?

CLIFFORD JOHNSON: Yes. It is hard. And it’s hard for us, too, as physicists. I think it’s important to realize that we have difficulties with some of these concepts, as well. We don’t have 10-dimensional brains that can think in 10 dimensions or what have you that he was talking about. We still use tools such as certain kinds of mathematics to help us limited creatures understand some of those things. The same thing as with infinity– no one has an understanding of infinity in an intuitive way. You either arrive at it by a process, or it’s a mathematical concept you can move around on the page because of the consistency of mathematics.

I should say, with the infinite stuff that’s happening at the beginning of the universe, those infinities are telling us that we have an incomplete understanding. Einstein’s equations, coupled with equations of the matter that are moving around, tell us that lots of these things are going toward infinity when the equations get to that point. And it’s telling us there’s some new stuff there that will actually resolve those infinities. Infinities in the actual universe are placeholders for physics we don’t yet understand.

IRA FLATOW: Well, we understand our number is 844-724-8255. Talking about the Brief History of Time with Priya Natarajan and Clifford Johnson on Science Friday from WNYC Studios.

CHRISTIE TAYLOR: So actually, Priya, one of the things that happens– we talk about physics on the show a lot, as I told Ira– as you guys probably know, but we get a lot of questions from our listeners that any time that we talk about these kinds of topics, they seem to cluster. So we get a lot of questions about the multiverse or like what happens at the event horizon of a black hole, really? Is travel backwards in time possible? People just seem really interested in these really extreme possibilities that seem to be presented when we talk about cosmos scale science. Why do you think people get hung up on these kinds of questions? Do you get hung up on these questions, Priya?

PRIYA NATARAJAN: Well, connecting up to what Ira and Clifford were just talking about, I think this notion of the limits of equations, such as beta infinities or singularities, also point to limits of our understanding. And black holes, because they encompass this singularity, it’s a place where our knowledge and understanding the language of mathematics, everything breaks down. They are tantalizing objects because they represent, if you will, the boundary between what is known and what’s not known, and that boundary has all these bizarre effects.

So I think people are really attracted to this strange behavior, which is not something that you encounter in your day-to-day understanding of physics. We just can’t really fathom what it means like to have time slow down or what it means like to have a very strong gravitational field that– the difference between falling into a black hole between your hair and your toes is so strong that it can rip you apart. So these are very non-intuitive kind of phenomena that happen around the event horizons of black holes. So I think they are really, really fascinating.

I mean, I find it very fascinating to really think through– for example, so classically, when we try to understand what happens when you start falling into a black hole. I’ve done these thought experiments– not just me falling in, because I’m a bit vain. I don’t want to fall in quite yet–

CHRISTIE TAYLOR: You don’t want to turn into spaghetti?

PRIYA NATARAJAN: Yeah, exactly. But if you throw a clock in, right? So this whole idea, this conception of what does it mean to say that time really slows down? So you have a far-away observer, who’s watching you with a clock, or just the clock, falling in. They will see that time on this clock is going to slow down and come to a complete stop at the horizon. And that is just super, super bizarre.

IRA FLATOW: Yeah, it’s hard to get your mind around what that’s like. But he tried to do, as best as he could, these great examples that you could relate to. And we’ll talk about more of those examples with Priya Natarajan from Yale University and Clifford Johnson, USC in LA. Stay with us. Our number, if you want to get in on the conversation, 844-724-8255. You can also tweet us @scifri. Maybe you read the book years ago. Maybe you want to read it again. It’s worth a second read, if you haven’t. We’ll be right back after this break.

This is Science Friday. I’m Ira Flatow. Back with our SciFri Book Club to continue our discussion about the late Stephen Hawking’s A Brief History of Time. And with me is SciFri Book Club producer Christie Taylor, physicists Priya Natarajan and Clifford Johnson.

And before we get back to the Science Friday discussion this afternoon, SciFri had a party in Hawking’s honor this last week. We invited New Yorkers to join us for a time traveler cocktail party in honor of one Hawking himself threw in 2009. We had hands-on physics demos, displayed the winners of our art competition. And to cap it all off, physicist and author Janna Levin remembered Hawking in verse, reading a work by poet Marie Howe, originally composed for the Universe in Verse Event held earlier this year at Pioneer Works in New York.

Here is Janna Levin commemorating Stephen Hawking Tuesday night.

JANNA LEVIN: So it occurs to me maybe to mention that I knew Stephen. I was in Stephen’s group in Cambridge for many years. And in the hallways, we used to joke about whose toes he ran over with his wheelchair when he was feeling impish. I think it was none of our toes, but we all pretended anyway. Just since we’re talking about him tonight, I should say that, knowing him, I don’t think that his prodigious mind, his unbelievable accomplishments, can be strongly enough contrasted against those obstacles he faced. He really was just an unbelievable person. He was also incredibly arrogant and belligerent and difficult.

Lenny Susskind said of his good friend Stephen Hawking, the man was arrogant, impossible, but then again, so am I. So this was my upbringing in theoretical physics. Just to say he is very much missed, and just to point out that he really did create a paradox, especially in the ’70s, over black holes that no one has yet been able to resolve. Everyone tries to resolve.

Even Hawking tries to concede occasionally that there was this resolution, and you brought it up earlier with the Hawking radiation and the evaporation of the black hole. But there are two contrasting, competing things that are going on in nature, and no one can figure it out. And the black hole is the terrain, and the only terrain, on which we’re going to figure it out.

And Hawking is the one who gave us this gift of revealing that to us, that that was the frontier. That is the frontier. If we want to understand quantum gravity, the ultimate theory of everything, the final chapters of Brief History of Time, we have to understand the black hole. And we don’t, even since he first proposed this in the ’70s, a couple of years after his diagnosis was supposed to be completely fatal.

So on that note, he was a loved man. He was a loved man. He was a difficult, but loved, man. So this is a poem by Marie Howe. And I’m honored that Maria Popova and Marie Howe asked me to read this poem, which was written for the Universe in Verse about Stephen Hawking, or at least inspired after Stephen Hawking.

“Do you sometimes want to wake up to the singularity we once were?

so compact nobody

needed a bed, or food, or money–

nobody hiding in the school bathroom

or home alone

pulling open the drawer

where the pills are kept.

For every atom belonging to me as good

Belongs to you. Remember?

There was no Nature. No

them. No tests

to determine if the elephant

grieves her calf or if

the coral reef feels pain. Trashed

oceans don’t speak English or Farsi or French;

would that we could wake up to what we were–

when we were ocean and before that

to when sky was earth, and animal was energy, and rock was

liquid and stars were space and space was not

at all– nothing

before we came to believe humans were so important

before this awful loneliness.

Can molecules recall it?

what once was? before anything happened?

No I, no We, no one. No was

No verb no noun

only a tiny tiny dot brimming with

is is is is is

All everything home”

Thank you.

[APPLAUSE]

IRA FLATOW: Physicist and author Janna Levin, remembering Stephen Hawking, reading a poem by Marie Howe, commemorating our event that we’re having, which is reading his famous book. Christie, we also commissioned art for this book club. How did that go?

CHRISTIE TAYLOR: That went amazingly well, Ira. So we threw out an invitation to artists on this platform called Ello for portfolios, and we got hundreds of submissions, people who wanted to create art that was inspired by some of the quotes that we picked out of the book. And we narrowed it down to six from four different countries, including the UK and Colombia. And you can see this on our website at sciencefriday.com/art.

But it’s this beautiful variety of abstract, sort of geometrical renderings that try to make you think about the Pauli exclusion principle and quantum electron spin. But then you also have illustrations of time dilation at the event horizon of a black hole and this sense of existential horror of that idea. So you have a lot of really beautiful things that came out of this, and we’re really excited to show those to you.

IRA FLATOW: That’s terrific. That’s terrific. A lot of people calling in with comments now. Let’s go to Huntsville, Alabama. Pat, hi. Welcome to Science Friday.

PAT: Oh, hey. I’m sorry. I’ve got my music on. So [INAUDIBLE] I’ve read the book probably three or four times. And the first time I read it, I was probably 12 or 13. And what it did, to me, was kind of– you know like the first time when you realized that doctors don’t know everything, and that maybe [INAUDIBLE] scientists don’t know as much as you think they– thought we knew–

IRA FLATOW: I think we’re losing– yeah, the line is awful.

CHRISTIE TAYLOR: So I think what he was saying– that moment when you realize doctors don’t know everything. And I know there are several moments where Hawking admits to being wrong about things in this book. He talks at one point about, if the universe contracts, are we going experience time backwards, for example? And he says, I thought so, but actually, I changed my mind. Clifford, does this happen a lot? Is this a rare thing for someone to admit in public in science?

CLIFFORD JOHNSON: It would be nice if it happened more often. It really depends. It really depends upon the scientist. There are some who are, I think, very open to discussion and back and forth and changing their minds, and I think that’s becoming increasingly so with new generations of scientists. But there are, indeed, famous examples of people who take positions and dig in at all costs. And I think Hawking was very, very gracious at a number of points when he changed his mind. There are a number of famous bets that you can read about, some of which he lost, concerning big issues in physics, and he’s been very good about that, especially in later years.

IRA FLATOW: A tweet from Jay Silvera, who says, “Would you discuss the concept of matter and energy being consumed by a black hole but not the information, and how that relates to the theory that the universe is holographic, another idea put forth by Hawking?”

CHRISTIE TAYLOR: Oh, Priya, I think this one’s for you.

PRIYA NATARAJAN: Right. Well, let me just quickly add to the changing your mind, because it’s related to this question, which is he famously changed his mind about the information paradox. So when he postulated this idea of Hawking radiation, there was this huge riddle that, because it’s believed that no information about the interior of a black hole or its formation could ever be extracted, it’s an essential property of the black hole. So but if particles were being radiated away at the periphery, as Hawking radiation suggests, then would they not be carriers of information? So originally, Hawking thought that they would carry no information at all, and the evaporation of a black would lead to total information loss.

But the nice thing about him, as you’ve all talked about, is not only did he change his mind on this big question– and as Clifford mentioned, he had a bet– but he also did so publicly. So he acknowledged that he was wrong, and that information could actually escape from black holes, after all. And so I think that was what was sort of very gracious about him, that he did so publicly.

Coming to the question of what really happens as a black hole sucks in matter. So matter that falls into a black hole, a small portion of the rest mass energy of that matter is converted into radiation. So one can think of it classically as the blob of gas, for example, is getting sped up as it’s being pulled into the intense gravitational well of the black hole. And it starts to radiate because it gets heated up, and it starts to glow in the X-ray. So a very small portion of the mass is actually left out as sort of a siren, as a signal, as it’s falling in. And this is how we actually see black holes at all.

And the rest of the matter, we believe, just falls right in through to the event horizon. And what it does, it increases the mass of the black hole. So as the mass of a black hole grows, since the size of the event horizon is proportional to the mass, as a black hole accretes– is a technical word; gobbles more mass– the event horizon become slightly larger.

So this is our current understanding of how we think black holes actually grow, other than the actual sort of collision between two black holes when they just go thwack. And they go thwack. They release gravitational waves. They jiggle the spacetime around them. And we’ve kind of detected the first sort of instance of two tiny black holes, not the supermassive ones in the center of galaxies like our own– we are yet to detect that collision– but this kind of matter falling into a black hole, pulled in from either a star that has strayed nearby or, in the case of supermassive black holes, when gas is sort of swirling around and held in a feeding disk around the black hole, from which it gets slowly siphoned in. That’s really where our current understanding is.

And in terms of the information, classically, we really do believe that once this matter causes the event horizon, we don’t actually know, after the black hole has “grown”– and I’m putting inverted commas in the air here– its size has grown. We just know that the mass has increased of the black hole. So we see the black hole. We can’t tell how it grew to be the mass that it has. So for example, if all our mismatched socks got sucked into a black hole, we wouldn’t know, when we saw the black hole, what actually went in.

IRA FLATOW: We’re not going to go there to find out, either.

PRIYA NATARAJAN: That’s right.

IRA FLATOW: I don’t want to do that. Let me just remind everybody that this is Science Friday from WNYC Studios talking about black holes and Stephen Hawking. One question I had that I thought I would try to get answered by you, Priya, and I thought maybe Stephen Hawking could answer it in his books, but the graphics weren’t there for it. You mentioned the event horizon, and you mentioned the disk– an accretion disk around a black hole.

PRIYA NATARAJAN: Yeah.

IRA FLATOW: Is it like the rings of Saturn? I mean, I’m trying to look at a black hole. I see a disk. Why is a disk forming in one spot as a ring and not going polar ring or instead of east to west? When I see a black hole, is everything equal around the whole hole, or is there some more preferable area for these things to happen?

PRIYA NATARAJAN: So I think there’s sort of a preferred geometry. And I agree. Really, it’s counter-intuitive, and it’s hard to visualize. It’s this sort of usual problem with having to plot on two dimensional paper things that are essentially three and four dimensional.

So the way to think about it, because the black hole is so compact, think about flinging a little baseball onto the black hole. The black hole is such a tiny spot in terms of the target– if you’re shooting the target, it’s such a tiny spot– that you are almost always going to miss it. So you’ll miss it, but then the grip of gravity is so strong that you get pulled back out. You come back in. And you’re kind of held by the gravity. And then you go back again.

So if you think about the continual sort of things falling into a black hole, where the size of the target is so tiny that you never hit bullseye, that you can imagine things being kind of captured around it. And that’s the structure that we refer to as the accretion disk.

CHRISTIE TAYLOR: And in the couple of minutes we have left– I apologize, Clifford– I wanted to make sure we were talking about how we talk about these things because, just as science has advanced in the last 30 years, we’ve seen so many books about physics and the way the universe works and the way particle physics work. We’ve had scientific advances, but we’ve also had maybe advances in science communication. Clifford, I know you’ve put out a book on this very topic.

CLIFFORD JOHNSON: Yes. Well, I think one of the great things that’s happened, and I think people like Hawking and Carl Sagan and others have really helped encourage this, is feeding that thirst that people have to learn what’s going on in fundamental research. And so there are many, many different kinds of scientists writing about many different kinds of topics. So even if you didn’t like A Brief History of Time, there are other books on the same subject matter, and there’s other books about exciting areas of other physics, as well.

And so I think that’s been a really wonderful thing. I think Hawking helped with that by showing that it was possible to get people to buy lots of copies of a book about abstract ideas, and so there are wonderful books, many of which you can find with an easy search. And we put some examples up. We suggested some, and I think you have them on your website.

CHRISTIE TAYLOR: Yeah. That’s at sciencefriday.com/bookclub. There are some examples. Are we ever going to completely explain everything? Like, is there ever going to be one book that really just covers it all? Clifford, Priya?

CLIFFORD JOHNSON: I would say no, and I think that’s good because I think there are many different ways of thinking about a topic. Not everyone thinks the same way, so it’s good to have many different kinds of books written by different kinds of scientists that bring different aspects of it alive. So I wouldn’t want there to be one book.

PRIYA NATARAJAN: Right. And I think this is the nature of science. There is no final answer. We always open up more and more questions. So I don’t think we’ll ever reach the position of being able to have the final word on everything. So things will always be evolving. Our understanding is constantly evolving. And I think that whenever there are lots of exciting new discoveries, I think physicists feel very excited to share and write books. So I think we’ll keep having lots of books written by lots of different people who think and imagine very differently and visualize very differently.

And I think technology’s also going to be really important. I think augmented reality, virtual reality are going to give us another very interesting canvas to start exploring these abstract ideas.

IRA FLATOW: Well, I want to thank you both for taking time to be with us. Christie Taylor, thank you for shepherding our book club.

CHRISTIE TAYLOR: You’re welcome.

IRA FLATOW: As always.

CLIFFORD JOHNSON: It’s a pleasure.

PRIYA NATARAJAN: It was fun. Thank you.

IRA FLATOW: You’re welcome. And you two keep writing books. Clifford Johnson, professor of physics at University of Southern California. The Dialogues, a great graphic history there. It’s wonderfully drawn. And your books, too, Priya Natarajan, professor of physics and astronomy at Yale. Thank you for both taking time to be with us today.

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