IRA FLATOW, host:
You're listening to TALK OF THE NATION: SCIENCE FRIDAY. I am Ira Flatow, and for the rest of the hour, the string theory rebellion.
If you've listened to this program, you've heard us talk a lot about string theory and how it among other theories has risen to the top as one of the most talked about solutions to a central problem in physicists, and that is how to unit all the forces and particles in the universe, especially quantum mechanics and relativity, gravity.
Countless books, papers, articles, TV shows have sought to explain it to us, but what we have not heard so much about are the critics of the theory, who are now openly questioning its usefulness in physicists. They say that string theory is not living up to its promise, that it offers no testable hypotheses and that's it's more hype than science.
Two new books are out that question string theory. One of the authors is here with us, Lee Smolin, as well as one of the most visible, I'd say certainly the most visible string theory scientist, Brian Greene. And if you'd like to talk with them, our number is 1-800-989-8255, 1-800-989-TALK.
As I say, Brian Greene is professor of physics and mathematics at Columbia here in New York. He's also the author of several books, including The Elegant Universe and The Fabric of the Cosmos. He joins us by phone. Welcome back to SCIENCE FRIDAY, Dr. Greene.
Dr. BRIAN GREENE (Columbia University): Thank you.
FLATOW: Thank you. You're welcome. Lee Smolin is a faculty member at the Perimeter Institute for Theoretical Physics in Ontario. He's also the author of The Trouble with Physics: The Rise of String Theory, the Fall of a Science and What Comes Next. He joins us from the studios of CBC in Canada. Thank you for talking with us today, Dr. Smolin.
Mr. LEE SMOLIN (Perimeter Institute for Theoretical Physics): Thank you.
FLATOW: You're welcome. Tell us why you wrote this book.
Mr. SMOLIN: Ira, I wrote this book in order to try to understand why string theory, which is a theory I myself have worked on, although not exclusively, why it was problematic. I was trying to understand why the ideas which seemed at first so beautiful, so natural, were not getting us where we expected to get 20 years ago.
I had another motive as well, which is more general. I was very interested in and am very interested in the idea that there's a close connection between science when it thrives, when it's doing well, and a democratic society when it's doing well. And I wanted to use the case of the theory that was not leading up to expectations as a kind of study to try to see how robust science is - and indeed science is robust - and to try to understand better this intuition that is a close connection between science and democratic societies.
FLATOW: Let's talk about your first issue. You're saying that the string theory has not lived up to expectations. Is that correct?
Mr. SMOLIN: That's the feeling of many people, certainly not just myself, and you know, when you in the introduction talked about rebellion or talked about new voices, there have always been people who were skeptical of string theory. Indeed there have been experts in the field who have been far more skeptical than I've been all along. I'm somebody who has been sometimes working on string theory, sometimes working on alternative theories.
And one of the stories that I wanted to tell that I think deserves to be told is that string theory, with the beautiful things about it and with its faults, is one of a spectrum of approaches to the deep problems of unification, of putting together quantum mechanics and gravity, and it's always been part of a spectrum of approaches. And that, situating it within that is a story that I wanted to tell and that I think has not maybe been told well enough.
FLATOW: Brian Greene, do you agree that string theory has not lived up to its expectations?
Dr. GREENE: Well, you always want to be further along than you are, because it'd be great to have the answers that we've been searching for. But the thing about science is you can't predict the rate of progress, and the best you really can hope for realistically is that you make progress toward the goals that you set for yourselves. And I have to tell you, where we are today in string theory is beyond what I had hoped 20 years ago.
Certainly we've yet to achieve many goals that I still hold dear, that many people in the field hold dear - namely to make predictions, that we can really go out and test and determine whether this theory is right or wrong. So certainly at this moment, skepticism is a healthy attitude towards string theory. But in terms of progress and in terms of being satisfied that the theory is making headway, absolutely, absolutely.
FLATOW: Tell us a bit about what string theory, the problems that string theory, Brian, are supposed to unite or to solve.
Dr. GREENE: Well, we have two main pillars of understanding in physics that were developed in the 20th century. One is the general theory of relativity, Einstein's theory that describes gravity. And gravity is a force that's relevant mostly when things are big - stars and galaxies and so forth.
The other major development is quantum mechanics, and it's a theory that describes the other end of the spectrum, the small things - the molecules and the atoms and so forth.
Now for a long time, we've recognized that these two theories have to talk to each other in a sensible way. There are realms, extreme realms, where things that are both heavy and small, like black holes in the center or like the beginning of the universe. And because those realms exists, you need to use both gravity, general relativity, and quantum mechanics at the same time.
The problem is for many decades any attempt to put the two theories together, to unify them, if you will, didn't work. It gave wrong, nonsensical answers. String theory is an attempt to fix that, to give us a theory that won't give nonsensical answers, that will give answers that make sense when you put gravity and quantum mechanics together.
FLATOW: Now Lee Smolin, you write that string theory makes no new predictions that are testable by current or even currently conceivable experiments. Is that your main issue with the theory?
Mr. SMOLIN: It's one of them, and I think that's not controversial, and I often agree with Brian, but I have to disagree with him about the expectations. Certainly I expected 20 years, and I think many people talked as if they expected, that we would see predictions rather soon.
And in - connected with this book, I was curious and I did a study of past revolutions in science and past attempts to make unifications of physics. And what I found looking at the history, which disturbed me very much - both about string theory, and I should say also for some other directions that I've worked on - is that history seems to show that when there's a good idea about unifying different parts of physics, it works fast if it's going to work. It takes some bold risks and the risk pays off. And within five or 10 years, there's experiments, even if those experiments are in domains that nobody would have thought of to look for before.
And so I think it is problematic that string theory is not making experimental predictions. There are certainly very beautiful things about it. On the other hand, if you look at some of the alternatives that have been explored, some of the alternative ideas, they're not - they're also, as is not string theory, fully developed theories, but they're ideas, and they do lead to experimental predictions. And those predictions are being tested.
So I think that this is the old standard on which science is judged, scientific progress is judged, which is to have a good idea you should be able to test it. And if it's the right idea, then the experiments turn out to support the idea and support the predictions of the idea. And I think we should stick to this standard.
FLATOW: Why not just let the string theorists continue doing what they're doing, and if they turn out to be wrong, they're wrong. Well, why not let time be the judge of what's happening?
Mr. SMOLIN: Oh, certainly time will be the judge, and I - it would never be it for me to say to somebody what you might be doing, what you should be doing. If somebody feels that string theory or anything else is the most promising thing they know about, certainly they should work on it.
But there is another level, and that's the level where we think about science as a very risky activity. And if it is a very risky activity, something like development of a new technology, the question arises - do we support only one direction? Do we put all of our apples or whatever it is in one basket? Or do we hedge our bets? Do we support all the people who are excited about the good ideas that they have?
And this is a large part of the issue that I'm raising in this book. It's not a question of what one individual scientist does. One individual scientist should do what they deeply believe in. But it is a question, when we step back from that and look at the range of science and look at it as a kind of community, as a collective endeavor, we can take attitudes where we encourage people to strike out on their own, to leave behind old ideas, even if there's still things about them we love, and to encourage the young people, especially the young people, to forget what people of our older generations have done and strike out for new directions.
Or we can encourage attitudes in which we try to keep everybody working along the directions that we feel comfortable with. And that's a large part of the issue.
FLATOW: So do you think that young scientists, graduate students, are going down a dead end if they get into string theory research now? Is that basically what you're saying, that we're not letting, giving oxygen to the other theories or that they aren't being encouraged?
Dr. SMOLIN: Let me turn it around because I would never tell a scientist what not to do. But what I do know and what I care very much about is that there are very good young scientists who are not working on string theory, who are not working, I should say, on the direction that I've invested a lot in, which is loop quantum gravity, who have their own ideas and their own directions and those people who are, in a way, kind of orphans.
But the analogs of the great physicists of the past who always struck out on their own, people like Galileo and Einstein, those people don't have an easy time because of the way that the university - universities are very adverse to risks. They're very adverse to hiring people who are working on their own ideas as opposed to ideas that large communities of people have been working on for decades.
And so my point is that we should try to find ways to help and support those people who have new ideas and have the courage to work on their own ideas.
FLATOW: Brian, how much time do you think that physicists need to see some of the predictions or to let string theory play itself out, so to speak?
Dr. GREENE: Well, there's no crystal ball, so it's really hard to predict, as I was saying before. But I would want to emphasize a couple of highly relevant points, which is no string theorist would ever want to change the standard of proof for a theory being its confirmation by experimental observation.
That's why I say repeatedly until I'm blue in the face when I'm out there lecturing, in my books and so forth, that you should not believe string theory is right because we don't believe it's right. It may be right and only experiment will tell.
How long will it take for those experiments to happen? I don't know. We could get lucky. It could be that the Large Hadron Collider, which will turn on in 2007 or 2008, there's a chance that we might see some of the fingerprints of string theories through something called super symmetry, certain particles that the theories suggest should be there but nobody has yet seen, through the possibility of seeing the extra dimensions of space that this theory requires by virtue of certain missing energy signatures in the data.
The possibility that we might confirm string theory through astronomical observations is something that I work on. That's what I spend my time on these days, trying to see where these strings might leave some imprint in the microwave background radiation, the heat left over from the big bang.
All of these are long shots. But we're doing exactly what Lee is saying one should do in science, namely work toward experimental verification. How long? I can't predict. Nobody can predict.
But let me just also, on this other issue of encouraging young students to strike out on their own and pursue their own ideas, I couldn't agree more. Absolutely.
I, for instance, in the last couple of years have had students that don't work on string theory. I've had students that have worked on relatively fringe ideas according to the mainstream point of view, something called modified Newtonian dynamics. I've had students working on that. I've had students working on more bread-and-butter particle physics.
So absolutely we need to encourage diversity of thought. We need to encourage the young students to express their creativity. Who would ever say otherwise?
FLATOW: Talking about string theory this hour on TALK OF THE NATION: SCIENCE FRIDAY from NPR News. I'm Ira Flatow talking with Brian Greene, professor of physics and mathematics at Columbia, author of The Elegant Universe: The Fabric of the Cosmos, Lee Smolin, faculty member at the Perimeter Institute of Theoretical Physics in Ontario, Canada, author of the new book, The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next.
1-800-989-8255 is our number. Let's go to the phones about what comes next. Hi, Jeffrey, in North Hampton, Massachusetts. Hi.
JEFFREY (Caller): Hi. I just had a question. If string theory doesn't pan out as Mr. Smolin's saying, what do you propose like the legions of string theory should do - like what direction should they strike out in? Is there any like -something to like stand behind string theory? Because it seems like it's been dominating the field for a while. And just like in general what would be the future if it doesn't pan out?
FLATOW: What else is there on the horizon, Lee?
Dr. SMOLIN: There are about half a dozen other active approaches. The names won't mean much to most listeners. But if you like I'll just throw them out. One of them is deformed special relativity. Another is dynamical triangulations -
FLATOW: Well, just give us a little sentence with each one what that might mean. Deformed special -
Dr. SMOLIN: Deformed special relativity is an idea that quantum gravity affects, alter the basic equations of special relativity. It turns out in ways that are testable by experiments that are going on now or are going to be launched next year.
Dynamical triangulations is one of several ideas on the basis of which space is made of discreet elements. And one tries to find effects that come from the fact that, the hypothesis that space is discreet.
Loop quantum gravity, which is a direction that I've been privileged to work on sometimes, is something that is a successful unification, at least at the level of the equations, of general relativity and quantum theory. And it has led to a very particular picture of space being made out of discreet elements. And there are consequences of that which people are exploring.
FLATOW: One of the - let me just stop you there and talk about your own work a little bit on loop quantum gravity, because one of its implications is, if I'm correct, I understand it correctly, is that there might be a time before the big bang. The big bang was not the beginning of time? Would that be correct?
Dr. SMOLIN: Well -
FLATOW: Or is that too hard for you to explain?
Dr. SMOLIN: No, no, no. It's an old idea, not an idea just to weigh-in of quantum gravity. It's an old idea that quantum mechanical effects remove that first instance of time that we call the initial singularity, where the density of matter, the temperature, everything is infinite, and allow time to proceed to the past so that there was a past.
The calculations that we have done so far using loop quantum gravity strongly suggests - I would not say mathematically prove - but strongly suggests that the theory predicts that that is the case. And it's one of several different ideas on which that expectation holds.
FLATOW: We're going to take a short break and come back and talk lots more with our guests, Lee Smolin, author of The Trouble with Physics, Brian Greene, you know him very well, author of The Elegant Universe, talking about the string theory and other possible competing theories. Our number, 1-800-989-8255. Stay with us. We'll be right back after this short break.
I'm Ira Flatow and this is TALK OF THE NATION: SCIENCE FRIDAY from NPR News.
You're listening to TALK OF THE NATION: SCIENCE FRIDAY. I'm Ira Flatow. We're talking this hour about string theory with my guests, Brian Greene, author of The Elegant Universe. He is professor of math and physics at Columbia University. Lee Smolin, faculty member at the Perimeter Institute for Theoretical Physics in Ontario, Canada, author of The Trouble with Physics.
Our number, 1-800-989-8255. Brian, you've invested so much time in string theory. Would this be terribly disappointing if you just keep waiting and nothing happens?
Dr. GREENE: Well, it would be disappointing if we're unable to determine whether theory is right or wrong and we just keep on developing it and we're unable to make contact with experiment.
And were that to really happen over the course of the next, I don't know how many years or whether one should measure it in decades. Certainly I would imagine interest in the theory would drop off because the people who work on string theory are physicists and physicists want to make contact with physical reality.
But what's happened over the course of the last 20 years of development is that the theory has gone through what we call revolutions in our thinking time and time again, which has given a surge of energy, a surge of interest in the theory, which has kept us going even though we've yet to make that desired contact with experiment.
If I just say quickly how we maintain that enthusiasm, I'd say there are really two main reasons. One, the theory is able to embrace all of the major developments in physics having to do with the elementary particles in quantum mechanics that were discovered before string theory in the middle of the 20th Century leading up to the end of the 20th Century.
They all naturally find a home within string theory. And that's very compelling to us because usually a revolution doesn't actually erase the past. It embraces the past but goes further. And that's what string theory seems to be doing.
The other side of it is even without the experimental confirmation, string theory has a very intricate mathematical structure that holds together with a kind of tight logical cohesion. There are checks and rechecks in the calculations, enormous number of consistency checks, and they're all passed. The theory comes through with flying colors every step of the way. And that again keeps us going, keeps us thinking that this theory is at least heading in the right direction.
FLATOW: Well, Lee, what would be wrong with that if things are working like that?
Dr. SMOLIN: You know, it's a delightful situation, because everything that Brian says is true. And because of that I'm, and many other people have spent time on the theory. There are things that, however, it doesn't come close to doing, apart from - I think we've talked enough about experiment and I'm very glad we agree about that.
If you really put quantum mechanics together with a description of space, then we know from general considerations that the notion of space should disappear just like the notion of the trajectory of a particle disappears in quantum mechanics into a more general notion of a quantum state, and then we have the idea that a particle is either a wave of a particle, depending on what questions we ask about it.
The same thing should happen to space in the geometry of space. Now, string theory may address that question. But so far it doesn't very directly whereas other approaches do address that very (unintelligible) - give us a new language to describe space in a way that's consistent completely with the idea that the classical description that we're used to, the idea we're living in this three-dimensional, fixed geometry, goes away.
And so I think the right way, the way that I like to think about it, is that different approaches have different strengths. We've learned something from the different approaches, including string theory, including the other approaches.
But each of them, including string theory, has run into barriers, things that it doesn't easily do. And because of that, I'm convinced - see, I see it something like mountain climbing. I see doing physics as something like a group of people trying to find the summit of a mountain, but in a fog.
And many of us, maybe most of us, who are well trained, know how to climb. You put us down on a hill. We go up hill and we find the summit that's nearest to us, that's uphill from here.
The problem with that is that the real summit is somewhere off in the fog somewhere. And so my sense of the field is that what we are as a field is where people who have discovered the tops of a number of hills and string theory is a very beautiful high hill.
And loop quantum gravity's another one. And dynamical triangulations is another one. And causal sets is another one. And twisted theory is another one. And meanwhile, the summit, maybe these are way stations on the way to the summit. But to get to the real summit we need to cross some perilous ridges or go through some swamps down in the valley and really find it.
And that's why above all what I'm encouraging is that we put the things that kind of work, that work beautifully but run into limitations behind us and we encourage ourselves as working physicists and the younger people to break loose and risk climbing over those perilous ridges in the fog and find the summit.
FLATOW: 1-800-989-8255 is our number. Talking with Brian Greene and Lee Smolin. Let's go to Brenda in Minneapolis. Hi, Brenda.
BRENDA (Caller): Hello.
FLATOW: Hi there.
BRENDA: My suggestion is that they need to get a bigger box, that -
FLATOW: A sandbox?
BRENDA: You know, that maybe it's not - maybe they don't need another big super collider. You know? Maybe there's some kind of systematic distortion in how the culture of the people researching string theory are thinking that is distorting their ideas about it or making them all - they need somebody to really think outside of the box and then to think outside of that box, if you understand what I mean.
Dr. SMOLIN: May I address that?
Dr. SMOLIN: Yes, I know exactly what you mean. And I agree with one strong proviso. And the but is that to be a good scientist you have to be a rebel the way you're suggesting. You have to be willing to think outside the box as you're suggesting.
But you also have to be a conservative. You have to master the tradition of all the knowledge and all the techniques that came before you, because as Brian said, I agree strongly, revolutions don't wipe out the past. They build on the past knowledge.
And to be a good scientist requires - and the great scientists have this, somehow this contradiction internally within each person as well as within the community of scientists, in which we are both very, very deeply conservative and very rebellious.
And that's the trick to doing science.
BRENDA: Well, maybe another way to think about it is it's like a decision tree, the branches. Maybe the tree you're on isn't a tree. Maybe it's just a branch. You need to go back further in the decision tree to find out where you made the mistake of thinking you were at the root when it was just another branch.
Dr. SMOLIN: The only thing I disagree - I agree with you. And the person who can do that and at the same time has mastered the past knowledge so when they find a branch that goes somewhere - your branches are like my hills. So when the person finds the branch that goes somewhere they have the training and the ability to climb it. That's the only thing that I would insist on.
But otherwise I agree with you. And Brian was saying, and I agree, when we make choices about which students, which younger people we encourage, we support, I look for those who are capable of going back in the decision tree, who wonder maybe quantum mechanics really doesn't make any sense. Maybe the problem is there.
And the evidence for that is that some of the greatest physicists alive do worry about those very foundational questions. For example, Roger Penrose or Girard Etoft(ph), they -
FLATOW: Do - I'm sorry. Go ahead.
Dr. SMOLIN: Go ahead. No, go ahead.
FLATOW: No, I was just wondering, I'm just following up on her thoughts. I mean, are we at a point now where you just have to sit and scratch your head and think we need some revolution. We may even need a revolution in physics. Maybe we need a new physics.
Dr. SMOLIN: Well, I think we do need a new physics. I think we need experiment and experiment is coming from several directions, from the Large Hadron Collider in Geneva, which comes online next year, from the glass experiment, which is a satellite that will launch next year that will be able to test very, very precisely whether the speed of light is really constant or whether that principle of Einstein's needs modification, from the observations of the cosmic microwave background, which I know Brian works on and I wonder about and people from all points of view in quantum gravity are trying to make predictions about as the experiments improve.
So we need and we are getting new experiments. And nothing can happen without experiment. And I also think we need a revolution or we need - the way that I would put it is we need to complete a revolution.
Einstein started this. Einstein started the revolution in the early 1900s when he - and he was the first person to declare that we needed a quantum theory to break with the physics that went before. And he also brought us relativity theory. And that was the launch of the revolution.
And we're still engaged in that same revolution. It won't be over until this problem of putting together relativity and quantum theory is solved, and not just solved in principle on a pad of paper, but solved in such a way that it leads to new experiments and new predictions for experiments.
FLATOW: Brian, any comment?
Dr. GREENE: Yes. Well, I full well believe that we will, when we do complete this revolution that Lee's referring to, have a completely different view of the universe.
I totally agree with Lee that everything that we know points to space and time not even being fundamental entities. The way I like to think about it is take the concept of temperature. We all know what it means for something to be hot or to be cold. We can experience it.
But scientists taught us that there's an underlying physics to temperature which has to do with how fast particles, molecules, are moving. Molecules move fast, it appears hot. It feels hot. Molecules move slowly, it will feel cold.
So the idea of temperature rests on a foundation of more fundamental ideas, motion of molecules. We think that space and time are like temperature in a sense that they rely upon more fundamental ideas as well.
Now what those more fundamental entities are, the so-called atoms, if you will, that make up space and time, we don't know yet. String theory has some vague suggestions. Loop quantum gravity has some vague suggestions. We're not there yet.
But when we get there, I think we will learn that space and time are not what we thought they are. They are going to morph into something completely unfamiliar. And we'll find that in certain circumstances space and time appear the way we humans interpret those concepts, but fundamentally the universe is not built out of these familiar notions of space and time that we experience.
FLATOW: Talking about string theory this hour on TALK OF THE NATION: SCIENCE FRIDAY from NPR news. Talking with Brian Greene, author of The Elegant Universe, Lee Smolin, author of The Trouble with Physics.
So much in the way that we used to think that gravity only happened here on earth, we expanded it out to, you know, to think of it having, being in other places besides the earth and also being able to measure it. That would be true of space and time? There's this underlying structure to - and is that the right word, structure to it that could change the speed of space, the speed of time, things like that?
Dr. GREENE: It would change the very notion of reality if you really want to be more precise because we all, I believe, most of us, at least, think about reality as existing in a region of space and taking place through some duration of time.
If we learned that those basic ideas, the arena of space and the duration of time, are not concepts that even apply in certain realms, the realm of, say, the very extreme of energy or the very extremes of small size and tiny intervals. If the notions of space and time evaporate, then our whole conception of reality, the whole container of reality, will have evaporated and we'll have to learn to think about physics in the universe completely differently.
FLATOW: So that our reality would just be one special case of all of reality.
Dr. GREENE: Precisely.
FLATOW: Lee? Sounds pretty Twilight Zone.
Dr. SMOLIN: It's not, it's not as far out as it sounds. Really, Ira, it's not. And seeing space is made up of something, atoms, of something more fundamental, you can go a long way with an image that the air looks smooth, the water looks smooth, and we discover that really it's made out of atoms.
But then there are two questions. One question, which Brian addressed, is how do you go from this microscopic description, from the atoms to the smooth properties that we observe? And that's an aspect of it.
Another aspect, which Einstein, part of his genius was to jump directly to, is are there consequences for experiment of the fact that, in his case, matter's made of atoms?
And that's why I keep pushing about experiment so much, because indeed it does seem that if space is made of atoms, there are consequences for how light propagates. And these consequences are checkable by experiments that use observations of light coming from very, very far away to look for very small differences in how light of different colors or different energies propagate.
Now I want to emphasize that we don't have a prediction that makes an absolutely precise prediction for what these experiments should see. And that's a source of great frustration to all of us.
But we have some general ideas about what the effect should be to look for and if those effects are seen, and this could be in as little as a year and a half, two years, from this experiment that I was talking about that looks at gamma rays coming from very, very far away.
Then that will indicate that what Brian is saying is absolutely right. That will be the discovery of the atoms of space in the same way that some of Einstein's discoveries really cemented the idea that matter is made of atoms.
FLATOW: Brian, how do you, as a physicist with things moving so slowly, how do you stop from being impatient?
Dr. GREENE: Well, they're not actually moving that slowly. It may seem slow from the outside because, you know, I've been on your program in the past few years and I don't remember but you probably asked me, are there experimental tests of string theory? And I had to say as yet there aren't. We're working toward it, which is more or less what I'm saying today.
But in terms of the actual field itself, our understanding of the underlying theory, our understanding of the equations, our understanding of the fundamental ideas and how they relate to one another, we've made great strides.
I mean, we have an international meeting every year, a string theory conference that has something like 50 talks. And these talks are generally amazing. They're generally showing how people are making great progress in spite of not having the guide of experiment.
So if it turns out, as Lee is saying, that some of the experiments he's describing or the experiments of the Large Hadron Collider, if in the next couple of years these experiments bear fruit and begin to show us some of the features of the theories that we've been working on for a long time, things will definitely take a major leap forward.
So it's a very exciting time, waiting to see the results of those experiments. And in no way would one want to say that the theory is moving slowly. It perhaps is moving slowly toward these experiments, which are coming online. But the theory itself is developing rapidly. In fact, it's hard to keep up.
FLATOW: All right. We've run out of time. Thank you. Brian Greene, author of The Elegant Universe, professor of math and physics at Columbia University. Lee Smolin, author of The Trouble with Physics, faculty member at the Perimeter Institute for Theoretical Physics in Ontario, Canada.
Thank you, gentlemen, for taking time to be with us today.
Dr. GREENE: Thank you.
Dr. SMOLIN: Thank you very much.
FLATOW: Have a good weekend.