Cumrun Vafa： Is String Theory Actually Science？

There is no best viewpoint, and that best viewpoint is subject to the question. We should not say this is the way to look at it. Everything else is bad and so on and so forth. Contradictory sounding views are sometimes necessary to understand the subject. Openness and the fact that duality shows us that multitude of attitudes and views It's important to appreciate and connect, not only in a scientific context, but in in a broader human society last week that I think would have a good applications.

Welcome everybody To this edition of the Into the Impossible podcast, I am your fearful host, Brian Keating. And today, it is a great pleasure, a treat in fact, For me to welcome none other than Kamran Bafa of Harvard University. How are you, Kamran?

Thank you very much, Brian, for having me your program. It's a Great pleasure. I'm fine and, looking forward to our discussions.

Yes. I've been, just devouring your book, which we're gonna Talk a lot about today, puzzles to unravel the universe. And I've been fascinated with puzzles my whole life, mostly my inability to solve them, but you are noted for having made tremendous contributions to the world of theoretical physics, and this is your 1st popular science book as I understand it. And I always like to say there's a piece of advice that you never should judge a book by its cover. But on this on this book, not only do you have A very mysterious and and puzzling imagery, but you also have endorsements in from none other than Edward Witten, Well, I've tried to get on the show unsuccessfully, but I'll I'll talk to you about that later. And also, Brian Green, another Brian. Actually, my kid's Favorite Brian in astrophysics. But I wanna ask you, how did you come up with the name of the book, Puzzles to Unravel the Universe? And how did you come up with the artwork that so beautifully graces the cover of this book?

The title, I think, was motivated by a course I'm Teaching, for Harvard's freshman called physics, math, and puzzles. It's a freshman seminar. And, so the book was Basically, the was drawn out of its course. And, so I decided I was thinking about what title to choose if I had Chosen physics, math, and puzzle sounded a little bit, maybe boring, so I thought maybe I should use some elements of it without Sounding too academic and a bit more kind of exciting in terms of applications to the real world and so on. So I thought that, which which involves actually the motivation behind the whole course, which is the connections with the real world. So I thought unraveling, the universe through Puzzles, puzzles to unravel the universe does justice to what I wanted to convey, and, that's why I chose that. As far as the cover, I got some help from some some people online, but, this whole design and all that happened during the pandemic. So I decided, during the pandemic, one thing I could do, is to finish this series of notes into a book, which I decided doing and the sub publisher just to go over, get it quickly out and get it done, so that it's people who may wanna be looking at it could could have a chance to do it during the pandemic as well.

So so So it was done in a bit of a speedy way at the end, but, so that's that's what it is. But I'm very happy with the with the the cover of the book as well as the way the book came out.

Yes. It's very, intriguing, and it matches the subject matter as well. I wanna make A distinction between mysteries and puzzles, and wonder if you do that as well. To me, there's a difference between a mystery and a puzzle, And I and I once discussed this with, Freeman Dyson, who I know you knew, the late great Freeman Dyson. And it was that, you know, a puzzle is something that could be solved. Maybe I can't solve it because I'm not as smart as you, but, a mystery might not be solvable. And I wonder, do you make a distinction between mysteries versus puzzles?

Well, in a sense, puzzles aspire to be mysteries. That's a good puzzle. Aspire to be like mysteries. That's not quite solvable, but gives you an creation to new ideas. So I view puzzles always like that. But I I I think for example, in the book I talk about the enigma of quantum mechanics, I still view it as a mysterious features that we encounter even though we think we understand quantum mechanics. You know, the features of experimentation within quantum mechanics are serious still to me. And so with that in that sense, I agree we we haven't solved it or it's it's not solvable at this point.

It might continue to be mysterious or maybe it gets resolved in a different form. Some other things happen like black holes. We have similar enigmas about black hole and mysteries about black Cool. Puzzles are pieces which kind of, as I say, try to get some features of these mysteries In some little nuggets of truth, and you can kind of wrap your mind around it and kind of understand it at least. So there's kind of There's a distinction, but there's this also this relation. They wanna reinforce each other that is you're hoping that the mysteries become like puzzles that you can solve. That's the way I look at it.

Yeah. I looked at, puzzles. I remember the most famous one perhaps is, Rubik's cube as a as a puzzle that I became infatuated with as a kid And then early 19 eighties, I think it's just about 40 years old and maybe a little bit older made by, I believe, a Hungarian named Rubik and became fabulously wealthy. And his whole life is wrapped up in in this particular, cube. And and it's, even such to the point that he cannot really Sleep when he tries to solve it faster than his previous record, etcetera. There are all these competitions, and he can't really do it as well as other people could. Or When he was a younger man, he could solve it even faster. I wonder, you know, if you look at your career, is there a particular puzzle or mystery that you're most fascinated by, among the many things you just mentioned, quantum mechanics, black holes, later, we'll get into string theory.

Are there things that just keep you up at night and that you won't rest until you Solve them or perhaps make some contribution towards the understanding

of them? Good problems have, interesting Reformulation in terms of things we can understand clearly in terms of the model that we are approaching. So there are many examples that what Comes to my mind, the computation of the entropy of the black hole, for example, using ideas about how you count the string theory, degrees of freedom in the using the geometry of string compactification. The work I did with my collaborator, Andy Strominger, is an example. But there are many such things, and I don't think I would Just pick 1 particular ones. I think even the some of the papers that may not be as well received or as well known in in general, I still might enjoy some of the puzzles that I can encounter. And to me, it's hard to calibrate it and organize it in terms of the ranking of which one is higher or lower in terms of interest to me. But even trivial sounding puzzles could be interesting and I find interesting. So So many of the puzzles that I discussed in the book, on the face of it might sound like, okay, so what? It's so simple.

What what do you want to learn? But Even those simple ones, I I I kind of think aft even after I've solved it and discussed it for 10,000 times, I still enjoy thinking about it. So I think it's like, the aftertaste of the puzzle is what, What attracts me to to thinking because it gives you a springboard for other ideas. It gives you say, oh, maybe this thing needs a bit more something else, and you begin to to think. So it might sound by itself kind of like a boring statement, but the connections and what what else it might relate to is what fascinates

Yeah. I think it was, that, maybe it was Albert Michelson, one of the I think he was the 1st US Nobel Prize winner, one of the first, Nobel Prize winners from America. And he said, you know, experiments are like puzzles to a kid. And just like a kid will Do a puzzle even once he or she has solved it, he'll do it again or she'll do it again because every time they do it, they get a little taste Of the thrill that they got when they solved it the 1st time, I feel like that was a as an experimentalist. I wonder though there are some puzzles and mysteries That are known to be unsolvable. I'll I'll say something like, Godel's incompleteness theorem. It's It's known that mathematics, a formal mathematical system is, is, you know, self inconsistent in a sense, Which is we know that to be true. We don't know why that's true necessarily.

I often find that about experimental physics as well that experimental physicists such as myself Have this desire to know what is scientific, what is worth pursuing, and some people don't wanna pursue things like string theory. I wanna, ask you, what do you decide is worthy of your limited we all have limited attention and time. How do you know when a mystery or a puzzle is worth solving or may have it be known that it's unsolvable. How do you divide your time, amongst these many activities?

Well, I think that, I mean, the that's part of having experience with various problems that we encounter. You get the sense of what is doable and what is not, And that's the difference between somebody who starts doing science at the beginning, like when I was a student, and now where I have seen many, many problems solved and some of them not being solved and so on. By seeing this through different through different kinds of projects and so on, you get a sense of what is doable and what is practical. So On the one hand, you know what is practical, what is doable, on the other hand, you have a sense of what is important and interesting. So then you take an overlap between these ideas. Okay. Among the one which are potentially solvable, which ones are potentially more interesting and impactful, and then you kind of based on that, overlap, You you decide what projects to work on. So so that's usually how I I go about doing it.

So there could be many interesting questions that I I would love to do it, but I have no idea, so therefore I wouldn't try those, but and down there and there are many things I I could do immediately, but they sound like not that exciting or impactful I won't Waste my time with. So so there's kind of, like, the intermediate line where you kind of try to do the most interesting thing you can do, and that combination of being able to and interesting is what what needs to be both for me to feel like it's a good project.

So I was thinking as I read your book and thinking back to a conversation I had with Lenny Susskind last week about, one of the most Impressive characters in his mind in history, Aristarchus. And you mentioned Aristarchus as well in the book, towards the end. And you talk about the fact that Aristarchus had these ideas about heliocentrism, which we now know to be true, but could not be proven because it was impossible Well, to measure, for example, the parallax of of stars, at that time. In fact, it wasn't proven, the parallax, was not proven Until, I believe, the 1700, even after Galileo. And and yet Galileo had tools to actually prove Copernicus, was right, and he didn't use them. Instead, he used other methods which turned out to be wrong. For example, his book, The Dialogue, Was originally going to be titled On the Flux of the Tides, and he contended that the tides on Earth's oceans were caused by the Motion of sloshing and revolution and rotation of the earth, not as we now know from the gravitational influence of the moon. So he was overwhelmed by the kind of notion That Copernicus was right so much so that he used incorrect evidence to, to justify and bolster the hypothesis.

On the other hand, you know, Aristarchus had the right idea, and Lenny calls him, you know, the most in interesting scientist perhaps in history, because he had the right idea, but the technology wasn't sufficient. What do you say to people who say string theory, or studying the properties of black hole singularities, which we'll get to in a minute as well. What do you say to those people that say it's not worth spending any time on it because you can't falsify The singularity. You can't falsify string theory. It's, so flexible it predicts or accommodates way too many outcomes. How do you justify that? Is there an opportunity to appeal to future technology, as in the case of Galileo and Aristarchus, Future, eventually technology caught up and prove them right. Do you think the same thing will happen with string theory? And if not, why should we study it?

As you say, Brian, many of the things about string theory are at the level of predictions, theoretical predictions that are very difficult to experimentally check with our current level of technology. So so it's in some sense that promise for the future. So the question would be, as you say, why should we spend time on something that we cannot check-in our lifetime as correct or incorrect and so forth? If there were no method to check our ideas, then we would have then I would have abandon doing string theory for the exactly that reason. However, due to the interesting interconnection of different ideas in high energy theoretical physics, you can actually check ideas theoretically. So you can check the validity of an idea from a different perspective and come to a conclusion whether that idea is correct or false without experimentation somewhat. Of course, that would validate the idea itself as being self consistent, logically correct, mathematically consistent. Whether or not that's part of the explanation of our current universe, we still have to wait. But we have seen so much encouraging results Strong string theory in term is lot consistent in information, different pieces of physics that we have discovered like strong interaction, What kind of forces are are working there, things about what happens for, cosmology, what happens for black holes.

We now know there are black holes ought to be very clearly. I mean there's no doubt about them, and the fact that these I ideas and strength theory come To get give a self consistent picture to many aspects of them makes us believe in them. And, like for example, the prediction that Hawking made about black holes, the fact that black holes entropy despite the fact that Einstein's equations predicts that they are unique. His, Taking to account of the quantum mechanics, the work of Bekenstein and Hawking in particular showed that now there must be some degrees of freedom which are inside the black hole. There's some microstates. And the fact that string theory was able to account for those degrees of freedom, At least the specific causes of black holes is already surprising and gives us a confidence that the theory hangs together. The details about how it would relate to our universe, then, you know, can we understand the electron has such and such a mass and so on remains to be seen. But even now even now, I will give you one example, which can make predictions Right now, Trump's string theory, which have experimentally been verified.

Now these expert these predictions are rather, in a sense, you would say not as precise a prediction, but still is a prediction. I will give you one example. So for example, you take the electron and it has a mass. And if you compute the mass of the electron in the fundamental units of physics, which is, Planck mass, It's a very tiny mass. And time unit is something of the order of 10 to the minus, I don't know, 22 or 23. It's a very tiny number. So you say, great. Do we have any prediction that the electron not should have been this small? Without knowing that there's an electron, and just by knowing that there is Electric charge, and by knowing that there is dark energy in universe, you find the bound for the electron mass.

You find that the electron mass A hectron mass should be bounded by 10 to the minus 1 on the upper edge, and it's above 10 to the minus 31 on the lower edge. So then the lower bound comes from the constellation of dark energy, and the upper bound comes from a constellation of what is called the weak gravity conjecture. That Gravity is always the weakest force in any any consistent universe. So putting these together, you find a range for the mass of the electron and lo and behold, 10 to the minus 23, which is the mass of the electron, is bigger than 10 to the minus 31 and smaller than 10 to the minus. So there are some predictions that you can see. Not as precise as you typically like intrinsic.

Right. I'm not gonna write a grant proposal.

Right. Exactly. But still, the idea that this is Has no falsifiable prediction is not correct. There are predictions that if the electron mass was somewhere outside this regime, you could have said, okay, this is inconsistent with these ideas. So, therefore, there aren't something should arise from this.

I might I might gently push back and say, you know, there are considerations in your book that You bring up from what's called naturalness that, that that you could actually get the black hole entropy to within a factor of pi or so, just based on dimensional analysis. So that doesn't require my, you know, any string theoretics at all. And you might also be able to push back. I might gently again with respect that, you know, that Weinberg made predictions about the, you know, value of dark energy, independent of the string landscape, but then it was eventually realized to accommodate that you'd have to have something like a landscape, which we'll get into in the multiverse. So is it unique to string theory or, you know, if my, smart undergraduate can derive it from her considerations of dimensional analysis, Does it really count as a prediction of string theory or could it equally be used by, Fermi to say it's a type of Fermi calculation?

Okay. So questions. So let's go over to the black hole question you raised. First of all, even there it's not clear, because consideration of, you mentioned analysis. You mentioned presupposes that we make an assumption that the entropy of a black hole is related to the area of the black hole. Diabally, you would have saw this relate to this volume, and that's not true. That was one of the surprising predictions of Hawking. So Another dimensional analysis without giving a totally wrong answer if you just use the the volume.

So you have to first assume its area. Okay. Let's assume this area. Why should we get that factor of 1 quarter of the area measured in plan Q and A? Why should we 1 quarter? We don't know a priori from that calculation. Hawking's Vision shows it does. String prediction not only gives you that 1 quarter, but actually gives you an infinite further correction. Instead, there's 1 quarter of area plus a coefficient times log of the area, plus other coefficient divided by the area, Plus other question, infinite expansion in the area. So not only it gives you Hawking's answer, it gives you all the possible corrections to it.

So it's not something that Hawking did not calculate. So from string theory, we not only get the leading term when the area is large, but subleading correction when the area is not huge. So these subleading corrections are shows you that there's a very clear picture of how you derive these statements and not just the overall coefficient in front of the area. So it hangs together. It is nontrivial, and to me these are the kind of examples that, bolsters our confidence. Mhmm. It's string theory and it's validity, and other approaches people have tried does not give you something as concrete and as precise as, as we have seen in string theory.

So thank you. That's a very masterfully explained. I actually came away just now with a new appreciation Of the depth of the mysteriousness of that particular puzzle. So you're unifying mysteries and puzzles for me, come on. You're we congratulated. My thumb's rather Occupied right now holding up good old Carl Sagan, but yours is free to push that like button. And don't forget to subscribe. It really helps us with the algorithm.

Now back to the episode. So we talk about unification and symmetry later because I wanna talk about hacking, puzzle solving later on. Do you solve do you do crossword puzzles? No. I don't. Okay. You know who does a lot of crossword puzzle? Marilyn Simons, who's, the wife of your good friend, Jim Simons, who I believe you've written Papers with, not too long ago. We'll get to that, in a little bit. But I wanna talk about a conversation I had with Lenny last week, Lenny Susskind, your friend.

And Lenny and I were talking about singularities. And I said to him, imagine if, you get a note from god, although He doesn't believe in God, so you'll have to take my word for it. And I said to him, imagine you get a note, and it says that, actually, there, there are no singularities at the center of black holes. Within the horizon, it's just purely classical. And furthermore, God gives you a note and it says, The universe, follows the, kind of cyclical eon hypothesis of, sir Roger Penrose who's been on the show many times. And or the, or a bouncing cosmology of my friend, Paul Steinhardt and yours at Princeton, who's been on the show also many times. I'll put links to that. And, and so there are no there's no singularity needed whatsoever.

Why why do we think that Quantum mechanics needs to be wedded to, married to, gravity. In those 2 cases, to my mind, those are the only cases where I often hear my fellow friends and physicists, theorists mostly, they say, well, we have to unite gravity with quantum mechanics because of singularities. Well, what if there are no singularities? Would you still say that we need to have a theory of everything in that way?

No. I wouldn't. My problem with unifying quantum theory and gravity is Star beyond even if there were no singularities, I would have thought that they should be saying like, because I have electrons which are quantum but proton which are not. To me it's like that. It's not because there are different forces. The gravity is one of the forces. You could say, well, how about gauge forces be classical quantum, but the other one be quantum. There's no form in which that makes sense.

You cannot talk about what is your form in them. Are you talking about how do you describe the physics in that context? It doesn't make sense. Now you can treat treat classical gravity if you assume the gravity is not dynamical. In other words, if there's no graviton, if there's no mode, basically that propagates. But But that's not the case. We do know that there are gravitational waves, for example. So gravity is dynamical.

Oh, we don't know that there are gravitons. But Well, there's

a there's a passive wave, I mean. So there's a fact that the wave comes, there's no doubt. So there's there's something moving. So that's what I mean by dynamical. In quantum mechanics, we call them made of gravitons, but Regardless, there's something moving. And so the question is how you describe this moving way in terms of classical physics or quantum physics? And And so you cannot say, okay, if electron, which is quantum interacts with this classical way, what does that mean? So that doesn't that that that is That is the conundrum. I don't think singularities is the reason I believe gravity has to be described quantum mechanically. However, since you mentioned the singularities of a black hole, If the gravity were just classical, then you might think, oh, okay.

This is bad and the Singularities are not possible, and therefore this incomplete, the theory. And therefore, one way out would be, yes, quantum mechanic resolves this this singularity. Another resolution might be as you say, for example, there could be higher order terms in Einstein's theory, which we have ignored, and if you put it back in, maybe gets rid of singularity or something. So to me, the nature of the singularity is not a convincing explanation of the existence of quantum description of gravity.

Thinking about the, other Property that people associate with black holes. Actually, Lenny suggested that to him, the singularity is almost less interesting than what he calls the stretched Horizon, in some, in some fashion in his books, hit the black hole war, his battle with, Stephen Hawking to make the world safe for quantum mechanics. He claims the horizon is much more, is much more interesting from a quantum mechanical perspective. What do you make about that? Is the horizon of of interest To those of us who are trying to unify gravity with quantum mechanics?

In a sense, I I sympathize with that view that somehow universal aspects of black Accold seem to be correlated with the properties of the horizon. So somehow a deep understanding of why and how that quite how that works seems to be A big piece of the puzzle is about black holes. We know that the nature of the singularities and the structure of them changes by little assumptions that you might make. And so that's that's in some sense unstable kind of a question. But the horizon is robust. Somehow the existence of the horizons and the properties of the horizons and What do we think about measurability or immeasurability of horizon? Those are more robust questions. So I agree with with that that viewpoint.

And I have, Juan Maldacena, who's another friend of yours, on the show, and we talked a lot about, about wormholes, and in fact, humanly Traversable wormholes. I wanna get your opinion on why do you think, someone as bright as one, who you referenced in the book. Why would he spend his time on something which is, you know, surely Inaccessible for for quite some time. Do you do you think this is a fruitful use of his time?

I think probably you ask him or you could ask him, but I think that The ideas of wormhole is just understanding wormhole is you try to understand what we think about quantum gravity can do. I don't think he's necessarily thinking about science fiction kind of wormholes even though he might even talk about those, the traversable ones. But the idea of studying wormholes, I think it was studies many many many decades ago, but even more recently in works that there was, for example, Lenny and Juan worked on And actually between Einstein Rosen Einstein, Pudelsky Rosen, Paradox, and Einstein Rosen bridge, which is this wormhole geometry. Mhmm. So the connecting them and so So for shows that certain things that might be understanding whose understanding is enriches connecting different parts of physics, Props motivates want to study the world more more, vigorously. Traversibility, whether we can send the spaceship, yeah, this and that and so on is, at this point, Not not in the cards for our universe. We don't see that under our understanding does not necessarily lend to that direction, but I think I would not be deterred nor would I find this more overwhelming reason to study wormholes. I think we should study them regardless.

Yeah. His his response to me on the podcast was that he He has found it a fruitful way to understand quantum mechanics and and, and gravitational fields. So he views it as fruitful and important, and and yet there there are criticisms of the the work on which that paper is based upon, a series of papers he's written on wormholes and traversable wormholes. In that, they rely on, results that are, are completely unproven and perhaps unacceptable by your Colleague and my friend, Lisa Randall, and her colleague, Sundrum, which are these, you know, 5 dimensional universes or they rely on, Yeah. Juan's major contribution is ADS, CFT kind of dualities. Those are things we we don't believe we live in 5 dimensions, and we We don't believe that we live in ADS. You know, if anything, it seems more likely after I read your book, that we live in a DS, not ADS. So, again, these these questions of are are they just merely, you know I I could also point to a crossword puzzle or a Rubik's cube and say, They're very challenging.

You're very smart. If you can solve them, my kids can solve them. I can't solve them. I I I take apart the Rubik's cube. It turns out you can put it back together, Take it apart and no one will know that you did it. Although I joked once, Kumrun, I wonder if you'll you'll you'll get this joke. I said I I got to the point where I could solve 5 sides of the Rubik's cube, but I just can't get the 6th side.

Right. That's a good one.

So, but anyway, getting back to this, Yeah. I mean, 5 dimensional random syndrome, you know, background space times, ADS where we don't live in an ADS. Again, it just seems like higher order adding on higher order speculation when, you know, I just I it's it's hard to to justify, and I'm not saying Saying that only as an experimentalist, there are theoreticians that that will say the same thing. Why don't they spend their time working out, you know, calculating some cross or or or whatever. I I don't know what theorists do, to be honest with you. But, but is it is it not, you know, kind of Speculative to study these things unless you feel like you're learning about math and that's important to learn about 5 dimensional, space time and ADS CFT. Where do you stand on that?

Let me say instead of that specific one because I think the the let me just change your question a little bit. The questions are why do we spend our time on theoretical questions which are not directly relevant to our universe. That's I think you're giving that through examples of, for example, 5 dimensions or Anti this interspace or this and that. So I will try to I will try to give you a a motivation for why how how how we come about. So what do we know about our universe? Well, we know it's made of, you know, particles, electrons, quarks, photons, this and that, and their forces between them. Great. What do we know about their forces? Well, we know quite a bit. We know what is called the standard model describes the forces between them.

The standard model consists of Various kind of forces, the electroweak forces, the strong forces, and so on. And within this context, we understand how these particle interact with forces. Okay. Now you come to asking why? Why do we have this particle? Why do we have this force? Can we have other kinds of forces? Could we have? So this is the beginning of a question. Could we have, for example, in our universe, instead of having this finite number of gauge billions of Blue ones or billions of photons or why do you have just 1 little photon? Why do you have only 1 strong force? Why don't we have much more? In fact, if you were to write a random theory in four dimension, which is consistent with quantum field theory, with I with finance rules of calculations and everything, We would namely say, okay. It could be like a gauge group with, you know, billions of gluons and this and that and this many particles and that many. But no. No.

No. We only see very few particles with very few forces around. Why? Okay. Now you might say, well, this is metaphysics. I have no idea why. I don't care about it. On the other hand, a lot of people have would like to have a deeper understanding of not only what are the forces And the dictionary or or geography or genealogy of the, what are the particle names and whatnot, but why? Why do we have so many few of them? Why do we have Why don't we have more exotic situations and so on? So that's that's the question. Now I'll give you a parallel question within strength theory for which we now have an answer.

You start with asking, okay. The situation we live in, this with all the particles, I don't know. This is very complicated. It's very messy. Can I idealize it? And the answer is yes. You can idealize it. Idealize, you still can be in 4 dimensions. We can be almost in flat space like the universe we live in, like Minkowski space, But let's add some ingredient which is not in our universe, and that ingredient is supersymmetry.

Suppose I say I have The maximum amount of supersymmetry to simplify my task subject to the only the assumption that I have some gauge forces around. So what is the maximum amount of supersymmetry I can have, which gives me gauge forces like Nuance and so on. That's what's called n equals to 4, supersymmetric theories in 4 dimensions. Fine. So you you restrict your attention to that. Then you ask, within this class, do I have any reason that the number of blue ones are finite? Now if you don't include gravity in the discussion, it turns out you have no bounds. You can perfectly understand these theories, and you can have a pretty large number of nuance in that theory. However, if you include the gravity, it turns out that the group choices are finite.

You cannot have our purely big group. So it turns out the rank of the group should be less than or equal to 22. So out of an infinite number of possibilities, somehow just including gravity, questions involving consistency of gravity mixing with the rest fixes what are the particle spectrum in that theory and what are the possible forces and so on. So that means the question of gravity in that context shows us crucial to answering these questions. So now you say, well, we don't need a supersymmetric theory, so why do I care about this? This proves the concept that gravity can restrict What are the possible content of the forces that we see around us? Of course we hope to extend these kind of arguments To the universes like ours, we have less supersymmetry or no supersymmetry, and that's but that proof of concept is what motivates us that yes, perhaps the answer is good. Toy model is a cherished approach in physics. We always start with saying, let's study the harmonic oscillator of this or that. That's a toy model.

The harmonic oscillator really doesn't exist. The idealized one is only idealized thought, but we always do it. That's physics. The physics is precisely modeling. So string theory is is at at the worst case, a model of what our universe could look like. And so at the very very rudimentary form is that you wanna say, okay, A structure which is like string theory, how could it potentially give a universe to like our universe? And so that kind of juxtaposition is very similar The well honored tradition of harmonic oscillator as toy models of certain physics concept we want to understand.

Is there anything, Any observation or lack of observation that would cause you to abandon string theory?

I think that abandoning is Strong words for it for me. I think for me there is right now there's no soft if you give me a theoretical substitute for string theory, which is better in some way, and has explained at least as much as string theory has done, then I will abandon. But I like, nothing nothing like this is in the cards. I think, We are if we understand that there are some obvious conditions of string theory which are, ruled out in some form, then we we go back I will go back and search my on my understanding of string theory. And perhaps we we we made a mistake somehow with our understanding. Because I think part of an issue is that we don't have A company's formulation what string theory is, so we are kind of on a difficult, platform to be that sure. Is string theory right? Is string theory false? To To do that, you have to know exactly what string theory is, and we don't know that yet. Mhmm.

So I would go back and check my understanding of the subject.

And, correspondingly, what about Supersymmetry, where would you say we are in terms of your credulity or prior, Bayesian prior on that, veracity of supersymmetry.

Well, I see that my priority right now is the supersymmetry is not there in anywhere near our energy scales and large hadron collider, but I would say that there is My high prior with the sufficient the high energy could be all the way to Planck energies. You might restore some supersymmetry. So I think that supersymmetry is in some sense a good point, but I wouldn't say that that's a necessary ingredient for string theory. We do have models in string theory where no supersymmetry arises. Some people some of my colleagues, I I don't know why they kind of say super smutty is a prediction of string theory. I wouldn't go that far. There are models within string theory which are perfectly fine and have no

I want to read as, the passage from the book towards the end about gauge symmetry. You say many important properties of particle physics involve what are called gauge symmetries. These involve somewhat different flavor, the more familiar symmetries we see all around us. With regard to translational symmetry, you might say an experiment performed in the 2 different points should The same result. With regard to gauge symmetry, we might say that these 2 different points are essentially the same point. What does that mean, and how do physicists use gauge theory or symmetry as sort of a hack to solve puzzles?

So first of all, what is gate symmetry? Gate symmetry is a symmetry that you kind of want to delete in a sense. It's a very strange symmetry. So let me explain what that means. An example of this discussed in that same chapter that you mentioned in the book, suppose you have you talk about the exchange rate, let's say, between the US dollar and Europe. You have some exchange, Like, you know, whatever $1 1.1 euro, let's say, is $1.2. Okay. Fine. Suppose the European Union decides tomorrow to But to change the to change the units of their money and the the what used to be €1 now becomes €100.

Okay. Then the exchange rate between the US dollar and the euro will change by a factor of 100. That's what we call gate symmetry. We will say in this context, there's a synergy which tells that rate has to get multiplied by a factor of 100 or divided by a factor of 100 appropriately. Is it a deep fact? Well, it's just the renaming of what you mean by your unit. That's all. So gate symmetry is like that. So it's redundancy of a definition.

It's not like It's not a fundamental number there. It's just if you change your units, that number changes. That's all. And so so gate symmetry is is is akin to that statement. Now why that should come up with so much power in terms of applicability in our universe? It's not obvious. Why should our universe be made of gauge forces and so forth? Why should we dealing be dealing with forces in that form? And this that that requires a further thought, and that turns out to be The basic statement is the is the following, is that if you look at your the property called unitarity, which is needed for consistency of a quantum theory, which basically means the probability of something happening is 1. It turns out that the spin of light particles is less than or equal to 2. And so if you look at the bosons with spin less than or equal to 2, there are only 3 choices, 2, 1, and 0.

And spin 2 is graviton, And spin 0 is like Higgs particle, and spin 1 is like a gauge particle. So the existence of gauge symmetry is needed to make spin one Here you work. So you cannot describe a spin one particle without this redundancy. So just from this picture, we are forced to have this redundancy. So I would say that The notion is to trying to make sense of a particle which has a spin one forces us to consider gauge symmetry.

And I was thinking about that in the context. I also talked about that Particular problem, with Juan, now the same, and he, he referred me also, of course, to the original. Some of the original work was, by Pia Malani and Eric Weinstein on that. A particular example of deriving, get, Maxwell's equations from it. I was wondering, you know, it's not so often I've got a chance to run on a crazy idea by someone as imminent as you, come on. But, Could could we not also use an example from language? In other words, as as Shakespeare said, a rose by any other name would smell as sweet. Is that another example of a gauge transformation and

Yes.

So is there anything we could do with it? I don't

know if you say any gauge you use. I think I I think that the main thing is Not that mention of that symmetry, but that that idea is needed for spin one to make sense, spin one particles to make sense. Spin one masses particles to make sense, need that. Now why need that? We can understand, we can explain it in the context of particle physics, but by itself, redundancy and a name should not be that important. And in some sense, Gate asymmetry is encoding redundancy.

Yeah. I had a conversation with Noam Chomsky about that as well, you know, kind of what we call something. And now in the words of Richard Feynman, who would say, you know, just because you know the name of something doesn't mean you know that thing. And I wanna get to Feynman in just a little bit. One of the other delightful things about this book, and we're talking with, professor Kunwar Rafa, Harvard University about his wonderful new book, Puzzles to Unlock, to unravel the universe, which is, just quite spectacular, is is this notion that, that there are the sort of hacks and tricks that we can use to to unravel certain puzzles, but that some puzzles by their nature, you know, have have this mysterious quality to them. And and one thing that you spend a lot of time on, which I'm very fascinated by, is is God and religion. And, I'm a I'm a practicing, a Jew myself, and I always say, I don't know if I believe in in God, but I believe in religion. I think there are things that we can that religion can do when it's Practiced, properly that can benefit a person's life.

The, the absence of working one day a week, is a very big thing in my life, and it contributes to my sanity, the Sabbath every day every week. I don't work. I don't send emails. I don't tweet. I don't text. Yeah. Those are that's kind of a commitment to a religion, if not a god. I wanna say, ask you a few questions about that.

Some of the greatest minds in history, we're religious believers. I Isaac Newton, you mentioned in the book, you don't mention this aspect of him, but his His biggest, accomplishment according to him, this is the man who came up with the Principia and met the calculus, the universal law of universal gravitation. He said His, biggest accomplishment was being Christ like. In other words, that he he never married, he never had relationships with women in that way, and that way he dedicated his life to Pursuit of knowledge. Of course, he also practice alchemy and did other things, but, what what can you say about the role of religion in in in your life, in in this book, what does it mean to you? And and obviously, you don't proselytize at all, but you seek a harmony harmonization, a consilience Between, between religion and and god. It reminds me of your former late great colleague there, Stephen j Gould. What what What can you say about the role of religion in your life and maybe even as a physicist if if that's applicable?

Well, I I did not talk about the role of religion in my life. I I try to keep it out of the public view. I keep that completely private, so I I would not discuss that aspect, but I would instead say that religion and science are Neither contradictory nor, reinforcing each other. In my view, there are 2 separate domains of thoughts or beliefs. And I just in that in the in that chapter or in that book, I try to explain why I felt that trying to prove or disprove The existence of God, the religion, and so on is a futile task in the context of science. And I tried to also, try to also say also the opposite that if if scientists feel that they can disprove or say that religion is useless, I also discounted that too by Giving counter examples including the Lamat, the understanding of proposal that the universe may have come from the beginning of of of some, primordial existence which something Einstein refused to accept and called, I do not know this how true the statement is, but The myth of that is, Christian mythology. I'm not sure if that is would actually happen, but the main point is that being motivated by religion It's not a necessarily bad idea as the example show. Newton is another example.

On the other hand, you know, some people do great without Religion, people like Hawking and so on were perfectly fine with doing, exploring their ideas completely free of any such assumptions, and they did great work too. So I I don't try to, I don't try to make a statement really about what it should or shouldn't be on my views. I don't like it to myself because I didn't feel I I have anything to offer in terms of advice or anything to anybody, so I just said there's no point me Sharing what I feel it should be or shouldn't be, but I think the listening to other scientists that who have felt strongly about it one way or the other, And seeing, okay, what does it tell us about the role of science for their life and and for religion and science, how they mix in their lives was useful perhaps. But then I also thought that it would fit with my book because, you know, it's a serious discussion in the science and religion. And the book I'm talking about puzzle sounds like a very, you know, You know, fun kind of thing is a little less less less serious. So trying to bring those 2 subjects, a very serious subject with a very casual topic, puzzles, I thought it'd be an interesting combination. I was trying to bring puzzles to to lighten up the mood, so to speak, that, okay, there are these serious discussions, but let's talk about puzzles in this context, and I offered a few puzzles. Some of my favorite puzzles are actually in that chapter.

So so I think, I I just use it as a springboard for discussions, really. I didn't want to offer anything specific. But I think I think the main thing I wanted to convey in that thing is we should be tolerant of viewpoints. And that was that was the that was basically I was driving in that chat.

Yeah. We hear a lot about the hostility of science to religion. I always point out that, The word Torah, which is a Hebrew word for the Bible, the Old Testament, it doesn't mean knowledge, which is what the word Science means in Greek. Science in or Latin rather means knowledge, and Torah means wisdom and and teaching. It, so There really are, as your late great colleague, Stephen j Gould, would say, non overlapping magisteria. They don't necessarily have to interfere with each other. Now I always also point out that in the book of Genesis, at least, again, I'm not prosthetizing. Again, I I consider myself a devout agnostic, which is which is something I think I have in common with, the late great Freeman j Dyson, who was a friend of mine and a friend of my show's man that many times that he appear on it.

He used to say, well, the the existence or lack thereof of God is a great mystery, and scientists love mysteries, and we love puzzles. And maybe you can solve it, maybe it's a mystery or maybe it's a puzzle. We don't know. But to give permission as you do, to at least consider it And and have an eminent scientist, such as yourself. Yeah. It's one thing. If I if I try to defend religion, but someone of your stature defend You're not right. Yeah.

Well, I'm just saying it it's delightful to have, to that you don't, you're not scared of it and that you Are are quite, are quite comfortable. But, again, you're not proselytized. This book is not a book about, you know, why you to believe in a particular religion, whatsoever. So I I just wanna commend you on that. I found it so refreshing and and delightful. I wanna talk, just in the Last few minutes. I know you're, super busy today, but there are, many mysteries that I think are in the In the theoretical physics world, there's a particular researcher who's a friend of mine, a friend of the show, her name is Sabine Hassenfelder. She's in Germany as a research scientist, And she made a video last week, kinda criticizing Lenny, Susskind and others and even Hawking, with the black hole information paradox claiming That in her words and she's had nothing much good to say about physics, theoretical physics' progress in the last 40 years according to her has been stagnant.

But anyway, she criticizes the black hole information paradox as, as the biggest overhyped, bit of of physics That's ever come along. I I think that's a little bit over the top, but her point is that these, the laws and so forth that govern this Are completely, you know, kinda more or less pedestrian. And furthermore, they can't be solved because we don't know if Hawking radiation exists And and we can never measure it. So a lot of these things, even from a pragmatist point of view, are some are somewhat pointless. Maybe this is, Relevant to what we talked about earlier. If so, we don't really have to dwell on it. But, why why do you think that there is so much attention to things like, like like black hole, information or the multiverse, which will maybe close out the scientific portion of the podcast with. Why is there so much interest in that? WERM and the double slit experiment, EPR, and all these things.

Why does the public get so wrapped up in this, and do physicists maybe do a disservice by by overhyping things like this.

Before we get to this, I think people, who talk about subjects like black hole and so on, and Especially criticizing or whatever from outside, they could do that perhaps if they had the scientific standing. And by that, I mean not just to say, well, I have read physics, I've got my PhD in physics, therefore I can say whatever I want. I think If you have not done sufficient research yourself in some direction to try to criticize somebody else, I think is a little bit of suspect. So that's some of the comments So it's like throwing a throwing stone at a building or glass glass or glass things because you're not inside, and so that to me is a bit of a childish reaction. As far as more seriously, okay, so what it is why is it that we think is an exciting subject and so on? Well, it's exciting because because it was a mystery. It's still to some extent, a little mystery. And mysteries always guide new physics. And so for us, that's the reason we study black Well, of course, black hole sounds, you know, captures one's imagination.

What if you fall in it? You know, why is what if a black hole is near us and this and that. So it can easily captivate public, but that's not necessarily the reason we are talking about it. The reason we are talking about is that many of the mysteries of Fundamental physics seems to be wrapped up in it. And that to us, that aspect to us is what is fascinating. And, yes, Of course, it will it will be interesting when you want to describe what we are doing to general public to explain that link because the general public can hold on to that Concept as being interesting because they can feel it. Oh, black hole, that's fun. That's cool. That's strange.

That's exotic. Let's see what we have to say about it. So So to say that we are we are excited about it is not because we want to kind of, get the public going with excitement. We are excited about it because I think Many of our deep questions are related. Enigma black holes, and a lot of them can be reformulated as properties of black hole. You lose information. If you throw something into the black hole, can you figure out later on what was it that you threw at? Or after the black hole evaporates, there's zero information. That's the information loss.

In other words, understanding that process tells you the meaning of fundamental meaning of whether or not theory can or cannot lose information. Black hole is a way to act ask that question, and that turned out to be deeply related to many other aspects of the theory. So for us, It is that aspect. Now to undermine it, to say no, it doesn't radiate or it doesn't radiate, we cannot measure it, therefore it's a bad question, all that, is again the kind of things that It sounds like this parallax that you mentioned, this experiment that later on was able we were able to do, but right now we cannot do, Was that, oh, yeah, are the stars really, you know, far away or infinitely far away? What is it? What what what is the connection with with with why don't they need to move and they indeed move, they just have no enough not enough accuracy. Same with black hole. If you try to say at that time, Thinking about them at finite distance on has has a meaning is would have sounded crazy during the Greek time perhaps to some people, but we now know that's not the right way of asking. Of course, the people who said that that's a bad question to ask because you cannot resolve it, we'd have 1 in the short term, because, yes, in the short term, you cannot measure it. The parallax was not possible to measure.

It was was it a bad thing to raise? No. It wasn't a bad thing to raise, so we have learned that through history, what we should pay attention to. And I think that, people who who throw stones rather than alternatives are never the ones who create the new science. And so There's one thing of it, constructive theory to say, oh, you know what? Your theory typically wants to have, let's say, 5 dimensions. Why not Four. Okay. Let's try to find the model why 4 dimensional space time arises and so on. That's a good question.

We are not saying we have understood that. But to say, oh, no. This is bad. This is bad and so forth without any given alternative. I think it's just disservice to science. And I to be frankly frankly, it's just, I think to try to, get publicity in the sake of from the sake of publicity to try to say something. And To me, controversial statement just to attract attention, I think, is unfortunate.

I mean, to be fair to her, she does say that she's written papers about the subject herself, but, yeah, she's, Yeah. Certainly, it takes takes out a lot of, aggression, but, no, I think it's it's important to hear the voices as long as you say they're acting Towards a, maybe not necessarily conciliatory, you know, perspective, but a congenial perspective. They're trying to do something constructive. I I agree with that. I wanna, conclude the scientific portion just asking, along the lines I talked with Shelley Glashow last week and he has a wonderful book, called Interactions written in 1988. And in that book, towards the end, he has a series of of questions for the future That he suspect can be answered in the superconducting supercollider and and other things, of course, that wasn't to be. But the the question of, Something like the Higgs, he he just assumed that we would understand the mass know the mass of the Higgs in not too distant future. Yes.

We didn't learn it from the superconducting supercollider, We found it out eventually, and, but he he goes through other other questions, which in my mind are much deeper, and it was Quite a treat and a delight for me to go over this scorecard with him and have have this eminent, you know, Harvard professor, Boston University group, give a score, you know, f f f. You know? Because some of the things that he listed on there aside from, you know, our neutrinos massless, which we now know, yeah, Which we didn't know back then that they're not massless. At least 1 of them is not massless, maybe 2 are not massless rather. But nevertheless, why are there 3, you know, generations of, of Quarks, why are there, so many fundamental parameters? Why are there so many particles? What is the, you know, fundamental dimensions of space time? Those things we we haven't really learned much about, and I'm not gonna ask you to comment on those. There was 1 or 2. As I said, the Higgs, wasn't even mentioned, but but the neutrino mass, being nonzero was, the protons lifetime, No. He thought, you know, at that time, it was, like, 10 of 28th years. Now I think it's much bigger, maybe a 1000 times longer, and that had some implications for supersymmetry.

I I wanna ask you your scorecard. What would you give, our understanding of things like the multiverse, the string landscape? What kind of grades would you give to such subjects currently, and then what kinds of things would you want when the next edition of, of puzzles comes out, Hopefully, in 30 years after becoming an international bestseller. Thank you. I think that, the scorecard, The the the

score you give to something is based on whether or not good attempts have been made and how much progress has been made compared to the difficulties ahead. So when you measure it against how much complication is on the way, I would give it a plus. If you ask me It's a scorecard is to try to measure how close we are to finally accepting it, I'll get it f or very close to f. So it depends on what is what is the scorecard for. So we are very far, unfortunately, still from making a prediction which is really precise and quantitative, and we can't say this It's a definite prediction of string theory is that it's either this or the whole thing falls apart and it's very precise. We're not there by far. So so it depends on that. I would say that as far as the scorecard, I will give a I would view it as what is possible to do in terms of theoretical, and huge huge things have been there.

I think to underestimate the dualities, that meaning of the dualities that we have learned. It's it's remarkable how much we have learned. For example, you mentioned this question that Shelley raised. We know the fundamental dimensional space time. We have learned something about this. We have learned that's a bad question. Why is it a bad question? We have learned that that constant question depends on which viewpoint you have. There is no fundamental answer to that question.

It depends on which parameter regimes you look at. So the dimension is not a fundamental concept. That even that realization that you cannot settle that, that that question is a bad question. It's only in 1 corner you can't say it's this, The different corners, the different numbers, so it's not an invariant concept. Those are progress. So for us, we have made progresses in that form. So conceptual progress is is is what I would say is certainly has happened. Holography is another amazing conceptional progress.

Pilots more generally is. And so I think we are learning quite a bit. I think Progress is going to be not super fast, and if we are measuring it against the yardstick of connecting to experiments, But if in terms of what new things we have learned, it's huge. We have learned a huge amount, and it continues to unravel.

Kamran, thank you. I'm gonna if you have just a few more minutes, I would like to ask you some questions I ask all of my guests on the show.

Is that okay? Sure. Please go ahead.

Great. So the first one In, in Judaism, in the Hebrew, language, there's a concept of what's called an ethical will, And that differs from a material will and that it is not bequeathing monetary or material objects To your offspring, but instead is bequeathing wisdom and and and discoveries that you've made outside the material world. And it's meant to benefit not only your biological children, one of whom put me in touch with you. So I wanna thank that particular Vafa son, for putting me in touch through with the magical medium of Twitter.

It's beyond my son. Yes.

Yeah. So thank him very much. And when this comes out, we'll send it to him to share. But I wanna ask you not only for for him and his brothers, but but for the whole world, what would you put in an ethical will, a a will of wisdom, Not only, for your biological children, but for your ideological children of which I count myself as as 1.

Thank you. It's a great question. I would say the following, and I was paraphrased by saying where this wisdom may come from. It's from the realization of the importance of duality in physics. What we have learned, and I think this is a broader application, is that the best viewpoint about the subject depends on the question being asked. There is no best viewpoint, and that best viewpoint is subject to the question. So that also opens up our mind to be open minded, That we should not say this is the way to look at it, everything else is bad and so on and so forth. We have learned that contradictory sounding views are sometimes necessary to understand the subject.

Contradictory sounding views which are nevertheless consistent, but in a subtle way Turned out to be the beautiful aspects that dualities have, has shown can happen. And so in my opinion, openness and The fact that duality shows us that multitude of attitudes and views is important to appreciate and connect, not only in a scientific context, but in in a broader Human society last week, I think is a good could have a good applications.

Nice. So I don't know if you're a science fiction fan, but, Shelley is a huge science fiction fan. And I asked him, about, Arthur c Clark, who is the namesake of the center that I act as a co director, and he had, he had written the the book on which the movie 2001, A Space Odyssey is based. So Have you seen that movie or are you like I

have seen it.

You have seen it? Yes. Good. So you might remember in that in that movie, in the opening scene, there are these primates in Africa And they discover this obelisk, this monolith, this black ominous structure Right. That's placed there. And then later, they don't know what to do with it, that they hit it with a bone or something. And then later, you see it's on the moon and astronauts are encountering it. You know, they've obviously developed. I wanna ask you, and it's sort of meant as As a time capsule meant to be discovered when humanity is ready for this knowledge, I wonder if you knew you could make a 1000000000 year long lasting time capsule, What would you put on it or in it? What would it what would it encapsulate?

I think many years down the line, what I would think now is probably gonna be irrelevant. And so, so one of the things I believe in is our knowledge is continually evolving, and almost none of the things that we think are correct now is gonna standards to be exactly correct. They're gonna be good approximations, they're gonna be modifications and so on. So to try to put something So solid for future, I would feel hesitant for this for for that reason, if nothing else. However, if we wanna brag about something we have learned in our society, in science, You know, you can put some aspects of, I don't know, this and that theory to to show that, yeah, we have a string, for example, we have understood this much. Of course, 100,000, 10000 years down the line, they might laugh at us. Okay. They understood something, not too much, but okay.

Just like the way We look at what, you know, scientists were doing 3000 years ago. We don't we don't think they were really, you know, at the cutting edge of of things. Now we kind of say, okay. That was fun. They were smart people, but maybe not for answering this and this and that. So I'll be hesitant to to put my word of wisdom in any form to for the future Generation, I hope that they will not laugh too hard at this. That's all.

Although 2 at least 2 ancient Greeks actually, 3 ancient Greeks, Plato, Archimedes and Aristarchus make very prominent appearances in your delightful book. Yeah. I this is just what you said reminds me of what Richard Feynman said about He I didn't get to ask him this question, but he said, if in some cataclysm, all scientific knowledge were to be destroyed and only 1 sentence passed on to the next generation of creatures, What statement would contain the most information in the fewest words? I believe it is the atomic hypothesis that all things are made of atoms, little particles that move around in perpetual motion, Attracting each other when they are a little distance apart, but rappelling barely being squeezed onto one another. In that sentence, you'll see an enormous amount of information about the world If just a little imagination and thinking are applied, and, of course, this is the Arthur c. Clark Center For Human Imagination. So I've managed to unify Fineman, Plato, circus, Aristotle, and the great Khmer and Baffa who will go down.

Sentence to that maybe.

What's that? I would

add maybe one little footnote to that sentence. Go for it. Attempts and extended objects like strings.

Ah, okay. Okay. Not a bulb. No. As Yogi Berra said, the great prognosticator said, it's Difficult to make predictions, especially about the future.

Yes. Exactly.

Okay. The last sentence, the last question I ask all my guests, Cameron, Is, relates to Arthur c Clark as well. He had these famous three laws. One of which was any sufficiently advanced technology is indistinguishable from magic. He had another saying called his 2nd law, which was that for every expert, there's an equal and opposite expert. And then his 3rd law says, the only way of discovering the limits of the possible is to venture a little way past them into the impossible, And that's the origin of the name of my podcast. I wanna ask you, what advice would you give to a young, Comran Bafa? What what thing Seemed impossible when you were a young person. But now because you had courage and you went into the impossible, now seems doable to you and On

if only in hindsight. To me, math was always always, attractive ideas of the math hanging together, The beauty beauty of Euclidean geometry, understanding the relation of simple objects. And it also was always fascinated by, you know, things around us, like, You know, how the how does the whole thing work? What why there are atoms? How does this work and that work and this one? And these 2 things sounded to me Like separate universes like math, Euclidean geometry and so on is there, and then you have this real world that's around us, has nothing a priori to this map. To try to bring these 2 universes together or closer, and so I noticed not only that there are already big links between them through centuries of work when I Got to learn more, but then I felt could they become even closer and in fact indispensable for one another. And so when in the context of String theory, the 2 have come together in such a way that you cannot do one without the other. You cannot do physics without math, and now also you cannot do math without physics. So the fact that these things can be combined is something that is really pleasurable for me in terms of my own interest, but I think anybody has their own interest and I hope that They don't they everybody follows what we are deeply passionate about, and, you know, there are things which are fashionable today or May not be fashionable tomorrow and so forth. But whatever you're excited by, if you follow it regardless of being fashionable or not fashionable, it gives you pleasure.

And Usually by that action, you're thinking deeply about it, you will convey something important to the rest. So I think Follow your dreams is is a cliche, but I think is a correct cliche in this case.

Yes. And as you say in the, beginning of the book, you dedicated to your parents, as well as your family, Simeon and Jabad, for nurturing your curiosity. And I think that's so, delightful that you, have now shared this curious, the investigator, perspective that you bring uniquely. You're a towering figure in science, and and I I really appreciate Your time I have to go now to paint, the surface of Gabriel's horn. It's gonna keep me busy. Right?

Yes. It will. A very, very long time. Maybe quickly time, but it's a pleasure, Brian, to talk with you and the, very enjoyable, discussion and questions. Thank you for having me on your