WGBH Forum Network; String Theory and the Universes Hidden Dimensions; Harvard Book Store

And now it's my pleasure to introduce this afternoon speakers Steve Naidus is a prolific science journalist currently serving as contributing editor for Astronomy magazine. His articles have appeared in numerous science and general interest magazines including nature New Scientist Scientific American and the Atlantic Monthly among others. And he has been a collaborator and author on over 20 books on a wide range of scientific topics over the years he has been a research fellow at a number of institutions including the Union of Concerned Scientists MIT the Woods Hole Oceanographic Institute and WGBH nova. Now is the chair of the Harvard Department of Mathematics where he has been a professor for over 20 years. His work in differential geometry has put him squarely in or in the intersection between mathematics and science mathematics and physics where his proof of the colossi conjecture and the related manifolds have been in fact instrumental in the study of string theory. His prolific work has earned him numerous prestigious fellowships and awards including the one thousand nine hundred two Fields Medal the most prestigious and well-known award in mathematics

a 1997 National Medal of Science and most recently a 2010 Wolfe prize in mathematics. Their new book The shape of inner space takes readers to the very border between science and mathematics explaining the role of geometry in string theory. But more broadly showing how geometry is fundamental to the underlying nature of our universe. Well now please join me welcoming Steve Naidus. Thank you Rachel. And I think everyone for coming. And also the Harvard bookstore for hosting the event this is the first kind of the kickoff for our new book. And I'm glad it's here because Harvard bookstore has been my favorite bookstore for many years. Well it's been a. Long haul. Four years ago I was contacted by a physicist at Cornell. The name of Henry Tai who told me that his friends in town you know wanted to write a book. And I'd heard the name before

but we've never met and I was kind of busy at the time but I thought well why not call Harvard's close enough. I live nearby in Cambridge so I called him and he said when you send me something you've written I send some articles. I called up a human half hour later said when can we talk. I said Well how about now. I came over his office and I use the last name you know he's a forceful personality kind of rolled up his sleeves he said let's get started. And we started working on the book pretty much. Right then and. Remember you know in that time there's been a lot of there a lot of long nights at the Harvard math department where nobody was around except for yes graduate students and were often nodding off and it's after midnight. I'm nodding off or hears and I'll say maybe we should stop and as you know keep going keep going. And so we did

took a little even though despite the fast heart it took a little longer than we expected. But I like to think that's not our fault it's the universe's faults. It's just seems to be very complicated now that perhaps we just need to understand things better. So tell you a little bit about what the book's about. And I can describe it in different ways. One what you could say is them about the mathematics of string theory. It's also a book about my co-authors ideas in mathematics particularly ideas related to what are called complex multi-dimensional spaces particularly the six dimensional spaces that are going to be talking about more. And so also as Rachel said it's a book about understanding the universe through geometry. And that's not a new idea. I don't know when it started but I know that Plato says

several thousand years ago subscribed to it and actually believed that the entire universe and all its constituents could be described by a fairly small set of geometric shapes that are named after him called platonic solids. Einstein also put some stock in the idea of Einstein's equations of motions are complicated nonlinear equations but one might simplify them perhaps grossly saying that geometry equals gravity. And the idea there was that set of thinking if gravity is the attractive force between massive particles. You could think of it as the curvature of spacetime or the geometry of space time. I went to the presence of massive particles and string theory which this books is about to a large extent takes that ideal a little bit further and could be simplified by an equation I don't want to burden you with equations but the equation would be.

Geometry equals physics and I and so that and that actually brings us to the shapes that are the subject of this book and we call the shape of inner space and they're named after my co-author. Columbia manifolds. I guess just a brief word about string theory. And it's a complex theory if admittedly and I don't claim to understand it fully but at its root there's a fairly simple idea is that everything you see in you know in the world everything in the universe. If you break it down to the smallest level it's a string in the same kind of string a tiny string too small for us to see could be a strand or a loop and the movement of these

strings in the wiggling in the vibrations of the strings. In space and I should say not just the space we know but in string theory that the space is a 10 dimensional space and it's not just space but includes time. So as the vibrations of these springs strings rather than tend to mention space time can actually give for a con for the diversity we think that there is in the universe that is all the forces and all of the particles of nature boil down to this. But as I said before it's not the space that we commonly think about sort of the three dimensional space left or right of backwards or forwards up or down. There's more dimensions to it and it has to. So the book is A. Lot about what those dimensions are. I was at the beach this summer and talking with a friend about it you know he said

what's it about. And I said well there's higher dimensions and he says oh yeah I was talking with my daughter about that and she said I know what the fourth dimension is. It's smell. That's not how Einstein had it but it might be on the right track in the sense that there are dimensions that we hadn't commonly thought about. That could be important. So in string theory theory we have the three spatial dimensions that we know and time that's counts for force so there are six extra dimensions that we cannot see and where are they. Well a string theorist would say they're everywhere hidden away in every point everywhere you point to every every place you can imagine. There's there's also this tiny six dimensional place tucked away and concealed from our view.

But it's not just the six dimensions it's important in string theory. They need to have a particular geometry or a particular shape to make the physics right. And some string theorist would say that if you figure out what the right shape is the right geometry you have pretty much everything that is all the particles and forces of nature. So the question is what is the shape or what is the shape of inner space. And we don't have the answer but the shape that seems to work the best so for is the thing we're calling a clubby a manifold or a club space. And that's sort of it very. At the heart of her book and nine hundred seventy six. My co-author yeah prove mathematically that these shapes these clever shapes exists. He didn't actually set out trying to do that. He

initially was convinced that these spaces that had been his existence had been conjectured by it and did you know Calliope. You thought that they could not exist. And many mathematicians thought that as well. Yeah I. Tried to prove that they could not exist and tried really hard and failed and after failing he realized that he must have been wrong that they were they must exist and then he turned it around and proved that they did exist. And after he prove that as I said nine hundred seventy six he had a deep conviction that this must be important for nature must be important for understanding the universe. He didn't know exactly what that was but. Shared his view with his many physicists who would listen to him. And eight years later in 1984.

Some physicists including Andy Strummer who works across the street at Harvard. Servitor came across as proof in a mathematical journal. And he's a physicist not a mathematician didn't wasn't sure he understood it well and he contacted Yeah and pretty excited and say Is this what I think it is. And after some discussion you know I told him that yes it was what he thought it was and strawman Jer and some colleagues realized then that this six dimensional shape is clever you know manifold might be the shape that they had been looking for in string theory that could explain the forces and particles. The story is not the case is not closed at this point because if if you limit to a clubby are manifold which is not yet certain. That's not just one shape it could have a very large number of possible shapes and maybe even infinite and that question is not yet settled so there's still a lot of work on that front to do

rather to be done. I hope this subject matter doesn't sound too intimidating. Yes we're trying to explain the inner workings of the universe. And that can get complicated. Perhaps you can take some comfort in the fact that one of the book's authors and never took a college math class. I don't have to say which one that is. I would say this book is not string theory for Dummies and it's not the Complete Idiot's Guide to string theory. And those are two real books. We're aiming a bit higher than that but I think an average civilian like me can understand it with an above average effort. Because the final point I want to make is that string theory is the name of a place is a theory. It's not proven to be the theory of nature in fact far from that.

But nevertheless that the mathematics that underlie Why is it in which we go into great lengths in the book. Much of that has been proven and is rock solid and that suggests to many people including my co-author Yeah that there must be something to this theory. And as to what that something is I'd like to turn the mike over to my co-author Yeah who may talk about that as well some other ideas. Thank you. Well Fast see if. Thank you all for your coming here to listen to me and see if. So Steve just mentioned that we met about four years ago that I decided to start the book with him you needed it. The reason I found out. The reason behind it was Steve of course is a singer and writer. No question about it. But more importantly he doesn't know much

math. And why is it important because I think if a repetition or even a fetus's want to write this book they will write too much technical detail to the extent that no general layman can understand a book. So he says he does not know as much as a professional mathematician know about math. So I have to explain in great detail how to convince him what I know and then he has to be able to write a uniform that you know laymen can understand. So I believe to a large extent and research it and I hope you take what about two comments yourself. Also I just say that this bill is different from many other books. I looked at many folks who write about math in general. They try to hire you. Most interesting part of mathematics. Either they write something which was discovered off

one got a feeling that years ago or so that we know what you see in high school or just write some numbers and couldn't really try to Carney's people that use what mathematics is about. Here we try to write what from TDL mathematics yes. And so as it is you you go for the spoke and understand about a boat. You would know very much about modern mathematics as a result you may be slightly more difficult to read than out of books but on on hand I fraying since Steve who did not know that much math can go up and even write it in such a nice way means that you take need to be more well for you to understandable. But more importantly one of the other reason I want to write about this book is to explain to you. They waved at him after he shook so very much different from many

movies books about mathematics. I remember I was in an airplane watching the movie at the wheel Hunter saying about MIT it was able to feed a guy who has a fuse mantle which seemed to be using portable. I think. We have learned a great deal from the great mathematicians in the past 2000 Yes and they are all genius. We ecumenism Skeel and order genius of this great man to be able to go on. I don't believe any janitor can Moscow all these ten years you know matter of a few hours and we need to study red hot although we have a lot of fun. And so. Also there are also folks who want to say that only people who have some mental problem could be a great my

physician. And. Of course I hope I can quote you on this book. And when I retire I'm a chairman. And so we have just signed he's one to understand us all. Many important ideas he signs for the way that we look at you from mathematics point of view. Some of them were difficult to go through but yet we overcome it. So we're hot on it. But some of them after we understand you so much how this ball is about my own experience about how I start from a college student which at the time I was in Hong Kong which I know where you to about math. When I come to Berkeley to study I learned much more. And I struck Oh for all the difficulty. For many steps for example I really did not know

much about physics and yet during the course of my research I Len that I need to know more physics in order to go on. So I got to learn it and I go through many different universities and many good friends including Komroff who are just good friends in physics department who I learn a great deal about probably all metaphors. Now he probably knows more than me. And I have many good friends that I cooperate with and in this book we explain how FMF Titian. I was working with people different disappearing and we were out to get a you know rare nice friend and he was extremely productive both for a subject like physics fundamental physics general right to a T.

Or to mathematics yourself. As Steve mentioned many important discovery in string field he may not be proof in the lap immediately at least not in the next few yes but. Demonstration. And then you speed Asian. All what he can do to MF. Yes extra ordinary. Probably never happened in the history in mathematics in the last 2000 yes. That nature also a subject in physics has so much impact on mathematics persay that many may read difficult questions in math some of them an hundred years old problem was solved only because of the inspiration that come from string for union. Now I just make it clear that this is mathematics that can be proved independent of whether string feeding is right or wrong and resell is so deep and difficult it is

impossible to believe that string Fredy is completely out of nowhere. It may not be x. You may not be able to explain exactly what the string feeders want to say but you better explain something interesting. Because the coincidence cannot be. That dedicate more than one or two problems that I solved in that way. There are numerous problems that will soften in based on the inspiration of a cornice in string Fredy and I'm mad that I being caught up with them for the last 30 string feed it a P.S. As I said as a refutation. I never thought of the SoCal copy I might have thought has anything to do with physics at the beginning but as Steve said that I always felt that is so beautiful and interesting. You must have some role in the understanding of the physics of nature. And you did you know a P.S. to my great surprise after

I proved that such a thing. And I should say that proving Caesar such a thing is actually a red difficult toss. Mathematics mathematically speaking we never fought that you should axes and in fact it was a pee rading believe that such an object cannot exist. And I try too hard to prove it until one day when I produce an example demonstrate that such objects do not exist and that I was challenged by who has a copy say that you should write down what you claim you know it to me that the opposite us NICIAS. So I start to write and I cannot reproduce the example that I fought and just hope we have sought at least two weeks. I could not sleep day and night in order to produce such a such example after such a fertile sure

icon is my show that mathematics cannot cannot beat that dedicate that whenever I fought. I have to see it to find such a simple document broke down. So I finally decide that it has to be right that such a space exists. And actually it depends on much more. F I stand what I thought. Case female Yes sot it documents and many days of non sleeping actually working with many friends and understanding a subject that was not so familiar to the friends of traumatized at that time. Now me I have to understand a great deal about differential equations and that was not so popular at that time and I got where hot fun to be able to hold nationally in Fiesta. Right after I got married I proved the finish Yes I was so pleased to know such a large set of examples came

through to acces to be X and I was very pleased by it because you immediately I was able to make use of this object to prove many important freedoms in mathematics by yourself independant physics and this whole experience to make me feel very excited because I feel that. Constant contact with nature will help mathematics a great deal. Many of the ideas you need from nature and nature is beautiful. So we see beautiful mathematics of it and the whole principle I've been teaching myself in the last 40 Yes and I'm still it still holds well into acting with physicist even with engineers as fast as true for you and nature. Natural true

and yet the mathematics that come out will be beautiful and I'm never hesitate to fing that the mathematics to all of this. Lively Shack will be useful. Back to nature to describe nature and in general relativity in string for uni and I hope my post with Steve can show the journey that I have gone for all up and down up and down some takes. Nighty night Thomas fail before I see it and at last. Tom and when I see it of course is very nice but the process of doing the research has been very gratifying. Although you fail you in between. But each time I fail I learn something interesting. So does one on the motorways and I wrote this book with Steve. I want light to sew my photo. My physicians my students all

my colleagues to understand that their research just being done by score us remember writings and I hope that food you can understand better that we are not we're not real just stand up press and squat our scientists but we need to be different angle from people who does experiment for us. Number us fake US and all those things on natural experimental data for us and thank you. Many people asked me oppression what is cobby L-Space including my children and it's not so easy to to explain but let me put it this way. So we have phase space just like the space we see. Now the obvious on the equation Einstein tells us space Tom.

You just described by some curvature and the curvature some part of the curvature is described by the matter distribution in the US so. But not a whole is described by Metis only part of it. Now we could have deaf or a space time where matter does not exist so its wreckage and yet the coaches to death are not complete is trivial. So a commie L-Space is one of such space. Yes vacuum and no matter. And yet the quality is still less strong. And so this is a short listen to the unsightly equation. And yet it has some internal symmetry and does internal symmetry is call supersymmetry by the string for years. So a wrecked him space. Tom we have some super symmetry.

And yet while he's not there I missed you still there. It's called Krave L-Space putting in that way and this is one of the building brought fall string for any where physicists want to give it up. A fundamental fear that come by quantum physics. We have General Relativity which is the dream of on a stone to do that and they fayne in terms of all the particles flows by small strings and then you're studying a quantum theory it is based on that and dad based on that you can derive a space time which satisfy you creations that a copy of space should satisfy. So it based on that you can describe the particle Mosse and the basic constants of well you know which copy of

space we are choosing but as Steve said to many of such problem spaces and yet still a big cost for us to figure out which one is the one that we will space off. Well I'm straying Freedia as we are describing is not describing the Big Bang but some people has been working on it. So what energy is he keeping the mosque as one Sanches Eagle Ramses Square. Yeah so but the whole you need data puppet is a major puppet is being studied and I'm no country was in the dock. Well no I mean we have to set you right. I understand you question my quality and I'm sorry because it does not you and dad. Attempts to give pet a base and to which we involve the curvature tensor. But there has not been done successfully competed

well into many kinds of mathematics. One just dumb Afridi number Fredy it does not is not guided by physics. Numbers are beautiful and you can count on it. But on the one hand more than DRAM on all number Freedia a great deal a great policy it depends on geometry geometry intuition and documentary intuition has something to do with physics intuition. And it's true that my fish and dusty read of extra free to you by yourself. Some of them has nothing to do with nature and those parks actually eventuate disappear in you know maybe in a bookstore but not in reality. Those which will come back to nature becomes important. For example when quantum mechanics was developed there was a concept of space and that was developed

by yourself for quite a while before. Quantum Mechanical physicists use it. So when you come back it becomes extremely powerful because now you get new intuition that come from physicists and it becomes much richer. Now Mexico is much richer and for physicists they cannot write we don't know math. I mean. So the founding fathers of quantum mechanics can write down some new creations but they need to solve the equation you know to be able to understand nature by let me show you venture a you have to know what a brave behave and you know all those things. And that depends on references and show you some drawing which you and I started right down to you crazy idea and we still want to solve the equations and you want to see what the equation tells you. And there has to be traumatized and we learn a great deal from them. As I said in the last 40

years most of my intuition come from physics in many ways and yet I'm still to a math and you know I learned a great deal from my friend. I never mean understand him. But still let's say the ten has any interest and I come from him. It's good enough for me to do it. So you see but on AI you comes off me because he doesn't need to know some math. So the interaction has been extremely fearful. Yeah well right from my point of view first of all when he read of his Newton's law one of the great important tool he needs is calculus calculus was one of the most spectacular discovery in human beings in the suit I season. And she was able to do a quick calculation based on

Calculus starting from with simple rules that he put down we don't know that calculus he was he would not be able to do the same kind of Calgary's and lead time that we compete take the planet move one which is read data came and complicate it. Coming so mathematics has already paid a very important role in fact I think there was a big fight between Newton and Hawke on the discovery of the Newton's law you know qualities of forces and one time to divide by a square. Newton High won the whole battle because he knows calculus. She was able to use the law to calculate it kind of go on and on and I should say that. I remember Crawford asked me this. I thought it would be from Keppra who is who. Who was the first guy. Why not a fresh guy who has done a great deal of operation on a compressed law which was important operation for

dependent movement until Newton actually right on it all it takes of us. Yes 200 yes. So there was a long time before a new fundamental law was complete understood. I think strong free to just talk about 50 s and string fetus. If yes right. Suppose we did describe the nature. Of the universe which is extremely compressed and complicated thing and I think many people are getting weary imposed and impatient just to try to understand the fundamental law of nature which includes everything in a matter Freddy Yes just a mathematics involved. Yes so come past and difficult to understand. Now along some very important basic physics intuition. But I fing. Sting free to hazard as Afridi has no contradiction and completely consistent. It's marvelous already. After all in the nature of beatings and Breeders a US set off to have a feed it that does

not contradict each other is absolutely spectacular I feel already well after experimentally trying to get a Nobel Prize everybody tried to try to make sure that you have debt and so the experiment may give some insight and. Comment on that just before the next question. Experiments at CERN at the higher change on Collider are not going to prove string theory is right they don't have a chance of doing that but there is some likelihood of proving things that are consistent with string theory like the discovery of super symmetry particles and perhaps evidence of. Higher dimension seeing particles that may disappear into we don't know where. And so there and then and so there's that possibility. And that wouldn't they would not say prove that string theory is right but we do see

more some validation or at least confirmation of ideas that are consistent with string theory rather than brute proving string theory out right. That's going to be a long process and you know it's going to take some patience some people are impatient and aren't willing to wait. Yeah my friend she you know she knows the way to derive it by calculus at the same time he tried to explain it by elementary drama teacher. You kept a secret she tried to explain it in most any mentum and I've seen some proof given some calculation by Newton. It was spectacular. Well yeah and I was amazed how she'd come up with those. And so I'm not surprised he did not use protocol he gets to do it. I do but I'm not Newton. But as far as I know she does calculus as she has major rep and two of those companies.

Well I actually probably when I got out of college I thought I might be a scientist and I was employed as a so-called scientist. I mean doing doing research on environmental issues and policy matters and thinking that I would do that for a little while and then go to graduate school. Probably some area physics but I didn't know then what area. And while I was doing that I I wrote a book and then wrote another one and then I kind of ever got into science and sort of stuck with the writing. See it was really a great writer. I'm reading a book again and again I was amazed how well he writes I would not be able to do anything close to it. As for myself I'm still working on mathematics related to string for you. So in particular probably all matter of course there are many many deep mathematics still related to

the subject which has not been discussed and in fact go to many different brands of mathematics including the Mafia on this whole subject. Some of them eventually come back to physics and also working in General Relativity classical generated beautiful somethings. Well there are many many problems you met him at a speed and problems you can create problems by generating problems by using a computer. The question is whether it interesting or not. Interest meant many Methodism to no concern for a problem to be interesting. Some of them do but many of them do not show you these depend on your taste in physics also damn many many problems you can come up on day to day life. While it depends what kind of faeces you are I can I suggest you can isolate time. So for me yeah. You know naman to just as I said at the very beginning.

To know what a mathematician lies to do and the journey that I went through myself from not fame to something interesting. So I generally make understand that you can skip the part which is more technical so to speak. Just shows how I struck the floor many different ways of understanding deep mathematics. So you got some feeling about how my physician. But also I faint if you read into it. You know we need to spend a bit more Tom. You understand more of mathematics and food that you can understand the beauty of it. You know they both were right. Well I'd say that you know that certainly the original aim of the book was to write a book explaining the mathematics that underlie string theory in a way that the you know an educated reader could understand my

motivation personally was that I had read several books on string theory. And when they talked about shape like of the club you know giving rise to the giving rise to particles and forces and usually a popular discussions never went much further than that. And I found that unsatisfying. So I said we're going to do something here we need to take it as a step further or a step deeper. And in a way it's like to open up the hood and look inside and you see these complicated 6 dimensional shapes with all kinds of folds and curves and holes in it and then trying to put that in words. It was challenging and so I think it's you know this but that was what I felt like to make a contribution and also to represent the work that my co-author did. That's what that's what the kind of book that we had to write so I feel like. I haven't read them all but I think this is them. Certainly this is the first book that presents this story and really this

first book about Calabria manifolds about the six dimensions spaces and how that. That may influence physics that's intended for a broad audience. Probably not for everybody but for people who are interested. And your question implied should you be interested in. I can't answer that for you. I would hope people wouldn't if this is how the universe works they'd want to know what we don't know that for sure the drama she has gone through many stages. When you create it and the Greek drama tested it is read different from the Newton did it because she got a new tool namely calculus. But then the concept was space Tom has challenge ahead of the 19th century dramatize stop I remark. She didn't have a concept so the space is no more the space that we can see is extra space and that was the rope we've

finking to be able to apply to nature and to understand us here. So you're traumatized. Better a new concept. It actually has a either. You need some kind of every onion physics or wash Rissa because our needs in physics Djama time has changed the concept of space time but now the string free to come up and a condom free space need to be unified we have General Relativity that calls for a new geometry which is good for quantum physics in a small. And yet also good for general as he did in the lodge. This we have never encountered before in the history of geometry and everybody tried to do it but nobody knows how. It depends on physics intuition from physics

and also depends on dramatize and people in mathematics. These are which probably take a whole century to finish this job and nobody can tell. But yes exciting because a new concept would be brought up and we hope to witness such a dram in our lifetime. Well you've got to be patient and you and I and also it depend on your belief for example in Dist case to copy conjecture. It should be hard to prove you wrong and then I decide it must be right and really depends on my persistence and I love this problem because it's so fundamental and so beautiful and I feel that all cos I need to solve this problem. So I find a soffit despite I feel many times I really true is a problem. People tell me what to do.

I used to. Moser most of them are fundamental problems is true. You either solve it important Does a problem which is developed in the last hundred years by many mathematicians to get it. So some of them are really absolutely fundamental. You can make a contribution to you it would be spectacular. But I as I said Are you sorry I sold a pup on a guy I consider to be exciting. And then I found that beautiful. And I will have strong motivation to do it myself. But they're out of tire my fish and they like to solve famous difficult problems. I don't follow that wrong. Well I mean of course in the many documents because sometimes I set these has to resign in disarray you know to make it to be accurate. Steve said that well you cannot do it otherwise nobody understands. So go for a

long tough fight in a couple of something which is accurate and yet understandable. That was a great experience because some of these I don't know how they spring in layman terms until I talk to Steve as TV's reputation. Maybe I should say something on that. Let your wife know. I mean I think you put it well. It was hard for me mortals to understand this stuff well enough to be able to write about it and I sort of set a standard where I didn't want to write anything down where I didn't really know what I was saying I think that does happen a fair amount and I without diminishing the input I got from my co-author I did find it was helpful to get other perspectives at time and in the course of writing the book. I spoke with more than a hundred twenty five people in different fields and some

outside his expertise in physics so it was an intense collaboration as you suggested but I did talk to a lot of people partly because I needed so much help that I needed a lot of people to give me a little bit of time. No one person could have done it. Come on would be a better person. But as far as I I can understand trying for you just to have a fundamental principle compare way of quantum physics or general relativity. Yeah. So it's a bunch of trying. I mean but things are beautiful and much more complicated. Well I mean you wouldn't get published. I mean did publish eventually but she didn't want to publish many things until much later.