The HLF Portraits: Edward Witten

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Video in TIB AV-Portal: The HLF Portraits: Edward Witten

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The HLF Portraits: Edward Witten
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2019
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Point (geometry) Observational study Variety (linguistics) Direction (geometry) Decision theory Multiplication sign Student's t-test Solid geometry Expected value Group representation Mathematics Goodness of fit Thermodynamisches System Term (mathematics) Descriptive statistics Physicalism Numerical analysis Category of being Ring (mathematics) Physicist Right angle Musical ensemble Object (grammar) Family Resultant Spacetime
Standard Model State of matter Multiplication sign Decision theory Direction (geometry) Mereology Perspective (visual) Mathematics Klassenkörpertheorie Many-sorted logic Different (Kate Ryan album) Körper <Algebra> Position operator Predictability Quantum chromodynamics Area Process (computing) Theory of relativity Moment (mathematics) Physicalism String theory Funktionalanalysis Flow separation Degree (graph theory) Category of being Phase transition Quantum mechanics Quantum Right angle Mathematician Abelsche Gruppe Resultant Ocean current Point (geometry) Computer programming Atomic nucleus Functional (mathematics) Variety (linguistics) Letterpress printing Gauge theory Routing Student's t-test Mass Quantum field theory Event horizon Theory Hypothesis 2 (number) Term (mathematics) Manifold Energy level Theorem Nichtlineares Gleichungssystem Spontaneous symmetry breaking Forcing (mathematics) Model theory Algebraic structure Cartesian coordinate system Numerical analysis Vector potential Supersymmetry Inversion (music) Physicist Asymptotic analysis
Point (geometry) Color confinement Group action Euler angles Standard Model Multiplication sign Decision theory Direction (geometry) Range (statistics) Feldtheorie 1 (number) Student's t-test Quantum field theory Mereology Distance Perspective (visual) Theory Mathematics Term (mathematics) Selectivity (electronic) Series (mathematics) Extension (kinesiology) Focus (optics) Process (computing) Fields Medal Forcing (mathematics) Projective plane Physicalism Algebraic structure String theory Faculty (division) Physicist Quantum mechanics Universe (mathematics) Gravitation Right angle Mathematician
Point (geometry) Statistical hypothesis testing Axiom of choice Standard Model Multiplication sign Feldtheorie Quantum field theory Mereology Theory Power (physics) Mathematics Different (Kate Ryan album) Term (mathematics) Theorem Körper <Algebra> Multiplication Standard deviation Forcing (mathematics) Physicalism String theory Limit (category theory) Proof theory Physicist Gravitation Quantum Right angle Mathematician Arithmetic progression Family Fundamental theorem of algebra Quantum gravity
Centralizer and normalizer Physical law Physicalism Water vapor
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[Music] professor I want to begin with the child you were I arbitrarily attend where are you living tell me a little bit about your family at that point well I grew up in Baltimore Maryland with a couple of younger siblings UDL is yes thanks as a kid I was very interested in astronomy and space you perhaps realized that or remember that those was the days of the space race yeah everybody was interested in space it made me very interested in astronomy but I can remember being worried but by the time I grew up astronomers would have to live and work in space which sounded dangerous so you were cautious yes we noticed that hasn't happened so space telescopes are extremely important both the astronomers who design and use them will live safely on the ground oh no I'm gonna stay with that 10 year old is he lucky enough to have had to have a scientist in the family or as my father as a physicist yes a physicist yes now was he the kind of father and your mother also would fall into this category of influencer who were pushed you or would let you follow your own carry house huh well I didn't actually say that my parents avoided pushing me very much they might have if anything well they weren't pretty far in that direction um my father did help me learn relatively advanced math at the age of about 11 but then nothing happened after that for years which actually had the result of the fact that was a long time before I realized that there was more interesting that than what I'd already learned huh I I'm still trying to characterize perhaps inappropriate this child that you were as where their self directed or framed in terms of expectation wasn't highly self-directed nor was I no word that that's from first one hangout I want to mention is that I was given a small telescope when I was about nine okay maybe 10 or 11 one of the highlights was seeing the rings of Saturn but I can remember as a child thinking it was hard to find Saturn which is something I can't understand in hindsight huh because eventually I helped our children see Saturn through a small telescope and I know it's been ever it's up in the sky Saturn is one of the most trivial objects to find so obviously I didn't learn very much about the sky I don't know were you called in your parents I the one who is most likely to succeed or were you all given a solid education expectations for your future oh I think there are I explanations for all the kids for all the kids all all the kids now I'm gonna put you in school is it a good school let's say at this point it would be elementary are you a good student for example well I was a good student but my interest in the main thing to tell you about my keen ears is that my interest in math and science stagnated for a few years I didn't really pick it up again until I was about 21 21 yeah when I realized that I just didn't have the talent for other things I might would do much better concentrating on math and physics wonderful so there was the default decision but not so okay what were you not good at enough well what were your interest is the real question well whatever I was it whatever else I might have interested in I didn't have the talent for then but was it so cultural things was a athletic what were what were the patent laws I wasn't going to be happy studying history which I'd major and that's an undergraduate you majored in history yes I wasn't going to be happy as a journalist anyway there was yeah there was a variety of things that weren't going to work I realized oh I'm with my police it was frankly clear that my greatest talent was for math and science even though I had for a few years my interest I flagged so at the age of about 21 I went back in that direction I'm still not gonna let you go to 21 I want I want that younger fellow before he's figured out his principle talents are you do you have any mentors anybody noticing you in school and saying well you might look into this or that are you you're just pretty much going according to your own interest instincts I would not say there was much guidance in high school years certainly not environment I could have been studying math at a much more advanced level but that didn't happen and anyway as I told you I actually went through a number of years where I assumed that what I'd learned was representative of math oh it seems a little funny at night segment if you don't come to math and science as your direction until 21 yes that means you would have majored in something else and in I said undergraduate I told you already I majored in history right it was I thought it was in high school that you were worried it was in and what kind of history well at Brandeis we didn't have to specialize very much so I didn't so I took a variety of history courses not just like industry or whatever been a whole honestly not too memorable and I type you said earlier in a way you weren't good enough in that and you switched interests I couldn't I'm okay and in some other things the infields that didn't require a lot of interpersonal relationships I could have probably done fine but but I realized I wasn't going to be satisfied row 21 is very often the point at which one decides on Graduate Studies where I don't think you you went to your first graduate study I think where it was in economics that's correct well I transferred after one year to applied math at Princeton right but as an economist the expectation was were you again expecting radical there would've been some reason why you would have taken graduate studies in economics opposed I would have told you at the time that I wanted to do something connected with development in third world countries it's hard to remember obviously but I think I was just wondering where there was a bit of a political decision about an engagement in the world or whether it was just I just don't your honor I think I was interested in economic development in third world our case and which I think I'll Renaud have been good at by the way well fortunately you you chose another pan up now you decide against economic subscribe you don't then immediately go to graduate school in I was lucky enough to be able to get into Princeton and applied enough immediately yes well that suggests to me preparation I need some preparation it's hard to give it a great description wonder at Michigan even as an economic surgeon I was able to take some math and physics courses okay so and I had those recommendations so when you entered graduate work in mathematics oh I'm sorry possibly in physics applied math at
Princeton is a program rather than a department but so people in the applied math programs get their degrees in different departments it could have been math but in my case by the time I arrived at Princeton I was leaning toward physics which was certainly a comment reason I think probably for students in the applied math program right so you had applied in physics you were in the physics department well I don't remember very well what the structure was but I was it originally it made it in applied math and after a year I changed to the physics department I say okay well the applied math program was flexible enough that regardless I could have actually done a physics PhD without officially changing to the physics department Wow because they just watch her Princeton want that there isn't an applied math department as I just told you I have accepted and applied math at least at that time but I think even today we're getting PhDs in a variety of departments right this is one of the decision points of your life obviously there'll be many and well a personal decision point was when I decided to do physics rather than math yes and I'd like to know why well the most significant statement to make is that it was based on very little knowledge of either field ok this is not unusual it wasn't a well informed decision I understand that but other of your colleagues have often said the same thing so anyway but the decision yes what I'm thinking in the interview we do particularly interested in finding out yes is this habit of thinking of it's more than a habit but thinking of physics and mathematics as quite separate was of course in the end in your career and you would show the relationship so at the point where you become a graduate student here the separation was considered quite dramatic the de separation was large and I show that when I was a graduate student a graduate student in physics would not be exposed to any topics in modern mathematics which of course in the 19th century would have been considered ridiculous I mean something had happened and I guess that's what I'm trying to try to even the legend and I as far as I know it's only a legend that the reason why there was no mathematics Nobel Prize was because Nobel assumed that that would be incorporated into physics whether that's true or not because there are also scurrilous stories about like there's no mathematics Nobel Prize but still by the end of the 19th beginning of the 20th century they would have been considered quite related subjects quite related but not nearly as related to the state pen a century earlier a century before that the same people were my physicians and physicists yes now by 1900 abstract math as we know today was developing in such a way that they were important branches of that by then seemed for move physics so it compared to 1973 when I started graduate subscription of 1900 is correct but even by then compared to a century earlier there was a lot of abstract math that was pretty far removed from physics just to give an example I don't remember what number there is developed class field theory but it was roughly that time and nobody working on that voted anything did it with physics to this women today it's only connect exactly to this only today it's only connected to physics by very long and roundabout route so you chose physics yes but I should tell you ok I told you that that was based on very little knowledge about the field but it was based on the excitement about the elementary particles that existed at that time because of all string of amazing discoveries that were made experimental in the 50s and 60s and early 70s so I'm gonna put it this way please correct me you were lucky in your moment to I mean in the the intellectual currents at that time well it's worked out fine for me yeah we all know what would happened if I'd made the other decision but it might have worked out fine too so you chose physics yes as the formal framework and so I got in education like other physics graduate students of the time that included very little exposure to any mathematics done in the last half century right because it wasn't considered necessary right so how do you how does under your curiosity take you back to politics a war oh well you see the only thing that happened I was attracted to graduate to physics because of the romance of the elementary particles but that subject was radically changing just at this time because the last major ingredient of the Standard Model of particle physics was actually discovered just a few months before I started graduate school that was the discovery of asymptotic freedom but gross will check and Pulitzer huh for which they won the Nobel Prize in about 2004 so well it took a while to fully appreciate the consequences so experiment had been way ahead of theory for a couple decades yes but by the time I was starting graduate school theory was catching up and in catching up in developing the standard model physics was put on new foundations which involves a lot of mathematical questions that haven't been relevant before this wasn't realized all at once they came to be realized a normal process that kind of started in the mid seventies and I think took at least a decade in my eyes before we really understood the implications I suppose I'm now going to be proving a little bit into your personality and the phases these options are are you pursuing your own interest in spite of directions given you by your professors all right you know are you finding professors who as it were at the moment first of all my my graduate advisor was one of the discoveries of mass photography David gross and his student Frank will check was so in the department I guess I said assistant professor when I was a graduate student will check with Cisco discover so anyway I was definitely completely within the mainstream but physicists okay working on the standard model and my thesis consists it is interesting but relatively minor detailed applications of the standard model the most interesting part of my thesis was that I worked out the standard model prediction for what's called deep inelastic photon photon scattering which wasn't really experimental immeasurable at the time but eventually was measured huh and the prediction is interesting the prediction is interesting because first of all you can calculate it in standard model but but it really doesn't give the obvious answer I thought of that project okay in those days before the internet journals of course were the traditional method of communication but they were so for the 1970s or mid seventies when I was a certain physicists for communicating white paper preprints you'd write a paper and send up paper copies to a few hundred colleagues who would read it long before it appeared new journal so the department had piles of paper preprints and i would sometimes just sit down literally with a stack of paper prints that live further and eventually got to a paper where a colleague had tried to work out the standard model prediction for this process but wasn't too hard to see it hadn't been done correctly and that
doing it correctly was interesting that was the most interesting part of my thesis but it was far from revolutionary it was an interesting I'm not trivial it was sufficient but not incredibly deep contribution to the Sanja ball so the discovery was the discoveries were not so great but the promise was clearly there but because you then got a position as a result of your of your work at Harvard as a postdoctoral Hall as a postdoctoral fellows I again something about the almost the sociology of your science is the collegiality of the inquiry important to you are you pretty much relatively isolated in the way you're pursuing problems I was young I was more collegial than I am now and I tend to think I lose something as a result oh good well we'd have to skip a few decades to explain that but maybe we should stick with the variable we were discussing at the time I was lively interactive art eh what was your postdoc direction so because as a student Dennett initial postdoc years I was obsessed with the problem of trying to understand better what's called the strong interactions which describes the nuclear force that holds together at the atomic nucleus so the breakthrough of us would probably freedom that I mentioned you earlier yes had enabled physicists to understand that the nuclear force is described by a theory that we call quantum chromodynamics it said non abelian gauge 3 with the gauge group su 3 yes so by the time I was a student we knew what the equations were but we didn't know how to solve them and um well that's actually a conundrum even today so I'd say that the understanding of the strong interactions even today is not what one would wish but at the time I was obsessed with the bobbin the fact that 40 years later the problem is still largely unsolved what's the perspective on the fact I was having trouble at the time so gradually I had to work on more modest problems that I can actually do and so I got some experience in working on what's called non perturbative questions made upon a field three ISO uh during the years I was Harvard but I learned a lot from all the professors there in theoretical particle physics but of the only one was interested in these non perturbative questions that was Sidney Coleman so I learned a lot from him I also introduced me to some of the math papers that actually were important from home all right okay this is is this increasing use of interest in mathematics seeming less and less odd for a physicist I mean you're at a time where where they it came to the Mossad but the process took at least a decade starting roughly also in the mid 70s really so gradually physicists learned that they could do interesting well first of all that the standard model was hard to understand I'm trying to understand non abelian gauge theories at the quantum level led to mathematical questions right that physicists hadn't been interested in before it also attracted the interest of mathematicians can you speak a little more about that because mathematics was feeling very much separate from physics well in general yes well there are primarily two reasons that mathematics were so separate from physics one is that in the 20th century mathematics had developed in rather abstract directions the second is that the most after the development of nonrelativistic quantum mechanics so nonrelativistic quantum mechanics emerged in the twenties it did have a big mathematical influence in the development of functional analysis for example but the biggest challenge in physics after that was the development of what became quantum field theory and ultimately the standard model and that was very difficult mathematically the foundations are difficult to understand mathematically they're not very well understood mathematically even today and the considerations of physicists working on it and what they were grappling with was rather far afield from the interests of my visions so this is a cartoon inversion little bits a lot of things but very roughly in a half century up to when I was a graduate student on the preoccupations of physics and math were rather different directions but non abelian gauge Theory which was the bread and butter of the central model was interesting to a lot of math editions and people like is singer Michael Taylor well Bob David Kashan and others who either were in the Cambridge area when I was supposed to talk at Harvard or Austin if his case were visiting there sometimes they were very interested in these developments became convinced that they'd be significant mathematically also made an effort to educate me and other physicists about your career I still detect this is an impression a sort of surprised that theorems and mathematics came from your work in physics they they still seem Sunday they don't doubt it anymore yes but they still seem surprised well I was surprised of course - and what happened - first it seemed like an exception so there was a summer school in car Jaws in 1979 were attea and bought we have taken it upon themselves to educate physicists about something called Moore's theory which I'm sure none of us had ever know something I thought not and I didn't think about it again for a couple years but then around 1981 and 82 I was trying to understand something in physics called spontaneous breaking of supersymmetry and I could see it was obstructed in a way I didn't understand a lot of models you think would want a nice event supersymmetry did not and trying to understand it I kept looking at simpler and simpler models and they all kept doing the same thing finally got down to the very simplest model but just involved a function with him saying that just involved a manifold with the function on it which physically was the super potential and it still had the same strange behavior at a certain point i dimly remembered what by vanity had lectured pros about in car chess and i realized whatever stumbling once he was Moore's theory so that resulted in my paper called supersymmetry and Moore's theory for physicists I explained the difficulty of supersymmetry breaking for mathematicians I gave a new interpretation of Moore's theory I think the paper the mourners were more influential for math and for physics in terms of communication yes across the fields um it's the habit-forming if that's the way to describe it of mathematicians reading more of the kind of work you were doing in physics and people in physics looking more in mathematics I mean for categories that had been separated and isolated I wonder about the communication of ideas in this way how one field begins to learn from the other in a very active way well I'm not sure I the answer in the abstract in the concrete case of math and physics during my career it's all just not very quick and proceeding a pattern but these things happened but they all seemed kind
of isolated right in part because okay in these years until the mid eighties listening my focus was really on understanding the standard model better yeah and other things seemed like digressions and well as I've already told you the problems I was most interested in are still largely unsolved what fascinated me most was to get a better understanding of court confinement and although I was eventually able to make some minor contributions there the fact is it's not understood even today in a way I considered satisfactory so the mathematical spin-offs coming from physics and the applications of math to physics were interesting but they didn't seem to penetrate to the core of what I really wanted to do so that's a quick summary of my attitude in the Jose the early eighties the main reason that changed was that string theory emerged as a framework for going beyond quantum field theory and unifying gravity with the other forces and when it became clear which was the case by 1984 that string theory was a very serious candidate and framework for trying to do that the perspective of physicists widened watt and the opportunities for interacting with math and the importance of doing so became much greater hmm now I'm also quite interested in just the structure of your career not just the problems you're addressing but your decision as to where to go you are certainly invited to be a member of faculties how are you making your decisions this is just the practical I apply to many decisions because I've been at the Institute here since 1987 so you pretty much yes it was a natural process as to where you were yes well we came to Princeton originally to the Princeton University in 1980 yes and the only change I made since then was moving to the Institute is although I was on sabbatical at Caltech and considered moving there at one point or when you've got young children Princeton is life and Princeton is comparatively simple so once we were so low in Princeton there weren't a lot of places we were attending it's because it was for a long time it's comfortable to stay here and of course intellectually challenging yes I spoke to some of mathematicians sorry been to the Institute there and I asked the question I'm about to ask you and it comes really from ignorances the process I asked whether a disadvantage of these marvelous places was the absence of students that you really are left relatively alone they're entirely alone if you choose tell me about about that the light of the absence or whether you in fact had students throughout all these years I did have students actually you did because professors here at Tech graduate students from Princeton so I wasn't teaching courses ah but I almost always had one or two graduate students occasionally three right now I only have one and she's about to finish is there is there a particular thing to be said or maybe nothing that interests you about this about the intellectual interchange that happens in teaching that affects the kind of work one does is their work it's a little bit surprising that you often think of things better when you're trying to explain something to somebody okay well
I should point out to you though but there's a very large group of postdoctoral fellows here at the Institute so they're not graduate students they've got their PhD right so they just passed that stage but interacting with them is not that different from interacting with students so that should be part of the answer to your question and do they do they I mean the explanation I get but do they stretch the range of questions you're asking yourself or is that something they're pretty much sometimes in the last couple years I've been working on enough with one of them how unfortunate is just left huh so it's not inevitable but it can't happen yes well we're still working together but nobody's a scam pure doesn't Stanford will finish this project but it will be harder to get start a new one long distance but maybe I'll start working with one of the other young people will say it's obvious to ask you about getting the field medal it's it was considered and is still considered and usual for somebody yes principally defined as the physicists together you I think I've been the only one physicists yes primarily a physicist who achieved it so were you as surprised as I certainly was quite surprised yes definitely what what was mostly said about the reason because they would have to explain that to the mathematical community as well this this kind of a selection do you remember specifically what was sight well of course you must remember but does it interest you to tell me what you were cited for that there was no official citation in those days ah but Michael tier the most traditional that somebody would give a lecture about the work of the recipients however in my case Oh an explanation was written by Michael to you and actually delivered by Isaac Fidel and if you're curious there's a written version in the Proceedings of the conference so you can read about it he addresses the surprise of it so to speak while explaining the contribution probably I don't remember that difficulty I think I saw a little bit of that in it but again that's not important what's important is that the the sense of what you had contributed and in a way maybe this is not the best way to describe it based on the work you had done yes mathematicians had to take account of it in the framing of problems well it's hard for me to comment on this fair enough um I was surprised when when I was awarded the Fields Medal but I'm actually a little bit more thoughtful when I cite then it was at the time because I feel that regardless of my work up till 1990 I made some further contributions after that right so you see the implications of that work right now in the work of others presumably hopefully um again it's a very general question which you can answer as you want and that is that all of us in layman's terms it seems like you were among the few looking for a single theory of the universe maybe I I'm sure you have various views of whether that's even possible but you are that expansive and some of the questions you're asking is that fair to say well sort of but what I really like to stress for you yes is that I would not have gone looking for a unified theory of gravity and quantum mechanics because I would have had no idea where to start and so if string theory hadn't existed no I don't think I would have invented it but I wouldn't have tried to invent it again because if not I mean ad word look but string theory was discovered it's kind of artificial to ignore the fact that humans stumbled upon a framework that does go beyond conventional upon field theory enforces those to include gravity well conventional quantum field theory makes gravity impossible yes yes yes and since they came to be appreciated which was in the mid 80s there's been a large community of people working in that direction so it's a bit misleading to characterize me as one of the few were one of the only ones but what is true is that we're all working in a framework that we don't really understand oh so I see string theory is this vast ocean of knowledge which has led to an incredible series of surprises okay which are about us in all directions were far from coming to grips with the most fundamental truths of the subject whatever they are it's often asked perhaps there's no easy answer to this but since your audience is mostly young mathematicians and scientists um what particularly excites you may be an extension of what you just said particularly excites you in the work now and in the direction that mathematics
and physics are going well I'm going to amplify what I've already said please so one of the main reasons that physics made so much progress in the 20th century yes is that the framework in which physicists were working is highly constraining so for example when the part of the standard model that describes the weak interactions was discovered by Weinberg LaShawn salon they actually had extremely maker experiments on clues but they were able to get a long way with very meager experimental clues because they tried to feed it into the framework of relativistic feel-good and that framework is extremely restrictive so the framework of brother su Kwong field theory was kind of force multiplier and they were able to find the right theory with what would seem like ludicrous a limited experimental clues so it's a very rich framework and part of the richness is that it's almost impossible to change it in any way without getting into some kind of contradiction yes rather mediate contradictions I think that this is one of the most important observations about 20th century physics that's something that very few people outside the field appreciate it's extremely hard to appreciate it I think unless you've learned cornfield theory it would be virtually impossible to understand what I mean and saying that it's a very restrictive framework that's very hard to change it at its power is one of the main reasons that the standard model was discovered based on limited experimental data right nope precisely because it's virtually impossible in tamper with the standard that the standard framework of relativistic quantum field theory without getting into contradictions one has to take extremely seriously anyway of tampering with it those presented self yes and the only interesting modification a relativistic quantum field theory that's been discovered that makes any sense is string theory and that alone would make it extremely exciting to study but the fact that it forces gravity upon us well the standard framework we can't really have quantum gravity apparently this isn't this even with the precision of the mathematical theorem well makes it extremely compelling to study and then pass the fact that in studying it one has uncovered so many surprises both where one gets a better understanding of existing physical theories and sometimes new insights in pure muffin-top dealt right so I think there's something very deep there that's very I'm just exciting to try to understand it better so where would you send a young person to a mathematics department to a physics department uh-huh see I think if you want to grapple with the questions I was just raising yes exactly that's what I'm asking if you wanna cop with physics you're really going to have to start with the physics education I see and then try to branch out into math but math obviously is great for the people it's great for us but in the end as a conceivable convergence it's just the framework in which you you begin that journey that intellectual journey well I'd say that there are a lot of times that concrete mathematical ideas are suggested by string theory and mathematicians appreciate those and put them into their own theories often formulate things differently come up with different proofs or different ways of looking at things yes but the conundrum in physics that's behind it all is actually extremely difficult to explain in mathematic language maybe the day will come where it can be explained in mathematical language but that's not the case as of 2019 so okay take the statement world test at quantum field theory apparently makes it impossible to have gravity while string theory forces us to include gravity and the second statement but the fundamentals of string theory are completely unclear now it's virtually impossible explain either of those two statements my vision while those two statements are the essence of what my physics colleagues is I believe yes so again this is too simple a way of asking but at this point yes were you entering the discourse still you might take the visitor the path of the physicist in terms of the problems that interest you sorry nothing to mathematics I as they say it may be just too simple to ask but it's back to this question of a choice for somebody who wants the larger picture yeah it's the physics of mathematics it's really the it seems like in physics as you were speaking of it it's more graspable as a path to get to this convergence well I've got no idea how close or far we are
from this convergence or from answering the really deep questions about string theory and or quantum gravity I can't
say all I can say is that at least eventually if in 2019 you want to understand that your sentence as I stated yes which live here is the central mystery step most powerful me yes the way to get to understand the questions although not the answers in law starting out as a physics assume water I understand thank you very much
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