 Just a few hours north of St. Peter lies one of the most pristine wilderness areas in the country, the boundary waters canoe area. At night there are no city lights, no house lights, no lights at all to obscure the dazzling complexity of the starry sky. The Milky Way stretches from horizon to horizon. Jupiter shines like a small moon. It is impossible not to wonder at the twinkling stardust, so infinitesimally small to our eyes, yet so incredibly stupendously distant. We see the universe at its limits on a still dark night, a mystery, a riddle on the grandest scale. Frank Wilczek is a man well acquainted with the mysteries of the universe. As a child he loved puzzles and games, so it was no surprise that he pursued a degree in mathematics at the University of Chicago, and subsequently graduate work in mathematics at Princeton. It was at Princeton that he learned of new work in theoretical physics that involved deep concepts from the mathematics of symmetry, in particular the gauge theory that was being used to describe electro-weak interactions. He soon began work with a young professor named David Gross on the peculiar behaviors exhibited by subatomic objects called quarks. Quarks are the building blocks of protons and neutrons, thus of matter itself. Wilczek returned to the notion of gauge theory to model and thus explain the wild antics of quarks. For this work he was awarded the Nobel Prize in 2004. Two things are immediately clear from even a brief review of Professor Wilczek's work. First, the sheer output of professional activity is truly stunning. Dr. Wilczek has published hundreds of research articles in a broad sweep of areas in modern physics. He has given invited talks at major universities and research institutions throughout the world. He has a rare gift for clear and engaging expository writing with publications in nature, the new scientist, physics today, and Scientific American as well as three popular books about physics. The second thing that is clear about Professor Wilczek's work is that it is infused with a sense of wonder about the world, a curiosity about what makes the universe tick. In his book, The Lightness of Being, he takes us on a journey from the Pythagoreans in ancient Greece with their motto that all is number, to the discovery of quarks and QCD, and finally to the frontiers of modern physics. It is a fascinating story. Professor Wilczek's playful and creative mind is evident throughout his career. In his book, Fantastic Realities, he describes how he came to predict the existence of a new particle called an axion. Axions might be the answer to the mystery of dark matter. When describing the origin of the name axion, Dr. Wilczek writes that, quote, I named them after a laundry detergent. Since they clean up a problem with axial currents, returning to the wilderness in our starry northern sky, we imagine all those throughout history who looked up in wonder and asked the question, what is it all about? This is the question at the heart of Frank Wilczek's work. It is my great honor and pleasure to introduce him today. Please join me in giving him a warm welcome. It's lovely to be here and lovely to have this cap to protect my hair challenge skull from the sun. But we're in close here so I can forego that. Today I'm going to talk about the universe at the limits of mind and matter. Where mind meets matter in the subject of geometry. Geometry originated in very practical concerns. In fact, the word geometry derives literally from earth measure. But geometry took on a life of its own. As people discovered it could be interesting, something you could play with, and that it led to very beautiful things. Perhaps the first great beautiful discovery in geometry was Pythagoras' theorem about the sums of the squares of the lengths of the two smaller sides of the right triangle being equal to the square of the largest side, or hypotenuse. We don't know exactly how Pythagoras proved that, but it's very likely to be something like this. This proof, by the way, was the subject of a wonderful story by Aldous Huxley called Young Archimedes, where Young Archimedes, this genius Guido, discovers it. He's nine years old or something, and draws the picture and says, So simple, he sees Pythagoras' theorem in a glance just looking at these figures. Let's spell it out a little bit if we're not quite Young Archimedes. These two squares have the same size, and furthermore, they share in common four little colored right triangles. That means that if you take away the four right triangles, the areas of the remaining things have to be equal. But if we look at the left-hand side, we have the blue square, whose area is the shortest side of the triangle, and the red square, whose area is the square of the second shortest side. Whereas on the right-hand side, we have a square, and we take away with the triangles, we have a square whose side is equal to the longest side of the triangle, and therefore whose area is the square of the longest side. And so the two little squares have to add up to the big square, and that's Pythagoras' theorem. It's an unforgettable proof of an unforgettable theorem, and it appears in an unforgettable story, which I highly recommend to you. Pythagoras' theorem has inspired people over the millennia. In Einstein's autobiography, he mentions that his scientific awakening as a young man occurred, as a young boy really, occurred when he came to grips with Pythagoras' theorem. I remember that an uncle told me the Pythagorean theorem before the Holy Geometry booklet had come into my hands. After much effort, I succeeded in proving this theorem on the basis of the similarity of triangles. That's not really enough information to reconstruct Einstein's proof. We don't know what it is, but I've tried to reconstruct it, and in any case, I think what I'm about to show you is the best proof of Pythagoras' theorem and makes it beautifully clear why it's the squares of the sides that appears. So here it comes. First, we have to make a preliminary observation about similar triangles. Triangles, that is triangles that have a right angle in them, will be similar. That is, they'll be magnifications or demagnifications, one of the other, if they have another angle in common. So if we have two similar triangles, and their sides are scaled up by some factor, one compared to the other, their areas will be scaled up by the square of that factor. Now, in this diagram, we have three triangles. We have the two sub-triangles and the big triangle. They all have an angle in common, namely phi, and they're all right triangles, so they're all similar. One of them has its longest side A, the other sub-triangle has its longest side B, and the big triangle, the triangle made up of those two, has its longest side C. Their areas are proportional to the squares of the longest sides, so the areas of the two little ones have to add up to the area of the big one, and so A squared plus B squared equals C squared. Again, Pythagoras' theorem. I can understand, really, how constructing this proof might have been an inspiration for Einstein's entirely scientific career. It's so beautiful and such a wonderful thing to discover. Now I'm going to sort of give you a brief historical tour through the evolution of geometry and how it's enriched our concepts of the world and how it's changed over time. When you first learn geometry in high school, you may think that it's a static subject, that it's never changed, that the rules are forever. The philosopher Kant even elevated that to a principle, that the rules of geometry were inherent in the human mind and would never change. That's totally wrong, of course. The first era in the evolution of geometry, once the idea that you could prove things and that it was beautiful to play with figures, came when people tried to construct the world based on beautiful elements of geometry. And used geometry as a source of intellectual standardized parts that could be models for atoms or structures in the world. The most famous attempt, and the most profound and fruitful, was made by Plato and involved what are called the Platonic solids. Let me briefly introduce you to what the Platonic solids are. Let me start with something simpler. These are the regular polygons in two dimensions. Regular polygons in two dimensions would be polygons that have sides all equal and angles all equal. The simplest example would be an equilateral triangle, but then you could have a bigger one, one with more sides, which would be a square, or a bigger one would be the design in Washington, the Pentagon, and then you have stop signs and so forth. And you can obviously have regular polygons with an arbitrary number of sides, so there's an infinite family of these things. When we move to three dimensions, we get something much more interesting when we try to extend this idea of regular figures. If we ask for figures in three dimensions, all of whose faces are regular polygons, identical, and all of which come together at identical vertices, then it's a great theorem of geometry. It's the last theorem in Euclid's elements and widely thought to be what he was building up to in this 13-volume work, that there are exactly five regular solids. These are called the Platonic solids. There's the tetrahedron, which has four equilateral triangles as its faces. The icosahedron, a wonderful figure that has 20 equilateral triangles. The dodecahedron, which has 12 pentagons and is widely used as a calendar for that reason. The octahedron with eight and the cube with six sides used, of course, in conventional dice. Plato, inspired by the fact that there are a finite number of these things, thought that that should have a profound meaning for the structure of the universe. And notice that the number five is quite close to the number four. And at that time, people thought it would take four elements to make the universe. Earth, air, fire, and water. So Plato postulated that the atoms of these different elements had the different shapes associated with these solids. The tetrahedron, which is pointy, would sting when you touched it, so that could be fire. The icosahedron is pretty smooth. Different icosahedron will roll over each other nicely. So that's water. For some reason, octahedron's air. And Earth can be made out of cubes because cubes kind of pack and get stuck and kind of are earthy. Now, an ordinary thinker might have been discouraged by the fact that four is not almost, but not quite equal to five. But Plato was a genius and persistence is a big part of genius. So he was undaunted by this. He found a use for the dodecahedron. The dodecahedron was meant to be the shape of the universe as a whole. So it also had a role. Plato later, who always tried to one-up, I'm sorry, Aristotle later, who always tried to one-up Plato, had a different theory. He imagined that the celestial regions outside of Earth, the so-called celestial spheres, had their own element, the so-called ether for the ethereal regions, and that the dodecahedra were actually the atoms of ether. Nowadays, it's difficult to agree with these theories in detail. However, the inspiration that symmetry determines the possible structures that we should use to describe the world and that when there are only a finite number of them, the suggestive of the classification of things that exist in the world has turned out to be extremely fruitful and, in fact, the basis of modern attempts at unification in physics and chemistry. Plato was very good at getting his name attached to things, but he didn't actually invent the Platonic solids. At the Ashmolean Museum in Oxford, you can find these dice, which were discovered at a site in Scotland and dated to about 2000 BC and which have the shapes associated with the different Platonic solids. So they're really in the nature of things and people knew about it quite early, at least in operational terms, even if they didn't have theorems. These were undoubtedly used for some early form of Dungeons and Dragons. This kind of thinking of trying to match geometric structures, and in particular the Platonic solids, to the shape of the universe, really took its final, and I have to say decadent form, in Kepler, where he tried to fit the orbits of the different planets to circumscribe and inscribe Platonic solids and thus determine the shape of the solar system. And it's a beautiful figure, but unfortunately has very little to do with reality. Because shortly after Kepler's work, and based on some of his detailed discoveries, a very different kind of approach to figuring out how the universe worked. Still geometric, but incorporating not the geometry of timeless perfection, but the geometry of things that change in time, took over. This was the profoundest aspect, I think, of Newton's revolution in physics. The idea that it's laws of change, laws, not static object, that are simple and fundamental. I think Newton first hit on this principle, not by watching an apple fall from a tree, but by thinking about something along the lines of this diagram, which is my favorite diagram in all the scientific literature, and is the first diagram in Newton's Principia. What is it? Well, you're asked to imagine someone standing on a mountain, on a planet, and on a body, could be Earth, and throwing a projectile horizontally, harder and harder. What would happen? Well, if you throw it not too hard, that's the familiar thing, it falls to the ground, but the harder you throw it, the further it'll go before it falls down, and Newton kept thinking, harder and harder and harder, and came to the opinion, thought it was plausible or maybe even obvious, that if you threw it hard enough, you'd better duck because it'll come back and hit you in the head. It would never have fallen enough to hit the ground. So this concept means that the same thing, the same kind of force that causes things to fall to Earth, could also be responsible for things orbiting. Furthermore, the mountain could have been bigger, so you could have bigger orbits, and for that matter, you could have other objects, not just Earth, but any object, having things falling into it or orbiting. So this suggests the universality of gravitation, that the terrestrial phenomena is the same as the phenomena that causes orbits, and gravity is a universal force, also suggests that orbiting is the same thing as falling. Just you're falling towards a target that's moving because you're moving, and therefore you never quite complete the process of falling. What's beautiful about this figure is not the shape of any particular orbit, but the thought that goes into it and the idea that the whole scheme of orbits makes sense and unites the idea of orbits and falling. Newton analyzed the motion mathematically as a series of small falls, so the object would move in a straight line if there were no force of gravity, but each time it tries to do that, there's a little force that deflects the orbit, the trajectory a little bit, and you can mathematically analyze the competition between those effects to determine the shape of the orbits mathematically. I think Newton, after considering the circular orbits, considered, suppose you threw it even harder, what shape would you get then? And that led him to the discovery of ellipses, which made contact with Kepler's work and drove the whole Newtonian revolution in classical and celestial mechanics. I really think it all comes from the visualization of that diagram that I showed you. And furthermore, the notion that motion can be analyzed most fruitfully from simplicities of its small bits, Newton generalized to a general mathematical framework for analyzing all kinds of things in terms of simplicities of their small bits. So for instance, to compute the area under this curve, you consider how fast the area is added to as you move along and add little bits to it, and you see that the area is going to be added to by the value of the elevation times how far you've moved, and that's the fundamental theorem of calculus from which so much flows. Newton's view of the world led to many triumphs and had an enormous impact on the surrounding culture, in many ways inspiring the Enlightenment. William Blake in particular was turned on by all this and imagined what Newton looked like as he was making his discoveries. I find this more or less plausible. I also like to work in the bathtub and looked very similar when I was discovering asymptotic freedom. You can see in the determined look here and in the attention to detail that the new ethos of science also aspired to precision as well as to overarching ambition in describing the world as a whole. And Blake extrapolated that because this was the right way to understand the world, it probably was also the way the world was built. And I find the juxtaposition of these two figures quite remarkable. So I've discussed now how geometry suggested building blocks for the universe through symmetry and how adding the time dimension really changed and enriched and made the picture more accurate. Now the next big idea in expanding what geometry means is the idea that geometry is not the science of space as given, but a realm where you can imagine other things and make models that are unusual. So, and in particular models where space is bent and curved. So in particular, you can not only imagine a flat plane as the arena for geometry, but you can consider two-dimensional creatures who occupied a horse saddle like that or who occupied the surface of a sphere. What would geometry be like for them? Well, they could have analogs of straight lines, the straightest possible path, the things that are locally the shortest distance between two points. But they would find, in the case of the saddle, that if you made a triangle, instead of the angles of the triangle adding up to 180 degrees, they always add up to something less. If you live on a sphere, they always add up to something more. And whereas on a flat plane, you can have exactly one line parallel to some other line through a given point. In on the saddle, you can have infinitely many and on the sphere, two lines always meet, in fact, in two points when you draw them, continue them indefinitely. So geometry expanded once we allowed space to become flexible. This idea was developed initially through the work of Gauss and Riemann describing the geometry of a curved earth and then extending it to many-dimensional spaces and brought to a new level when Einstein, combining these ideas about flexibility of space with the idea that geometry should also include time and the element of change developed the idea of flexible space time. So not only can space bend, but time can also bend and distort in response to physical perturbations in particular to the influence of large bodies. So the ultimate example of this perhaps is the black hole. What I've shown here is I'm not supposed to use that, sorry. Time runs vertically here and you're supposed to imagine space running, oh this is fun, space runs horizontally. So a curve like this represents the surface of a star moving through space as time gets passes and ending up in a collapse to a much smaller object. So this is a stellar collapse and what happens according to general relativity to Einstein's theory is that when that happens the collapsing matter pulls along space and time so that these cones which indicate the paths of light rays the paths that light would follow and far away represent the speed of light. You go a certain distance as time travels so you get 45 degree angle lines those things tip over get distorted and eventually you reach a situation where light can't escape no matter how hard you try the light cone has tipped over so light moving into the future instead of going off to infinity where you can see it collapses like the matter into the singular point. Well this is just one particularly dramatic example of the power and the strange things you start to encounter when you combine the idea of flexible space with the idea of combining space and time to have a flexible space time. Another direction that's quite remarkable and has an unforgettable picture associated with it is that if you can bend space and time you can start to blow bubbles also known as creating universes. So this is a picture of a model of cosmology called eternal inflation where universes once in a while sprout new universes roughly speaking new big bangs and as time goes on universes sprout universes that sprout universes and you have this enriched picture the multiverse for what the ultimate reality of cosmology is. So that makes space very big in the sense of volume and also very various in different directions. Now I'd like to add one more idea to the mix the idea that not only can it be big in extent but nowadays we have to consider that the universe is very very rich in the sense of having many many different possible directions. We're accustomed to thinking that there are three kinds of directions two horizontal directions north south and east west and also vertical so three dimensional space and you can throw in one extra dimension of time if you want to add the dynamical element but there's nothing conceptually to prevent you from thinking about larger dimensional spaces you can even draw what a four dimensional cube would look like for a three dimensional cube the sides the faces are squares for a four dimensional cube the sides are cubes and mathematically it's not difficult to figure out the relationships that connect the different points and make a four dimensional cube of course you have to project it down to two dimensions to display it on a computer screen and apply considerable imagination to lift it up twice to four dimensions but the information really is all there what did these higher dimensional spaces help us describe well many things some of them are quite subtle and profound in quantum mechanics but also the experienced world of a mantis shrimp human vision is sensitive to three averages of intensities of light from the electromagnetic spectrum we have three so called photoreceptors that respond one mainly to blue light one mainly to green light one mainly to red light in reality they all respond to a continuum but with different colors and so if you want to make a color photograph that humans will regard as being fully accurate you only need three kinds of ink because you only have to satisfy these three averages or if you want to make a computer display that has all the colors that human can sense you only need three different types of light generating elements we say human visual space human color visual space is three dimensional well the mantis shrimp puts us to shame it has 16 receptors so its color world is 16 dimensional things that look the same to us could look very very different to a mantis shrimp it's capable of making much finer distinctions it can also see considerably into the ultraviolet and even make distinctions among different kinds of ultraviolet light so if you want to do justice to the visual world of a mantis shrimp you need a 16 dimensional space to describe the intensity in all these different channels well I can't allow the opportunity to pass to show you what this creature looks like this genius of color space as you see even humans can see that it's quite colorful and also that it has very very strange eyes kind of googly-eyed creature but now we realize that not only strange but extraordinarily powerful and insightful eyes that in some ways put us to shame but we have one advantage over the mantis shrimp we have a much bigger brain and using our brain we can imagine not only 16 receptors but an infinite number of receptors we realize through our brains that color space is actually infinite dimensional there are any number of frequencies there's a continuum according to Maxwell's great discovery of the identity of light with electromagnetic radiation of different wavelengths there is a continuum of different possibilities we only see three averages the mantis shrimp seems 16 averages but our minds could allow us to imagine an infinite number and in fact we can even extrapolate and using Maxwell's equations bring in new phenomena that are not seen as visible light at all and one wouldn't naively think had anything to do with light such as radio waves infrared radiation ultraviolet x-rays and gamma rays so nowadays you also cook with it not only see it and listen to rock music with it so now I'd like to introduce yet another idea from the expanding realm of geometry this one is absolutely central to our best description of the physical world it's the idea of something called internal space this one is not very widely known outside of physics and not very widely appreciated even within physics so I'm hoping you'll help me popularize it so we've discussed various complicated geometric objects this one may look paltry by comparison just a cylinder let me introduce however a little more structure to it drawing a line and now let me ask you to imagine that you are or that you're imagining creatures whose world is one dimensional that live on that line imagine that line is very long and they're pretty big so that the cylinder seems quite small to them and their eyes, their senses are incapable of resolving directly the structure in that second dimension which looks like an extra dimension to them what would things occupying different places in that extra dimension look like to creatures in this world well they might look like different colors but if they had different properties of other kinds such as not the colors of the rainbow but the colors we talk about in QCD, the colors of quarks then what would happen is that you would see the same fundamental object in different places as being a different kind of particle so instead of having many independent kinds of particles within modern physics even within the standard model and also in more elaborate forms in unified theories we imagine we postulate and make successful use of the idea that many different kinds of particles can all be the same kind of particle just in different places seen in different places in extra dimensions so as this particle moves around if it's seen in different places we don't sense those as different places in the normal sense but as different particles this is the profound idea that what you are derives from where you are so I've described now several different ideas I hope quite a few ideas about the encounter between mind and matter where mind has adapted geometry and changed it as a result of its confrontation with the realities of matter now I'd like to discuss very briefly the frontier of where mind and matter meet and the distinction between them starts to become blurry and I think where we're working towards a unified concept where both mind and matter are part of this are the same entity at some level, the same deeper unifying entity this wonderful object is an example of a fractal I think any human artist who came up with this would have been regarded as an extraordinarily creative genius who dreamed up something essentially new and quite beautiful just at the sensual level but this is a mathematical object that's generated by the computer following very simple rules I won't tell you exactly what the rules are but trust me they're so simple that even a computer can follow them in fact they're so simple that even a vegetable can follow them you see this also has this kind of broccoli kind of structure that follows by iterating simple rules of growth over and over again to make this kind of fractal self-similar structure so simple rules can give complicated objects and we have to expand geometry to allow the operation of simple rules of new kinds this network is a representation of a piece of the internet a rather small one telling who's connected to who and we're developing new kinds of geometry to describe these kinds of connections and networks this is another network which superficially looks similar but this is the kind of network you have inside your skull this is the pattern of nerves neurons that are connected to each other you can see if you look carefully a few cell bodies and it's actually much denser than this but only some of the neurons get stained there's not much empty space but presumably it's wired up in a pretty structured way so that this thing actually does useful computations such as taking input from the eyes running through the network and then being able to decide whether what you saw was Julia Roberts or this other person or a baby ideas of geometry and quantitative descriptions of the effects of one neuron on another and on the effect of the architecture of the network are a fascinating and very fruitful and fast growing area of research so nowadays geometry has become very flexible not only bringing in the time direction not only bending space and time not only allowing spaces of arbitrary dimension but even changing the notion that it's the description of space in any very direct way now it describes relationships but the same kind of mathematical techniques and rigorous approach are allowing us to understand also the neural networks and the social networks that are so important to humans and so finally the end of this story mind and matter are becoming united as mind by studying matter finally realizes what it actually is thank you thank you professor Wilczak for that fantastic lecture at this time I'd like to ask the rest of a panelist to join us up on stage here for the question and answer period and as they come up I'll remind people how we do the Q&A sessions here at Gustavus the ushers will have small tablets for you to write questions on pieces of paper and you can submit them write your question on them and hand them back to the ushers they'll bring them to the front where we'll collect them and get them to the moderator if you're on the internet you can submit questions by clicking on the submit a question make sure you submit the question for me and Google moderator will help you sort those you can vote for other questions that people have already submitted as well and as we gather our panel up here we'll begin the question and answer period very shortly thank you so coin is not in town yet he's flying in but apparently went out to look for his wife and somebody is trying to find him so we may just go move with what we've got we'll make it work and if he shows up we'll wire him up if he walks up we'll wire him up great thanks John so no I'll in the moment when we open I'll moderate first shot and then I'll have questions from the audience and questions from the internet we'll just sort of and Frank can peer over my shoulder and see here's the questions that are coming in the multiverse was the first question that came in yeah I mean maybe Tom's with him yeah and he missed the briefing at dinner last night maybe and doesn't know the routine smile for a brand yeah who knew what what please when you're speaking okay straight ahead initiate this whole thing and you'll also do the when it's over okay please find your seats folks we'll get the question and answer period started in just a second here okay Professor Melano will start us off okay thank you thank you again professor for an amazing lecture and I think we usually give our panelists the first shot at questions so does anyone from the panel want to ask so Frank do you think ultimately geometry is everything well well yes because geometry by definition will be everything every all the concepts that are used to describe the world will ultimately want to visualize and play with the way we play with figures so they'll become geometric even if their origin wasn't anything we'd recognize as geometry today thank you go ahead so Frank I was intrigued by the last part of your presentation in two ways you talked about the notion of internal space yes and then you at the end you drew this very strange figure with the you and a number of us have seen that one of the eyes sort of representing that operation of the mind so are you one of these people who thinks that what the mind does which is process data has something to do with the universe that is an idea that we're starting to see emerging physics well first of all I should say that that figure was stolen from John Archibald Wheeler I'm aware of that who loved to draw those kinds of strange profound figures some more profound than others but well I do think it may be a fruitful way to look for new laws of physics or understand implications of physical laws better to think of them in unconventional ways now suggested by the study of neurobiology or by computer science because it's given just as in the early days it wasn't obvious that what geometries were doing measuring the earth would turn out to be so fruitful for understanding the physical world but they were doing a lot of stuff that you could exploit now I think similarly neurobiologists and computer scientists are developing ideas and information theory and analysis of networks that are very very powerful ideas and so we can look forward to stealing from them in physics and also we can we can repay because we have ideas in physics that I think can be very powerfully and fruitfully exploited in those realms and haven't yet been sufficiently appreciated Frank when you developed quantum chromodynamics was there much data upon which it was based was it largely mathematical like string theory right now and without that much experimental grounding there was enormous amount there were enormous amounts of data about how the strong interaction worked and in fact in many ways the hardest part of discovering asymptotic freedom and realizing its importance was to separate the signal from the noise because most most of the data most of this enormous accumulation of data about the strong interaction turned out to be well not wrong but not central I had a great advantage I was only 21 years old at the time I had the great advantage of not knowing very much so I didn't know all this irrelevant stuff and I was lucky enough to focus on just the stuff that led in the right direction there were crucial experiments in fact pioneered especially by people at MIT Kendall Taylor was not at MIT and Friedman of course who's still very much with us and a good friend of mine at MIT that showed some very unusual behavior of quarks that when they're close together they interact very weakly although when they're far apart they interact strongly and also that when you hit them very hard although they have very powerful interactions usually and you would think that therefore if you hit them very hard they would radiate a lot of stuff in fact they radiate very little and it turned out that those were the right phenomena to focus on and just by trying to understand those and make them consistent with general principles of quantum mechanics and special relativity we were led to a unique theory now the unique theory we were led to was a highly mathematical theory of symmetry but it was definitely informed by very concrete experimental facts and it wasn't long before Sam Ting and others did experiments that really started to give new kinds of confirmations of the theory so it didn't go through this long period of being a promising theory that hasn't delivered that some other theories we might mention have been going through Professor Shears has a question so Frank I have a really simple question for you so I'm an experimentalist and I've heard many many theorists talk about the beauty of symmetry and the beauty in geometry what is that beauty for you is it the simplicity is it the compelling nature of the laws of symmetry well I'd like to quote Solieri here in the movie Amadeus Solieri looks at one of Mozart's compositions in the manuscript form and is in wonder at it and says if you changed a note it would be diminished and if you changed a phrase and that's a form of beauty everything fits you can't change it without making it worse and that's what symmetry in physical equations gives us it gives us equations that can't be changed without making them worse because their different parts have to be perfectly balanced so that when you make the transformations that the symmetry says you're allowed to make you still get equations with the same content so that mathematical idea leads you to unique very structured equations and then the miracle is that those equations are actually the ones chosen by nature so it was the same instinct that led Plato to the platonic solids as models of atoms but this time it's right other questions from the panel I'll try this a little differently so you can rattle Frank this way in fact a lot of the history recent history of physics the last 40 or 50 years has been about understanding symmetry and exploiting of starting this from another theorem and in fact it seems to me people have pushed that to an extreme limit with supersymmetry even though the data has not yet supported that theory even it's quite beautiful and just because it doesn't look like the real world you have some spontaneous symmetry breaking or something to get out of it but geometry has a lot of symmetry in it but it's different and I've been thinking for a while that people have exploited symmetry enough that they know it a lot better than I do so I should think other ways and I'm with you I think geometry is a way of doing it and geometry has some built-in symmetries but it has some other factors and so when you were giving this talk on geometry I was so eager to hear what was going on are you thinking the same thing that we need this new approach well in broad terms I think I think you're touching on a theme that actually was implicit in my talk which is that the original idea of geometry as a static perfection doesn't do justice to the possibilities when you add dynamics you get enriched possibilities when you allow the structures to bend you get enriched possibilities so and now when you consider networks and things that don't have a continuous structure you get additional possibilities so so I so it's a balance you have to on the one hand have structure that gives you something to work with building blocks and using those building blocks I guess and a lot of well you alluded to this but a big theme of physics in the last few decades is that symmetry can be very deeply hidden in the phenomena you can have symmetry in the equations that doesn't show up in any very direct way in the phenomena you have to look very very hard to find it but then once you found it you can build back up to reality so physics as it's developed has come to use longer and longer chains of deduction getting from the basic equations to the phenomena that you observe I mean it's famous for instance that in Newtonian gravity you can solve the two-buddy problem and get Kepler's law for planets in general relativity you can solve the one-body problem to get the Schwarzschild geometry in quantum field theory you can't even solve the equations for empty space okay so and yet that gives us the deepest description of the world and so we have to use more and more chains of deduction between what we can between the starting point and what we actually observe other questions from the panel I have one more since implicit in the discussion of the last few minutes has been the notion of symmetry I want to describe an experiment and get your response to it one can take a human face and cut it in half and throw away half of it and then invert and then glue back together to get an apparent human face back but people's reaction to that is actually very very different than the original face so do you think that this is some indication that we are so wired to regard symmetry as humans that it's a force in how we think about things far beyond the laws of nature well yeah I think symmetry is certainly part of the notion of beauty well of course the way we use the word in science is somewhat different and more precise than it's used in general usage but it's still the same word and there's a reason for that and symmetry in art and so forth has always been associated with more general ideas of beauty and human well as you said humans are very attuned to symmetry or lack of asymmetry especially in other humans I'm told although I'm not an expert at this I'm told that movie stars for instance typically have much more symmetric faces than the average human beings because that is a sign of health and attractiveness that people use in assessing possible mates let's turn to a question from our audience today the questioner writes regarding the theory on internal space you said that different particles may actually be the same particle viewed at different angles should there not be an infinite spectrum of angles and therefore an infinite spectrum of particles in classical mechanics there would be but in quantum mechanics the infinity gets broken down to a finite number so it's quantum mechanics that really enriches the picture and allows you to get a discrete number of possibilities out of a continuum of angles another question from the audience if time is the fourth dimension can you speculate on how dimensions 5, 6, etc. well I can certainly speculate but I don't have to speculate even within this well within the standard model I wasn't just making up this idea of internal dimensions it's in accepted physics it's the central concept in the standard model that for instance a quark a particle in different directions in color space will be seen as either a red quark or a white quark or a blue quark will be seen as having different properties so that's what three extra dimensions look like it's the dimensions that not all particles can move in quarks can move in those directions but it turns out electrons can't move in those directions theoretically but we use very flexible ideas of what dimensions are in our equations so they can look like almost anything we use these extra dimensions as playgrounds for our equations so you can use different equations based on those extra dimensions to describe a wide variety of things in principle in case people get a little confused by what we said when you talked about red we use the words color but we don't mean color maybe not dimensions but we run out of words well it's a very unfortunate choice of words actually but Murray Gelman chose it and now we're stuck with it but when applied to quarks the concept red white and blue really have absolutely nothing to do with visible colors they're much more like different kinds of charge electric charge but instead of in electricity we have just one kind of charge it comes in positive and negative varieties but it's just one axis so to speak it's a strong interaction it's kind of electrodynamics on steroids and we have three different kinds of charges and they're called colors for historical reasons basically because Murray likes to be clever let me turn to a question that came via the internet today from Alex in Sheboygan, Wisconsin he asks can we discuss multiverse theory and its relationship to geometry in some more detail okay there are actually two important multiverse theories in contemporary physics one of which I think is well even it is controversial but I think it deserves not to be controversial having to do with quantum mechanics where the wave functions that we use in quantum mechanics describe many many possible outcomes of experiments that don't occur when we make a measurement we find out one result occurs out of many possibilities with different probabilities a possible interpretation of that called the many worlds interpretation which I really think is the only consistent interpretation is that what's happening when we make a measurement is that the wave function describes many worlds when we make a measurement we discover which of those worlds we belong to and so that's a kind of many worlds that's implicit in quantum mechanics and well maybe I'll leave it at that and let other people talk but the second use of the multiverse is much cruder and it just means that there could be structures, spatial structures that are very very far away that we haven't seen yet where physical laws look quite different multiverse has different nuances but that's I think the main idea and this of course flies in the face of everything we know about the observed universe which seems to be uniform and obey the same laws everywhere and that's a very profound discovery in itself but there are theoretical reasons to think that if we did persist and wait long enough we might see different laws acting elsewhere or that it's fruitful to consider theoretically the possibility that we're only sampling a small part of a much much larger structure when we sample what we call the universe so that's the multiverse theory another question from our audience the questioner asks if mind and matter merge then can we alter the state of our experience with discipline directed thought for example the practice of meditation sure but I think more effective than meditation is studying physics or mathematics so why not a related question from the internet also you should exercise it's very good for your brain we talked a bit about the geometry that describes the physical aspect of the mind in terms of networking and neurons this question from the internet is there any geometry that describes the mental space itself yes yeah I mean there's a whole discipline called neural network theory which is rapidly developing and very exciting these days that describes well it's too early to say that it really describes how we think but it describes a rich kind of mental universe that is capable that allows machines to recognize patterns to recognize faces things like this in absolutely explicit mathematical terms as the operations of these mathematically defined imaginary objects there are no real neurons it's a mathematical construction so it's geometry in a generalized sense and the underlying geometry is the geometry of networks between units that I sort of sketched another question from the internet we've talked a lot about symmetry and perhaps seeing beauty in symmetry the questioner asked what about imperfection isn't that beauty as well if properly done yes done perfectly no I should emphasize that symmetry is only one form of beauty and there are certainly additional forms in fact if we look at that fractal which I think by any standard has a lot of symmetry it's very beautiful its symmetry is quite subtle you can't turn it some way and get the same structure it's certainly not spatially uniform it's very very structured it has a kind of symmetry if you blow it up parts of it may look the same as the whole thing but you know and of course if you look at any of the classical art objects they're not perfectly symmetric Michelangelo's David is not symmetric so there's a lot more to beauty than symmetry I mean well maybe I should leave it at that but symmetry is one thing that can lead to beauty just add if the universe was perfectly symmetric we wouldn't be here so yes I mean that's right I'm here and you're there therefore different points in space are different right one more question from our audience for Professor Wilczak what happens to geometry inside the black hole well no one knows for sure since no one's been there and done experiments but the straightforward application of general relativity which has been tested in other ways leads to the idea that if you did fall into a black hole you might not even notice if the black hole was big enough you would feel some tidal forces as you pass through the surface but basically nothing is there anymore it's all been swept into the middle and you can describe those tidal forces they get more severe as you get towards the center of the black hole squished into a spaghetti like shape as you fall into the singularity well you can describe the geometry in terms of equations but I think it's better to think about it it's easier to think about it in terms of how you would sense it if you were moving in this space-time geometry that's what would happen if the black hole is really big you would hardly notice when you first fell in in fact the whole universe might be a black hole and we might be inside it but nevertheless you can't send signals to the outside world anymore that's what's really happened when you fall in and your fate is sealed eventually you'll fall into the middle and shortly before that you'll notice that you're being squeezed into a piece of spaghetti one last question from our audience is does time actually exist or is it just a measurement of change wow well I think I reject that question questions about actual existence are kind of loaded questions they have more to do with the use of the English language than actual questions the kind of thing Wittgenstein called language games so I'd be much more comfortable with concrete questions about phenomena okay well I happen to have maybe a last from the internet that relates to time but is perhaps that kind of question this questioner Lauren from Salk Rapids asks if time and space are flexible is there any possibility that something like time travel is possible or maybe a faster way to travel through space well exploiting those the flexibility of space time is actually very limited you have to use extremely massive objects and concentrate a lot of energy in a small place to get significant bending so for instance whereas we use electromagnetic radiation for all kinds of practical purposes of communications and microwave cooking not to mention sensing the external world to date our evidence for gravitational waves which would be the corresponding effect of bending space time are very few and indirect and very ambitious difficult experiments are being planned and apparatus constructed to detect gravity waves at all and the gravity waves they'll detect will be things triggered by violent effects in the universe so it seems very far fetched that you'll be able to magnify those kinds of effects in a practical way to speed up space travel or even more drastically to do anything like time travel there may be fundamental limitations where there may not be the possibility of time travel but I think as a practical matter don't hold your breath thank you all for being patient here I would just want to remind people as we close this session we reconvene at 12.45 with music and one o'clock with Professor Shearer's talk have a great lunch