Science 5

This is science five and we come to Niels Bohr and a pair of contemporary physicist Stephen Hawking and Roger Penrose. It's a curious focus. And what this particular set is trying to do in science is to make a bridge between the first pair of books that we had. Mary Leakey Discovering the Past and Richard Feynman's book on QED with the last Pair. The third pair in science. One of them will be by a science fiction writer, Nancy Kress. A series of her short stories and a book by Kip Thorne, who teaches at Caltech, called Black Holes and Time Warps. So these two books form a pair in the middle of two other pairs. And if you look at this sequence, we have three pairs, which is the methodological procedure that we're using all through the education. We're using a triangle of pairs so that the set of those three pairs of books together make a six. And this set of six is a universal form. Not only is there a six part to the hexagrams of the I Ching, but all snowflakes in the universe. All snowflakes of water are six pointed. There, in fact, was a monograph written 400 years ago by Kepler called the Six pointed snowflake. And it's one of the simplest ways, 400 years ago, that a great mathematician was able to discuss why it is that mathematical theory. Coagulates in a universal existential, and that you can go from the universal existential shape of snowflakes and go back and verify and reify the theory, the mathematics. It was a stroke of absolute genius at the time when Kepler did this, and he meant it as a monograph that would sensitize his generation of people to something that was so unfamiliar to them that they didn't even realize that there was method in this madness. And the method is that the mind's theory, when it can be quantified, can be applied to the physical world. And that experiment in the physical world can come back through its quantification and have a verifiable Correspondence with theory. So that theory and experiment can work together. And as they work together, they form a self-correcting tandem. Now, the very first university in the world to ever do this was Oxford University. And they did this 800 years ago. And the master at that time at Oxford. His name was Robert Grosseteste. Grosseteste means great head, and Grosseteste at Oxford was one of those intellectual Franciscans who, because of the English stubborn personality, to want to see things for themselves and not just to have Beautiful doctrines or convincing arguments. The experimental science quality of English Thought 800 years ago was put into an educational format by Robert Grosseteste, and his prize student was Roger bacon. And Roger Bacon's works are some of the most perspicacious works in the history of science. It's hard to believe that he did his work 800 years ago. There was an edition of Roger bacon, his big Opus Majus, his major work about the turn of the 20th century. And it astonished people to find in his private notebooks he had sketches Is of microscopes made 800 years ago, and that he made them himself. We know because he had in the margins of some of his notes, pictures of the egg and the sperm from human beings, with all the detail of a laboratory microscope that one would have had 750 years later. But Grosseteste and Bacon were ahead of their time. There was almost no follow up, and things in the 1200s became medieval again all of a sudden, because it was only like a little isolated pool of liquid insight that eventually evaporated and left very little trace. But in Kepler's day, when he wrote the six cornered snowflake, which comes back to the shape that we're using all the way through our education, there was a tremendous follow up. But the follow up didn't come from someone in Kepler's circle. It came from a man named Descartes, René Descartes. And Descartes will show up in our history of science several times, maybe today, certainly next week. And what came out of this was the conviction that there must be a way to tune thought to the actual experience of the world, and that the actual experience of the world can confirm thought, and therefore thought was the medium, the common denominator, by the way, in which the mind and the world are brought into a focus, into a logicality, into an understandability. In our time, for the last 50 years, we have not had a single great physicist who is also a single great experimenter. Physics has been divided into those who are theoretical physicists and those who are experimental physicists. And the last individual who commanded both aspects of physics together was Enrico Fermi. And he died in 1954. And if you go out just west of Chicago, you will see the Fermi lab Fermilab with its great Tevatron circle. And all of that development comes from Fermi being both a great theoretician and a great experimenter at the same time. The development of the Cavendish Laboratory Laboratory in England was largely due to a sequence of great masters who were hands on physicists who did their own work, from J.J. Thomson through Ernest Rutherford to William Bragg. All of the great work in science before the middle of the 20th century was done by individuals who did laboratory work as well as theoretical work. And since then it has been split. And because it's been split and literally Become excluded. A great deal of misunderstanding through the last several generations and science has crept in. And unfortunately, meeting that kind of creeping in the in the 40s, there was a at the beginning of the beat movement in New York, there was a phrase that a radio show host named Long John Silver used to use. He called it creeping meatball ism that instead of something really beautiful, you just had it all smashed together in meatballs that could be served quickly. I heard this story from two friends of Long John Silver, a Theodore Sturgeon, the great science fiction writer, and K.D., the great Daoist actor. So we're trying to keep away from the creeping metabolism. And what made it so enticing is that the general population began using as buzzwords selected terms from the development of high powered science, without understanding that one has to have a meeting of theory and practice, and that it is not only just a meeting, but that they form an interface that exchanges and that they modify each other to the extent that there is a tunability of theory and practice when brought together. And it's that tunability that allows for a focus so precise that one can quantify to any extent of precision whatsoever. That there is no lower limit whatsoever to exactness when theory and practice exchange centers and come together. And this is not only for the very small, but also for the very large. And this is largely disappeared. So we're coming to a six part. Presentation, six books to make the science. We've had one pair already. There's another pair to come, and now we're at the middle pair. Niels Bohr I'm choosing a book by Abraham Pius because he was a physicist himself, and his understanding of events are quite excellent. Niels Bohr's times in physics, philosophy and polity. And we'll see that there indeed are some very interesting things about Niels Bohr. There was a book written about two years ago called Redirecting Science, about how Niels Bohr's institute in Denmark was funded by Rockefeller funding, making it possible for a tremendous advance in science at the time at that particular institution. And one of the models for the ability of Niels Bohr's group to make such tremendous advances, or the Cavendish Laboratory in Cambridge, making such tremendous advances, or places like the Fermi lab today or CERN in outside of Geneva today. Why science makes such tremendous penetrative advances. Part of the model for this, though philosophically, people say it goes back to Francis Bacon's advancement of learning and his idea that there should be some scientific utopian community where all the disparate people working on aspects of a problem come together. But the real model for this was a university in Germany called Göttingen, and the university at Göttingen in the early part of the 20th century, had 3 or 4 of the greatest mathematicians of all time in the same place working together. And it was an incredible ability of those theoretical mathematicians to change the nature of the way in which theory was mathematically enunciated to change the grammar and the syntax of mathematical language, so that it meant a radical change in experiment. And we'll find that Niels Bohr is an example of that radical change in experiment. One of the really great things about Niels Bohr was his ability to see into the results of experiments and bring out of that a most precise, quantifiable exactness of what actually was happening, actually occurring. And to bring that to an interface with the brilliant mathematical developments symbolized and characterized by Göttingen. Now the figure who was the king at Göttingen was the greatest mathematician of his age, and his name was David Hilbert. And David Hilbert. He was born in 1862 and died in 1943, so he lived over 80 years towards what became the end of his life. David Hilbert was beset by several difficulties, one of which was the Nazi takeover of his native Germany. Actually, he was born in Königsberg. Königsberg is a part of East Prussia, and really, it's not technically a part of Germany today. It's a part of Russia. They still claim it, but it is a port On the Baltic Sea, which in more powerful medieval times was set aside by the Teutonic Order of the Knights to make sure that they had access to the sea, to the Baltic Sea for evacuation, or for sending out their own troops. Evacuation, because they were always trying to take over that central part of Europe, and also because from time to time there would be generations where they would be under siege from the competition. And so Hilbert was born in a part of the Baltic coast, which was always an entrance and exit for whoever was in power. And he grew up having the sense that there is a mysterious interplay between circumstance and life, and you don't want to be too forceful as an aggressor because your time for being a refugee will come. Also, his grandfather's middle name in German meant fear God and love life. David, fear God, love life Hilbert. And that was his grandfather. And so he grew up in a very odd household. He was a German language Protestant, but the kind of Protestants that came from what is called historically, the Pietist sect of Protestantism. That means that they were esoteric, mystical personages who looked to see the old doctrine for them was the life lived. Is the doctrine received you? Whatever it is that you understand about your relationship with the divine, you will only know by being able to observe your life. If you only go by what you know that you believe or what you think you believe, you can be deceived, that the mind alone can be deceived. And so David Hilbert grew up in a milieu that was very interesting. He always held very lightly his genius, and he became the greatest mathematician of his day. In fact, one can run across these kinds of books all over the world here. Published by Cambridge Cambridge Mathematical Textbooks. An introduction to Hilbert space. That space is not just space, but there are many kinds of space. And one of them is Hilbert space. Here is a recent book. David Hilbert, a translation of his The Theory of Algebraic Number Fields. Not only are there different kinds of space, there are many different kinds of numbers, and that there are algebraic numerations which generate, in fact, fields. And his greatest book, one that's still in print. Geometry and the imagination. One can also find the foundations of geometry. Notice here that Hilbert and his mathematics saw that there's an interface between algebra and geometry, and this goes back to Descartes. Descartes in the 1600s saw that algebra and geometry algebra as a theoretical special abstract language, and geometry as the abstraction of form from the world have an interplay, and that you can calibrate the one in terms of the other. So that theory and practice can mingle together. If you bring algebra and geometry together. So that Hilbert is famous for this book, also brought into print principles of mathematical logic. And all of this came to be characterized, of course, by the fact that if you look at the interpenetration of algebra and geometry, the interpenetration of the world and the mind. What characterizes the interface is that there are common transforms that govern both at the same time, and that these transforms, as operators, are able to translate one to the other to the extent that they meld together and form a continuity. Now for Descartes, he was convinced, as almost everyone of his age, people like Kepler with such exceptional outlaws, that almost no one believed the farther reaches of what Kepler had exposed in experiment and in math. Kepler's genius was not appreciated by anyone until the young Isaac Newton, doing his own experiments, doing his own mathematics. His own theories discovered that Kepler had seen something so startling that it would change the foundations of thought. But the confidence that Descartes had was the confidence that was there from Aristotle, from ancient times, that there was a continuity in nature, that nature between one thing and another is so continuous that you can't tell the difference between the most of one state and the least of the next, that in fact they overlap, and that all of this is not only a continuity, but is a chain. The great chain of being and that nature is continuous was not questioned And publicly permanently until about 1900 by a man named Max Planck, who showed that nature in fact, in both experiment and theory, is discontinuous. And that nature, as far as the existential great chain of being, it is not a chain that has overlapping links, but is even less than a line that's just continuous. Forget the overlapping, but that even the line has blanked out portions that never occur. And what does occur then only occurs at that particular quanta, and that especially energy. Electromagnetic energy only occurs in discrete quanta and in between those discrete quanta. There is no registry of existentiality at all. At the zeros have a place along with all the oneness, and that this discontinuity is the quantum realm. Hilbert did most of his great math about the time when this was being mooted, and one runs across a collection of essays here. Fourier. Fourier. Hadamar and Hilbert transforms in chemistry that it not only applies in physics, it applies in chemistry, it applies in math, it applies in biology. And finally, the last next to last Hilbert thing that I will show here is something published in 1932, published in New York, the American Mathematical Society. Linear transformations in Hilbert space and their applications to analysis, so that by the time we get to the great age of Niels Bohr, which is the generation before Hawking and Penrose. And so we're pairing two books is like pairing two generations. We're pairing Bohr, who at the same time as Einstein and Hilbert, are learning that theory and practice have a mysterious accuracy that one needs to own up to. Exactness is that quantification quantization of theory is possible to almost any degree of exactness and the one dimension that forbids the exactness are the infinities that occur in calculations when one looks to see the all. When one looks to see the larger the spectrum rather than the particular, uh, discrete quanta. If you look at the spectrum, if you look at the spectrum, you will find that at certain parts, existence in theory and in practice acquires a densification. And like the spectral density of quanta, is noticeable to almost infinite exactness. The confidence in that has extended to the fact now that All six members of a matrix of quarks have been identified. All six members of the lepton family of particles have been identified the electron with its opposite, the positron. The muon, its opposite the tau, and its opposite that. Here one has a set of six again, and even on another order on the neutrino level, each one of those particles has its own neutrino. And there are six neutrinos that there are matrices of sets. There are groups of existence in quanta down to every level and up to every level that one could imagine. And so one of the qualities of working with the high powered science of let's stay with the 30s for a moment, was the fact that almost no one understood what was going on, and the few who did were actually in a position of paradoxical humor vis a vis those who pretended to know. Hilbert was the man that Werner Heisenberg sent his computations to, because he couldn't understand how to read what he was able to develop. And Hilbert, of course, um, was, uh, quite Humorous about the fact that all of these people were dealing with things that they almost didn't understand at all themselves. There is a biography of Hilbert by Constance Reid, and there's a photograph of the almost 80 year old David Hilbert in there. And. Hilbert stopped giving public lectures in 1933. He wasn't bothered by the Nazis because he was a Protestant, but he always considered it an absolute, um, travesty that they didn't incarcerate him as well, not only because all of his great students were Jewish, but he was at one time in an operation, and the only person that had his blood type was Richard Courant, another great mathematician who was Jewish. And so Hilbert got a blood transfusion. And he always used to privately joke and say, I'm a Protestant who has Jewish blood in his veins. In 1937, on his 75th birthday. This is from constant. Read her biography of him, a newspaper reporter. A Nazi newspaper reporter came to interview him and asked him about places to go in Göttingen, connected with the history of mathematics. I actually know none, he said, with without a trace of embarrassment at his ignorance. Memory, he said, only confuses thought. I have completely abolished it for a long time. I really don't need to know anything, for there are others, my wife and our maid. They will know. He's talking to a Nazi reporter. He's putting them on. You see, as the reporter then began to express a courteous doubt whether one could so eliminate memory and history, Hilbert put back his head and gave a little laugh. Yeah, probably. I have even been known to be especially gifted for forgetting for that reason. Indeed. Did I study mathematics? Then he closed his eyes. The reporter refrained from disturbing any further. The great old man, the honorary doctor of five universities who was such easy serenity, could completely forget everything houses, streets, cities, names, occurrences and facts, because he had the power in each remaining moment to derive and develop again a whole world. Someone with a differential consciousness on the level of David Hilbert is extraordinary, and even reporters for the Nazis don't stand a chance because it's like, um. It's like a technician from a delivery service trying to get the best of Groucho Marx. It you just ain't going to do it. It was a curious thing. Because when Hilbert developed his mathematics, one of the great developments in geometry at the time was due to a man named Riemann. And it's a little book on Riemannian geometry, published in 1926 by Princeton, very formative volume on Riemannian geometry. There are such things as books more recent on Riemann surfaces, and there are such books, just to give you examples the Riemann approach to integration. Local geometric theory. Cambridge University Press, just a year or two ago. We're talking about algebra and geometry. We're talking about theory and practice. We're talking about forms of learning and knowing. We're talking about the way in which sets or groups or matrices are able to bring together both the integral and the differential. Both the theory and the practice, and that when they are brought together, when the integral and the differential are brought together in a matrix, in a grouping in a set, one has the opportunity to go to a higher order of understanding, not a meta order at all. Aristotle is quite naive. There's no such thing as a metaphysics. But there is, as Niels Bohr saw, an almost infinitely refinable physics that one can be conscious to any degree of specification whatsoever. And if you can't at that particular moment, we now have the capacity to create scales and In spectrums and orders and inner penetrations, and we can learn to understand anything whatsoever, anything whatsoever, even infinity. Because one of the most powerful things in the 19th century was the idea that the infinite, the infinite makes a closed set in itself. One of the mathematicians that Hilbert learned from Georg Cantor in his dealing with sets, came up with an an astonishing ability to be able to express this particular idea, and it haunted thinkers of the day. So when we come to understand how it is that theory and practice in science, the mathematics of theory, the physics of experiment, come together and form discrete aspects of sets of groups that themselves have theory and practice. You begin to see that there are layers, not boxes within boxes so much, although sometimes it's expressed in that way. One of the strangest examples of a of a mathematical form is called the Hawaiian earring of circles within circles, having a tangential Meeting at one of the points, the way in which the mathematics and the experiment came together into sets, into matrices in the late 20s and early 30s influenced in particular a man named Werner Heisenberg, who was a student of Niels Bohr, who was a confrere of Niels Bohr, who was famous now for the rather glibly used uncertainty principle, as if people understood. Came out with a special kind of mechanics to mathematically explain the quantum world, and it was called at that time matrix mechanics. And about six months later, another confrere of Bohr's named Schrodinger, Erwin Schrodinger, came out with yet a different way of expressing the relationship. It was called wave mechanics, and matrix mechanics and wave mechanics were finally seen to be, though they were completely different in orientation that they said the very same thing about the very same thing. And it was Hilbert in a book written before either wave Mechanics or matrix Mechanics, written with his friend Richard Courant, his student and friend in 1924 already showed that this was not only possible or feasible, but was real. And when it was discovered that this was true, there was a tremendous development in the way in which our understanding of reality not took a quantum jump, but became available for a kind of a language of inquiry that has led to our own sophistication at this particular time, this particular moment, but that our sophistication at this particular time, in this particular moment, about 25 years ago, reached a dead end, because the language that was used at that time exhausted its ability to penetrate further. And this is where Roger Penrose came in about 25 years ago. 35, maybe. Now, Roger Penrose developed a new theoretical language that could interface with a new level of experiment, and he called it twistor theory. Twistor theory for Riemannian manifolds. And it caused a great deal of difficulty, and still does. And the person who disagrees with him most is his prized student, Stephen Hawking, who happens also to occupy the Lucasian Chair of Mathematics at Cambridge, the very chair that Newton himself held, named for a man in the earlier part of the 1600s who was a mathematician, and that Lucasian chair is the most famous chair in the world for mathematics. But Hawking, holding the Lucasian Chair for Physics and Mathematics, is a theorist and does not believe his teacher's twistor theory has any validity whatsoever. Not only that it is not right, but that it is not relevant. And we'll take further looks at this. Let's come back and maybe I can Rechoreograph. We're in a learning process that has a methodology, but the methodology is not one that has rules. If we had a methodology that has rules, we would have to learn the plan. And there is no plan and there are no rules that hold. But our method is one of inquiry, and continuous inquiry is a logic, but the continuous ness of inquiry for it to be logical truthfully must be discontinuous in terms of its discursiveness. If the points were always clear, they would be dots that need to be clearly connected, and you would have then a form of geometry which would sound good and look good and think good, but not be real. It's called a game. One of the most powerful mathematicians of the 20th century. His Great Collector's Item two volume published by Princeton functional operators. John von Neumann. John von Neumann, volume one measures and integrals and volume two the geometry of orthogonal spaces. Shapings of space. But his most powerful book, Theory of Games and Economic Behavior, 1947, that the powerful application of mathematical models of game theory changed the way in which the political economy of the world works, and it was just in time for the Cold War. Towards the end of his writing career, John von Neumann did this tiny little book that Yale put out 1958, The Computer in the brain. So that the instructional form of conditioning the brain, the mind, the economy, the politics, all of it is of a seamless plan which is not real at all. And what we're learning is how to be real behind, beyond, above, below, and through the faltering game plan of the world. Because the illusions have long since dug in as delusions and are not serving anyone. And our regression into medievalism by 2001 is an abject object of failure. So we all have to learn again, and we are learning again. But the first thing we need to learn is how to learn. And so we're starting from scratch. In January of 2002, we'll start one more time from scratch with nature one. We'll start with Thoreau and the itching and just begin to generate like reality generates. There is an emergence out of what can only be characterized as a mystery. And that emergence is the first objectivity, and it's objectivity does not register as things, but registers as action, so that action is an objectivity on that ritual level. And if you follow the action, you can develop a path integral. And one can understand a great deal along that way. One of the difficulties is to understand that no matter how refined that path integral is, it also carries within its own expressive form and process, a lot of zeros in blank spaces, a lot of not meeting and not touching. One of the most beautiful Chinese landscape scrolls from about a thousand years ago from the Southern Song, one of the greatest painters of all time named Ma Yuan. He used to be called One Corner Ma because he would put a lot of plants and ink and mountains and streams in one corner, and the rest of the scroll would be wide open space and maybe way off in the distance. There might be some sawtooth, jagged Razor Mountain in the mist, and that would be all. And he at one time painted one of the most profound temples. And when you look at that landscape scroll, if you look at a detail of that temple, none of the posts and beams of that temple meet. There's space in between all of the elements of that structure. And when you see that. You realize that every time a human being is journeying through a ma yuan landscape, his feet are never touching the ground, and the immediate context of where he is is not touching the rest of the context that there's always not a broken ness, but there's also a way of saying that there's an articulation so that the quantum world is articulate, especially in terms of action, that its ability to move is because the posts and beams don't touch, so that the joints are mobile in all dimensions all the time, and that the distribution of the dynamic does not follow a causal line at all, but takes over as a re-emergence literally from nanosecond to picosecond to I guess now it's down to femtosecond or even the next level attosecond that the quarks never touch, that make the particles, that never touch, that make the atom, that all of this has a very peculiar quality. And when it comes to structures like ourselves, the billions and billions of cells that make us up do not touch in a wall to wall way. But they interface in a membrane fashion so that there is a mysterious legerdemain of structure, especially in the organic level of the cosmos. Our life forms on this planet, in this star system, have a predilection for structure on the politeness towards water. Every cell membrane in this particular stellar system likes to have either a water loving or a water repelling paired quality, so that cells hold their structure largely on the basis of an attitude towards water. Philosophically, about 300 years ago, a man named Leibniz understood that the most powerful ways in which to talk about mathematical forms is in terms of some being bounded and others being unbounded. And if they are bounded, they have boundary conditions, and the boundary conditions are not contingent upon definition, but upon function. Function is an action, and functional operation becomes indexed by operators, and one can follow the action if you know the transform operators and the detailed quanta exactness. Otherwise, you're dealing with guesswork. So that the causal post and beam construction people are actually guessing, whereas in actual practice, conscious Application of attentiveness includes knowing the probabilities, the odds, and that those probabilities are informed by certain boundary conditions. One of them is initial starting point. And there are several others. And we talked last week about four that together make a beginning matrix. In the late 20s, in the early 30s, there were two geniuses. They were quite dissimilar in personality Heisenberg and Schrodinger. Heisenberg loved the position and the authority and liked everyone to know that he was the boss. Schrodinger was surreptitiously a Playboy who liked to really have fun, but if you have to think, he would quickly think exactly right and then move on from there. And this is what the biography of David Hilbert has to say. The matrix mechanics of Heisenberg was followed in short order by the wave mechanics of Erwin Schrödinger. Two different mathematical theories about how the quantum world worked, and eventually they were put together, and matrix mechanics and wave mechanics became quantum mechanics. The two papers, although they were on the same subject and led to the same results, astonished physicists. For as one of them marveled, they started from entirely different physical assumptions, used entirely different mathematical Methods that seem to have nothing to do with one another. The equivalence of Heisenberg's and Schrödinger's theories, however, was soon established. The whole development gave David Hilbert a great laugh, according to one of his biographical buddies. When Max Born and Heisenberg and the Göttingen theoretical physicists first discovered matrix mechanics, they were having, of course, the same kind of trouble that everyone else had in trying to solve the problems. They couldn't do the math and to manipulate and really do things with matrices. So they had gone to David Hilbert for help. They went to the big professor at the big university, these famous historical people. And Hilbert said the only times he ever had anything to do this is his reply, because they couldn't get the math to work with matrix mechanics. What's wrong here, professor? And so he laughed, and in his own oblique way gave them the clue. But in this kind of a form, he said, well, he didn't deal with matrices very much. The only time he had to deal with them was in a very special condition, very intelligent man. He said the only times he ever had anything to do with matrices was when they came up as a sort of byproduct of the eigenvalues of a boundary value problem of a differential equation. It's the only time he ever paid any attention to them at all. And of course, this is like monumental clue. But just reading this and hearing this and we can read some more. She says. Constance Reed says. That Hilbert was saying he was only concerned with matrices as a byproduct when he looked at eigenvalues of the boundary value problem of a differential equation. And you can go to the encyclopedias and you can see eigenvalues and eigenfunctions. If an equation containing a variable parameter possesses non-trivial solutions, if there are real solutions only for certain special values of the parameter, the parameter is the boundedness. These solutions are called eigenfunctions, and the special values are called eigenvalues. In other words, no matter how minuscule, if they are not trivial, then they are real And you should be able to find them through experiment. They may be incredibly small. It just means you have to refine your equipment and your instruments, refine your experiments, and that you will should be able to get there. And the results should not only match, they should be a cinch so that if you can figure it out theoretically in the quantum way with matrix mechanics, it means then that you're dealing with a situation that has a boundedness, and that you have to have a way to stay out of the other kind, the unboundedness. You have to stay out of the infinities, and if you can stay out of the infinities, then you should be able to think and experiment and mesh and confirm to any degree of specificity in the universe. So Hilbert. So if you look for the differential equation which has these matrices, you can probably do more with that. They had thought it was a goofy idea and that Hilbert didn't know what he was talking about. So he was having a lot of fun pointing out to them that they could have discovered Schrödinger's wave mechanics six months earlier if they'd paid a little more attention to him. As a result of his almost miraculous recovery, Hilbert at this time underwent an operation and got Jewish blood in his Protestant veins. Hilbert lived to see what had been called one of the most dramatic anticipations in the history of mathematical physics. In fact, it was the most astounding thing since Newton's Principia mathematica. The current Hilbert book on mathematical methods of physics, which had appeared at the end of 1924 before both Heisenberg's and Schrödinger's work, instead of being outdated by the new discoveries and the new theories seem to have been written expressly for the physicist who now had to deal with them. Hilbert's own work at the beginning of the century, 1890s 1900 1903. Beginning of the century on integral equations. The theory of eigenfunctions and eigenvalues, and the theory of infinitely many variables turned out to be the appropriate mathematics for quantum mechanics. So at the math was there was done before any of this came about. And this brings in Roger Penrose. This is in a little book. This is monograph number 156, The London Mathematical Society. Twistors in Mathematics and Physics, 1990. Penrose's introduction twistor theory after 25 years its physical status and its prospects. Meaning. Where is experiment now? Where is theory now? And what he will say in this? I have provided the next phase of mathematical language for theories and experiments that will come in the 21st century, and the math that I have done, like Hilbert's math that he did in connection with his student, Richard Courant. The math is already there, folks. Twistor theory, twistor language. But we haven't got there yet in our refinement to be able to speak of this language. Yet we don't speak it the language yet. This is Penrose about ten years ago. The primary objective of twistor theory originally was, and still is, to find a deeper route to the workings of nature. Yeah, that's what it says. So the theory should provide a mathematical framework with sufficient power and scope to help us towards resolving some of the most obstinate problems of current physical theory. What are they? Such problems must ultimately include one. Removing the infinities of quantum field theory. Two ascertaining the nature and origin of symmetry and asymmetry in the classification of particles and in physical interactions. It's a pretty big questions. Three. Deriving from some fundamental principle the strengths of coupling constants and the masses of particles. If you write an equation that includes a constant, say, Max Planck's constant h, which we'll get to next week, why there is such a thing? How in the world? And why does that couple with the theory, experiment, detail of particles? And how does some universal constant, which is a consciously derived quantification of a relational situation? How does that meld and work in equations with particle stuff at all. Why does that work? It's a very big question, by the way, for finding a quantum gravity theory. You can't find it without that. Without what? Without a new mathematical language, which Penrose has developed for a long time now. And no one has been able to work with it. Because speaking a language is not a matter of learning rules. It's a syntactical acrobatic. It's a grammatical courage, and it takes an artist to be able to do that, because it's like developing a role that no one ever played before, before someone wrote the part or even built the theatre. And so you're dealing with something that has to emerge whole, Spontaneously out of the mystery of zeros. And that takes very big magician called an artist that mathematics on this level is an art. It isn't about rules, it's about aesthetics. It's about beauty. In the ancient Plutonian sense. It's about someone who knows how to love deep enough so that their conscious historical activity elicits a response from the cosmos. It's like courting Mother Nature and having her kiss you, that that's the only way that we're going to go anywhere further than the dead end that was reached in the 1960s. And it takes an acclimation to learning about learning in a new language way in order to access that. Penrose goes on. He lists more. But he says, I shall comment on these issues individually in a moment. But as things stand, it must be said that the success of twistor theory to date has been almost entirely in applications within mathematics, rather than in furthering our understanding of the nature of the physical world. I would think of twistor theory in its physical role so far as being something perhaps resembling that of Hamiltonian formalism. Hamilton was a great mathematician. That formalism. That Hamiltonian formalism provided a change in the framework for classical Newtonian theory, rather than a change in Newtonian theory itself. In other words, you're not modifying the theory, but you are modifying the context in which that theory is able to hold its boundedness in the first place, so that the transform of it is not just that you modify it, but you morph it into something else, not by causing it to happen, but by allowing for it to reassemble in a new emergence from that mysterious place in which all theories happen in the first place. And what is that? It is an unbounded infinity. We need a footnote here. Theory is a Greek word theoria. Theory does not mean mental plan theory means contemplative, attentive focus that the contemplative attention focus in the classical Greek. The greatest exponent of this in the early times of its genesis was Pythagoras, that Pythagoras power of contemplative attention saw, for instance, the relationship of the Pythagorean triangle. The square of the two sides equals the square of the hypotenuse. A three, four, five right triangle will always have this universal shape and it doesn't matter what star system you're in. It takes a deep contemplative focus, though, to continue its stamina to see that that relationship, which is not only true geometrically, is true for any scale of harmonic analysis. And so, out of that kind of form, Pythagoras developed the first musical theory. The first harmonics, and saw rightly, that there is involved in this process the contemplative, the theoretical, the theory, deep attentiveness in its stamina by allowing for reemergence to occur so that they're not just aligned, but that they are resonant, which is why there's a harmony and one of the most mysterious and yet profound Pythagorean sayings that was remembered and always kept is, he said. And because he was so revered, the Greek word is ipse dixit, he said. And literally everyone in antiquity knew the only person that spoke this way was Pythagoras. He, that guy, the cook in there, the chef, the iron chef of ideas. And he said, this geometry is history. This geometry is history because the way in which time Space happens for us is cognate with this happening so that when we make music and sing, nature dances with us to our tune, and that this is not the pipes of pan charming nature in some ooga-booga way, but this is us learning the music of the spheres, because one could see even Pythagoras by his time, could see the geometry of lines and points and planes, reveals a threshold which is not on the plane, not in terms of lines, and doesn't reduce to dots. And that threshold of points and lines and planes reveals to us spheres, because harmonics deal with spherical deities. And so in the 20th century, one of the greatest artists of all time, Kandinsky, writing a textbook for the Bauhaus where he was teaching teaching, called his book From point and line to plane. And he followed the old ancient Pythagorean way, but was showing that there's a new harmony that is able to come. And that is by understanding that tone tones have an interface with colors. And that colors sound. And therefore there is not only a harmonics of color, but that harmonics of color can be expressed in music as well as in painting as well as in architecture, in poetry and whatever one does. Can be expressed in the development of a human personality that one is not just colloquially a colorful character, that there are human beings who are so conscious that they are kaleidoscopic because they show the infinite differential diffraction of light into its rainbow array and put that into motion. And it's like a kaleidoscope of rainbows, because and we now have light bulbs that are have filaments that are tuned to the exact frequency of the light from this particular star, so that the light that comes out of them is not electric light, but is sunlight. And there will be sunlight lamps within about 5 or 6 years on the market, where the light at night will be sunshine and not at all electrical. It will lose its mechanical tinniness. And what's interesting is we know now how to make light bulbs tuned to any star in the cosmos. If you are on a planet around the star Procyon, about nine light years from now, you could have light fixtures tuned to that star. So you could see by that star's light, so that when we say that the conscious cosmos is a gift of beauty without bound, we're just speaking in terms of the headlines of the ad. It's absolutely true. Here's what's interesting about Penrose. He was able to bring his deep, appreciative theoretical understanding into play in such a way that his math condensed and formed into a transform that could be used to test physical experiments. It's called the Penrose transform. Here's a little monograph from Oxford. The Penrose transform, its interaction with representation theory. Because as long as one is working with representations, you will always be in a game. Which is characterized by the images, which is indexed by the symbols which can open out into momentary visions, but they don't stay there. They can't be there. They bounce back into the symbols. They bounce back into the image base. They bounce back into the ritual comportment actions because that's how they do. If they're not transformed. And so there is no such thing as quantum gravity. There's no such thing as twistor geometry and field theory, though there are books on it because it hasn't been done yet, but it will be done. It's not measuring up to something that's a fantasy. It's not pursuing something that is theoretical, only it's not daydreaming. It's as practical as one can get, because there will be a quantum gravity and a quantum field theory QFT. When we ourselves can inhabit and speak the language of it adequately, it will be there. It's like that. It's mysterious like that. Our particular beauty is that we have always learned how to sing, no matter how unusual the language is, and we're very close, and we'll be able to sing in this way. I plan to show a few other things today, but I think we've gone as far as we need to go. We'll come back next week and go deeper.