*~ Lorraine Walsh*

**Selections from Portraits of the Mind:
Visualizing the Brain from Antiquity to the 21st Century by Carl Schoonover**

**Visual system.
**Ibn al-Haytham, circa 1027 (published in 1083).

The oldest known depiction of the nervous system seems reassuringly well ordered: a large nose at the bottom, eyes on either side, and, flowing out of each eye, a hollow optic nerve that meets the other for a moment before they part ways and continue on to the back of the head— all of this meticulously named and cataloged. From this unadorned sketch, drawn in eleventh-century Cairo by Ibn al-Haytham, comes a premise that is so elementary as to seem almost trivial: In the nervous system, information travels. From here we go on to formulate the more exciting—and more explicit—hypothesis: At each stop in its path, signals from the world outside are somehow processed, interpreted, or put to use. How information travels from one part to another inside the brain, and how it is processed at each step, is the business of neuroscience.

Al-Haytham’s drawing was based in part on the teachings of Galen of Pergamum, a second-century Roman physician and anatomist who, although dead for eight centuries, continued to exert an outsize influence on the world of brain science. In ancient Rome, Galen worked in an environment of relative permissiveness when it came to cutting through bone and flesh to study the organs underneath, an activity that religious and legal restrictions subsequently rendered taboo for centuries thereafter. Since human dissection was off limits, he employed as his subjects a veritable zoo—apes, dogs, bears, stags, camels, and one elephant. Otherwise, his exposure to human anatomy was restricted to wounded gladiators and rotting or deteriorated corpses that he came upon by accident.

**The shape of ventricles. **

Leonardo da Vinci, circa 1508.

With religious authorities issuing blanket bans on dissection after Galen’s era, many anatomists relied on interpretation of and commentary on his findings, which he meticulously cataloged in a series of hundreds of treatises. Many of these were lost in a fire, and if he did draw figures summarizing his findings, none are known to exist today. Thus, our vision of Galen is one that is necessarily mediated by the eyes and minds of his followers. His fragmented output, from an era more open to exploration, crystallized, amplified, and took on baroque characteristics of its own as it bounced around the libraries of Europe and the Middle East throughout the Dark and Middle Ages. His words were dissected under the pen; his theories were bent to accommodate the leading views of the time. Occasionally his views were challenged—especially in the Islamic world—but by and large his theories became dogma.

An early proponent of what would soon become a forceful return to the study of actual anatomical samples, the Italian polymath Leonardo da Vinci often conducted his dissections in secret, as restrictions began to be cautiously relaxed. Dissatisfied with Galen’s description of the ventricles, and seeking a way to more accurately determine their structure, Leonardo realized that the brain was sufficiently complex that cutting and looking alone would not succeed. To circumvent this problem and study ventricles in their unadulterated state, he turned to a statue-casting technique, injecting melted wax into the ventricle of a freshly killed ox while siphoning off the excess fluid through holes poked in the other end. After the wax had cooled and solidified, he carved the surrounding brain away until nothing was left but the shape of the cavity. Leonardo’s drawings of ventricles, c1508, (not shown here) depict his rendering of the cavity from both the vertical and horizontal view. If the history of neuroscience is a history of seeing, then Leonardo ushered in the conviction that our eyes alone cannot do the trick.

**The Fabrica frontispiece.**

Andreas Vesalius, 1543 (image taken from 1555 edition).

Frustrated by the limited opportunities during his time in medical school to, as he delicately phrased it, “put my own hand into the business,”[1] Vesalius overcame any moral qualms—and the occasional pack of wild dogs—to scour local cemeteries for human remains. In response to this bold departure from traditional anatomical study, Vesalius’s former mentor, Jacobus Silvius, once implored his colleagues to “pay no attention to a certain ridiculous madman, one utterly lacking in talent who curses and inveighs impiously against his teachers”[2] and urged the powers that be “to punish severely… to suppress him so that he may not poison the
rest of Europe with his pestilent breath.”[3] Clearly, Vesalius was onto something. Yet in a town still in the thrall of Galenic theories, Vesalius’s unsettling obsession with performing his own dissections raised eyebrows and led him to settle in Padua, Italy, where his research program received a greater measure of support. There, he was supplied with a reliable stream of corpses fresh off the gallows, whose deaths were occasionally timed to accommodate his workflow. Vesalius’s dissections occasionally became massive public affairs, bordering on the ceremonial, for the benefit of students, colleagues, dignitaries, and assorted gawkers. The frontispiece of his 1543 magnum opus, *De Humani Corpus Fabrica (On the Workings of the Human Body)*, seen here, hints at the flavor of these events.

It was his dissections in Padua, and an epiphany induced by a side-by-side display of human and ape skeletons, that put the proverbial nail in the coffin on Galen’s anatomy. Vesalius realized that while his Roman predecessor had claimed to be characterizing human anatomy, the structures he had described more closely matched the anatomy of other animals—a fact that is hardly surprising in retrospect, since in Galen’s Rome human dissection was prohibited. What Galen had failed to account for was the possibility that his findings in apes, stags, and dogs might not prove true for humans, as well.

**View of a human brain from below. **

Thomas Willis and Christopher Wren, 1664.

Descartes’s vision of the nervous system as mechanism would find its experimental realization across the English Channel in the work of Thomas Willis and Christopher Wren. Willis, who wielded the scalpel with consummate virtuosity, generated a mass of anatomical knowledge that set the new standard for neuroanatomy after Vesalius. Wren is perhaps best known for having designed Saint Paul’s Cathedral in London, but when he wasn’t drawing up building plans, he found the time to make significant contributions to the fields of mathematics, astronomy, and—assisting Willis—anatomy. Together, they synthesized their observations into a single, coherent, three-dimensional whole, as shown here. With human dissection now increasingly mainstream in most of Western Europe, they provided an account of neuroanatomy that was vastly more precise than that of Vesalius, shifting the emphasis away from the ventricles and back to brain substance itself.

The ventricular theory fell apart when Willis, who pioneered novel dissection methods noticed that the ventricles collapsed the instant the organ was

removed from its case. Concluding that the ventricles were merely “a complication of the brain infoldings,”[4] Willis turned his interest to the arterial system, the dense web of blood vessels that innervates the

tissue. He believed these served as the conduits for a “nervous juyce” of animal spirits sloshing around in the brain. In order to examine the vasculature’s labyrinthine structure, Willis would inject a dyed solution into an artery and follow its tortuous path through the brain, echoing Leonardo’s prescient method for studying the ventricles, and confirming once again that the unaided eye would not be sufficient to the task of studying this organ. His ingenious method of observation, which illuminates arteries and relegates the rest to the background, finds a direct expression today in *cerebral angiography*.

**Pyramidal neuron. **

Santiago Ramón y Cajal, 1899.

Modern neuroscience begins with the neuron,
a cell that collects, processes,
and transmits information to other neurons in the brain. This illustration shows a *pyramidal neuron* drawn from observation by Spanish neuroscientist Santiago Ramón y Cajal in 1899. Its nucleus and DNA reside in the *soma*, the thickened area at the center. What distinguishes a neuron from other cells in the body is the striking set of long appendages that radiate from it—think of them as antennae that neurons use to communicate with one another across the expanse of the brain. The thicker *dendrites*, the cell’s “receivers,” rise upward and outward in this illustration, while the thinner *axon*, the “emitter” of a neuron, drawn here only in part because of its considerable length, shoots downward. Unlike with antennae, however, transmission in the brain is not wireless, and the infinitesimal spaces between these neural appendages gave rise to an epic scientific battle one century ago.

The hypothesis that a neuron could
be discrete—distinct from yet connected to others—once divided the most credentialed voices in neuroscience, and the schism ultimately made its way to the august podium
of the 1906 Nobel Prize awards ceremonies.
The committee had chosen to honor both Cajal and his scientific rival, the eminent Italian Camillo Golgi, for their respective contributions to the study of the brain. Golgi believed the brain was continuous, made up not of individual parts but rather an uninterrupted reticulum, a single mesh. Cajal, on the other hand, argued that the existence of the neuron as a self-contained entity supported a view of the brain as a network of distinct, interconnected units. He reached this conclusion, ironically, using a chemical staining technique pioneered by his rival. Named the *reazione nera* (black reaction), Golgi’s method stains a very small fraction of individual neurons in brain tissue, while, crucially, leaving all others invisible. Why only approximately one percent of neurons incorporate the black stain—a mix of potassium dichromate and silver nitrate—remains a mystery to this day, but this selective viewing rendered invisible the impenetrable tangle of brain tissue and facilitated previously unthinkable access to the neural universe. In their Nobel lectures, the two scientists laid out their respective visions of the neural world, while taking shots at each other—some of them courteous, others decidedly not.

**Purkinje neuron.**

Santiago Ramón y Cajal, 1899.

By the time Golgi and Cajal’s argument made its way to the Nobel celebrations in Stockholm in 1906, scientific opinion had mostly turned against Golgi’s theory, and the audience was reportedly dumbfounded as he proceeded to attack Cajal’s views from the stage. That the Spaniard won the neuron-versus-reticulum debate, along with a host of other skirmishes, is a testament to his prodigious knack for synthesis. He apparently did not sketch what he saw with a pen in one hand and the microscope’s focus knob in the other. Instead, he is said to have drawn from memory, in the afternoon, after a morning of observation. Though the details were of course of great importance, what mattered most to Cajal was the general form, the common properties, the essence of the specimen’s overall architecture. Studying tissues ranging from birds to humans, he focused on the commonalities, uncovering deep principles of brain organization. His amply documented interest in the visual arts suggests why his renditions of biological samples are so exquisite and hints, perhaps, at why he was able to identify

underlying forms where others saw only lines.

This drawing shows a *Purkinje neuron* that is strikingly different from its pyramidal cousin in the previous drawing but built along similar lines. Although the two types of cells play very different roles in the brain, they share the same blueprint: at the center, the soma; radiating up and out, its many thick, branching dendrites; traveling down and beyond the frame, a long, thin axon. ·

[1] Stirling, W. Some Apostles of Physiology. London: Waterlow and Sons Ltd., 1902: 2.

[2] O’Malley, C. D. O. Andreas Vesalius of Brussels, 1514–1564. Berkeley: University of California Press, 1964.

[3] Ibid.

[4] Willis, T. *The Anatomy of the Brain and Nerves*. Feindel, W., ed. Montreal: McGill University Press, 1965.

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Chairman of the SCGP Board of Trustees

*Interview by Maria Shtilmark*

* *

*The recipients of the 2017 Breakthrough Prizes were announced on December 4th, 2016, marking the organization’s fifth anniversary recognizing top achievements in Life Sciences, Fundamental Physics and Mathematics. Dr. Cumrun Vafa, along with Drs. Joseph Polchinski and Andrew Strominger, was awarded the 2017 Breakthrough Prize In Fundamental Physics for his research in transformative advances in quantum field theory, string theory, and quantum gravity. Dr. Vafa has a rich history with the Simons Center. He joined our Board of Trustees in 2005 and has served as its Chair since 2009. He has also served as the Scientific Director of the annual Simons Summer Workshop since 2003, and visits the Center regularly. The Simons Center is pleased to formally congratulate Dr. Cumrun Vafa and all of the winners of the 2017 Breakthrough Prize In Fundamental Physics. Our heartfelt congratulations to all!*

**Congratulations on becoming a laureate of the 2017 Breakthrough Prize in Fundamental Physics “for transformative advances in quantum field theory, string theory, and quantum gravity.” As this definition is a bit broad, what do you consider your main contribution?**

Thank you. I don’t take the credit personally and view this as recognition of not only my own work, but the work I’ve been doing with many people, with many different ideas. I’ve had over 150 collaborators, close to 170 now, written over 250 papers, and I can’t say that one particular paper was the reason. It may have been the combination of them. I feel part of the group, where there is camaraderie between colleagues. The fact that they have chosen my two colleagues and me is kind of them, but I view this as not just us.

As to my work in general, the overarching theme has always been the connection between physics and mathematics, particularly in the context of geometry. How can we learn physical facts from geometry, and how we can learn geometry from physical facts? Many of my works are at the interplay between these two subjects, which cover a wide range of topics in physics, quantum field theory, quantum gravity and string theory. It seems to me that the bulk of progress in string theory lies in these relations between geometry and physics.

**You graciously acknowledged all your collaborators on the Breakthrough Prize web page and thanked them. Not everyone does that!**

Thank you. I specifically contacted the InSpire and asked if they could help me collect the names, which was at the time when we were not supposed to let the news get out, so I couldn’t tell them why I needed it. Unfortunately, in the InSpire’s database, they can only list the collaborators up to a hundred. And I knew I had more than a hundred, so I asked them to find a way to actually increase the number and give me the names of all my collaborators. So, after a couple of weeks, they kindly forwarded to me the full list. Thanks go to them!

**In your beautiful acceptance speech you thanked your parents, your sons, and dedicated this prize to your “wife and best friend,” Afarin, whose unwavering support and love has been a steady pillar in your life.**

That’s correct. I think my family (my wife Afarin and my kids, Farzan, Keyon, and Neekon) has played a special role in bringing inspiration and happiness to my life. I remember working on concrete physics projects and being inspired by the interactions with my sons when they were very young. “What is the relation?” you might say. I don’t quite understand it, but I certainly owe them a lot of my inspiration.

**You also mentioned Iran, “home of many eminent scientists, such as Khayyam and Biruni.” Could you perhaps remark on the impact these two have had on your perception of the world?**

I think in my acceptance speech I mentioned that science is a timeless, borderless adventure. If we take a snapshot of science today we’ll see various centers of excellence, and some places that may be relatively quiet, but we should view this as not the property of science, but as transient phenomena. Sometimes science is strong in one place, sometimes in the other. It is not a territory of a particular area, and it’s not a territory of a particular people, it’s an adventure for the entire human kind. In this sense, I want to emphasize the fact that it’s timeless — in different times, different cultures contributed more to the development of science and math. And it’s borderless — it doesn’t matter where knowledge originates. People from different parts of the world can contribute, and do contribute. This open culture of science — the fact that it’s borderless — is one of the main reasons science makes advances, and interacting with all these different people from different cultures and different backgrounds is one of the most fun parts of being a scientist.

As far as the names you mentioned, they are two among many ancient Persian mathematicians and scientists. Khayyam worked in geometry and math, trying to geometrize algebraic equations, among other things. That was one of his talents, in addition to being a philosopher and a poet. That to me defined that he was multifaceted, but deeply interested in the connection between geometry and algebra. The other person you mentioned was Biruni, who was a very perceptive physicist, in today’s language. He knew deep math, but he applied it with precision to the world around us. For example, he used some simple and beautiful ideas from geometry to measure the radius of the Earth with unprecedented accuracy for his time. And this is late 10th — early 11th century! The fact that he actually applied geometrical ideas to the real world is what I found fascinating and inspiring.

**As someone who was born in Iran, could you tell us a little about how sciences were proportioned with other subjects in your school, and the system of education in general?**

Yes, I was born in Tehran in 1960. I had the fortune of attending a very good school, the Alborz high school. But the education we were getting was not necessarily at the same level as in the Western countries, and in particular, we were behind in science education. Some parts of math were covered well; we had excellent classes on Euclidian geometry and appreciation of proofs. Understanding what mathematical proof meant helped me when I was learning more modern math. But at that time there was one textbook for the whole country, and that textbook wasn’t that great in science. I was studying a little on my own, learning things like Einstein’s theory of special relativity. I was so eager to go to college in the US that I applied one year early, so I started MIT in 1977. I was planning to study engineering and economics, but I took courses in both subjects and didn’t like them. I was taking math and physics courses at the same time and those I loved, so by the second year I decided to switch. I graduated from MIT in 1981 with a double major in math and physics, and went to Princeton for a PhD in physics. Edward Witten was my advisor. I completed my PhD in 1985 and came to Harvard, becoming junior faculty in 1988, and senior faculty in 1990. I have been at the Harvard Physics Department since then.

I love going back to Iran. I enjoy visiting my relatives and giving lectures on physics and math. Scientific life has improved quite a bit since I was growing up; they have good groups working on string theory and modern aspects of mathematics. They may not be the leaders of the subject, but they have people following recent developments and writing good papers.

**Talking about string theory, you mention mysteries (of confinement of quarks inside atomic nuclei) and enigmatic properties (of astrophysical objects, such as black holes). Is solving puzzles and uncovering mysteries your driving force?**

Perhaps what summarizes my interest is the word magic. The very simple things we see around us, like this big moon out there in the sky which is not falling down — that’s magical. It doesn’t mean there is no nice and simple explanation to it. What I like about the beauty of science is taking this magical reality and making it understandable. Magic exists, even if we understand it. The way it is put together, the presentation of the reality in the form we see it, is magical. So trying to decipher the magic and understand how it comes to be so beautifully presented to us, combined with the rational explanation, often based on elegant mathematics, be it in the form of geometry or other ideas in mathematics, is very attractive to me.

We are curious as human beings. It is natural to be asking questions. But why we would direct our innate curiosity towards something like string theory, that will have no application in our lifetime, is a question that some people may ask. How can we be spending so much time on a subject so disconnected from physical observation of day-to-day life? It is a good question, and it is our sense of aesthetics that tells us that there is truth behind this theory that attracts us, and some of the application of it comes secondary. Because, after all, we are trying to understand how the truth of nature works. We also know that we will not finally understand it, as science only works in increments. In terms of the amount, we know the amount we can learn is very tiny, and we know that from looking backward. Also, it is a little disappointing that the human lifespan is so tiny compared to the age of the universe and all the beautiful reality. The maximum distance we travel is a distance on the globe; compared to the vast scale of the universe it is almost nothing. Connecting ourselves to sets of reality, which transcend space and time, gives us some kind of satisfaction of going beyond the reality of our finite lifetime. It is a minor satisfaction in view of the fact that we are not going to be able to visit everywhere and be around all the time.

That is why I am attracted to fundamental science, though I know and I appreciate the fact that the contribution that I am going to make is going to be very tiny, compared to the portion of the unknown.

**We started this conversation in 2014, when the discovery of the Higgs particle was a big topic, and I asked you if it answers major questions, or if you expect more to come? What do you predict CERN can bring in the future to the type of research you do?**

If the Higgs boson discovery is the only discovery of the Large Hadron Collider, then this situation is very unfortunate. It means that whatever has been going on for the past 40 years is useless in the context of experiments. Of course, it is great that such a fantastic machine was able to discover the truth. It is a remarkable achievement, and the scientists who did it should be congratulated to the max. But nature could have given us more hints about string theory. We have not been as lucky as we wished. There still is room, though, as LHC has 5-10 more years before we can be sure if there is new physics at LHC.

**Is there a question that you wish you were asked, but you were not?**

I think there might be forums where a person who is not a physicist, and is not interested in forces and particles per se, could ask a scientist “so, what does it all mean for regular people?” Not so much explaining the laws of physics, or how forces of elementary particles work but “how does it affect my life?” or “how do you think about this?” or “does the way you look at the whole universe change your daily life?” In my opinion, these kinds of questions are not raised as much. Perhaps scientists are also a bit shy to venture into these areas because they don’t consider it their area. Perhaps it is philosophy, or poetry; these domains are some that scientists don’t wander around, and people don’t expect them to. They usually focus on matter of fact things, such as types of particles and kinds of forces, and it’s a little too mechanical, or too technical, in my opinion. That’s just my taste.

What I find a little bit strange in the attitude of scientists of this century, or of the past few decades that I have been working, is that in some sense it’s not only not philosophical, it is sometimes anti-philosophical despite the fact that the foundation of science is philosophy. Many scientists do not recognize the underpinning of their own ideas as philosophical. They don’t venture into those areas. Whenever this discussion arises, they dismiss it as useless and just put it off the discussion table. I think that’s neither faithful to how science is being developed, nor good for the development of science. For example, during the early days of quantum mechanics, or relativity, there were discussions that were mixed with as much ideas of science as ideas of philosophy, and I think that aspect of science is missing today.

**If we could return to collaborations — the majority of your work is in collaboration, but every 2 or 3 years you write a sole author article. Is that intentional or incidental, and what conceptual difference do you see in your papers alone vs. with collaborators?**

I love collaborations. To me, science is about understanding things, and therefore getting help from other people and collaborating with them is perfectly good. Trying to build the “I did it!” kind of attitude is not good, and to me there is no loss in trying to get into collaborations. I like the diversity of talent that is brought in through other people and collaborations, so I enjoy that human aspect of trying to deal with different people, as well as the ideas they bring to the table. I come up with one idea, and my collaborator suggests another, and it makes it far more exciting. Occasionally, though, there is an idea that starts in my own head and gets finished in my own head. I didn’t need collaboration; there is a case of a sole author paper. But it’s not like I design it like I have to do this by myself. If it happens when somebody else contributes, then it’s collaboration. So, to me, that is the nature of science.

Often in science, we see this unfortunate view that we are after heroes. Human sight goes into the direction of hero building, in political scene or other areas of human endeavor, like art, music or film. Somehow it gets translated to an idea that a sole author paper means you have a hero. I don’t subscribe to this view of science. To me science is by far more interesting and meaningful when it is the result of collaboration. This is what I like about the Summer Workshop that we run at the Center. Many of the people I like to collaborate with are here. I use this opportunity to start or continue collaborations, and it is fantastic in that respect and fits very well with my attitude about science.

**This year marks the 15th annual Simons Summer Workshop that you have directed. What are you especially proud of?**

Yes, this is the 15th year of the Summer Workshop, and with every year it becomes even smoother and more effortless. It is by now well-recognized in our field that at the Workshop there is an atmosphere of discussion, collaboration, and top-notch people, as well as eager students and researchers, all gathered in one place. So not a specific topic, but that atmosphere is what drives us forward. The Center does an amazing job in making this a friendly environment. Every time I get feedback from the participants, they are always amazed how smoothly things run.

**And we must thank you for that! How do you see the future of the SCGP? How will it and should it develop in 10 years?**

String theory is under a great amount of pressure in terms of funding. Since it has not been connected to any experiments, there is tension for this field to be supported indefinitely by physics departments (which are supposedly based on physics experiments). On the other hand, mathematicians have seen that this subject is useful to the development of pure mathematics. A lot of them like to see the continuation of the development of string theory

research, except they feel that a lot of things that are going on in string theory are not rigorous enough to be called mathematics. Therefore, many mathematicians view this as a good activity by the physics departments. So, subjects like string theory fall into the crack between two areas, and do not get supported.

This is where the Simons Center and similar institutes come in, playing a critical role in filling this void by the amazing workshops that take place here. The diverse group of people that come and interact here at the Simons Center has already brought a lot of impact into the joint area between physics and math, and I hope it continues to increase the number of activities and interactions in the future. I am very optimistic about that! ·

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President SESAME Council

*Interview by Maria Shtilmark*

**Thank you so much for the fantastic talks you gave at the Simons Center. The Della Pietra lecture series has also hosted David Gross, with whom you have written your article “High Energy Neutrino-Nucleon Scattering, Current Algebra and Partons,”[1] which resulted in the Gross-Llewellyn-Smith sum rule (GLS). At your birthday conference at CERN, David spoke about how “cavalier and bold you both were working on the frontiers of high energy physics when you knew almost nothing!” Could you tell us a little about your collaboration with David and the fate of this article?**

In early 1969, when I was a postdoc at CERN, David arrived as a visitor. He was talking about the new ideas that were going around about deep

inelastic electron scattering experiments at SLAC. I was working on neutrino scattering on heavy nuclei (with the late John Bell, of inequality fame, who had pointed out that, very counterintuitively, neutrino scattering must exhibit nuclear ‘shadowing’). I thought, “I will test my understanding of the ideas David described by applying them to neutrinos.” I went to see David and asked whether I had the right answers, to which — to my great surprise — he replied: “Nobody has looked at it.” So we started working together on neutrinos, and came up with certain results. I followed this with some other papers[2] in which I showed that combinations of data from deep inelastic scattering of electrons and neutrinos demonstrate that partons have non-integral charges (not a fashionable idea at the time), and that about half the proton’s momentum must be carried by neutral particles. I think this was the first evidence for gluons. It all started as an accident of timing. I was in the right place at the right time thinking about neutrino scattering, which was being studied at CERN.

**I am amazed by how you always manage to find yourself at the crossing of all possible borders — not only between theoretical and applied physics, or between economics, education, politics, and science, but also literal ones, like the border of USSR in 1967 — Lebedev Physical Institute…**

FIAN. [Physical Institute of the Academy of Sciences]

**Yes. How did that happen?**

My wife, Virginia, was writing a PhD on the relationship between the treatment of women in Chekhov’s works and the women in his life, on which she later published a book[3]. She needed access to the archives in the “Biblioteka Lenina,[4]” which is probably called something else now, to read some of his correspondence. Chekhov’s letters were published, albeit in censored form, but the replies were not. This was not regarded as a suitable subject in the USSR in the 1960s. Her supervisor in MGU[5], where she was living when I arrived, told her that he’d only heard of one even more ridiculous thesis topic, on which a visiting American was working: “Pushkin kak Gastronom” (Pushkin as a Gastronome).

**Nowadays there is a lot of research on Chekhov’s treatment of women. Virginia was clearly ahead of her time!**

Anyway, to conclude I had just finished my PhD and applied for a Royal Society — Academy of Sciences Exchange Fellowship, so that I could join Virginia.

**You were Director General of CERN, when the LHC was approved, and have been President of the Council of SESAME, which brings together countries such as Turkey and Cyprus and Iran and Israel. You’ve managed the UK fusion program, led energy research in Oxford,
and served as Provost and President of University College London. During your varied career, what have you found to be the key to successful communication between people with different economical, political and scientific backgrounds?**

Communicating across disciplinary boundaries depends on learning through experience, what you can assume that others know and don’t know, and what metaphors and similes will strike a chord. The universality of science is the key to communication among scientists with diverse political and cultural backgrounds and views. As Chekhov wrote, “There is no national science, just as there is no national multiplication table. What is national is no longer science[6]”. I have observed at CERN and at SESAME that scientists, engineers and technicians who work together develop professional respect, which leads to greater tolerance of each other’s views on other matters.

**David Gross also mentioned in his talk at your birthday conference at CERN how enthusiastic and hardworking you are, and how you haven’t changed in the many years he has known you. How do you do it? How do you get things done and avoid disappointment?**

I think I’ve had my share of disappointments. To cite just one, I worked very hard to get funding for the final stage of the upgrade of LEP (the Large Electron Positron collider at CERN), and for an additional year of operation, because there were good reasons to think that it might discover supersymmetric particles (this was also one part of the case for building the LHC, Large Hadron Collider). It’s puzzling and disappointing that Nature seems to not make use of this beautiful option, at least in a simple way.

**When Oxford University refurbished the Geography Department, its Lower Carbon Futures team, which is one of the largest collection of experts on building efficiency in the UK, wasn’t consulted. And in the end, the building uses more energy than before the refurbishment – and I am sure this is just one example of the frustrations you’ve faced.**

It was ironic and ridiculous. I don’t usually work in that building and was not aware of what was going on until it was too late. Afterwards I tried to draw people’s attention to what had happened in the hope that it won’t happen again. But you can’t fight, let alone win, every battle.

**If you could put your Director of Energy Research hat on for this one: As a former Director of the UK Atomic Energy Authority’s fusion laboratory at Culham, which houses JET, what is its future beyond 2018?**

The UK has decided to leave Euratom along with leaving the European Union, in principle in March 2019. Continued operation of JET, and UK participation in the global fusion project ITER, will depend on putting in place some arrangement for continued UK association with Euratom, which funds the operation of JET, and through which Europe belongs to ITER. This will not be straightforward because the European Court of Justice (ECJ) is responsible for the adjudication of disputes related to Euratom. The UK has announced that it will no longer accept ECJ arbitration on any matter, but it is hard to see the EU agreeing to anything else. The lack of any form of UK association with Euratom would have very serious consequences for fusion research. In preparation for the operation of ITER, more experience is needed with a mixture of deuterium (D) and tritium (T), the fuels that are almost certain to be required if fusion is ever used as a source of power. A D-T run is planned in late 2018 at JET, which is the only device in the world that can operate with D-T.

Most alarmingly for the UK, Euratom is responsible for nuclear safeguards and movements of nuclear materials (it actually owns all non-military materials held by its members), and for overseeing nuclear safety in Europe. Unless alternative arrangements are in place by then, the nuclear power production in the UK will grind to a halt on April 1, 2019.

**Today is a very dramatic time to be speaking about changes in energy system. The US had its own view first on the Kyoto Protocol and now on the Paris Accord. A lot was said today after your talk – was there a question you liked or you wish that you were asked?**

The questions straight after my talk were mostly about details, but later, over lunch, someone informed me that the President was considering

reversing President Obama’s decision to strengthen Corporate Average Fuel Efficiency standards for US cars[7], which I had mentioned in my talk. This led to a discussion of the likely effects of the President’s retreat from the Paris Agreement. My own belief is that the transition to low carbon energy now has enough momentum that it will continue whatever Trump does, although it may go a bit slower. Part of the Paris Agreement was to transfer funds to developing countries to help them get away from carbon-based energy, and that will presumably suffer from US withdrawal. However, in the US, the States control energy policy as much as the Federal Government. I assume that California, which is the sixth biggest economy in the world on its own, is just going to keep going, and not going to pay any attention to Trump.

**The New Yorker compared the Paris Agreement to the tale of the Stone Soup**[8]

Like Stone Soup, the Paris Agreement depends on voluntary contributions, or at least pledges, but it does not require that everyone does the same thing and the analogy is not complete. In fact, rather than encouraging others to pull out, US withdrawal seems to have strengthened the resolve of China and of the European Union. In the Stone Soup case, everyone puts something in and gets something out of the pot. In the case of de-carbonization, inputs and outputs have been very unbalanced. Germany, for example, poured subsidies into wind and solar energy, which produced a lot of renewable power, in a country where the potential is limited. However, this did not have a big impact on carbon emissions, because of the decision to close down nuclear power, or, as had been hoped, benefit German renewable companies (although German machine-tools are used to make solar cells worldwide). But the rest of the world benefitted enormously because the experience of large-scale manufacturing drove down costs. Actually, China captured a lot of the solar PV market, and Denmark and others took the lead in wind. I would be surprised if US withdrawal from the Paris Agreement has a major effect on US market share. As I said, the transition to wind and solar has a momentum of its own, supported by many States. It’s interesting that not only the big tech companies, but also the oil companies have been criticizing the decision.

**In your opinion, to what extent is the choice between fossil fuels and renewables more a matter of culture or economics? **

Attitudes are very important. For example, I’ve noticed that among the rich in Santa Fe it’s socially unacceptable to have a green lawn when it’s very dry, whereas not so far away in Albuquerque, green lawns are seen as a desirable sign of affluence. However, in most of the world, economics will determine the speed and extent of the move to renewables.

**How important is it to get the public more educated, interested and involved in sustainability and the use of renewables? Where do you start? **

The more the public understands the need to move away from fossil fuels, the better. Most people have probably made up their minds about climate change. But it’s also important to decarbonize to reduce air pollution which is a major cause of death in developed countries, such as the US, as well as in countries like China and India. Also to reduce international tensions by rebalancing relations between major exporters of fossil fuels (Russia, the Gulf States) and importers. Public appreciation of these arguments can help speed up the energy transition, but the key is to develop clean alternatives to fossil fuels that are also cheaper.

**I know people who have gone vegan partly because they believe modern animal agriculture is a very aggressive polluter, and livestock and their byproducts account for at least 32,000 million tons of carbon dioxide (CO2) per year, or 51% of all worldwide greenhouse gas emissions. Do you think this is true?**

It’s true that if we all became vegetarians it would make a big contribution. I myself don’t know anyone who became a vegetarian because of concern about emissions – it’s interesting that you do. Those I know became vegetarians for health reasons or concern about animal welfare.

**When you spoke of the dire need to decarbonize, you mentioned that one way is to rethink the industrial processes. Do you know if these attempts to rethink it are being implemented at the ITER construction at all?**

While ITER is surely being built in an environmentally responsible manner, I’m not aware of any novel steps that are being taken to reduce the project’s environmental impact, but that may reflect my ignorance.

**The reason I asked was this quote from the brochure on the official opening of SESAME: “When SESAME’s solar power plant comes into operation, SESAME will be the first accelerator in the world powered solely by renewable energy.[9]”**

The use of renewable energy is necessary to allow SESAME, which is currently paying $375/MWh for power, to operate at a cost that the Members can afford. It’s also a good example, which I hope will be followed by others — accelerators use a lot of power. While SESAME is not the highest energy or the brightest synchrotron radiation facility in the world, it will be a good facility that will enable good experiments by a large community which up to now has not had access to a light-source, and someone with the right idea could use it to win a Nobel Prize. It’s good that it will also lead the world in at least one way.

**In 2015, my colleague Elyce Winters spoke with Eliezer Rabinovici, whom you also mentioned in your talk. He spoke of three things critical for SESAME’s success: that science is a common language; that SESAME has top science; and that the members participate on an equal basis. Would you like to comment on the various difficulties — political, financial, even inclement weather — that the project encountered, which you mentioned in your presentation? **

I was President of the SESAME Council for 8.5 years. You would expect some difficulties over a period like that. But the really remarkable thing is how few there have been and that we’ve managed to get around them and surmount them. When the political situation in the Middle East was particularly bad a few years ago, someone asked whether we should give up. My reaction was that the worse the situation, the more we need SESAME, as it shows that people of goodwill can work together to achieve common ends across some of the deepest divides on the planet, in the most dire of circumstances.

**If we could go back to ITER – it is obviously not the project for someone who likes instant results. How do you deal with such a timeline?**

That’s a very interesting question. I was surprised that nobody asked me about the prospects for fusion after my talks here. Let me deal with that unasked question first. Ten years ago, I would have replied that I’m reasonably confident that we will be able to make a fusion power plant, although we need ITER to be sure, and the real question is can we make one that’s reliable and competitive? The question of reliability will remain unanswered until we try, although operation of ITER will provide clues. I used to think there was a reasonably good chance that fusion could compete with other low carbon sources of power, but, while I would not say that it’s impossible, the situation has changed. The cost of wind and solar power has decreased faster than anyone could have dreamt. Meanwhile ITER has gone way over budget, partly because of the way that the project was set up and because it’s the first of a kind, but probably also because fusion reactors will be intrinsically more expensive that we thought a decade ago. I think we need to finish ITER and establish once and for all whether fusion really is a viable option. We will then have to reassess the likely cost of fusion power in the light of the experience gained with ITER and in comparison with the cost of alternatives before deciding whether to go ahead and build a real fusion power station.

On the timescale, the ITER management are now talking about deuterium-tritium plasmas in ITER in 2035. So it’s a very long time before we will be able to establish the viability of fusion. Your question whether people will be willing to commit to projects with such long time scales is a good one. Can you, should you, motivate people to get involved, and devote their careers to projects that won’t produce results until after they’ve retired? A similar question arises in high-energy physics. I gave the first major talk on what physics it might be possible to do with the LHC if we ever built it in 1984, but it didn’t start to operate until 2008, and even then not properly. How do you deal with these long-time scales?

This issue is not new. During the Middle Ages, people in Europe designed and started building cathedrals, which often took hundreds of years to complete, knowing they would never see them finished. They presumably considered that they were doing it for the glory of God and the spiritual benefit of succeeding generations. Likewise, people may be willing to devote their lives to fusion, or other very long-term projects, with no expectation of seeing them working in their lifetimes, if they are convinced that they may provide a better world for their great grandchildren. On the other hand, people work in high-energy physics to satisfy their intellectual curiosity, and presumably want to live to know the answers to the questions they are addressing. If the timescales get very much longer, I think it will become increasingly difficult to attract people to such fields. I certainly would not have wanted to become Director General of CERN in order to start a project which I knew would not be finished for

50 years.

**Thank you very much, good luck and hope to see you again at the Center.** ·

[1] High Energy Neutrino-Nucleon Scattering, Current Algebra and Partons (D. Gross C. Llewellyn Smith), Nuclear Physics B14 337 (1969).

[2] Current Algebra Sum Rules Suggested by the Parton Model, Nuclear Physics B17 277 (1970). Inelastic Lepton Scattering in Gluon Models, Physical Review D4 2392 (1971).

[3] Anton Chekhov and the Lady with the Dog, Virginia Llewellyn Smith, Oxford University Press (1973).

[4] The Lenin State Library, now the Russian State Library. The Moscow subway station is still called the Library Named after Lenin, though – M.S.

[5] MGU – The Moscow State University.

[6] (Quoted by wikiquote.org/wiki/Anton_Chekhov)

[7] On 16 March Trump said he was ordering the EPA to reopen a mid-term review of Corporate Average Fuel Economy Standards that currently require the industry to deliver a fleet average of at least 54.5 mpg by 2025. The President’s goal is to make Detroit “the car capital of the world again” and save automotive jobs, which would be lost if (as claimed by some in the industry) meeting the standard were to increase vehicle prices and hence depress sales.

[8] http://www.newyorker.com/news/daily-comment/au-revoir-trump-exits-the-paris-climate-accord

[9] SESAME Official opening under the patronage of His Majesty King Abdullah II, 16 May 2017, pg.13.

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*Interview** by Elyce Winters
Edited by Maria*

**Welcome to the Simons Center. Could we start with what is your area of research? **

Thank you. Well, I am a particle physicist, one of the breed that you know very well: totally megalomaniac. We believe that somebody owes us a simple description of the Universe, so we try and search for it. We got away with it until now, but there are still many holes. Our picture is not full. However, we have had quite a few successes condensing the knowledge of the material world into one slide of PowerPoint.

I am trying to understand how the physical laws that we know well — electromagnetism, strong interactions, weak interactions, and gravity — even though governed by one set of laws, manifest themselves in enormous varieties. We call this “different phases.” In short, you have one set of laws, with parameters like temperature, or else, and when they vary the system totally changes its character. I studied the phase structure of gauge theory, which gave us electromagnetism, weak interactions, and strong interactions, as well as something more exotic called oblique confinement, which manifests in condensed matter physics. That’s one area of research that I’ve contributed to and have done some work. Then I studied string theory, which is an attempt to check how the world would be different if the elementary constituents of nature wouldn’t be just points, but one-dimensional objects: strings.

I could ask you what do you think is the basic ingredient of a painting? You could think it’s a point. Are you familiar with art?

**Yes. **

Who painted points?

**Ah, pointillism! **

Yes, you have George Seurat. From far away it’s just a painting, but if you come closer it’s a totally different structure. Up to now we’ve accepted the point of view that the fundamental building blocks of nature are point particles. There was no reason to try anything else because this was so successful. But when faced with how gravity manifests itself, things begin to look different. From there it seems worthwhile to entertain a Van Goghian idea, where maybe it is the basic brushstroke that makes a painting of nature. And it turns out that this has dramatic impact on how nature could behave, and these things, called symmetries, or dualities, they fascinate me and I’ve worked for years on uncovering and trying to understand them.

The Simons Center is also an institute of mathematics, so I would say that if you think your eyes are not sending points, but are sending strings, then there is no concept in mathematics that remains untouched. Every concept of mathematics that I know of has become ambiguous, or, if you wish, symmetrical. You would think that large universe and small universe are totally different concepts. Imagine how many territorial disputes you could settle if you could just agree that one person could call it large and the other person would call it small. But it turns out in string theory there are cases when you view things from a string theory point of view, you don’t know if the universe is large in one direction, or small. Each narrative is equally valid. And this goes on to concepts like topology, number of dimensions, commutativity, and associativity. Let’s say there would have been an end to the Universe, which we call a Big Crunch. This appears very dramatic, very painful. But it turns out that you can have an alternative description of that, in which nothing happens. You are lying in a hammock on a South Pacific Island, experiencing no drama. So, these different narratives that describe exactly the same thing have existed also when there were point particles, but they’ve become much more pronounced and much more powerful when the constituents were larger than point particles, that is strings and even membranes.

The latter in the painting metaphor would be thinking of Monet, or Pollock, who experimented with basic two-dimensional ingredients, just splashing blots of color. That’s called membranes, which also leads to various interesting consequences.

**Is that what they are doing with the Heavy Ion Collider? Would you consider that splashing?**

(Laughs). It’s different. These symmetries are amazing to me, and I want to understand their origins. Of course, being a physicist, I am interested in what actually happens. Like most of my colleagues, I’m holding my breath waiting for what the Large Hadron Collider, which is now starting to work again, will give us. Will it bring some new results or not. In the next 2 to 5 years [said in 2015] we should know if there is anything new in the near energy range, the accessibility range, or we will have to fish in much deeper oceans to find something. And as of 2017, we have reached India, that is when the Higgs particle was discovered, but deep inside it is America, a new continent of particles, that we hope will be discovered, and as far as we know that hasn’t happened yet.

**Can you tell us about your collaborations at the Israel Institute for Advanced Studies?**

Nowadays there are big institutes that are full of collaborations, and there are different types of those. Take a picture of a lone wolf, as mathematicians are usually lone wolves. There is a type where collaborations are just weak interactions between lone wolves, who from time to time want to sense what’s going on around them, but actually they are much more interested in what’s happening in their own territory. And in that case, in order to foster excellence in their research, you must give them the environment where a lone wolf can move back and forth without feeling the constraints of everyday life.

**What do you think is most key in providing that environment?**

I think you should invest in the physical structure, so it becomes accommodating for that. And I think at the Simons Center there has been a lot of effort in considering the physical environment. I am very impressed by that. Give them the appropriate financial conditions, free them, so they don’t have to spend their time looking for housing and thinking about mortgage, and could really dedicate their time to the research.

So, these are lone wolves. Now, look at *The Dance *by Matisse.

**That’s one of my favorite paintings!**

You like it? Good. That’s collaborative research. And our Institute [for Advanced Studies] did a lot of effort. We had a few lone wolves, but we mainly focused on the collaborative effort and the way we did it was the following: we would ask two or three people to present a proposal of the research they want to do, for which there is enough evidence – as you know, research is always a high risk, and you may end up with nothing – in fact, most of the time you end up with nothing really new, but sometimes you do succeed. But you have to present a case that bringing together a group of people could change, and in a quantitative and qualitative way lead to the progression of the field. So, sometimes it can be changing or really creating a field. There is a field of study of migrations, from various points of view. We took a risk, we brought a group of people, who together really helped found a field. It was many years ago, I take no credit for it. It was about brain research by methods of physics. We had a breakthrough meeting. The field changed by having these people together, a year later it wasn’t the same. The field is not the same because the progress done in the place changed the map of the field.

And another example of that is we brought together Christian and Jewish scholars of… what are the first five books of the Bible?

**The Pentateuch. **

Exactly. I hadn’t realized how different Jewish and Christian interpretations are. Big differences! The value of being together was building a common language.

**Speaking of common language – SESAME, which is being built in the Middle East, and with which you are involved, is another level of collaboration, across political spectrum, and across nations.**

You’ve heard it many times, but I believe it, so I’ll say again – we scientists are lucky that we have some understanding of what’s going on in the universe. Society helped us, it didn’t happen on its own. And most of us, especially in physics, we do collaborate. So, we have the skills of collaboration, and I think it’s our duty in cases when we are needed to bring these skills back to society. And unlike these guys from the Bible, who tried to form a common language, we already have it, it is there – science. And if you accept the fact that there is a common language, science, then you can try to use it to bridge these enormous differences in narratives of what really happened, of how people pursue what happened, and to build responsibility. Now I’m talking about science for understanding. Science for understanding, first of all, must be top quality. You should not do mediocre science – it’s better not to do it at all. It should be that all parties bring something to the collaboration. It should not be in a patronizing form, not somebody coming to teach ‘the natives’ what to do. It’s really about everybody bringing something essential to the collaboration. And everybody should have an interest, his own interest, not only to bring, but to also have an idea of what they want to take out of the collaboration. I think when you have these circumstances the hearts can open a little, and one can make some progress.

It has now been twenty years, and what we did succeed in is that this is not a fluffy dream anymore. SESAME was opened on May 16th, 2017, and aims for science this same year. My next dream is for it to produce top quality science. SESAME is a light source, and hopefully, the light source will bring some light. In mathematics there are such things as existence proofs. No matter what’s going to happen, just the fact that all of us, Iranians, Israelis, Jordanians, Egyptians, Pakistanis, Palestinians, could work together for twenty years proved that it’s possible, no matter what the leaders say. I believe that scientists in different countries took their leaders to a place they never expected to be. I don’t think anybody in Jerusalem or Tehran thought this was going to happen. But up until now even when they realize where they are they did not yet blink. They didn’t run away. They may, eventually, because anything is possible in my region. But we have shown it’s possible.

**Beautiful! Thank you so much for your time, and I truly hope to see you again at the Center.** ·

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The Simons Center for Geometry and Physics is pleased to announce the latest issue of SCGP News, a biannual publication which reflects the Center’s mission, scientific and cultural events.

Download the Newsletter HERE!

Director of the C.N. Yang Institute for Theoretical Physics

Most of us would agree that addition and subtraction are simpler than multiplication and division, at least for big numbers. And this is not just for people who lack an affinity for math. When quantitative astronomy began in earnest, astronomers like Tycho Brahe and Johannes Kepler were faced with multiplications and divisions involving very large numbers, when they used trigonometry to deduce the motions of the planets. As seen in many other cases, this “practical” problem in the pursuit of pure science stimulated a solution with uses and implications far beyond its original inspiration. The unwieldy numbers of observational astronomy led to an innovation that reduced multiplication to addition, and division to subtraction. This invention was the logarithm, developed most influentially by John Napier around the beginning of the seventeenth century.

What are logarithms? Well, for every number *“a”* we define another number, log(*a*) , “the logarithm of a, ” which has the property that if *c* and *d* are two numbers, then the log of their product, log(*c*x*d)* is the sum of their two logarithms,

log (*c*x*d*) = log(*c*) + log(*d*).

How would this be used in practice? You have a table with a list of the (approximate) value of the logarithm for every positive number. Then, when presented with two large numbers with many digits, it’s not necessary to multiply them. Instead you go to that table of logs, look up the logs of the two numbers, add those two logs, and then return to the table to find out what number has that log. That new number will be the same as the product of the original numbers.

In days gone by, this property of logarithms was built into the scientific calculation tool of choice, the slide rule (see Figure 1).

*Figure 1. Slide rule. [From the office of C.N. Yang, Stony Brook University.]*

A slide rule consists of two bars, one moveable (thus the name “slide”), with numbers marked out at points whose distances from the point marked 1 are proportional to their logarithms. Matching up the 1 on the moveable scale with any number *X* on the fixed scale does the multiplication of *X* times every number on the moveable scale automatically. From the figure, we check, for example, that 2 times 2 is 4 and 2 times 3 is 6, and so forth. Notice that in the picture the bigger numbers are getting closer together, which suggests that as the number *N* increases, log(*N*) doesn’t increase nearly as fast. To be specific, for large numbers, *N*, which means that *1/N* is small,

*log(N+1) = log(N) + log(1 + 1/N) ≈ log(N) + 1/N**,*

where the “wavy” equals sign means “approximately equal to.” We see that as we increase the number whose log we’re taking by 1, then to a very good approximation, the value of that logarithm increases only by *1/N*. In fact, any time we identify a function *f(x)* that changes by *1/x* when *x* changes by a unit, that function is proportional to log(*x*). [Note: here we are using what is called the “natural log.” There are other, equally good logarithms, but they are all found from the natural log by multiplying every natural log by the same number.]

Logarithms aren’t limited to their use in multiplication and division. They often occur in the description of natural phenomena, in quantities that change with distance, time, momentum or energy. But no matter how we measure these quantities, they can’t appear all by themselves in a logarithm, because you can find a log for the number 2, but not for 2 meters. A log can depend on a distance, but only if it is the distance measured in some unit, so that it is really the logarithm of a ratio, like

*log (2 meters/1 meter).*

But log*(2 meters/1 meter)* is the same number as log*(2 miles/1 mile)*. Thus, if we change both the scale of the quantity (2 meters) and the scale of the unit of measure (1 meter) in the same way (meters to miles), we don’t change their ratio. We say that such a logarithm of a ratio is “scale invariant.” For most purposes a mile is very different than a meter, but in applications of the laws of nature, some measureable quantities can be scale invariant, at least approximately. In fact, scale invariance is a signal for the quantum field theories of the Standard Model. To see this, let’s talk about particles.

In the world of classical physics, we think of an isolated particle as stable in time. If the particle experiences a force, its motion will be changed, and Newton’s laws tell us just how this happens. Our classical particle knows about forces, but experiences them only if they are applied from the outside, or if the particle happens to move into a region where these forces act.

In the quantum view, things are much more lively. There is no such thing as a truly isolated particle. All quantum systems are restless — any particle will at all times experience all the forces to which it is sensitive, emitting and reabsorbing other particles that are associated with those forces. For electrons, the force is electromagnetism, and the associated particle is the photon. For quarks it’s the gluon of the strong interactions. This really means that a picture of nature in terms of isolated particles is inadequate, and that the “true” particles are more complex combinations of all these possibilities. Still, it’s convenient to think of an electron, for example, as emitting photons of specific energies, one at a time.

Such an emission changes the status quo, or “state,” consisting of a single electron to a new state, in which there is an electron and a photon. This state, however, has more energy than the original one. Classically, this forbids the whole process, because energy must be conserved, but in quantum mechanics such a state with the wrong energy can last for a finite amount of time, given on average by the ratio

T = (Planck’s constant) ⁄ (Photon’s energy).

So, an electron is never really alone, it always populates its neighborhood with such “virtual” photons, and we describe this situation as a “virtual state” of the electron.

Do virtual states really exist? Yes, we have good evidence that they do. Imagine that an electron in a virtual state is suddenly deflected by a force. For example, it might absorb a photon from another source. This can happen when our electron passes close by the nucleus of an atom. The process is illustrated in Figure 2, where the electron, represented by a straight line, comes in from the left, and emits a “virtual photon,” represented by a horizontal wavy line.

*Figure 2. Feynman diagram for the Bethe-Heitler production of a photon.*

* *

Before it encounters the nucleus, the combination of the electron and photon doesn’t have the right energy to be “real.” (If it did, isolated electrons could emit photons, providing a kind of perpetual motion machine!). The energy is adjusted when the electron passes by the atomic nucleus, and the electron exchanges the other virtual photon (the vertical wavy line) with the nucleus (the black circle), so that both the virtual photon and the electron now have just the right energy for their momenta, and off they both go on the right of the figure, in a state that can last indefinitely. When this happens, the process is called the “Bethe-Heitler” production of a photon. This is basically how X-rays are produced for medical imaging and other purposes.

In the Bethe-Heitler process, the nucleus in effect “shakes loose” the photon from the electron, and the two separate, as would any other virtual partners that happened to be “in the air” of the particular virtual state at the particular time the electron passes by the nucleus. A photon is, however, by far the most likely virtual partner, because it can carry just a little energy, thus occurring in virtual states that can last a long time.

A picture like Figure 2 is sometimes referred to as a “Feynman diagram,” which illustrates quantum-mechanical processes like this one. These diagrams help us picture such quantum processes intuitively, and they also come with rules that tell us how to turn the intuitive picture into quantitative predictions. How likely is the Bethe-Heitler process, and how does it depend on the energy of the virtual state? This depends on the theory and on the energy transfer. The rules for Feynman diagrams in each theory are used to compute the answers.

Famously, quantum mechanics makes predictions in terms of probabilities, numbers that have to be somewhere between 0 and 1, where 1 indicates “a sure thing” and 0, “not a chance.”

The probabilities that tell us how elementary particles behave in isolation or in collisions actually depend on the number of dimensions in our world, because whatever its energy, the virtual photon could move in any direction, and the range of possible directions depends on how many dimensions there are. This is where the logarithms come in. When we calculate the probability of finding an electron in a state with a photon of energy *E*, summing over all directions in three space like *1/E*, the telltale sign that the total probability is a log. The same goes for finding a quark accompanied by a gluon, in the theory of the strong interactions that is part of the Standard Model.

This *1/E* dependence means that the total probability for the Bethe-Heitler production of photons between any two energies is given by the logarithm of the ratio of those energies. Suppose, then, we ask for the probability for encountering photons in a range of energies, say from *E**min* to *E**max*. For a single photon the answer is of the form

*Probability to find one photon* = *F* x α^{2} log (*E**max*/*E**min*),

where *F* depends on the velocity and direction of the electron before and after the collision, and α is a number called the “electromagnetic coupling.” It is a measure of how easily virtual states change one into another. It is one of the fundamental constants in nature. Its value is small, about 1/137. It is a “pure number” with no units, and if it were not, the energy dependence would have been different.

The Bethe-Heitler logarithm exhibits the property of scale invariance — if we multiply the smaller and larger scales by the same number, we get the same probability. The probability of finding a photon emitted between (say) 2 electron volts and 4 electron volts is the same as between 4 electron volts and 8 electron volts. This feature also appears, at least approximately, at much higher energies for all the components of contemporary particle physics, that is, the Standard Model. Approximate scale invariance is a direct result of having dimensionless coupling constants and of being in four dimensions (three space, one time).

So far so good, but there is a surprising consequence of this picture. After all, the electron isn’t always so unfortunate as to pass by a nucleus while its photon companion, of energy *E*, is in a virtual state. Left undisturbed, after a time proportional to *1/E*, the electron reunites with its virtual friend. But using just the same method, we can calculate the probability for all such “unseen” photons between two energies, *E**min* and *E**max*, to be emitted and then absorbed. When we do, we get the same log(*E**max*/*E**min*), as in the Bethe-Heitler process. But if we don’t see these virtual photons, there really is no limit to their maximum energy, *E**max*, and we end up with the logarithm of infinity, which is itself infinite. This is a property shared by all the quantum field theories in the Standard Model; they all have infinities, which emerge through logarithms, from the hidden lives of their elementary particles. In effect, the electrons of the Standard Model are spendthrift with energy, loaning it freely to their virtual photons with no limit. And yet, these loans are always repaid. Technically, this problem is avoided by a method known as “renormalization,” which can be applied successfully to theories with dimensionless couplings. Renormalization “hides” whatever it is that keeps virtual photons from carrying infinite energies to and from their parent electrons.

After renormalization, approximate scale invariance has a tendency to isolate low energy phenomena from the influence of whatever lies at higher energies or shorter distances. In fact, the Standard Model may turn out to be difficult to improve upon, simply because its approximate scale invariance makes its predictions self-consistent up to energies far beyond those directly accessible to accelerators. The emphasis here is on the word “may,” because this scale invariance may fail past a certain energy, indicating the presence of new fixed energy scales beyond those we know today.

Einstein felt that dimensionless constants ought not to be a basic ingredient in a truly fundamental theory[1], and over the years the logarithmic infinities associated with them have displeased many illustrious physicists. The very first natural force law, of Newton’s gravity, is defined with a dimension- full number, known as “Newton’s constant.” The most influential modern “completion” of the Standard Model including gravity is string theory, in which the basic constant is the string tension, a quantity with dimensions, related to Newton’s constant. The logarithms at the heart of the Standard Model may yet yield to compelling experimental or theoretical evidence for new, dimensional scales that can tell a meter from a mile, or a gram from a ton.

[1] Ilse Rosenthal-Schneider, “Reality and Scientific Truth: Discussions with Einstein, Von Laue, and Planck.” Wayne State University Press (1980), pp. 36, 41 and 74.

]]>*Recently there has been a discussion among mathematicians, as well as in press and several blogs, covering the developments in symplectic geometry. Professor Fukaya expressed interest in giving his opinion and we are happy to present it here:*

The set of the solutions of the equation *x*^{2} + *y*^{2} – *z*^{2} = 0 has ‘singularity’ at the point (*x,y,z*) = (0,0,0). On the other hand, *x*^{2} + *y*^{2} – *z*^{2} = -1 has no such singularity. *(See the figure)*. Singular objects, such as *x*^{2} + *y*^{2} – *z*^{2} = 0 are very popular in algebraic geometry, the branch of mathematics that studies the space defined by

algebraic equations.

On the contrary, it is always difficult to include ‘singular spaces’ in differential geometry, or topology. A ‘manifold’ is the main target of research in those fields. The notion of a manifold goes back to Riemann, who introduced this concept as a space which looks like Euclidean space everywhere, locally. In other words, a ‘manifold’ is a space that has no singularity. It seems to me that there is still no reason to change this situation and shift the main focus of the field to the study of singular spaces. However, for the purpose of researching a manifold in differential geometry or topology, it also becomes important to study certain ‘singular spaces’ as a tool of the study.

In the 1970s, studying nonlinear differential equation on a manifold became an important part of differential geometry. In the 1980s it became important to research not only an individual solution of a nonlinear differential equation, but also the set of all solutions, as a whole. Such a set is called a ‘moduli space’. Using moduli spaces in differential geometry or topology was especially successful in two areas. One is the mathematical study of gauge theory and its application to the topology of low dimensional manifolds (such a study was initiated by S. Donaldson), and the other is the theory of pseudo-holomorphic curve in symplectic geometry (which was initiated by M. Gromov). Symplectic geometry is an area that started as a geometric study of the equations of classical mechanics.

Moduli space appeared in algebraic geometry much earlier than in differential geometry. When the foundation of modern algebraic geometry was built by the works of A. Weil, O. Zariski, A. Grotendieck, etc., the study of moduli spaces was one of the important reasons why extremely singular objects are included among the spaces to be researched.

In the differential geometric study of moduli spaces, people need to extract certain algebraic information from moduli spaces. The simplest information to be extracted is the number of points of such a space. Later on people started to extract more sophisticated information from spaces. Especially A. Floer, who found several versions of ‘Floer homology’, where he obtained groups rather than numbers from moduli spaces. With time, adding more structures to Floer homology became an important area of research and produced many applications.

To ‘count’ the number of points of a moduli space is actually a tricky problem. The number of solutions of the equation *x*^{2} = 0 is naively one since 0 is the only solution. However, it is more natural to regard it as two, since for any ϵ ¹ 0, the equation *x*^{2} = ϵ has exactly two solutions. In the world of algebraic geometry such a way to ‘count’ the number of points is known as ‘intersection theory’, and is closely related to the foundation of algebraic geometry. In the realm of differential geometry, singular objects are harder to study.

In the 1980s people used rather an ad-hoc method to find correct ‘count’ of the number of points of a moduli space.

When the study of moduli spaces in symplectic geometry made much progress it became necessary to find a more systematic way of such ‘count’. In 1996 several groups of mathematicians found it. We (K.F. and K. Ono) were one of them. Other groups included G. Tian, J. Li, G. Liu, Y. Ruan, and B. Siebert. This method is now called ‘virtual technique’.

By this method, two of the important problems of the field were solved. One is Arnold’s conjecture about the number of periodic solutions of Hamilton’s equation, an ordinary equation appearing in classical mechanics. The other is the construction of Gromov-Witten invariant, which is a basic invariant in the ‘topological version’ of string theory. When certain Floer homology is nonzero, it implies existence of a periodic solution of Hamilton’s equation. Gromov-Witten invariant is a ‘count’ of the number of solutions of a differential equation, non-linear Cauchy-Riemann equation.

These two problems had previously been solved under certain additional assumptions. By the new way to ‘count’ the number of points, it became possible to solve it in complete generality, in 1996.

When we found it, I believed this method would become a basic tool of the field. During the years 2000-2010, several important works used our version of virtual technique, which we called Kuranishi structure. J. Solomon’s and Melissa Liu’s important PhD theses both studied ‘open string analogue’ of Gromov-Witten invariant in two different situations and used Kuranishi structure. Ono used it to solve Flux conjecture, a famous open problem in symplectic geometry. Fan-Jarvis-Ruan built an important new theory, which they called ‘quantum singularity theory’. In the technical part of their theory, they used Kuranishi structure.

However, using Kuranishi structure did not become the standard of the field. Y. Eliashberg, H. Hofer, and S. Givental proposed a theory which they called Symplectic Field Theory. It uses the same kind of moduli spaces for its foundation. Hofer, together with K. Wyscocki and E. Zehnder, were building a version of virtual technique. They called it Polyfold. In those days, various people working in symplectic geometry mentioned on various occasions that Polyfold theory would soon be complete, becoming the standard by which all the previous approaches would be replaced.

I thought there could be many different approaches, each of which had its own advantage, to establish ‘the foundations of symplectic geometry’. On the other hand, for us (myself and my collaborators Y.-G. Oh, H. Ohta and Ono) the only way to persuade people to understand the importance of our approach was to continue working and to produce more applications.

As I mentioned, putting more structure to Floer homology was an important direction of our research. For this purpose, we needed to improve our method so that it could be safely used in more difficult situations. We were working on ‘Lagrangian Floer theory’, which is a version of Floer homology, and is related to ‘open string’ and ‘D-brane’. Our study was completed in 2009 and we wrote a two-volume research monograph. Soon after that, this theory was generalized by M. Akaho and D. Joyce. Joyce was not satisfied with our version of virtual technique and started a project to rewrite it. His way had various advantages compared to ours (and ours also had various advantages compared to his approach.)

We continued working on Lagrangian Floer theory. Our book in 2009 provided a foundation of the theory, but it did not contain much concrete calculations of the Floer homology we produced. For example, the notion called ‘bounding cochain’ is a major player of our theory. However, in 2009 the example of useful bounding cochain we knew was only 0. Later on, we found the first example of bounding cochain, which is far from 0 and is useful in the study of symplectic geometry. It was a solution of an equation *x*^{3} – *x* – *T*^{α} = 0 and is a complicated power series of *T*. Bounding cochain is a parameter to deform Floer homology. We found that, only at that particular value, Lagrangian Floer homology of a space (called *CP*^{2}#* – CP*^{2 }) becomes nonzero. I was very happy when we found that an abstract notion ‘bounding cochain’, which is difficult to define and is hard to calculate, actually has highly nontrivial examples and is useful in symplectic geometry.

We thought that those generalizations and applications clarified the importance of our version of virtual technique in symplectic geometry.

Around that time, some people who had been ignoring our results, started asking us mathematical questions directly and suggested that there was a gap in our work. I was very happy to hear that, since serious mathematical communications with those people became possible at last, 16 years after we found it. A Google group called ‘Kuranishi’ was started in 2012, whose moderator was Hofer. There D. McDuff and K. Wehrheim posed several questions concerning the detail of our approach to virtual technique. We stopped our research on applications and concentrated on answering their questions in as much detail as possible. We replied to all of their questions. After 6 months no more questions were asked and the Google group was terminated.

I moved from Kyoto to the Simons Center for Geometry and Physics (SCGP) in that year. In

2013-2014, together with McDuff and J. Morgan, I organized a full-year program in SCGP on ‘foundations of symplectic geometry’. My motivation to organize this program was to provide people an occasion to present objections or questions to various approaches to virtual technique. We had two conferences, two lecture series, and many seminar talks. Many people visited SCGP during the conference, or other various periods of the program. During the program, Solomon presented an example which was related to certain issue in our approach. We wrote a paper to clarify this point,[1] which is recently published. Other than that we did not hear objections to our approach.

Hofer and Joyce gave a series of interesting talks presenting their approaches. There were other various approaches appearing around that time. Tian, together with B. Chen, wrote a paper to continue his way of studying virtual technique around 2005. Chen, together with B. Wang, also gave a talk on their approach at the SCGP during our program. One difference between their approach and ours is that we reduce problems to a finite dimensional geometry but they work directly in an infinite dimensional situation. D. Yang studied the relation between our approach and Polyfold theory. J. Pardon wrote a paper that put more emphasis on the algebraic side of the story. I think all of these different research methods contain various new and significant ideas.

The whole construction of ‘virtual technique’ consists of 3 steps. We start with nonlinear differential equation, Analysis. We then obtain some ‘singular space’ and study them, Geometry. Finally, we produce some algebraic structure, Algebra. If one works harder in one of those three parts, then in the other two parts the required amount of the work is smaller. In Polyfold approach, people work harder in analysis, and so less in geometry and algebra. In Pardon’s approach he works harder in algebra, and less in analysis and geometry. In ours and Joyce’s approach, we work harder in geometry, and so less in analysis and algebra. The difference between our approach and Joyce’s is that we study ‘singular space’ in a way closer to ‘manifold’, while Joyce studies it in a way closer to ‘scheme or stack’, the notion appearing in the foundation of algebraic geometry.

I think depending on mathematical taste and background, various researchers have different opinions on the version of virtual technique that is easier to understand and use. This is one reason why I think it is useful that various approaches will be worked out in detail — so that each researcher can choose their favorite one.

I think at this stage of 2017, it is becoming a consensus of the majority of the researchers of the field that, for the purpose to prove Arnold’s conjecture and Gromov-Witten invariant, all of those approaches will work. (The disagreement is mainly on when, where and who completed it. This is not related to mathematics and further discussion would be coarse and vulgar.

I am afraid to say, however, that for more advanced parts of the virtual technique such as those we have been developing since 2000-present, the consensus on its rigor, soundness, or cleanness is still missing. For example, McDuff and Wehrheim, in a paper arXiv:1508.01560v2 page 10, said that their version of ‘Kuranishi method’ is applicable only to Gromov-Witten invariant. Especially they denied its applicability to Floer homology. The purpose of much of my research since 2000 is to improve our version of virtual technique and widen the scope of its applications. Various people are now working on research in symplectic geometry and related areas such as Mirror symmetry, using various versions of virtual technique. I firmly believe that most of that research is based on sound, rigorous and clean foundations.[2] Unfortunately, this is not a consensus of the majority of the researchers of the field.

Together with my collaborators, I am trying to do my best to change this situation. I believe this effort contributes to the sound development of the field.

In this article I compared ‘the foundations of symplectic geometry’ to ‘the foundations of algebraic geometry’ several times. While I do think that symplectic geometry is as important as algebraic geometry, as regards to the foundations of the subjects at this time those of algebraic geometry have existed longer, and are broader. The foundations of symplectic geometry are parallel to the part of the foundations of algebraic geometry dealing with moduli spaces. One very important aspect of ‘the foundations of algebraic geometry’ is its application to number theory. There is nothing comparable to it in ‘the foundations of symplectic geometry.’

My dream is that in the future, virtual techniques will make some serious contribution to establishing the mathematical foundations of quantum field theory. If this dream comes true it could be comparable to the application of ‘the foundations of algebraic geometry’ to number theory. One could then say that ‘the foundations of symplectic geometry’ are comparable to ‘the foundations of algebraic geometry’. I believe there is a significant possibility that in the future this will actually happen.

[1] Shrinking good coordinate systems associated to Kuranishi structures, J. Sympl. Geom. 14 (2016).

[2] When we wrote the book on Lagrangian Floer theory in 2009, we made a few corrections to the definition of Kuranishi structure in our paper 1996. However none of its applications is affected by this correction. The definition we use now (2017) is equivalent to the one in our book of 2009.

]]>* Director of the C.N. Yang Institute for Theoretical Physics*

* *On October 9 and 10, the C.N. Yang Institute for Theoretical Physics (YITP) at Stony Brook University celebrated its fiftieth anniversary with a symposium of talks by faculty and returning alumni, held at the Simons Center for Geometry and Physics. The Institute for Theoretical Physics was founded in 1966, when Chen Ning Yang came to the then little known Stony Brook University, providing it instantly with an international profile. The concept of an ITP (renamed YITP after Yang’s retirement in 1999) was developed by the Physics Chair Alec Pond, by faculty member Max Dresden, and by Stony Brook President John Toll. Early faculty included Ben Lee, Gerald Brown, Ernest Courant and Max Dresden. Its first postdocs were William Bardeen, Hwa-Tung Nieh, Michael Nieto and Wu-Ki Tung, each of whom went on to make important contributions in particle physics, as did many of their successors into our own era. Bill Bardeen was among those who returned for the event.

The Institute is associated with milestone advances in gravity, including the discovery of supergravity, in particle physics and quantum field theory, as well as early work on the renormalization of gauge theories, in neutrinos and QCD collider theory, in statistical mechanics, and the Yang/Baxter equation and solvable models. Over five decades, YITP faculty have supervised approximately 250 doctoral graduates, and hosted nearly one hundred postdoctoral fellows, in addition to numerous visitors. Among doctoral alumni, Luis Alvarez-Gaume, long of the Theory Department at CERN, has taken on the role of Director of the Simons Center for Geometry and Physics, whose physics faculty are also members of the YITP. Other returning participants with current leadership roles included alumni Eric Laenen, head of the Dutch National Institute for Subatomic Physics NIKEF Theory Group, and Kostas Skenderis, Director of the Southampton Theory, Astrophysics and Gravity Centre, and former postdocs Stephen Libby, Leader of the Theory and Modeling Group at Lawrence Livermore Laboratory, and Jianwei Qiu, Associate Laboratory Director for Theoretical and Computational Physics at Jefferson Laboratory.

The symposium involved short reviews by current faculty, covering much classic material, combined with a variety of talks from returning participants on their experiences and current work. Reports on new results included those by Bernard de Wit (Utrecht/NIKEF) on the construction of N=4 superconformal theories, and by Shoucheng Zhang (Stanford) who spoke about topological insulators. At the end of the second day, the symposium concluded with a public lecture by alumnus Ashoke Sen (Harish-Chandra Institute) titled “What is String Theory?”.

At the symposium dinner, participants saw a short video by the YITP’s founder, C.N. Yang, who now lives in China. Yang recounted that in 1966, “the opportunity and challenge proved irresistible” to found the ITP and take part in “building up a new research university” at Stony Brook. Referring to his years at Stony Brook as a “second career,” after the Institute for Advanced Study, he recalled the origins of supergravity and informal lectures from Jim Simons, which eventually “contributed to the increasingly close contact between the world communities of physicists and mathematicians.” At Stony Brook, this contact is facilitated by the Simons Center, and Jim Simons, founder of the Center and former chair of Mathematics at Stony Brook, was present at the dinner to recall his many conversations with Yang that led to those lunchtime lectures, and their friendship over the years. Yang concluded his video message by stating that, “at this celebration of the first 50 years of the ITP we can look forward to the next 50 years of close and fruitful collaboration between the ITP and the Simons Center, and we can also look forward to great advances in the unravelling of the fundamental structure of the physical universe.”

The symposium provided the chance for participants to meet with old friends and with new faculty, whose arrival has added to the breadth and depth of theoretical research at the YITP. In the past decade, seven faculty members have joined the Institute, beginning with Leonardo Rastelli, Director of the new Simons Collaboration on the Non-Perturbative Bootstrap, and followed by Patrick Meade, Rouven Essig and Christopher Herzog, all working in aspects of high energy theory; Tzu- Chieh Wei, in quantum information and condensed matter; Marilena Loverde, in cosmology; and just this year, Alexander B. Zamolodchikov, who has joined as the first C.N. Yang – Deng Wei Professor of Physics. The YITP is fortunate to be able to look with pride at the sweeping contributions of its past in research and in training, with a strong sense of momentum and optimism for its role in the future of theoretical science.

]]>*Interview by Maria Shtilmark*

**Let us begin with Stony Brook where you obtained your PhD in 1981. How did your thesis and your advisor influence your future in theoretical physics?**

There was quite an influence! I came to Stony Brook at the end of August 1978, passed the qualifying exams in January, and started working at the C.N. Yang Institute for Theoretical Physics (then called the ITP). My idea was to work in supergravity. As an undergraduate, I had read a nice article on supergravity by Dan Freedman and Peter van Nieuwenhuizen. At the time there was a student exchange agreement between my university and Stony Brook, which had just started as Spain was coming out of the Franco period. So first I went to the army, and once I finished military service I was fortunate to be accepted here, and to start working after the qualifiers with Dan Freedman. That was a very nice experience, he was a wonderful advisor, and when he moved to MIT in 1980 I went with him. I finished my thesis at MIT, as I was working on projects that he suggested. The only issue was whether I should have defended my thesis at MIT or Stony Brook. At MIT they said that if I wanted to defend the thesis I would have to pass the qualifiers again. We thought this was nonsense and my defense took place here, March 12, 1981.

In fact, in December 1980 I was already granted a fellowship at the Harvard Society of Fellows, so fortunately, I had a postdoc position to go to, even if I didn’t pass the thesis. It is a society of scholars, and to become a Junior Fellow you were supposed to be good at what you do, but also be able to interact with people in other areas of academic activity, and a PhD thesis wasn’t even required. But I passed the thesis, and obviously Dan Freedman’s letters to the Harvard Society of Fellows was important for my access to this privileged position. Dan Freedman has always been a great support in my whole career. I am in great debt to him.

**It is fascinating to learn about your service in the army! What was your rank?**

Second lieutenant. First, I was in a boot camp for three months, and then at A Military Academy, close to Madrid. I went to the Artillery Academy, ending up as a second lieutenant, and then six months of practice. And I was doing it while I was studying for my BA in Physics. At the time there were so many strikes at the university that I could only take few real courses. Either students, or professors were always on strike. So, I worked at home and decided I would complete my military duties (as at the time it was mandatory) while also working on my university degree. I had two six-month breaks, in the fourth and the fifth year of studies. Fortunately, I finished the army at the same time as I finished my BA in physics. At the time physicists and mathematicians were sent either to naval or artillery academies. At least, they trusted we could do some ballistics.

**I noticed that a lot of your interviews are in Spanish, and you are greatly involved with science in Madrid. How important is it for you to come back to Spain and support science?**

Ever since my PhD I’ve been visiting Spain regularly. I even took part in the construction of “The Institute of Theoretical Physics” at the Autonoma University in Madrid. I did my best for this to happen, but of course the locals had the biggest responsibility and credit. I went there frequently to lecture and teach graduate courses. When I was at CERN I directed some theses from students coming from Spain. I felt it was my duty towards the young people of my country to help them get an opportunity. I’ve had quite a number of Spanish students, and many are professors in Spain, or elsewhere. At CERN we can’t grant PhDs, but we can share students with member states, and here at the Center we can probably share students with the faculty in the Mathematics or Physics Departments. This way we are not officially PhD directors, but morally we are co-directors.

**Since CERN has been brought up − During your time at CERN what was the most exciting discovery there, in your opinion, the one that meant the most to you and was special for your work?**

In a sense, there are positive and negative discoveries. I think the best discovery of all has been the fact that now we all talk about the standard model of particle physics. Of course, many laboratories, e.g., SLAC, Fermilab, Brookhaven, CERN, etc., have contributed to that. But LEP (Large Electron-Positron Collider) set the standard model on its feet. It allowed for precision measurements, essentially for all aspects, except for the Higgs. The interesting thing is that because it is a machine based on leptons, electrons and positrons, you could actually predict the mass of the top quark, and interestingly enough, that information was passed to Fermilab which eventually made the discovery of the top quark around 1994-95. This information was important because it is a very difficult measurement and there is a large background, so for Fermilab that was a very useful piece of information. And finally, although LEP was made, among other things, to try and discover the Higgs particle, the scalar particle of the standard model, we had to wait until 2012 to have a machine discover it: LHC. So, in a sense I think that the last nearly 20 years of CERN have been to vindicate and to close the standard model. Then, of course, pushing the boundaries for dark matter, pushing the boundaries for supersymmentry, but I think the important legacy for these 20 years has really been to leave the standard model standing on good ground. And to see that happening was very exciting.

**Could we talk about your book, “An Invitation to Quantum Field Theory”1? The goal is very well explained — “We have selected representative topics containing some of the more innovative, challenging concepts, presenting them without too many proofs or technical details;” “the book tries to motivate the reader to study QFT, not to provide a thorough presentation;” and you also “focus on some conceptual subtleties,” and you mention realization of symmetries in particle physics. Are you happy with the results in general, and of this particular focus on symmetry?**

There are topics in QFT that somehow pass from one book to the other without any critical revision. Then some archetypes, or mantras, are created, and the reader is not asked to think thoroughly about some of those concepts. Unfortunately, this has led to some misconceptions propagating in time. Some of the deeper aspects of QFT concepts, discrete symmetries, e.g. breaking of parity, matter-antimatter asymmetry, CP violation, and CPT, one of the holy grails of the subject, are not explained in enough depth, the approach to them being often more of an engineering approach. We believe it is possible to explain to the reader that the CPT symmetry follows from three simple things, which are properties of our current knowledge: special relativity, quantum mechanics, locality. These three things are enough to prove the CPT and to study its consequences in particle physics. And this is one of the reasons we came up with the book — we don’t have to use the engineering approach with the symmetries. You can understand them at a deeper level from fundamental principles in physics. The interplay between symmetries and conservation laws, the properties of broken symmetries are often presented in ways that we did not find satisfying. We were trying to explain not the standard recipes, but what are the underlying concepts behind them.

**Please, tell us a few words about how your article on Gravitational Anomalies, written with Ed Witten, came about, as it made a big impact on string theory.**

That was when I was a Junior Fellow at Harvard. You could spend one year wherever you wanted, and Edward was kind enough to invite me to spend a year at Princeton. Edward had just come from a conference, I think it was in Texas, where he had been speaking with Sir Michael Atiyah precisely on this type of issue, so he drew me into this work. Clearly, at the time I was fairly ignorant on anomalies, so it was a great privilege to be working with Edward and to complete this work with him. We showed that the type IIB supergravity in ten dimensions was anomaly free through a rather remarkable cancellation of different contributions. Somehow we did not study other possible cancellations in more detail, and we missed what is called the Green-Schwarz anomaly cancellation mechanism. A real pity. We also worked on different things, like the descent equations and more mathematical formal structures of anomalies, and we missed, or at least I did, the possibility of exploring other anomaly cancellations, the ones that eventually led to the formulation of the heterotic string. Of course, working with Edward Witten is always an awe-provoking experience.

**Let us return to Stony Brook — what are your memories from your student years here?**

At the time graduate students were living in a place called Stage 12, not what you would call a ghetto, but something different from a normal American campus. It was a very international community. Many people made successful careers, like Ashoke Sen, who came in the same year as I (1978), Sunil Mukhi, Rohini Godbole, Rabindranath Akhoury, Ergin Sezgin… it was serendipitous to have all these people in the same place at the same time, and we really enjoyed being together. It felt like an extended family away from home. We shared life together, not only scientific interests.

At the time I was married, and my first son was born, so as soon as my family joined me I had to leave campus, because children were not allowed on campus housing. With the immense salary we were getting as teaching assistants, we had to share a house with an Italian mathematician and an American physicist. We used to call the place where we lived “Selden Horror.” The house was in really bad shape, and we could pay a good fraction of the rent by remaking the house, so we spent one year doing that, from the plumbing to the roof, new floors, etc. We really re-built the house, and eventually the owner sold it for a very good price. There was also a lot of conflict between different clans, or families in the area, but fortunately, we got along with them well.

For Christmas we would go back to Spain to see the family (of course the family would send us tickets as we couldn’t afford them). Before my trip, I went to one of the clan leaders, who was our neighbor, and I asked him if he could keep our keys and keep an eye on the house while we were away. He was so surprised that someone would put so much trust in him that he was our protector for the rest of our stay. People were very friendly and nobody disturbed us…

**How does it feel to be back?**

It feels like coming home. Many professors that I worked with as a teaching assistant are still active, and I have plenty of fun memories. I was here at the beginning of my scientific life, then I was away for 30 years, and now, at the dusk of my life, I came back. It feels like opening a new cycle, it feels nice. It is a homecoming in a sense. The place has changed, but not that much. And I’ve also known the people who are at the Center from outside the Center many years ago. Now I also need to get acquainted with the University administration. Something that one usually does not do as a graduate student.

**Could you share your vision of the Simons Center’s place on the international map of the similar institutions?**

I think that the Simons Center is unique in many respects. Clearly, one aspect is service to the community (programs, workshops), and that works extremely well. It is very well-financed and very well-organized. The staff of the Center are great. They are a small team of people who are very efficient and very motivated. This service component has been very successful, and will continue to thrive in the future. I believe we need to strengthen the research that is produced at the Center itself. We want to have it not only as a great place for meetings, workshops, and discussions, but also as one of the top centers for high-quality research. So far we’ve had great people hired, hence the initial conditions are excellent. But, given that we are a small group, it is important to share common goals with the Math Department and the Physics Department, especially the YITP. I think it is important to see how we can all collaborate, like a symbiosis. How we can use the Center’s resources and facilities to help in the common plan. There are various ways to go about it, and I have a number of ideas on how to proceed, but we will see. Last May I presented some of these ideas at the Board of Trustees, and their reaction was quite positive. So, I think it’s possible to implement them and take the Simons Center to the next level. I think we’ve reached the cruising altitude, but now we have to determine the height.

**I love the metaphors you use — is literature important to you, the written word?**

Very important. Literature has always been my passion. You can’t work, or at least I can’t, only on physics, because you become less efficient. It is always good to engage in creative or artistic activity that allow you to relax and return to your research problems with renewed energy. And for me these have always been literature and music.People who do research are very obsessive, almost neurotically so. And you need some strong attraction to remove your attention from what you’ve been working on for weeks, months, maybe years. For me literature has such power of attraction, along with music. Some of my favorites are Russians, like Dostoyevsky, Tolstoy, Lermontov, Pushkin, and Bulgakov and Andreyev, among the more modern. From the Spanish I would name the classics, and more modern ones, such as Borges, Cort.zar, Garc.a M.rquez, Vargas Llosa. My all-time French favorite is Balzac. I also enjoy reading essays, biographies, and history books.

**Do you prefer an e-copy or a paper copy?**

The good thing about e-copy is that I can travel with it. But I like to touch the book. It’s a good feeling to have it in your hands and to be able to browse it. So I buy both, hard copy and e-copy. The physical feeling of satisfaction of touching a book can’t be obtained by electronic media yet, but of course it allows you to carry thousands of books around in a very small device. Or when you can’t sleep, you can read without disturbing your partner.

**I also know that you play piano?**

I do my best. I started playing music, or shall I say learning music when I was 40. I didn’t know how to read music before, so I do my best, but age does not help…

**This is very unusual and shows very broad talent.**

Perhaps more obsession than talent. When I am at home we always have classical music playing. There are pieces that you know essentially by heart, note by note, and to play them in the background while you work is very soothing, it helps me concentrate. When I am little distracted I can latch on to the music and I know how it unfolds, it allows me to focus. But after listening to music so much I developed this yearning to play it and I said “before I am 40 I have to start,” as after 40 your brain begins to lose plasticity at a higher rate. I started to learn music theory, then took playing lessons, and eventually a wonderful professional pianist in the Geneva Conservatory decided to take me as a student. She found it amusing that this old guy had so much interest. I was one of the few non -professional students she had. I took a 90-minute class weekly, and practiced at home for an hour every day. My aim was to play Beethoven sonatas, and I am getting there. Some are already accessible, and this gives me immense pleasure. I have tried pieces of varying difficulty from mostly classical authors. I haven’t gone into jazz, I am absorbed by music up to the beginning of the 20th century.

I have to look for a teacher now, and of course I would love to have access to a piano. Being able to play music is very important for me, as I will be alone a lot. Cinzia [DaVia] is going to be at the Physics Department 50% of the time, starting January 2017. Until then she will be going back and forth from the UK. She will be based in Manchester where she is a professor of Physics. So, playing music will keep me company.

**What upcoming programs at the Center are you especially looking forward to? **

I am interested in the program on Entanglement. I’ll have to see what happens with Mathematics of Gauge Fields, since most organizers are mathematicians… I fear the worst (laughs). They may not be discussing the aspects of gauge theory that I am more interested in, their quantum properties. I am looking forward to a number of them, like the one on Turbulent and Laminar Flows, certainly looking forward to that. The programs are great, as for the workshops, I will attend most of them, time permitting.

**You have already become an organizer of one — on gravitational waves. **

I am organizing the Universe through Gravitational Waves with an expert on numerical relativity, Vitor Cardoso, and one of our local experts on gravity and cosmology, Marilena Loverde. I think it will be good, not just for the mathematics, but all aspects on how to detect them, what can we learn, and there are things about the sources of gravitational waves that are going to surprise us for decades. In fact, in different ranges gravitational waves will open windows to the universe that are not accessible otherwise, e.g. the Big Bang. We could even nearly see how the Universe begun. String Theory and Scattering Amplitudes are organized by two of my former graduate students at CERN, Katrin and Melanie Becker, so it will be fun to collaborate with them again. I will be involved, at least initially, in both of them, and then depending on the time available, I will see how involved I can be. I think it is important to go to the opening talk. And I want to make sure that every time there is a workshop, there is also a colloquium, accessible to Physics and Math Departments, which should highlight the reasons why this workshop is taking place, so that not only 30 specialists, but the Stony Brook community at large can appreciate it.

**What is your main acknowledgement of your predecessor, John Morgan and the work that he did? **

John started the Center, under his mandate very good people were hired, and some of them are still here. All are accomplished and world famous. So, to get it started and to bring it to this level, is already a great achievement.

*September 6, 2016 ** *

*Interview by Maria Shtilmark*

**You are a theoretical physicist, but the topic of the Simons Center workshop you spoke at was “Automorphic Forms, Mock Modular Forms and String Theory” (Aug 29-Sept 2, 2016) which sounds, at least to me, more like abstract mathematics. How did you become interested in aspects of number theory?**

Well, my interest in certain aspects of number theory has come as a surprise to me. My background is in physics. I studied for my PhD in the Physics Department in Cambridge, and my initial interests in string theory were very much related to experimental physics of the strong interactions, which is where string theory originated. At that time I viewed my mathematical training as a tool for helping to advance the physics that I was interested in. In those days, it would have seemed unlikely that I might talk to mathematicians, let alone take part in mathematical conferences. But over the years, as string theory developed, not only have I come to a greater appreciation of mathematics as a tool in understanding theoretical physics, string theory in particular, – I’ve also come to appreciate why mathematicians do what they do. It’s always been a puzzle as to why the laws of physics can be reduced to elegant mathematical statements — as famously emphasized by Eugene Wigner, who called this the “unreasonable effectiveness of mathematics.” In recent years, as I have edged closer to the math community, I’ve been able to get a deeper sense of the elegance and the beauty of mathematics for its own sake. However, the language used by mathematicians is quite tough for a physicist to master, and it has been important for me that certain mathematicians are able to adapt their style in order to communicate with theoretical physicists. Of course, there are also certain theoretical physicists who have a natural ability to communicate in either of these two cultures.

String theory has evolved in spectacular ways, and now touches many areas that were not part of its initial purpose. And several of these diverse areas have deep connections with developing areas of mathematics, which is one of the reasons why the theory is so fascinating. So, my interest in string theory has followed a path that makes it impossible not to be interested in the kind of mathematics that is going on in this workshop, which is intrinsic to the structure of string theory in several ways.

**Having just spoken of the spectacular evolution of string theory, could you comment on how modern theoretical physics compares with the pre-war period, when it was more converged, unified? Is it harder for a present day researcher to grasp all areas of theoretical physics? **

It is of course extremely difficult to imagine what theoretical physics was like in the period before or just after the Second World War. Just in terms of the sheer number of people in the subject, it is a hugely bigger and more diverse field. Many subfields of theoretical physics have evolved into major fields in their own right. Recently, in the process of reviewing Dirac’s achievements, I studied some literature about what kind of physics was going on at the turn of the 20th century. Most of the research of that period has long been forgotten. The major advances in that era—the beginnings of particle physics, quantum mechanics, special and general relativity—were not only astonishing, but they involved a relatively small number of researchers. And now, of course, that is no longer true. It is impossible for any one person to follow the advances in all areas of theoretical physics. In many senses, research is a more communal activity.

One of the impressive things about string theory over the last 20 years is the way it has come to be viewed not so much as a theory of particle physics, which is where it started, but as a theoretical umbrella which contains the mathematical ideas needed to attack a very wide variety of problems in theoretical physics. So, there are people who call themselves string theorists, but who are attacking problems ranging from nitty-gritty condensed matter physics to early universe cosmology. Although many of these ideas are very speculative, it is imaginative speculation motivated by the rich structure of the theory. A key aspect of this structure involves symmetries, known as dualities, which relate apparently very different descriptions of the same system. The most powerful example of such dualities is the so-called “gauge-gravity correspondence.” This is a deep property of quantum gravity that identifies a theory of gravitational forces, which is described by string theory in a certain volume of D-dimensional space, with a non-gravitational theory on the (D-1) dimensional boundary of that volume. This has suggested the possibility that some aspects of condensed matter systems, which are described by non-gravitational forces in three space dimensions, might be described in terms of properties of gravity in one higher dimension. Conversely, puzzling aspects of string theory, or quantum gravity, may be explained in terms of properties of the boundary non-gravitational theory. This idea has opened up a whole range of possible interconnections between what we would normally think as very different disciplines.

It is intriguing that the same mathematical structure describes such different-looking physical systems. For example, a system of condensed matter at finite temperature is described within this holographic framework in terms of a black hole in an extra dimension, with the temperature identified with the temperature of Hawking radiation.

However, I don’t think that anyone really believes that when you are measuring the viscosity of a hot liquid you are looking at a black hole in higher dimensions. One should distinguish a real physical system from the mathematical framework that is used to describe it.

This evolution of string theory into a theoretical structure within which a wide variety of physical systems may be described has significantly broadened its scope. I sometimes think of an analogy with what was happening shortly after quantum mechanics was finally formulated in the 1920s. That was a dramatic breakthrough in fundamental physics, which had immediate applications to atomic physics. However, the subsequent development of quantum field theory had an even bigger impact. This involved the idea of quantizing the electro-magnetic and the electron fields. Although quantum field theory was invented as an explanation of quantum electrodynamics, it was not understood well enough to calculate any of its consequences for a long time. However, it quickly became a hugely successful tool for calculations in other areas of physics, such as condensed matter physics. Feynman diagrams, which came along later, became standard tools in quantum field theory that are useful for studying particle physics, but also a wide range of other physical phenomena. I like to think of this as an analogy to what string theory might do. String theory has a close relationship to quantum field theory — indeed in some sense it encompasses all interesting quantum field theories. From this viewpoint it is an overarching structure within which a range of interesting physical systems may be described.

Another series of recent developments in understanding the structure of string theory involve a reexamination of the role of quantum entanglement, which is a fundamental property of quantum mechanics that distinguishes it from classical physics. There are strong indications that this is at the heart of the black hole information paradox and may be an essential ingredient in understanding how space-time emerges from a more fundamental formulation of the theory. These ideas are still quite primitive, but the aims are very ambitious.

**You spoke of philosophy in physics, do you have an explanation as to why string theory causes certain controversy or denial?**

Some of my colleagues are disturbed by the fact that other theoretical physicists are antagonistic towards string theory. But I think it is fine for people to argue about its merits — scientific progress always involves argument. Actually, since string “theory” is not really a theory, there is no sense in which it can simply be “wrong.” However, it could turn out that it is not a useful approach to understanding theoretical physics. It has not yet been of direct use, but indirectly it has inspired some very novel ways of thinking about problems ranging from cosmology to condensed matter physics.

If people who understand enough about string theory don’t like it – that’s fine, although from my perspective they have bad taste! My problem is with people who are antagonistic to it without understanding its structure. Sometimes you get emails from people claiming to prove that Einstein was wrong. And then you discover they don’t actually know what Einstein said even though they know he is wrong. That is also often the case with people who attack string theory. But I don’t think there is a substantial antagonism to it among those who have studied it, other than a few individuals who enjoy publicizing their views. My US colleagues seem to view this as a problem but I don’t think this affects the way academic appointments are made in the UK. I don’t feel people fail to get jobs because they work on string theory.

**Is it true that your collaboration with John Schwarz started in the CERN canteen in 1979?**

Yes, it started in the CERN cafeteria in 1979, which illustrates a great virtue of CERN as a meeting point for people from all over the world. We had known each other earlier, when I was a postdoc at the Institute for Advanced Study in Princeton and John was Assistant Professor at Princeton University, but in that period we didn’t interact much. In 1979 we were both in CERN for the summer, and we simply started talking about what we thought was interesting. It turned out we were both interested in the same thing, so we started to work on it – which led nowhere that first summer! But our interactions were sufficiently interesting, and we decided to get together at the Aspen Center for Physics the next summer. The following couple of years he invited me to spend some months at Caltech and one year he spent a term in London, where I was a lecturer at Queen Mary College. That was a wonderful place with a Head of Department (John Charap) who really appreciated the significance of research and made it possible for me to take leaves of absence, so I had a very flexible research schedule. In addition, the fact that both John and I were unmarried meant that we had quite flexible lifestyles, which was important in scheduling long absences from home.

**Speaking of collaborations—as I understand, one reason you came to the Center was to collaborate with Erik D’Hoker? **

Both Eric and I received invitations to this workshop, organized by Boris Pioline and Steve Miller (among others—M.S.), both of whom have been my recent collaborators. Steve is a number theorist from Rutgers who has been very important to me as a source of mathematical wisdom over the past few years. He is the first real mathematician that I’ve collaborated with. So, I wanted to come here because of the workshop. The possibility of continuing the project that Eric and I have been working on together with Pierre Vanhove, who is also here, made it particularly timely to be here.

**What do you think of this new format for the Center, namely independent visitors?**

That’s a very good development. Last week, before the workshop started, was very different from this week, as we didn’t have a full program of talks. This allowed time for more intense one-on-one interaction, which has been very fruitful. But this week is interesting in another way, as there is such a diverse collection of experts at the workshop. This includes mathematicians whose talks I can’t always understand, but several of their observations have been very useful.

Putting mathematicians and physicists in touch when they have something to say to each other can be very fruitful. However, it can fail miserably unless an effort is made to communicate across the culture barrier. It is not very useful if they are incomprehensible to each other, even if they are great mathematicians or physicists.

**Yesterday Ken Ono, who had opened the workshop, presented the recently released film “The Man Who Knew Infinity,” on which he had worked as an Associate Producer and Consultant. It was a story of Srinivasa Ramanujan, one of the greatest mathematicians of the last century. Among many achievements, he introduced mock modular forms, one of the topics of this workshop, and he is famous for his work while at Cambridge. In your opinion, how authentic was this representation, did it render the atmosphere of the place, and how has Cambridge changed?**

I think the image of Cambridge in the early 20th century portrayed in the film is probably quite accurate — the formality of the place, and the all-male nature and mild racism. I don’t know that much about Hardy and Littlewood, but their lives in Trinity College evidently had some weird aspects. They were both bachelors who lived in the College, but communicated largely by sending letters to each other. Hardy would write a letter and a servant would come and pick it up and take it to Littlewood, living practically next door! That’s what you might call old-fashioned.

Cambridge has changed hugely since the days of Ramanujan. For a start, in Ramanujan’s time Trinity College was a male enclave, whereas now it has as many women as men. Until the early 1970s only three out of about thirty colleges were women’s colleges, so when I was a student men outnumbered women by about nine to one.

The film was a very worthy attempt to portray something which is almost impossible to explain to non-mathematicians – to try and give the public some insight to why mathematics is such an amazing subject. It was much better than several other recent films with scientific themes.

**Thank you very much for your time, and hope to see you again soon at the Simons Center! **

Yes, and in conclusion I would like to thank the Simons Center for providing such an ideal environment for meeting with other researchers in fields related to my own, but who I would not normally get a chance to meet.

*August 31, 2016*