Almost lost to history, these toys quite literally put quantum mechanics at one’s fingertips. In episode 35, Jean-François Gauvin from Université Laval in Canada, discusses how he came to understand the purpose and value of unique toy blocks that ended up on his desk at Harvard University in 2014 as the director of the Collection of Historical Scientific Instruments (CHSI). His article “Playing with Quantum Toys: Julian Schwinger’s Measurement Algebra and the Material Culture of Quantum Mechanics Pedagogy at Harvard in the 1960s” was published in March 2018 in Physics in Perspective.
Websites and other resources
- “For Some Reason, These Quantum Mechanics Toys Didn’t Catch On” (IEEE article on Jean-François’ study)
- “Appendix: In the Makers’ Lab” (instructions for making your own set of quantum toys)
- The Quantum Toys:
- Interview with Costas Papaliolios (circa 1987):
- Freeman Dyson – How difficult was it to understand Schwinger?
- Harvard Gazette Memorial to Costas Papaliolios
- Select papers by Julian Schwinger:
Press and blog coverage
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Hosts / Producers
Doug Leigh & Ryan Watkins
How to Cite
Leigh, D., Watkins, R., & Gauvin, J.-F.. (2018, October 30). Parsing Science – Playing with Science History. figshare. https://doi.org/10.6084/m9.figshare.7273064
What’s The Angle? by Shane Ivers
Quantum toys photo credit and copyright: Collection of Historical Scientific Instruments, Harvard University
Jean-François Gauvin photo credit and copyright: Samantha van Gerbig
Jean-François Gauvin: The objects stored in museums are resources, the same way that manuscripts are books’ primary source.
Ryan Watkins: This is Parsing Science. The unpublished stories behind the world’s most compelling science, as told by the researchers themselves. I’m Ryan Watkins…
Doug Leigh: And I’m Doug Leigh. A package containing 21 aluminum boxes forgotten for over 40 years arrived on the desk of our guest, Jean-François Gavin, at Harvard University’s collection of historical scientific instruments in 2014. With little more to go on than the cryptic symbols inscribed on them, he had to decide whether these objects warranted inclusion in the museum’s collection. Today on Parsing Science, Jean-François talks with us about his efforts to uncover the provenance, and use of these objects in teaching students an important principle of quantum mechanics. Here’s Jean-François Gavin.
Gauvin: Bonjour! I am Jean-François Gauvin. I am professor here at Université Laval in Quebec City, and I have a chair in Museum Studies. As you can hear, so I’m a French-Canadian. I grew up in Montreal and after that, I went to Harvard University, where I was able to do a PhD in history of science. And for basically the past 20 years, I had a foot in both the museum field and also in academia. And my specialty is the history of scientific instruments. At Harvard, I was the director of administration of the collection of scientific instruments over there for seven years, before coming back to my native country, and leading that chair position.
Watkins: We began our conversation with Jean-François by asking how it was that the cubes ended up on his desk at Harvard, and how he came to recognize their relevance in teaching quantum physics.
Gauvin: There was a box that came into the collection in late 2014, and on the box it says: “Julian Schwinger, Phys 251a.” And it was given to us by the Department of Physics, and of course, Julian Schwinger is someone that all physicists know he is this great quantum physicists, won the Nobel Prize in 1965 with Richard Feynman and Tomonaga, for the discovery of quantum electrodynamics. And so, he was teaching at Harvard, from the late 1940s to 1973 I believe, and so he was this big scientist. And I was looking at those little toys, and as I figure out later, they were called quantum toys, and those things were just boxes with some kind of filters in the middle, and I just couldn’t make any sense of them. But I knew that they had something to do with quantum mechanics, because on the top of them on each side, there were those quantum notation that you find from Dirac. And I knew that they had something to do with teaching quantum mechanics, but I just couldn’t figure it out. And for about two years, a little bit more than two years, I, on and off, when I had some time, I would look at those, and I would play with those until I was able to figure out how they worked. And a lot of the figuring out came from playing with those objects, just trying to put them together, and trying to see what it would happen. But also, I was able to find some of the archives at Harvard, because the person who invented those, his name was Costas Papaliolios, was a physicist at Harvard who did his PhD at Harvard, and he’s the one who invented those, basically thinking of Schwinger and a very idiosyncratic way that Schwinger was teaching at quantum mechanics at Harvard starting in the 1950s.
Leigh: Next, Ryan and I were curious to learn how the cubes — which you can see at: https://www.parsingscience.org/e35 — were intended to be used in the classroom, as well as how they were received by students.
Gauvin: The set that we received at Harvard, they were small cubes, I think they were made of aluminum, and I think that there were 13 of those, for a complete set. And in each of those cubes, you have filters, and I was able to find in the archives all of the different filters that were used in each of those cubes. The idea is that when you put the cubes together, and when you look through those cubes, you either see through or you don’t see through, and this is what would we replicate a two-state system. Basically, it’s on or it’s off, it’s like a binary system. And so, those cubes would replicate that. And so when you’re putting cubes that go together and see through, so it means that is one special quantum state. But if you don’t see like going through, then you have a different quantum state. And so, you could put two, three, four of those cubes together, sometimes even five, and then by looking through, to see if you see light or not. It is gonna tell you something about the state of the system in which you’re trying to understand. And Papaliolios, who in 1959-1960 taught physics 251a that Schwinger was teaching, wanted to use those to teach the two-state system that the Schwinger was building as all concept of quantum mechanics on. And so, he sent a set of those cubes to another physicists in Maryland and said just try them and then see if you can make sense of them. And six months later, he received the cubes back with a note saying that they are really firm but the students don’t understand how they work, they don’t understand how you can understand quantum mechanics with those. And so, it seems that indeed when you know quantum mechanics in the beginning, you can have a lot of fun working with those cues. But, if you don’t understand quantum mechanics at first, then it’s really difficult to understand quantum mechanics by playing with those cubes. So, I think that he worked with those cubes for a couple of decades, trying to make them work, but I think it was always unsuccessful with the students.
Watkins: In his article, Jean-François writes that Schwinger’s aim in teaching was to completely rethink and reconfigure the basis on which quantum mechanics was founded. Doug and I were interested in hearing how the topic was most typically taught in the 1960s, and also what Schwinger’s new approach involved.
Gauvin: What is interesting is that he wanted to change the whole way of teaching quantum mechanics. He didn’t want to start with the history of quantum mechanics, going back to wave particle equations, Schwinger’s equation, those kind of things. And in many ways, this is how I was taught quantum mechanics, because I remember when I was an undergrad and I used the textbook, Cohen Tannoudji textbooks, and this is basically all you understand the quantum mechanics, you have this Schwinger equation and then you’re taught how to use that. But you don’t really understand what’s the foundation behind that except for the fact that it looks similar to some of the equation that you find in classical physics. So, there is this transition between classical physics and quantum mechanics But, how do you go from classical physics to quantum mechanics? It’s not quite clear, and so I think that’s why I wanted to just get rid of all of that and really start from one specific experiment, the stern-gerlach experiment, which was able to determine the spin of particles. And from that, building from the ground with algebra building the whole concept of quantum mechanics. So, he’s talking about induction and the whole important thing about the way that you understand quantum mechanics from Schwinger is that you didn’t need to have any background in quantum mechanics to understand quantum mechanics. It’s really principles, it’s really the algebra that is natural. But it was strange for students have this very nice quote in the paper from the physicist, Jeremy Bernstein, who took the course when he was a senior at Harvard and he just couldn’t understand anything that was happening in that course. It was already hard enough to learn quantum mechanics and trying to learn it the way that trainer was teaching it. It was a brand-new way of teaching it and he just couldn’t do it. So, what Papaliolios wanted to do, a few years after he finished the course with trainer, he wanted to use that formalism that trainer was teaching and trying to invent something that would be at zone that you would be able to use with students, so that they can be able to understand what Schwinger was trying to do on a more formal way, in a more tactical way.
Leigh: As mentioned earlier, Papaliolios’ quantum cubes are inscribed with symbols used to describe various quantum states. These symbols, known as Bra-ket notation, were introduced in 1939 by the theoretical physicist, Paul Dirac, for whom the science library at Ryan and my alma mater, Florida State University, is named. So, we wondered how Jean-François was able to make sense of these brackets, numbers, and arrows.
Gauvin: So, if you’re looking at the cubes, you have the bra, and the ket, and notation. But, what the symbol you find inside, instead of the psi for instance – or instead the h-bar that you could find in quantum mechanics – you had a series of 0 and 1, plus and miners, and the arrow up and down. So, Papaliolios dubbed them quantum toys but also polycubes, because basically what you can do with those cubes is that you can find the polymatrices that help you understand the spin of the electron. And so, with those cubes if you put the cubes in different ways and you do that several times, you understand indeed out those polycubes can be generated. And one of the things I was able to do – and I think this is where I really got what those cubes were meant for – is that I was putting those cubes together, and indeed when you look at those matrices from Pauli there are two by two matrices. And then, you have zero or ones in different corners, and by putting those cubes together, I was able to find those zeros and those ones in the real polymatrices. And I said: “oh my god this is how it works.” And by doing that, Papaliolios tells you that you can extract from those by putting them together. You can see out the mathematics of matrices works, because you can see that if you put those two matrices together, then you get this third matrix that gets the result. And so, you can extrapolate, and you can deduce basically how it worked, and this is how he was able to recognize that they were indeed used for teaching physics is because of those symbols. If those symbols had not been on the cubes themselves, I would have had a hard time figuring out what those things were. So, that was for me, it was a sign telling me that indeed that was something that you could use to teach quantum mechanics; because of those symbols that are recognized by any student who has done any course of quantum mechanics.
Watkins: The quantum toys aren’t just a peculiar anomaly from the 1960s, but rather are tied to a project at Harvard University, aimed to reform the teaching of physics and science more broadly as Jean-François explains next.
Gauvin: As a grad student in physics, Papaliolios was able to become a teaching fellow for Gerald Holton who was teaching a course called natural science at Harvard, and the basis of the course was to be able to teach basic notions of science. But the way that Holton was teaching that was with a lot of history of science which was a different way of doing that – instead of just looking at the sciences – and he was really going back to Galileo and Newton, and he was having the students read some of the original publications by those, by those scientists. And at the same time that Holton was doing that he got involved with two other professors into a reform of the physics curriculum in high school in the United States. There was a general consensus in the US at that time in the 1960s that teaching of physics was terrible, and that the students were not learning that much, and that not enough students were actually graduating with the physics background from high school. But Holton wanted to do something that would be different from that, and from 1962 to 1968 they were able to get some money from the Carnegie Foundation, and also from the National Science Foundation to build this new complete new program – which is called “Harvard physics project” – and they had to drop the Harvard because people told that it would be too elitist. So instead of the “Harvard physics project” became the “physics project course,” and so Holton worked on that. And this is when to me it came together the fact that Papaliolios was a teaching fellow for Holton in one of those courses in 1962, and Papaliolios himself says that he designed those quantum toys around 1962, and Papaliolios was involved with the “Harvard physics project” from the very beginning from 1962. So everything comes together around that project. So the idea is that without that project perhaps indeed that Papaliolios would never have invented those toys. The question remains though is why were those toys not incorporated into the “Harvard physics project” and that’s a question I was not able to answer, and again, it goes back to this idea that the course was targeting mostly high school students, and the quantum mechanics was perhaps too difficult to introduce at that level. So maybe that’s why they were not incorporated into the project, but I know that a lot of the things that were designed, and that were tested for the “Harvard physics project” were tested into some of those courses, like the natural science course to that Holton was teaching at Harvard. But again, there is this kind of discrepancy between this course and the way that Papaliolios was thinking about teaching science in the 1960s, and the fact that those cubes didn’t make the cut to be able to fit in such a course that would be for the general audience.
Leigh: With more than 20,000 scientific objects in Harvard’s collection, Ryan and I asked Jean-François what it was about the quantum toys that drew – and kept – his attention for so long. We’ll hear what he had to say about this question after this short break.
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Leigh: Before the break, Jean-François was about to explain what interested to him most about Papaliolios’ quantum toys.
Gauvin: If you look at the sector – for instance a 17th century sector – which is a mathematical instrument on which you find different scales on it, and you can do some calculations dealing with sines, cosines, calculating the area of squares, and those kind of things. When you know how one works, you know how all of the others work. So there’s nothing new in trying to do that. So you have different makers, you have different materials in which they are made. But when you know how one works then you know all of these are, they work. But when I saw those stories, I became almost infatuated with them. I wanted to know how they worked. It’s just that thing was so strange, those toys, those cubes, were so strange, were so different than anything else we had in the collection that I just said I have to understand how they work. I don’t know, it’s just something that just came up, and for about two years, not full time of course because I had too many other things on my plate, but I spent a few hours here and there, I could stay at night one evening, and looking at those cubes playing with them, spend a few hours in the archives looking at what I could find to help me understand what they were, and be able also to understand the fact that they are mostly linked with an important curriculum reform that started at Harvard which is the “Harvard physics project.” So, all of those things when I started looking at those just made me feel at home with something that I knew of about astrophysics that I liked, and so I just said I have to figure it out, and I just have to write about it, because if I don’t do it I’m not sure anybody else will do it. So, I said why not.
Watkins: The most recent data from the Association of Science-Technology Centers indicate that attendance at science centers and museums increased from 81 million visits in 2013 to 120 million in 2016. Nevertheless, scientific instruments can present difficulties to museum curators, since the purpose of such objects might not be intuitive to visitors, as Jean-François discusses next.
Gauvin: When you’re in the Science Museum and you see an object that is behind a case, you see the object, you see how nice it looks, but you can’t really learn anything because you can’t touch it. You can’t really have an idea of how this lever works, what’s the friction, how difficult it is, or how easy it is. You can break something or not. Of course, when you are in a museum collection you try not to break anything, but you know what I mean. It’s that if you don’t play with something, if you don’t have it in your hands, and you try to have this kind of manual knowledge from it, you won’t learn much from it. And so, this is why it’s so difficult for a science museum to attract people, because most of the time they don’t know what is behind a case. And so, if you go to an art museum you see a sculpture, or you see a painting, you can relate to that because you know what it means, and you can light the colors, you can light the design. But when you look at some kind of a big oriole, you look at an astrolabe, most people don’t have any idea how those things work. So if you don’t have this concept of touching, and this concept of trying to figure out for yourself how it works the same way that I did with those quantum toys, then you won’t learn anything about those objects. I think that it’s not easy to go to a museum and try to understand something about an air pump from the 18th century, how it works, if you can’t really understand how you can make it work for yourself. And this is why you do those labs in high school, when you are doing labs, and you are playing with those instruments. Because if you want to learn something about the vacuum, if you want to learn something about electricity, well, you need to produce those charges, you need to be able to get electrocuted by something. If you really want to feel how electricity is an hour to produce, but if you’re just looking at the textbook, you won’t have any clue what that thing is. And so this is why you have labs in the high school, and also in college.
Leigh: Having been tasked with identifying which parts of its bombers should be reinforced with armor, the Hungarian mathematician Abraham Wald delivered eight secret memoranda to the US military in 1943. Wald reasoned that planes which didn’t return from their missions must have sustained fatal damage to their most vulnerable components, and so advocated armoring places where bullet holes weren’t found in surviving aircraft – their engines. Here, Jean-François explains how wear and tear on scientific instruments can yield important insights into just how those objects were used in the first place.
Gauvin: The objects stored in museums are resources the same way that manuscripts are books’ primary source to the study of history. And so when you’re surrounded by a collection of scientific instruments, then the first thing you do is to look at those, and study those, and look at the marks, look at the way they were built, to look at the makers, look at the environment in which they were built. So by looking at the objects, that’s the type of revelation that you usually won’t find in a manuscript or in the published article of a scientist. It’s by looking at the object that you see where perhaps he had some difficulty with a piece, if it’s something that was bought off-the-shelf, but you look at the object that the scientists use, and there are a few pieces that have been removed, I’ve been exchanged, I’ve been added. You start getting an idea of how you use that object, and now I modified it to be able to get the results that he needed, and sometimes at the kind of stuff that you don’t see in the published record. So that’s why looking at objects gives you an idea of how an instrument has been used by its owner. And so this is how it gets you to understand how the science is produced in the 18, 17, or the 20th century. So, I think that’s for a lot of Eastern scientific instruments. We get our first knowledge from the objects themselves and after that, then you can find of course archives and some other books and publications from those people. But the objects are really a primary source and this should be dealt with this way.
Watkins: “The subject is born from the object.” This epigraph – by French philosopher Michel Serres – opens the article “Thing Theory,” published in 2001 by the critical theorist, Bill Brown. In it, he argues that an “object” becomes a “thing” when it stops working in the way that it was originally designed to. So we asked Jean-François whether historians of science are equally as interested not just in how scientific instruments were used, but also in how they are maintained and repaired over time.
Gauvin: So, when Frank Oppenheimer developed and also opened the Exploratorium in San Francisco, one of the first thing he wanted people to see was the workshop. The workshop is open, so you can see people working in the workshop and working on new exhibit designs. So it tells you how those things work, and for Frank Oppenheimer when one of those exhibit designs was working too well, it didn’t like that for him. Stuff needs to break if you want to learn something about anything. It needs to break and you need to repair it to learn something. So all of those ideas of hands-on, and also to be able to build, and to repair something, it’s really part of how you learn about the world, and how you learn about the sciences. And this whole movement is not only in science museum, science centers, and those places, but also the way that people are thinking about history of science as well. Over the past 15-20 years, but especially the past 15 years, there are a lot of scholars who have started looking at artisans, and laboratories, and experiments. There was a big shift in the 1980s, instead of looking at theoretical physics you’re looking at experimental physics, and all you make experiment. And now, it’s really about the makers, the artisans, and now you have this big boom of articles and books. For instance, there is a colleague of mine who’s published a book about recycling in the early modern period. His name is Simon Werrett. The book is coming out next year, and what he’s saying is that in the early modern period you were not always buying new materials, you were recycling, you were just cannibalizing what you could find around the kitchen, around the living room, in the scrap yard, and when you need a piece of wood, then you just use what is lying around, and you would reuse it, repurpose it to your own new purpose, so that you can make your experiment work. And so this concept of recycling, and cannibalizing, and making something out of nothing. Basically this has been going on for centuries, and now there’s a lot of people who are looking at that not only as a new way of pedagogy to teach sciences, but also to look at the history of that over the “longe journée” – if I can use that word.
Leigh: Los Angeles, where I live, is infamous for its obsessive “car culture.” So, it’s little surprise that the region has at least three auto museums recognized as among the best in the United States. My favorite, though, is the unassuming Automotive Driving Museum. Despite its relatively modest collection of vehicles, the museum is unique in that, each Sunday, staff roll vehicles out from the garage and invite visitors to drive them around town. After sharing this story, I asked Jean-François why museums don’t generally embrace the idea that ongoing use might actually enhance the public’s interest and understanding of science and technology, as well as their impact on our past, present, and future.
Gauvin: Well, when I was working at Harvard, I was living in Montreal. So, I was driving back and forth Montreal in Cambridge every week. And so for seven years I had my little Mazda 3, and it was working perfectly, and I knew exactly how that thing works. I recognized all the sounds, I recognized all the little tweaks, and how it behaved. And when you change a car and you go into different cars you don’t know how to drive it, because it’s so different. It’s the car, but it’s not the same car. And so this is why people when they are doing some labs, and they have their own instruments, they don’t share those. They don’t want anybody else to touch them because it’s their home they have tweeted, they have calibrated it for their own purposes. And if you have somebody else that comes in, he won’t know how to use it, whether he’s gonna break it, and or whatever. And so this is what I’m saying that I was playing with those cues, because it’s not instinctive to be able to see what those cubes are doing. And so by playing with those and putting two, four, six of those together trying to see if light goes through or not, I was able to get a sense of what they were meant to be for. And to extrapolate a little bit from that concept of playing that I’m talking about, and the role of the the tangible objects themselves, when I’m surrounded by old scientific instruments I’m like a kid just playing, and to me I think that this is how you can really get to know something from the past. It’s really to look at those objects, and trying to play with those objects, because a lot of the things that I’m trying to do and trying to study in my own work, it’s looking and at indeed that people were playing with objects, and also what they could learn from those instruments in the past – in 17-18 century. And the only way that you can put yourself and try to understand how they were learning something, is by trying to work with those objects the way that they were working themselves with those objects in the 17-18 century.
Watkins: “Tinkers” – or “tinkerers” – have been applauded and derided in nearly equal measure since long before the American author and musician Paul Harding published an award-winning novel of the same name in 2009. Originally a reference to door-to-door tinsmiths who mended kettles, pots, and pans, the term today is as likely to conjure inexpert dabblers as it is ingenious – if not eccentric – innovators. Since Jean-François began to first make sense of Papaliolios’ quantum toy cubes by playing around with them, Doug and I were curious to learn how historians of science go about figuring out the purpose of enigmatic objects such as the quantum toys.
Gauvin: One of the things I’m trying to make clear in the beginning of the paper is really that concept of starting with an object. And this is what I’ve been trying to describe in this podcast is saying that those objects, those cubes, just came on my desk. And so, without knowing anything, I started with these cubes, I really started looking at how they were made, and trying to play with those together. And when I started looking at that, I just couldn’t figure everything out of them. And after that, I went to search for paper traces of those objects, and fortunately I was able to find a paper trace in the archives at Harvard. And so, after going to the archives, I went back to the objects and I was able to figure something else more. But the idea is that when you start with those objects you get to the science because of those objects. I went back to Schwinger the way that Schwinger was teaching quantum mechanics. Because of those objects I was able to look at Papaliolios, how he was involved with teaching basic courses in science at Harvard, with Gerald Holton which is one of the people behind the “Harvard physics project.” So, because of those toys I was able to make a lot of different connections. So, when you start with the objects, it leads you to different places, and you always come back afterwards to those objects. And I think that this is why it’s so important to start with those objects. I would be very much surprised as someone at some point went to the Papaliolios’ papers at Harvard stumble, on that folder of quantum toys, look at the few diagrams and write the same paper. I think it’s impossible to write such a paper. You need to start with the objects themselves and after that you find all the leads. You can’t be able to explain what’s the origin of those objects and what’s the context in which they were invented.
Leigh: Ryan and I were both trained in instructional systems, the discipline of analysing, designing, developing, implementing, and evaluating materials for use in education and training. Given this, we wondered if Papaliolios’ quantum toys failed to catch on not because they didn’t work, but rather because people didn’t know how to make use of them for teaching – and learning – quantum mechanics.
Gauvin: In some manuscript that I found in the archives, he described all of the things that you could do with those cubes. But it’s not easy when you don’t know how to do that, trying to use the cubes and trying to figure it out for yourself. And so why he didn’t do any papers, I don’t know, it was suggested to him – you should do that and publish in the physics journal – but why didn’t do it I don’t know. I think that he’d use them for his own personal use, maybe with his own teaching. But again, I just couldn’t find it in his own archives, a good sense of how often he used them in his teaching. But in the paper, I compared what Papaliolios was doing with those stories with the famous Feynman lectures that Feynman gave again in the same time period in 1960s, and then they were published. And I was telling myself that if you add those final lectures and then you had somebody was teaching you with those quantum toys, if you combine those two then they become fun and you could have in these sections in the course with those little toys that you could perhaps make yourself, and then after that you could play with those, and you could have a lot of fun understanding those systems. So, this is why in the paper at the end there is an appendix, because the editor, one of the editors of the paper, asked me to add this makers section, this makers lab, to tell people out to reproduce them. Because he thought that it would be nice to be able to reproduce and play around with different people around the table, and trying to understand how two-state system can behave, and also what do you mean in the physical sense. So, I would appreciate, indeed, if physics professor would look at that and make his own her own, and give a list of ways of using that. Because I’m not good enough with quantum mechanics to write those instruction myself, but I believe that the paper gives enough information about the history, and the use of those stories to be able to start someone who would like to be able to use those, and make instructions. So, I really believe that you could have a lot of fun doing that if someone would be willing to do that. But hopefully they’re gonna send those to me, because I would love to be able to see instruction, and be able to continue my playing around with those toys.
Leigh: That was Jean-François Gavin, discussing his article “Playing with Quantum Toys: Julian Schwinger’s Measurement Algebra and the Material Culture of Quantum Mechanics Pedagogy at Harvard in the 1960s,” which he published in the March 2018 issue of the journal Physics in Perspective. You’ll find a link to his paper on: www.parsingscience.org/e35 along with bonus content and other material he discussed during the episode.
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Leigh: Next time on Parsing Science, we will be joined by Marlene Behrmanm from Carnegie Mellon University. She’ll talk with us about the case of a child with medically intractable epilepsy, who after surgeons remove the region of his brain responsible for visual processing, was able to regain the ability to recognize people’s faces and without otherwise impacting his language and visual perception skills.
Marlene Behrmanm: This has allowed us to provide evidence for a view in which there is not absolute hardwired innately specified dedication of a brain region for a particular function.
Leigh: We hope that you’ll join us again.