Our guest this week is Hamilton physics professor Kate Jones-Smith who joins us to discuss the evidence for the claim that drip paintings of Jackson Pollock contain fractal patterns. This hypothesis originates in a paper by Taylor, Micolich, and Jonas titled Fractal analysis of Pollock's drip paintings which appeared in Nature. Kate and co-author Harsh Mathur wrote a paper titled Revisiting Pollock's Drip Paintings which also appeared in Nature. A full text PDF can be found here, but lacks the helpful figures which can be found here, although two images are blurred behind a paywall. Their paper was covered in the New York Times as well as in USA Today (albeit with with a much more delightful headline: Never mind the Pollock's [sic]). While discussing the intersection of science and art, the conversation also touched briefly on a few other intersting topics. For example, Penrose Tiles appearing in islamic art (pre-dating Roger Penrose's investigation of the interesting properties of these tiling processes), Quasicrystal designs in art, Automated brushstroke analysis of the works of Vincent van Gogh, and attempts to authenticate a possible work of Leonardo Da Vinci of uncertain provenance. Last but not least, the conversation touches on the particularly compellingHockney-Falco Thesis which is also covered in David Hockney's book Secret Knowledge. For those interested in reading some of Kate's other publications, many Katherine Jones-Smith articles can be found at the given link, all of which have downloadable PDFs.
Data Skeptic
Jackson Pollock Authentication Analysis with Kate Jones-Smith
We'll welcome back to the Data Skeptic Podcast. I'm here this week with my guest Kate Jones-Smith. How are you, Kate? I'm great. How are you? Doing excellent. Thanks for joining me. Thank you for inviting me. So I'm especially excited to have you on because you're my first guest for whom the topic we're going to discuss is around, I guess, a rebuttal to a peer-reviewed publication. So it's not only an interesting data and math topic, but it gets to kind of delve a little bit into the peer-reviewed process and how scientific conversations take place. Yeah. So I know your background, at least for my perspective, is a little bit outside our central topic. So maybe you could start by telling us what you do in your day job. Sure. Well, my day job nowadays, I am a physics professor at Hamilton College. And prior to this, when I was working more heavily on research, the art and physics angle, the Jackson Pollock stuff only made up a component of the types of things that I looked at. So I'm more interested in theoretical cosmology and particle physics, particle astrophysics. Also a branch of quantum mechanics called non-hermitian quantum mechanics where we relax one of the fundamental assumptions about the Hamiltonian operator. So I am more interested in, I guess, standard fair physics topics. The Pollock thing, it was my very first paper. And I think I have two publications on this topic, and then I continued to be involved in a number of authentication disputes. It is not entirely irrelevant to my day job nowadays because I will be teaching, for example, a course in the spring here at Hamilton on physics and art. And I taught the same course when I was a visiting professor at Oberlin College last year. So it has worked itself into my day job a bit. But as a graduate student and as a postdoc, it really wasn't my research focus. So maybe we could get into exactly the first, the claim that was made and then your response to it. Would you care to summarize what the first authors said in their work analyzing Jackson Pollock in the context of fractals? Sure. So the claim is basically that Pollock's work contains fractal characteristics. As a result of those fractal characteristics, in fact that they were so unique that a fractal analysis could be used to identify authentic Pollock paintings versus fakes. Now that sounds like what the heck do these things have to do with one another, especially if what comes to mind for you when you hear the term fractal is something like the Mandelbrot set or all of these really pretty pictures. It might seem at first that there's no connection whatsoever between the thing which is a drift painting by Jackson Pollock or somebody else and fractals. But the connection comes through chaotic motion. So the claim was basically that Pollock was undergoing a certain type of chaotic motion as he created his paintings. And as a result of that chaotic motion, the drips and splatters contain fractal characteristics. This is because some types of chaotic motion do leave fractal trails. So if you propose that he was moving chaotically, then you could seek fractals in his work. And that is essentially what they did. Then they found the fractals that they had assumed were there. And furthermore, they found a set of characteristics, a set of criteria that every painting they studied, you know, obeyed, met these criteria. So then they said, here's the fractal signature that Jackson Pollock was creating unknowingly, of course, because fractals weren't even invented until 20 years after he died or so. So it wasn't like an intentional signature, but they claimed that they could understand his work in the context of fractal analysis and authenticate it because he had this fractal signature, if you will. So, yeah, to my understanding, there's a certain subset, there's some of Jackson Pollock's work that has provenance, and we know it's absolutely his, and there's a certain set that are claimed Pollock's with not the same authenticity. So I guess it was the original authors hope that they could give some official authentication to the uncertainty. Yes, I would say it is more than just their hope. They did engage in authentication disputes and as far as I know they still do. Wow. So maybe we could take a quick aside, just in case any listeners don't know Jackson Pollock, could you give a rough description of what his paintings look like? Yeah, absolutely. The thing he's best known for is these drip paintings. He is trained as a classically, if you will, as an ordinary painter to paint objects using a paintbrush on canvas in the traditional way. And his early work is very pedestrian, I would say, but he was trained in a well-known group of artists and by a very well-known artist, but he started to depart from the traditional painting technique in these significant ways and that is what he is best known for. So he started to create drip paintings and his technique was to roll a canvas, a large canvas out on the floor of his studio, which was essentially a barn as far as I understand in Long Island, and he would fling paint onto the canvas. So you can imagine what this looks like, it's just a bunch of drips and splatters. Now his paintings are quite large, and the drips and splatters occupy the entire canvas more or less. So the canvas itself might be painted and then there's a layer of, say, black drips and then a layer of white drips and then another layer of blue drips or yellow drips. So the resulting image is a dense layer, dense layers of drips and splatters of different colors. To many people it looks quite childish and I think it is really the quintessential abstract art that makes people wonder like what the heck my three-year-old could do this type of thing. It's absolutely that type of thing. Now it was controversial even when he started doing this and became known for this. So it's not like people were universally in support of this being aesthetically pleasing and they still aren't. So it remains controversial and some people just absolutely love it. To me it's more about the message. I think his art was more important in what it did. It was this drastic departure of saying, "Hey, this is art too. This is me splattering paint around and this is art too." So I guess that's kind of where it fits in for me and maybe hopefully it brings up to my individual of what his paintings look like, but of course a brief Google search will turn out many of the canonical paintings. Yep. Including your untitled number five of my Google searches. Yeah. Good. I'm glad that that comes out. Yeah. Well that's, you know, I mean, I think the thing that is the best part of Untitled Five is that it's also very childish looking and it looks like something that a parent might hang on their fridge from preschool drawing time or something. But that contains the same fractal characteristics as the best Pollock painting. So those fractal characteristics, to my understanding that first authors, their approach was the sort of divide and conquer grid system. Is that right? Where they'd look at smaller and smaller sections to see if you're seeing the repeated pattern that we expect from a fractal? Was that their approach? Yes. And you know, I, there's enough problems with this work that, you know, it's worth pointing out some of the things that are well motivated and are reasonable things to do. So a box counting technique of a, of an image to see if it's fractal, that would be pretty standard. I would say that they were doing standard practice there by employing a box counter to determine whether an image is fractal. So the motivation for this work is reasonably compelling. I think, you know, I mentioned this in my email, but when I first came upon the work, I thought, wow, this is great. You know, I've never liked Jackson Pollock and here's some physics and math to, you know, to connect to. The original connection was based on a visual similarity between the way Pollock's paintings look and a chaotic paint dripping pendulum. So if I understand correctly the history of, of what happened, the lead author on this paper, Richard Taylor, was engaged in some type of art training program, like a master's degree or some type of program where they, you know, somehow he had an assignment to create a natural work of art or something along these lines and, and they did something like suspend a can of paint from the branch of a tree and left a canvas underneath it during a windstorm with the intention of paying, you know, creating a painting that was, you know, made by nature, if you will. So okay, you know, the thing that resulted there reminded him of a Jackson Pollock painting. Then he constructed a chaotic, three dimensional chaotic paint dripping pendulum and you can see the similarity between Pollock strips and splatters and the chaotic paint dripping pendulum. It's much more like a chaotic pendulum, for example, than a harmonic pendulum, which does not jerk around back and forth and therefore does not contain any blobs. So the link visually I think is there to say, oh, look at this, you know, Pollock strips look like a chaotic paint dripping pendulum. Maybe he was moving chaotically around the canvas. If he was, then maybe there's fractals there. That is not a terribly unjustified or crazy thing to do in my mind. And it would be a great idea if it turned out to be true. It would be very cool. And that, I guess, was how I first saw it was like, hey, this is very cool. I just assumed it was true, especially because it was in nature. I mean, you don't think that something you're reading in nature has any, you know, flaws or short companies. So I thought it sounded great. And you know, like I said, visually, the link is there, but it just doesn't hold up under scrutiny. Yeah, it's funny. I kind of came to it in a similar way. I was a very lazy headline reader of science articles, you know, some years ago and had this one stuck with me. I didn't read at the time, Taylor and McCollich's original nature paper, but there was a certain plausibility to that claim. So I think I read a headline two sentences and moved on and something reminded me of it recently. I said, you know, that's an interesting topic I'd like to do on the show and sought it out and found the original paper and found my way to your work, which I thought was much more telling of the whole situation. Good. I'm glad that you think that we were very interested in being completely transparent with our methods and our analysis so that other researchers could look at what we did because that's what science is about. That's how science should be practiced, in my opinion. And yeah, you know, we are very critical of what they found. I think it does, you know, you said at the beginning about like the peer review process and the fact that this was a refereed publication, that is an interesting microcosm of how science works in this day and age. I don't know how many things have been published in nature that are just blatantly false, but this certainly isn't their first time publishing fraudulent data. I don't think that there was any intention of being fraudulent in this case, like some of you. I mean, there was this, you know, dog-poning scandal that I think, you know, was somehow people that just make up data, I don't think this was a case of that. But there certainly wasn't a lot of transparency and we had contacted the authors, you know, asking them to share their data with us, which they never replied to. And there's things that about this that are just not exactly how scientists normally communicate. I mean, you usually don't withhold data or techniques. So yeah, there is a lot of interesting, I guess, sociology in this whole debacle as well. So we talked a little bit about the original paper's claims. Maybe we could get deeper into your analysis of it. How you went about reproducing what they've done and how your findings differed from theirs. Sure. Yeah, so essentially what you went about, I guess, without access to the same data set, presumably you had to try and generate as close to it as you could, getting a body of work and doing those color separations and then reapplying the same box counting process. Was that how you guys went about it? Yes. Well, it started with my scribbles and Adobe Photoshop. So like I said, I was intrigued by this work and I assumed it was right. I was preparing a presentation. Of course, this was like the night before the presentation or maybe two nights before the presentation that I'm trying to figure this stuff out because it seems cool. I wanted to demonstrate that not any old image has these fractal characteristics that, you know, that in fact these, that the box counting data and the criteria from a polypane were unique in some sense. So that seemed like a nice little, you know, blank to fill in when presenting this to my colleagues. So rather than turn into an actual polypainting in that, you know, to make that point, I came up with some average images. So I made these scribbles and Adobe Photoshop and box counted them with the intention of showing that they were not in fact fractal. But you know, to my surprise, they all came back as fractal. And that's when I, you know, so that was very early on in the preparation of this presentation and the whole work altogether. So that was where we started. We didn't start by analyzing polypaintings, but it became clear immediately that there were, you know, significant flaws in this box counting technique because if any old scribble does appear fractal, then, you know, you're doing something wrong. And it kind of became obvious in retrospect when you think about a box counting definition. I don't know if you want to talk more about this later, but they, you know, the key feature of fractal behavior is a fractional dimension, you know, non-integer dimension. So for example, a line is one dimensional and a completely filled in box would be two-dimensional. Something a fractal, say a famous, the Von Cox no flick, for example, has fractal dimension of, I think it's log four over log three, it's about 1.26, some repeating decimal. So it's a non-integer number and that's what makes them fractal and that's where they get their name, of course. But what dawned on me during these, you know, when these scribbles started to come back as having a fractional dimension was that that's going to be true for any partially filled in canvas. You know, if you take a perfectly straight line and you box count it, then you should get one. And I did get one. If you take a completely filled in box and box count it, you should get two. But if you take something that is, you know, not just one line on the canvas, but a bunch of lines criss-crossing, then you're going to get a box counting dimension of something between one and two because that image is partially filled. So it's, you know, it's basically working in a fractional dimension to the definition that is the, you know, the flaw that became immediately transparent here. Now we did eventually look at actual Pollock paintings and intentionally fraudulent ones created by students at Case Western Reserve, where I was in graduate school. So we eventually brought in to look at things that weren't my scribbles in Photoshop. But that's where we started was with the scribbles. Yeah. So how then do you find the same fractal patterns in these fraudulent ones or maybe just someone trying to paint in the style of Pollock? Yeah. So it has to do with the actual numerical values that you get when you make this box counting curve. So perhaps I'll describe what that is and then it'll make more sense to talk about the actual numbers. So what you would do with any image that you choose to box count is you just write a program that starts with a certain box size. So maybe you start with large box sizes and you take your image and you divide it into two separate boxes. And you know, chances are the image is in part of both of those boxes and so you say both of these boxes are filled. And then you would go down to a smaller box size and maybe all four boxes now are still filled. And you go down to eight boxes and 16 boxes and you reduce your box size by some factor and you count how many boxes are filled at each box size. So as the boxes get smaller and smaller, you'll have some boxes that do not contain part of the image and therefore they would not be filled. So the box counting curve really is a measure of how the image fills the space that is available to it. And it's not inherently a bad way of determining fractal behavior. But as the only indication, it's very bad, it's very unreliable. So when it comes to Pollock paintings, what you would do is you have to color separate the images. So you'd have to get a high resolution image of a Pollock painting high enough so that you can resolve a single speck of paint, which is about one millimeter approximately. So you get a high resolution image of a Pollock painting, then you color separate it just so that you can look at the individual layers. This is because they claimed each layer was fractal as well as the composite image of all of the layers. So we would color separate and then just do a basic box counting algorithm on the individual layers and the composite image. So once you have the box counting data, you just make a log, log plot, log of the filled boxes versus log of the box size, and the slope of that line is the fractal dimension of the object. This can be very reasonably and accurately done for known fractals. You can test your box counter by doing, you know, a Cepinski gasket or something from, you know, the Von Cox Nolff, like something where the dimension is known analytically. You can see that your box counter is giving you the right dimension and that of course we did. So you get this plot, the plot of log of N, the number of filled boxes versus log of the box size, is some plot that you can then fit a line through and the slope of that line is the fractal dimension. So that is easy enough to obtain if you have high resolution images of Pollock paintings. It's also of course easy to obtain if you have your own images like scribbles that you're doing. So once you've written the box counter program and made the plot, it's really just a matter of getting the slope of the line that you fit through that data. So the key criteria that you can say whether something is authentic, these were of course developed by the Taylor group, and those have to do with the actual values obtained for the fractal dimension. So there's a key point which I've not mentioned here yet, which is that the data are, they claim are better fit by two lines than a single slope. So of the data, they do like a broken line, a line that has a certain slope in one region and then a different slope in another region. Now... With it, so like a piecewise linear kind of thing? Yes, piecewise linear, which of course any data set is going to be better fit by two parameters than one, right? So these are the types of things that are glaringly obviously, you know, in retrospect, and perhaps in whatever. So yes, so any set of data is going to be better fit by two parameters, but they claim that this was actually, you know, part of the genius of Pollock, that he was able to create two fractal dimensions, not just one, but two fractal dimensions in every layer of every painting, and that so that he's consistently able to create these two fractal dimensions, and that the dimension that dominates at large scales, large physical scales, always has a particular relation to the dimension that dominates at small scales. So they dubbed the dimensions D sub L and D sub D, and I think that D sub L is always greater than D sub D, not the other way around. So it's that transition between the two dimensions. It's really the broken fit or the piecewise fit that is key to the criteria because that's how you say, okay, is D L greater than D D, and if it is, then it's an authentic Pollock. So the transition between the two fractal dimensions always occurs at the same place, physically corresponding to about one centimeter, and the chi-squared, which is of course a measure of how well the data are fit by the line that's passed through them, is very small. So as long as you find the broken fit, you have the right relationship between the values of the fractal dimensions, and you have a small chi-squared, then your painting is an authentic Pollock. That was what they claimed. And how many of the fraudulent ones you examined qualified as Pollocks by the metrics? Oh, both of them. So there's different sets of fraudulent paintings that we, well, I should say paintings that we analyzed. The set that I think is perhaps the most interesting and humorous is a set of nine paintings that were done by undergraduates at Case Western Reserve University in 2007. These were students that just heard about the work and were interested, they had studied Pollock's technique. So we hooked them up with some canvas and some house paint and a studio, and they just made fake Pollock paintings. And we have nine of those. We analyzed, we started by analyzing two. The color separation can be a bit time consuming, so we started with just their two simplest ones. One just had black paint and the other had black and red paint. So of those two, both of them were authentic Pollocks. You know, they passed the criteria without any, you know, fudging at all, and they were beautiful examples of the point we were trying to make, which was, you know, that this is bogus and you can't identify real Pollocks. Now the reason we were interested in doing that is because, Untitled Five, which is the stars, the scribbled stars, that has the same fractal characteristics in the sense that it meets the criteria. But an art authenticator would never, or even just any human being, would never confuse that with a Pollock painting, right? That's not going to land on anybody's desk with a real question mark of like, geez, you know, is this a real Pollock painting? There's no question that it was some scribble. So we wanted to study actual drip paintings, so that's how we wound up, you know, I was going to do them at first since I'm the artist here, but then we, you know, these students kind of approached us and they wanted to do it, so we let them do it. Now we also looked at the very interesting case of these matter paintings as they're called. And those are, you know, those are real disputed paintings. The provenance on them is excellent. They belong to Alex Matter, who is the son of Herbert and Mercedes Matter. Those were dear friends of Pollock and Lee Krasner, his wife, during their lifetime. All four of them were artists. They all, you know, had a lot of artistic exchange and lived together for periods of time. So Alex Matter is the son of Herbert and Mercedes Matter, and he found these paintings in like a storage locker after his parents had passed away. So we did analyze some of those paintings. We analyzed three of them, and I can't really comment on whether those are authentic or not. You know, some people believe they are, some people believe they aren't, but the reason that we were interested in doing that is we knew that the Taylor group had studied some of them. We don't know which ones they did, but the Pollock Krasner Foundation had commissioned the Taylor group to look at them with the, you know, goal of determining whether they are authentic. So we had access to three of those, and we looked at three of those as well. So yeah, I mean, if you have an image, all you have to do is a box counting program or algorithm on it, but then you can compare with the known criteria. So of the ones that the students did, we had nine, the first two that we analyzed passed, so we didn't analyze any more, of the disputed ones in the matter cache, we analyzed three, and we found that one meets the criteria, one does not, let me see if I grabbed it, or sorry, we only, we only analyze two of those from the matter cache, and one meets the criteria and the other does not. Interesting. Yeah. Yeah, because one would assume that real or not they were probably produced by the same author. That's right. Yeah. There is simply, in my mind, I think we have demonstrated conclusively that there is simply no robust feature of an image that is described by the box counting data in the case of a drip painting. You can tweak the magnification factor of your box sizes, you can change the resolution of the image, you, and you change the numbers that you get when you do a fractal analysis. So they're just, it's just not a robust feature. You know, I don't think it is sensitive to anything that is particular to the artist at all. If it is, you know, I don't know, this gets back to what your definition of a fractal is. If this is how you want to define a fractal, then everybody can make them and they're everywhere, and therefore they're not special, so they shouldn't be used for authentication. Yeah. Yeah, when I first heard, like I said, read the headline many years ago, one of the things that gave me the subconscious willingness to say, "Oh, this sounds plausible" was that they had fractal stuck in there, and that there seems to be almost this, in my opinion, borderline superstitious nature to when you see the golden ratio or a fractal and something, it sort of lends it this credibility, I don't know. But I guess I wanted to appeal to you specifically as a physicist. Those sorts of patterns we hear about all the time, does that seem to be peridolia or is there a good reason to expect that we're going to find golden ratio and fractals throughout nature and things like that? You know, I mean, I'm quite jaded, especially by this whole affair, and I agree with you that there is an unwarranted willingness to look for these things, and sort of a mysticism that tends to excite people, I guess. That does not preclude the possibility of finding good, solid fractals in nature. And so, whether it's appropriate to look for these things, I don't know. I think if you pursue the golden ratio and things like fractals in good scientific efforts, and you find one, then great, then that's really cool. But I don't know. I tend to agree with you. I think that there is a zealousness or a zeal for finding these things that is unwarranted and just does not do a good service to perhaps the few examples of robust presence of fractals and physical systems. Yeah, along the lines of robustness, one thing that kind of bothered me as I looked at the whole topic was that ultimately, Pollack, or really any other creator of art, is going to have a small sample size of positive training cases available, just because they only live so long and were allowed to create so many works. So whether you look for fractals or some other feature, and especially when you're open to playing around with how many parameters you fit in, it seems like if you exhaustive search something, you're likely to find some characteristic whether it's meaningful or not. So do you think that this sort of analysis, whether it be these techniques or more robust ones, will ever be useful in art analysis or trying to establish who the author of a particular work was given that we have such a small set of possible examples to give us a training basis for? Yeah, no, that's a very good point. That is a point that was not lost upon us in our critique of their work. My general answer to this question is I think it depends. It depends on the numbers, it depends on the thing that you're claiming to find, and the other features of the analysis. So I wouldn't, you know, the sample size issue, I think would be a drawback of any, you know, limited sample size, that's going to be a drawback of any real experiment. As a physicist, those are things that you just, you know, have to accept, and you can set your bar for statistical significance very high, or you can set it very low. In the case of Pollock painting, the numbers are, you know, they analyzed something like 15 paintings, and there's something like 180 known drip paintings, so that's not a hugely representative sample. If the work held up in other ways, I think it would be worth considering whether this is statistically relevant, or the, you know, the limiting, the fact that the sample size is limited. So in other applications, I don't have anything in mind, but, you know, future applications of people trying to do this type of thing either with art, or, you know, you've got these things about Shakespeare, and the Bible, and all sorts of stuff like that. I mean, in principle, I think that does not have to be a deal-breaker aspect of the analysis, but I would have to be sold on other features, other robust features. You know, if you, in the case of fractals, the presence of fractals would be driven by some scale and variant process that is going on in your system. So if you have an understanding of the system, and you can show that you've got some a priori reason to expect fractal behavior, then something like, okay, we only analyzed 15 paintings, and there's 180, that would be less of a problem for me in that case. Or if you had a vast range, I shouldn't say or, I would rather say and if you had a vast range over which the behavior was observed, that would also ameliorate this problem of limited numbers. So I think, you know, the limited numbers, that's something I would be willing to accept in conjunction with a strong indication in other aspects of the analysis that whatever the claims are are in fact true. So that, you know, if this was the only problem with the Pollock stuff, I don't think there would have been, you know, I don't think I would have tried to write a paper about it just based on the fact that the numbers aren't great. Yeah, there's so many other problems with it that we don't even need to worry about the fact that they only analyzed 14 or 12 paintings or something like that. So in principle, I think that that's, I don't know, you know, interdisciplinary science, like you're going to have to relax some of your rigor at some point. I would prefer to not relax the basic components of the scientific method like a control group, or, you know, sharing of data and transparency and reproducibility, those things I'm not willing to relax, but I would be willing to accept something that was robust, modulo, small, sample size. Yeah, speaking of sharing of data, I read another paper on the topic for which I believe your data sets were shared to these authors, and my apologies in advance for butchering their names, but I believe it was Irfan and Stork, who took a more machine learning approach that looked at multiple features, one of which I think was this box counting approach, but they looked at other feature extraction methods they could do to get data out of it. And if I were to summarize their findings, to me as the reader, it was that they felt they had a classifier, they produced a classifier, which was better than random, but not perfect in the validation, the hold-out set that it used for training. So it's pretty hard, as we've been talking about, to put any really concrete numbers around it with so many few data points, but they seem to have found some of those features to have some explanatory power in classifying a legitimate versus a non-legitimate Pollock work. Can you have a chance to review their paper? You know, I have looked at their work. Let's see, I'm not sure what I can actually say on the air and so forth. I am familiar with their work. I have argued against it for a number of reasons, so I don't know if this is the same paper as what you've looked at, but yeah, you know, you can torture the statistics to tell you anything that you want. Being able to do something marginally or pathologically is not good enough in my book. There's also the, I guess, overcoming the shortcomings. I think that their approach does not obviate any of the criticisms that we have levied, in my opinion. And I don't think that what we have shown is that the box counting data are not robust. That does not mean that they can never detect anything, but that does mean that they are not good at detecting Jackson Pollock authentication pieces. Yeah. Yeah. Yeah, and that, I mean, you know, there's, I have been since numerous papers to referee. I'll put it this way. I've been sent papers to referee in which the authors try to come up with a new way of identifying quantitative features of Pollock's work. And I have not seen any of those be published in peer-reviewed journals. Thinking about people who are going down that path to look at, whether it be Pollock or other artists, do you think there's any, well, I don't want to say any use because there's probably always used to something, but given your work and your research and literature research on these topics, when it comes to visual art, is there really something worth pursuing there from these sort of algorithmic approaches or deep analysis, or is there something just intrinsic about visual art that makes it not as readily quantifiable? You know, again, I think it depends. It depends on what you want to do. There are certainly cases where I think there's been a fantastic intersection of art and physics or art and math that benefits our understanding of the artists. One example that comes to mind is Peter Liu and Paul Steinhardt discovered these quasi-crystalline patterns in ancient Islamic arts that suggest the artists understood math that we did not have a good understanding of until the 20th century, not Penrose-Tiling patterns specifically. That case I think is really beautiful. I think it is a great intersection of art and math or physics. But there was really no authentication disputes. I think you get into dicey area when it comes to things like authenticity or like creativity. Some of the papers, I don't know if you've read Taylor's papers, but they would get very sort of philosophical and saying things like the polycat master of the chaotic motion that is the language of nature. That's where you've got to draw the line. I don't think that science and math should start talking about creative processes in a quantitative way. I don't think that that is useful. I don't even think it's necessary. Let creative processes be creative processes. There's plenty of natural stuff to study that is fascinating and that does yield itself to scientific analysis. I would prefer to just leave works of art alone when it comes to looking at the artists or the creators' motivation and things like that. There's other sort of materials type things where of course physics has had a great deal to do and things can be done very robustly. You can radio carbon ancient things and find out whether the Dead Sea Scrolls were from a certain era or things like that. They can do material science very robustly, not without error bars and so forth, but some things regarding the context of certain art can be studied very robustly with high-tech scientific quantitative approach. It's more when you venture into what motivates the artist and whether they had mastered certain things or whether something's authentic, that's where I think you get into trouble because it is a creative process and this person or these people or whatever are not bound by any logical enterprise in their creations. I don't think it's necessary to try and circumscribe an artistic body of work with a set of quantitative parameters. That makes a lot of sense to me. On the similar lines, can you give us a sneak peek about what's on the syllabus for the physics and art course you mentioned? Oh gosh, we do really amazing stuff. I had the pleasure of teaching this class last semester at Oberlin and I chose to cover topics based on my own interest. One of the things, well of course we talk about Jackson Pollock and fractals and chaotic motion. We talk also about Peter Lew and Paul Steinhardt and Quasi crystals and Islamic arts. Another fascinating, fascinating topic in this area where you will find much of Irfan and Storck's efforts are regarding the controversial Hockney Falco hypothesis as it's called. Oh I was going to bring this up, I'm glad you got to it. This is great, I mean this is another excellent case in my book of, you know, intersections of art and physics, they're well done. So this is the proposal by David Hockney primarily who is of course a very famous British painter. So Hockney spent years sort of studying some Renaissance paintings and drawings and eventually came to the conclusion that many Renaissance artists were actually using lenses and mirrors to more or less trace certain key features and render very lifelike portraits and still laughs and what not. So this hypothesis, I mean it's just amazing, I would highly recommend his book. Also Charles Falco is the physicist with whom he has worked most closely and Falco's website, he's at the University of Arizona, just contains a lot of really compelling things. So those are three episodes as I call them that we studied in detail. But we also studied some other things, for example, radiocarbon dating, which I think is important for, you know, very early art, like I'm very intrigued by cave arts and some of the art that we find in caves throughout Europe is just incredibly old, you know, 40,000 years old and older, which is just extraordinary. So I wanted to teach people how it is that radiocarbon works and how it is that we know these caves are, these paintings and these caves are as old as we say that they are. That also factors into authentication disputes, believe it or not, because radiocarbon is quite sensitive, the amount of radiocarbon that there is in the atmosphere is sensitive and it actually went up during the atomic tests in the upper atmosphere, the level of radiocarbon went up in the mid 20th century. So you can do radiocarbon of sort of more modern things to tell if they are from that era of time or not. So that was another thing that we discussed. We also discussed, there's an interesting case of Van Gogh, or yeah, Van Gogh brush stroke analysis. So some folks have claimed that they can identify authentic Van Gogh paintings using a brushstroke analysis or trying to look for repetitive patterns in Van Gogh paintings because he had a certain brushstroke style. That's actually something you might be interested if you like algorithms and whatnot. There's a pretty good paper by these people who did the Van Gogh work and I haven't looked into that as much as some of the other topics, but it seemed much more reasonable. They did a much better job of transparency and reproducibility with the Van Gogh stuff than with the Pollock stuff. They were trying to identify real Van Gogh versus potential fakes and also Van Gogh paintings from a specific era of his work versus another era of his work. And they were able to do that with some success. And that's all computer science based, it was pretty interesting. Those are the types of things that we talked about in the class. And then I had students do a project at the end, so I got some cool projects, things like the history of Prussian blue paint, Tom Stoppard's play Arcadia, which is a really well-known sort of play with scientific themes and sound waves and space and just lots of cool stuff. Very neat. Yeah. Is there a chance of gallery where listeners could check out some of those? No. Unfortunately, there is not. I could, at the moment, there is not. Part of that is due to the fact that I was only temporarily at Oberlin, so all of my stuff there is now shut down. I'll be teaching the course again in the spring at Hamilton and I would probably make a website at that time. Cool. Well, let me know. If you do get around to it, I'll be sure to put it out there on Twitter and wherever else my listeners are finding me. Great. Speaking of which, are you on Twitter? No. I'm not. I started to try to keep a low profile here. I don't do Twitter, I don't do Instagram. Yeah. No worries. Yeah. Is there anything on the topics you think we've missed? No. I mean, this is one of my favorite topics. I obviously have a lot to say about it and I think we covered a lot of the key points. You had asked where people could look for more information. I think, you know, if you're interested and I have a few things to recommend in that regard. First of all, you know, if you are a scientist or you want to read about the more technical aspects of what we did in the Pollock approach or in the Pollock case, I would recommend our paper and physical review E as well as the less formal and perhaps more barbed exchange of words that is on the archive between my co-authors and the Taylor group regarding their critiques of our criticism of them. So I highly recommend people read that exchange because I think it really, you know, we just get down and right down to the points and so I usually direct people there. But that's quite technical. If you're looking for more general art authentication type of stuff, there is this fantastic article in the New Yorker from 2010 that is not primarily about Pollock, but it is about a purported da Vinci drawing and the quest by some individuals to get it deemed as authentic. And now there is also a long NOVA special on PBS about the same drawing. So, I would check out both of those if someone's interested in art authentication. The article is called The Mark of a Masterpiece. It's by David Gran, it's in the July, one of the July issues, July 12th, maybe 2010 of the New Yorker. There was, of course, a lot of media coverage when our paper first came out. So I think the best articles are, there's one in science news that came out a bit later. The first stuff in science news is really kind of disappointing. But the New York Times piece and the USA Today piece do a pretty good job, I think. You know, there's a movie about Jackson Pollock, of course. Oh, you may know who the blank is, Jackson Pollock? Oh, no, so that I have, yeah, I have actually seen you. So that movie, that's a documentary, and that is about a woman who has, in her possession of painting, she thinks is an authentic Pollock. If you like that movie, that actually, her story figures largely into the New Yorker article that I mentioned. You know, the case of the da Vinci drawing is paralleled by some of the Pollock authentication disputes. So it's a nice sort of framework to discuss art authentication. And Terry Horton, I believe her name is from that movie. Her painting is discussed in some detail there and her efforts to get it authenticated or at least accepted by the art community. The movie I'm referring to is a Hollywood film starring Ed Harris about Jackson Pollock and his life. So that, you know, is more, that wouldn't contain any of the math. I believe the matters have a little cameo in that, not the real matters, but, you know, people playing the matters. So that might be a place to- I think those are all great resources, and I'll be sure to get those in the show notes for people to check out. So Kate, this has been great. I usually like to wind up shows by asking my guests for two different recommendations. Can be anything, you know, a book, a documentary, a website, whatever. The first I ask is what I call the benevolent recommendation, which is something from you that you have no affiliation with, but you think would benefit from a little exposure, something you appreciate. And the second is the self-serving recommendation, something that hopefully you can get direct benefit out of from getting exposure here. Oh, geez. I would say for my benevolent recommendation, man, there's so many good things out there. Neither of these things are particularly lacking in recognition, but I will again mention the Lou Steinhardt paper on quasi-crystalline patterns in Islamic architecture, I think, is just fantastic and an absolutely wonderful story. And also the Hakni Falco hypothesis, I think that those are both cases of interdisciplinary science being done responsibly with fantastic, fascinating results. So that's what I would say for my benevolent recommendation. For the self-serving one, geez, I've already mentioned the New York Times in the USA today. Let's see, I think, for self-serving, you should check out my papers on non-hermitian quantum mechanics. All right. Yeah. Well, just a quick aside there, I like to especially guess who are working in the physical sciences ask how, you know, a lot of my listeners are data scientists, they're into things like big data. Are there any things that are lacking in what you need as a physicist that someone like that might be able to step up to the plate and contribute in terms of tool sets or analysis implementation of algorithms, anything like that you think might inspire one of my listeners to go out and build something useful? Oh, God. Actually, yeah. So I'm working on a project now. So I've, you know, sort of started to dabble in this interdisciplinary thing. And this is great from the liberal arts standpoint because this is exactly why people want to go to liberal arts colleges is to, you know, work in all sorts of crazy stuff. But I am working currently on a project that is based on the findings of a music theorist. This guy essentially claims to have found a geometry of musical chords, that's the title of his paper. And I'm very intrigued by that. I'm currently trying to figure out how to take MIDI files and deconstruct them into just chords reliably. So I have a basic mathematical code that can do this, but I would like to take a large sample of music, and so I think, you know, MIDI files might be the best way to go about getting these because they're generally available and they're also free, but I'd like to look at, you know, like jazz, for example, as an entire genre there is, you know, can we see any features, are there any quantitative features that can be assigned to jazz versus classical music? I think, you know, music theorists can identify differences between these genres, and it would be interesting to see if any of those features can be explored quantitatively by looking at the chords and the voice leading patterns, especially in the context of this work by Dmitry Tomochko, who is the music theorist at Princeton, who's work I am currently looking at. So yeah, if you have anybody who works with MIDI files, tell them to look me up. Yeah, what's the best way to reach out to you? The best way would be at my Hamilton email address, which is, I think, the first eight letters of my name, K Jones SM, so K J O N E S S M at Hamilton.edu, and, you know, I'm on the webpage there as well. So that would be the best way to find me. Excellent. Well, thanks again for joining me, Kate. This has been really fun and interesting, and I'm sure the listeners are going to enjoy as well. Great. Thank you for inviting me.