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00:00:04 Right. Yeah well origami has a surprisingly rich mathematics and geometry to it.
00:00:16 It's I originally got interested in origami because it just posed a lot of interesting mathematical questions you have
00:00:23 this sheet of material and you have very simple rules you can't stretch it and you can't tear it
00:00:27 and what can you do just by a reconfiguration just by folding and so it's very kind of a simple set up
00:00:35 but the answers turn out to be surprisingly complicated and you need to use a lot of powerful geometry
00:00:41 and algorithms to figure out what you can fault in many senses of you can really fold anything out of a sheet of paper
00:00:48 and you can prove that mathematically. And that's sort of where we got started.
00:00:52 It's very exciting
00:00:54 and finding more interesting ways to make structure the fold between different shapes also has a lot of practical
00:01:00 applications in science and medicine
00:01:03 and engineering where you want to build some kind of structure that can change transform it shape from one thing to
00:01:10 another so maybe you want to fold it down to some small size for storage or transportation.
00:01:17 Like if you want to put something inside the body.
00:01:20 Maybe you need to transport through small blood vessels and so you need to make it very compact
00:01:25 or you want to deploy something into space.
00:01:27 You want to fold it small so it fits inside your space shuttle and then going to unfold it when it gets there.
00:01:34 I think it's even more exciting is you imagine like buildings or gadgets
00:01:40 or things that can transform from one shape to another and serve different functions depending on what you need.
00:01:44 Maybe your house a room in your house can transform from a kitchen to a bedroom and this kind of thing.
00:01:53 One of a couple of the areas that we were exploring are things like printing. Now to robots.
00:02:00 So there are a lot of rapid prototyping machines that are designed to make flat sheets of material.
00:02:09 And how can you use them to make three D.
00:02:11 Robots and other structures
00:02:13 and folding is a good way to do that you can transform your two dimensional sheets into some cool three D.
00:02:18 Structures so we one of our goals in this printable robot project is to make robots that can for like ten
00:02:26 or twenty dollars of materials you can cut them and make them within a couple of hours.
00:02:32 So everyone can make their own robot and customize their robot to do whatever they want.
00:02:37 Another fun application is in making nano scale structures so we have out of the whole computer chip fabrication
00:02:46 technology we have really good ways to pattern two dimensional surfaces at with nano scale features like nanometer
00:02:52 resolution. But we're not so good at making three D. Structures at that scale and so folding offers another way.
00:02:59 That's more in process and experimental but. An exciting possibility for folding is for you something that is.
00:03:11 What makes your position as a professor sort of roses. Yeah.
00:03:19 Yes I know lots of different players interested in different aspects of folding maybe more practical side I'm more on
00:03:25 the theoretical side and developing new mathematics
00:03:28 and tools to show to help those sort of kind of underlying technology for people to build on to make useful things.
00:03:39 So we especially like to prove what we call universe ality results where we say in this kind of regime of origami
00:03:45 design or folding design.
00:03:47 You can make anything you want and we give you a computer algorithm to do that
00:03:51 and so you can come in with your specifications like oh I'd like something that looks like this and it
00:03:56 and the algorithm will give you how to fold exam. Actually that thing.
00:04:02 And you know we get very general results they're not always the most practical because often we don't take into
00:04:09 consideration things like the thickness of the material or other kind of structural issues
00:04:14 and something we're trying to get to but by kind of simplifying looking at the core geometry we can get very general
00:04:21 and powerful results and then that those can be adapted to more practical scenarios where you are going for something.
00:04:34 You would think that there's a limitation but I don't know every year it.
00:04:38 I'm amazed at what origami artists come up with there's new people with new ideas
00:04:44 and it seems like almost limitless possibilities
00:04:48 and especially if you start with a large enough sheet of paper you can really fold really really complicated things
00:04:55 and there's still aspects we don't understand.
00:04:58 For example area we look at a lot is curved crease folding so most are Grammies made with straight creases curved
00:05:05 creases are a lot harder to understand and analyze and we're starting to make progress on the mathematics
00:05:12 but there's still a lot we don't know we don't have any good design algorithms to say Oh I'd like to fold something
00:05:16 that looks like this. Here's the curve creases you need to do that.
00:05:20 So instead we've been experimenting a lot with just playing around trying different curve crease patterns
00:05:26 and see what they produce and trying to be able to model that mathematically.
00:05:30 And that led my father
00:05:32 and I into the sculptural side of paper folding so most of the sculpture we made is make is around curved crease
00:05:40 folding initially we're just experimenting trying to figure out what's possible and what what can be done
00:05:46 but we kept making all these beautiful forms and so I started to embrace that as a purely sculptural.
00:05:53 Endeavor as well but there's a lot of back and forth.
00:05:56 I think that will do something sculpture really that will inspire new mathematics.
00:06:00 We discuss we understand something better about curved creases mathematically that inspires new sculpture
00:06:04 and so it's a lot of fun to go back and forth between the two cards right between art and science I think in general.
00:06:12 That's a big appeal to why people like to explore origami
00:06:16 and mathematics together because you have this sort of scientific purpose maybe an engineering application
00:06:24 or the beauty of the mathematics but then one of the applications is also to make sculpture.
00:06:32 So it's really exciting to see these kinds of collaboration is a lot of engineering teams are bringing on origami
00:06:37 artists at to help design new folding structures so artists have a lot of practical experience of how to make
00:06:45 interesting folding structures and then they know the the literature which is a lot of people folding stuff
00:06:52 and then that can inspire and inform new scientific discoveries. So your work your age. These are.
00:07:03 Yeah that's where we like to live is right on the edge of knowledge where we we have a lot of tools
00:07:08 but there's still something we don't understand.
00:07:10 And so we try to push push that frontier of what's what's known on the scientific side
00:07:16 and we use sculpture to kind of help explore that area more tentatively we can we can often make things that we don't
00:07:24 yet fully understand.
00:07:25 And so that lets us go a little beyond the frontier and sort of explore what's out there and see what's possible
00:07:31 and then.
00:07:33 Hopefully eventually understand that part mathematically where you where your science part formed you well what was it
00:07:40 like for you just what was there. Yeah well in general we're looking at unsolved problems.
00:07:50 I mean part of some sense one of the hardest parts is to figure out what the right question is. So you might want.
00:08:00 Two types of questions about folding structures one is I give you a structure
00:08:04 and I want to understand its properties and sort of analyze what it does how good it is what it folds into
00:08:10 and the other side is the design side so you have some more high level specification of what you'd like to fold
00:08:17 and then you want to automate the design of a structure that folds with those parameters designs maybe the more
00:08:24 exciting side
00:08:25 and there's many different ways you might formulate what you want to fold sort of the classic origami design problem is
00:08:34 is shaped design. I say I give you a three dimensional shape. I want to fold that thing.
00:08:40 What's a good way to fold that thing.
00:08:41 And we're still we're still finding good algorithms for that we have some general procedures that work
00:08:47 but they may not be so efficient as one of the standard measures of efficiency is if I have a square of a particular
00:08:54 size material. How large of a version of that shape can I fold.
00:09:00 I don't want to fold a really tiny thing because that means I'm kind of wasting a lot of my material five a big square
00:09:05 filled with little microscopic things not very efficient material usage.
00:09:10 So how can we optimize that scale factor we still don't know the best way to do that.
00:09:15 There's a sense in which we can't know exactly how good we can do that
00:09:18 but we can hope to approximate the best solution.
00:09:21 So that's something we're still actively working on for example our current.
00:09:25 Favorite technique is called organizer and it's it's also free software
00:09:31 and it's an algorithm we've been analyzing over the last several years to give an arbitrary three D.
00:09:37 Shape that gives you a way to fold exactly that shape.
00:09:43 It seems to be a good method but we don't know it's the best method
00:09:45 and then there are many other questions based on other types of goals you might want like maybe you want to have a
00:09:52 folding structure that can make two different shapes.
00:09:54 We don't know much at all about that question or you want to make a folding that actually.
00:10:00 Works with really thick material because you're making out of sheet metal
00:10:02 or you want to make a practical mechanical structure.
00:10:07 We're still understanding that we've made some progress on
00:10:10 but there's still a lot of questions we don't know the best way to deal with with these kinds of practical issues
00:10:18 and so that as becoming really relevant these days because a lot of people are trying to build these structures
00:10:23 and sometimes it works sometimes it doesn't like to understand that threshold then
00:10:28 and ideally automatically design structures that always work really well in practice.
00:10:42 Yeah I mean I think we like to build objects and we.
00:10:46 And it's even cooler when those objects can change shape so almost anywhere you imagine a gadget of some sort.
00:10:51 I think folding could offer some interesting perspectives on on reconfigure ability.
00:10:59 C one one area we haven't talked about is protein folding which is a kind of origami it's a little bit different
00:11:09 but it's kind of essential to how just understanding how life works and also potentially drug design.
00:11:16 So every living thing that we know of in this world is built up out of lots of little proteins kind of making life
00:11:22 happen and proteins are centrally one dimensional pieces of paper that quite a lot into complicated three D.
00:11:28 Structures in that three D.
00:11:29 Structure kind of determines how it interacts with other proteins and what what its function is.
00:11:34 And we don't really understand that process of folding kind of a one dimensional strip of paper into these three D.
00:11:41 Structures how nature does it how we could do it how we could design proteins that fold into geometries that we want to
00:11:47 like combat. You can imagine some disease comes along new disease.
00:11:51 You could design a protein to fight specifically that disease but we don't know how to design.
00:11:58 Proteins that folded the way we want to.
00:12:00 And so we're trying to understand how proteins fold in order to sort of just understand how biology is functioning
00:12:06 but also so that we can kind of control it in useful ways to kill viruses and things like that.
00:12:12 So that's that's an exciting but difficult interaction.
00:12:17 I would really like a sort of universal programmable gadget you know like we have lots of gadgets where you can
00:12:24 download software updates like your smartphone you can download software updates and it does new things
00:12:30 but we don't yet have a gadget where we can download new shapes
00:12:34 or new geometries you can imagine a kind of universal gadget that can take on any shape I mean it has to preserve mass
00:12:43 that you could imagine it unfolding and becoming a large thing at folding into a more compact.
00:12:50 Structure changing shape maybe it's a chair or one one moment and it becomes a bicycle the next moment
00:12:56 or I mean anything in principle is possible.
00:12:59 It's we need to figure out what the practical regimes are
00:13:01 but instead of having a separate gadget that does different functions
00:13:06 or separate separate furniture that does different things you could imagine having fewer objects that are more
00:13:12 reconfigurable so that that excites me like I really like gadgets.
00:13:17 But I can have a gadget that can do more different things or be more customizable I think that's really exciting.
00:13:26 I owe a lot of people in the field.
00:13:28 Got into folding because they've been folding since they were kids and doing origami
00:13:32 and then they learn about mathematics
00:13:34 and think oh oh maybe we should combine these two I came from the other side so I was a beginning graduate student at
00:13:42 University of Waterloo and I was just curious. I was looking for interesting problems to solve.
00:13:49 I knew that I really like geometry and algorithms and. My father remembered an old.
00:14:00 Unsolved problems that he had read about
00:14:01 when he years ago from a column by Martin Gardner who used to write for Scientific American about mathematical games
00:14:10 and it's a problem that comes from the magic community and the concept is you take a piece of paper you fold it flat
00:14:18 and make one complete straight cut and then unfold the pieces
00:14:22 and magicians like Houdini could produce a five pointed star lots of different simple shapes
00:14:29 and Martin Gardner I was wondering you know what are the limits can you make anything by this process
00:14:35 or what can you do
00:14:36 and so that's the problem we started working on like OK I've got geometry in algorithms now seems like a cool unsolved
00:14:44 problem to work on and it turned out to be fairly challenging took us a year or two to solve
00:14:50 but it also was very exciting that we got our first universality result
00:14:55 and we showed that you can make any poly gun any sheet metal straight sides
00:14:59 or actually you can make several shapes all at once. Just by a one straight cut after folding. So those very exciting.
00:15:07 It's fun problem motivated by magic.
00:15:09 It turns out to have some practical applications also there are some designs for airbag folding collapsing airbags flat
00:15:16 that are based on the same kind of algorithm that we didn't intend that at the time
00:15:23 and it really got us excited about this world of folding where it seems to have very rich
00:15:27 and complicated mathematics but also those kind of fun and visual
00:15:31 and you can you can demonstrate these things you know you can fold a piece of paper make a kite and make a swan
00:15:37 or whatever shape you want to so it has an attendee ability that everyone can kind of appreciate even if they're not a
00:15:45 mathematician you can say hey look we solved this magic problem that's cool.
00:15:50 You know something for you where it was well before right. Well. Yeah it's going to start.
00:16:08 I guess my father became a single parent when I was two years old
00:16:13 and so we've been close for a long time especially from when I was ages seven to eleven
00:16:20 and we started traveling together and visited many different places.
00:16:25 Mostly east coast of United States and just traveling for fun.
00:16:29 There was no particular reason other than seeing different cultures within the United States
00:16:34 and exploring which was really fun and throughout that time my dad treated me as a peer. So we would.
00:16:42 Jointly decide where we're going to go next to how long to stay in a place some places we'd stay just for a few days
00:16:48 other places we'd stay for years and that was a really fun and bonding experience for us.
00:16:55 Growing up and also because we're traveling a lot.
00:16:58 We try to at home school and home school turned out to work really well for us.
00:17:04 I would spend only like an hour a day doing sort of the breadth of regular school
00:17:09 and so that I have many other hours during the day to explore things
00:17:13 and very quickly for me exploring was computer programming.
00:17:17 I got really excited about that essentially how to video games I played a lot of video games I was curious how they
00:17:24 were made and my dad knew a little bit about computer programming to get us started
00:17:27 and then we'd go to the library to learn more.
00:17:30 This was all before the Internet and so I was sort of racially learning about computer programming
00:17:37 and having a lot of fun there and then when school got out I would go and play with kids and things like that.
00:17:42 So that was a really great time for me growing up and I went very fast in the computer science
00:17:48 and eventually mathematics side of things right. So right. Yeah I asked over that when I was.
00:18:00 Five or so and six years old my dad and I had our first collaboration we like to say with the Eric
00:18:07 and dad puzzle company.
00:18:08 So I helped design wire take apart puzzles and my dad would make them bending wire
00:18:17 and then we sold to twenty stores across Canada and we split the income fifty fifty and it was a lot of fun.
00:18:25 That was definitely the beginning of my interest in puzzles which is still to this day something I had like a lot
00:18:33 and probably also the beginning of my interest in mathematics and geometry
00:18:37 and things like that although that came much later as we were twelve. Yes yes. So after we ended this travel.
00:18:48 I wanted to learn more about computing in computer science I learned was a thing
00:18:54 and you have to go to university to learn about it.
00:18:56 So there was some complication but I started undergraduate at twelve
00:19:02 and took lots of classes because I at that age you can really soak in a lot of material and so I ended up finishing
00:19:08 when I was fourteen and then went to graduate school and got a master's and Ph D.
00:19:15 By the time I was twenty and then went on the job market and became a professor here at MIT. You're right. Yes.
00:19:32 Yeah it's really. We really value. Having fun and enjoying the work that we do.
00:19:39 There's a very there's essentially no line between the work that we do and the things we do for pleasure.
00:19:46 So it's all mixed together just with different kinds of outcomes maybe becomes a math paper maybe it becomes a
00:19:54 sculpture maybe it's there's no outcome we're just doing it for fun but.
00:20:00 It's all for fun and the philosophy is that if we do work that we enjoy
00:20:06 and find pleasurable then we'll do it very well excel at it and that has been a useful guiding principle
00:20:15 and I would encourage everyone to do the same it's definitely it may seem risky at times
00:20:19 and certainly there was a worry that the work that we do is to recreational like you know we're studying the
00:20:25 mathematics of a magic trick how could that be useful for anything but it turned out to be unexpectedly.
00:20:33 But I think a lot of specially in mathematics there are just a lot of basic questions that are very curious
00:20:40 and you want to know the answer to
00:20:42 and if they're basic enough the sort of very simple set up like paper folding is a very simple set up a very few rules
00:20:47 about what's what you're allowed to do and yet it's very complicated to understand it's a nice context for.
00:20:55 I think basic research tends to become useful eventually even though you may not see the applications ahead of time
00:21:01 and so mathematicians tend to be attracted to like very simple questions that have complicated answers.
00:21:07 Those tend to be also useful questions to answer always but if you solve enough of them.
00:21:12 Many of them will become practical and so even though you do it for fun.
00:21:17 It tends to have useful applications as well so that you might be worried by a lack of applications
00:21:24 but turns out to be OK. It's for real life. It's really sweet.
00:21:35 I mean we have pretty much ideal set ups where we can work on what we enjoy and get paid for it
00:21:41 and have fun doing it and have all the resources to do it. We're very lucky.
00:21:52 Yes So the glass blowing interest comes from.
00:21:55 My dad's background which is more on the visual arts side so before I was born.
00:22:00 In the late sixty's early seventy's he had the first glass studio in Canada.
00:22:04 It's called the father of Canadian glass
00:22:07 and so he had to have a studio made lots of glass work it was it was the early days in the studio movement of glass
00:22:15 blowing in North America
00:22:16 and so he was experimenting exploring what's possible trying different recipes to make glasses and glass colors
00:22:23 and things and then he didn't blow glass for many years until
00:22:30 and I never really saw him blood last until we came to MIT fifteen years ago
00:22:35 and we discovered he'd MIT has a glass blowing studio called The Glass lab and so my dad got curious to try
00:22:44 and glass flying again.
00:22:45 And so he started teaching there became one of the instructors and started blowing glass again
00:22:52 and I got to see him blow glass and watched him make things and it's so beautiful and amazing to watch
00:22:58 and then eventually like maybe maybe I should try clasp like that said Yeah you know you should at least see what it's
00:23:05 like but be careful. It's addictive.
00:23:07 So I quickly got into a glass blowing and now we blow glass together and make things together and it's a lot of fun.
00:23:22 It's a little more difficult because there's a lot of physics going on with glass blowing which is not exactly my forte
00:23:28 but we're always looking for interesting math and connections between mathematics and glassblowing and we've found.
00:23:36 We've found some interesting books there I think there's still a lot more to be explored.
00:23:40 I would love to have algorithms to automatically design interesting because this sort of operations you can do are
00:23:46 glassed in glass blowing a very simple. You know you can.
00:23:50 You're turning your piece you can swing it around you can play with sort of gravity in this way you can heat different
00:23:56 parts and cool other parts and that totally changes the shape that you produce.
00:24:00 But it's a very complicated relationship and so it's hard to model all of that mathematically.
00:24:06 But we've found some interesting regimes where it's simple enough that it's mostly geometric what's going on
00:24:13 and so we can use computers to help design new patterns in glass.
00:24:18 So we have some free software called virtual glass that we've been developing where you can design what are called
00:24:24 Glass came patterns very simple.
00:24:29 Conceptually simple but hard to visualize where you set up some essentially straight lines of color and glass
00:24:35 and then twist them.
00:24:36 And so you get some really cool twisty patterns they've been used in glass flying for for centuries. But.
00:24:45 Pretty much everyone who makes glass cane follows one of standard set of patterns
00:24:50 and so we were curious whether there were more patterns for Glass can that were possible in the software lets you
00:24:56 explore those patterns and lets you try new things and sometimes you try a new thing
00:25:00 and it looks kind of like an old thing.
00:25:02 So it's not really interesting but other times you try a new pattern and it looks amazing in the software
00:25:06 and that tells you here.
00:25:08 This is something we should spend the time to actually learn how to make in real life software doesn't tell you exactly
00:25:13 how to make it but it gives you a kind of schematic and then you have to do the glass blowing hard work
00:25:19 but at least you know that the thing you're trying to make is really beautiful and so it's worth working towards.
00:25:26 So you can rapidly try lots of different designs and software to find the one you want and then go physically make it.
00:25:33 So it's really hard.
00:25:38 Yeah I think it's I mean I think in general working on the boundary between two different fields you find interesting
00:25:44 areas that.
00:25:46 People tend to specialize in just one area and so they miss the things that the boundaries
00:25:52 and so we've had a lot of fun exploring these boundaries
00:25:54 and I think it comes partly from our different backgrounds my dad with the art background me with the more math
00:25:59 and science. Background and we're always talking to each other and so we see we see the connections.
00:26:06 When I started graduate school I was doing this sort of more theoretical mathematical work my dad's side
00:26:12 and saying looks. That's interesting.
00:26:14 This kind of creativity you're going through
00:26:16 and solving unsolved mathematical problems is very much like the kind of thing that I go through in designing new
00:26:23 sculptures or thinking about new art to build
00:26:27 and so we started working together then he got he I taught him to become a mathematician.
00:26:33 And he taught me to become an artist and so now we work on both together
00:26:37 and it's really it's a lot of fun for us to collaborate in that way but also leads to really interesting questions
00:26:44 and inspirations where instead of just thinking OK the math is the serious stuff
00:26:50 and everything else is just you know side project we think of everything is like main projects
00:26:55 and they inspire each other in ways that we couldn't predict. So I'm just working for years. We're definitely.
00:27:15 Yeah I mean you could say frontiers of science and art maybe.
00:27:20 Or that interplay but you know we're always as scientists we're always excited about the unknown
00:27:26 and I mean that's as soon as we understand something fully it becomes almost boring
00:27:33 and we want to move on to the next thing I mean we write down what we know and publish it
00:27:37 and share it with the world so they can build on top of it
00:27:40 but then we're always excited about the next question which we don't understand that's that's really what drives us is
00:27:48 the price that we don't quite understand or like that seems a little strange. And we're curious about and.
00:27:57 Yeah that's that's where we explore next. You know years at. Wells you might. Yeah it's a good question.
00:28:18 I think in the in the folding regime. I work in many different areas but in the folding world.
00:28:26 I think the biggest challenges right now are taking the nice mathematical geometric design algorithms that we have
00:28:34 and adapting them to to real world materials.
00:28:38 So we're starting to look at how does the thickness of the material affects what we can fold.
00:28:44 How does the rigidity of material affect what we can fold off and you're making things out of plates and hinges.
00:28:50 So you can really only fold at the creases whereas on paper it's more flexible.
00:28:55 Between the creases So this is a world called rigid origami still trying to understand how to design within that space
00:29:02 but it's very practical and exciting and for us it's nice
00:29:05 and challenging because we don't know that's what that's what we don't know how to do
00:29:09 and so that's where we're attracted So I think in the next couple of years we'll make a lot of progress in that kind of
00:29:14 trying to take the rich and very general mathematics and adapting it
00:29:19 or how to deal with the parameters of real world materials where you know other areas where you
00:29:29 or where you're working well yeah I see there are a lot of so I mean like the traditional origami set up is you have a
00:29:45 square paper and all you can do is fold and it's really interesting to see what you can do just by folding
00:29:52 but there are a lot of practical setups like in our printable robots project where it's.
00:30:00 Also find to cut the material I mean why not. It's folding is very powerful it's a good way to go from two to three D.
00:30:06 but We don't have to start from a square of material probably we're starting from some kind of rectangle of sheet
00:30:12 material and why not also cut it in two dimensions before you fold
00:30:17 and that's exciting because it can lead to much more efficient foldings potentially use all of the material now
00:30:24 and you can make structures you couldn't make just by folding or you can you can make them much more efficiently
00:30:30 and in different ways it's also a little it's tricky from a mathematical perspective because now we have so much more
00:30:36 freedom we can cut and fold in some sense it's more freedom than we know what to do with
00:30:42 and so that's that's kind of a new direction of folding where we also are cutting because why not.
00:30:48 It's a practical thing you can do
00:30:51 and maybe there are some settings where you want to add lots of cut some settings where you want to add fewer cuts we
00:30:56 don't know the right balance between us and I think that's a new frontier we're still exploring
00:31:01 and trying to understand but potentially leads to much better ways of folding structures.
00:31:07 And going back to your you're very free for. Case don't have this space. If you go.
00:31:35 I think it played a big role I mean it's hard to know exactly
00:31:38 but I think growing up with so much free time unstructured time where I could just explore what interested me really
00:31:47 gave me a big edge. Instead of sort of wasting time which a lot of schools do just filling that time.
00:31:56 So as a kind of child care. It's set up.
00:32:01 There's social aspects which are good too but a lot of time I feel like is wasted in school
00:32:07 and so having the home school opened up this window where I could explore what interested me and
00:32:13 and really dive in deeply and that let me go far ahead in the computer science world
00:32:18 and I think in general could let students go really far ahead in the thing that excites them the most you still have to
00:32:25 add in the breadth and socialize with other kids and so on but really
00:32:31 and then going to university at a young age I think really gave me another edge whereas you can learn so much at a
00:32:39 young age and so when you get to university.
00:32:41 Suddenly there's really interesting things you're learning and it's really exciting
00:32:45 and I still remember the things that I learned back then.
00:32:50 So that's really powerful as a way to to get started and I think a lot of people could do it.
00:32:58 There's also a more general sense of.
00:33:02 Because we were improvising if we want a long travelling around we would talk to our neighbors learn about what they
00:33:10 knew about and if they knew some interesting topic they would teach me and teach my dad.
00:33:15 So I learned different aspects about the magic that way.
00:33:17 I learned different kinds of cooking that way
00:33:21 and that was a fun way to say it to appreciate different people of different backgrounds
00:33:28 and different knowledge sets and I think in directly that influenced me
00:33:33 and my dad to think a lot about collaboration
00:33:38 and in current day we we collaborate with a lot of different mathematicians
00:33:43 and different papers I've written papers I think over four hundred people at this point
00:33:48 and on the art side we're also looking for collaborators interesting ways to combine different ideas from different
00:33:54 minds we collaborate a lot with each other. Of course but also looking for outside inspiration. I thing.
00:34:00 When you combine multiple people together you can really you can solve problems that could not be solved individually
00:34:07 on the mathematical side this is because there's just so many areas of mathematics. You can't really know all of them.
00:34:13 But some problems require lots of different tools to solve and so you can either go
00:34:19 and learn about that tool it takes a long time
00:34:21 or you could just collaborate with the person who ARE THE knows the tool
00:34:24 and they can solve that piece of the problem really. Well you can solve your piece you combine the right people.
00:34:29 You can solve big problems relatively easily
00:34:32 and on the art side you get inspiration things that no one person could make because they have the creative voice from
00:34:39 multiple people you have to be willing to let go of your own ego to do this and I think that probably for my dad
00:34:47 and I came from this period where we're just kind of exploring together and being open to the people that we meet
00:34:52 and learning from them. Not that I know of. And it's an interesting challenge to try to model.
00:35:06 Fun or humor or surprise. Mathematically I've heard.
00:35:10 I know I have some friends who are trying to answer that question but I don't know of one sort of I usually go by.
00:35:21 You know it when you see it kind of definition. So it was like. Each Other. Large I see here.
00:35:37 Yeah it's certainly a fascinating topic to think sort of at a high level of like mathematics for example has a kind of
00:35:48 a branch mathematical logic where tries to understand where we try to understand mathematically what mathematics is
00:35:55 and why it works or when it works when it doesn't work. But.
00:36:01 Of course the mathematics we practice in real life is a kind of a social dynamic you know do you believe
00:36:08 but someone claims they have a proof written down there
00:36:10 but to really check the proof you have to check it very carefully and it's humans are perfect
00:36:16 and so it's there's a social dynamic to the.
00:36:20 The body of research we we create and in some ways it makes it more fascinating
00:36:27 and colorful that that kind of mind share of what we know
00:36:31 or what we think we know is always kind of changing usually we're adding things we think are true
00:36:36 or that we claim are true.
00:36:37 Sometimes we take them back away we look at an old theorem and people have been building on
00:36:42 and realize oh actually that proof is wrong
00:36:45 and then there's this flurry of activity trying to fix the proof make a new proof so that the results that are built on
00:36:51 it are the result may still be true but sometimes we need to find a new way to prove it.
00:36:56 Sometimes the results and being false. That's that's more. It's occasionally scary but it's exciting.
00:37:04 Always trying to discover new things but also make sure they're really correct.
00:37:09 And definitely to me one of the appeals of mathematics is that you there is at least a sense of real truth of ultimate
00:37:17 truth that in principle if you're doing it correctly
00:37:22 and you prove something you really know that it is without a doubt true.
00:37:25 There's no other area where you can be as certain but still even then
00:37:30 or stuff like quite certain because humans make mistakes all the time. Yeah.
00:37:37 So I mean certainly we can see a lot that we can kind of build up lots of evidence that something is true by
00:37:45 constructing lots of examples and sculpture and and more practical engineering structures and so on
00:37:50 but to know that it's always true is a little bit different to know that it's usually true. This start.
00:38:01 Well you're right.
00:38:09 You have puzzles of remained an active interest
00:38:11 and in some sense all the mathematics we do is a kind of puzzle we have some set up of like what you're allowed to do
00:38:18 say with paper folding are some other simple mathematical structure
00:38:22 and the puzzle is you know what's possible what can you make these are kind of met a puzzle set sense
00:38:28 but even puzzles themselves like the kind of board game puzzles you get or the like sliding blocks
00:38:35 or these kinds of things are actually really interesting to study mathematically as well.
00:38:39 And so my dad and I and many collaborators like to explore the mathematics of games and puzzles
00:38:47 and we do it for video games like we studied Tetris and Super Mario Brothers
00:38:52 and other Nintendo games that I grew up playing now I can study them mathematically
00:38:57 and the sorts of things that we prove are that it's really hard to play these games perfectly.
00:39:03 So if you if I give you a level of Super Mario Brothers and say can you get from start to finish.
00:39:09 That's actually computationally difficult problem
00:39:13 and you can prove that solving that problem is really hard for a computer to do
00:39:18 and my philosophy is that humans are essentially a kind of computer
00:39:22 and so that tells you that it's also really hard for humans to play these games perfectly
00:39:27 or to solve these puzzles to play a Tetris game optimally
00:39:31 or to slide blocks around to get one block out of the box all these problems are really really hard
00:39:37 and I think it helps explain for humans.
00:39:40 Why we enjoy them because humans like a challenge things should be challenging but not too difficult
00:39:47 and proving these problems are computationally difficult.
00:39:50 They're still solvable given enough time
00:39:51 but in general you need an amount of time that grows exponentially with the size of the puzzle and so.
00:40:00 It means it's beyond a certain size it really becomes intractable and even in a small size it's a challenge
00:40:05 but still feasible.
00:40:07 I think that's why it's fun to have this kind of mathematical justification for why we like playing games
00:40:13 and puzzles and it's also a fun way to explore puzzles and games that I grew up with or know or love
00:40:20 and be able to study studying them from a mathematical perspective lets me essentially play the game
00:40:27 but in a more interesting way in some ways.
00:40:30 Usually we have to design new levels new puzzles within a design space in order to show that.
00:40:38 Oh we can build like logic gates and we can essentially build a computer within this game or puzzle.
00:40:44 And that's how you show that it's hard for a computer to play because computers are not it's really hard for a computer
00:40:50 to simulate a computer sexually.
00:40:53 That's sort of the hardest thing that they can do
00:40:55 and so we get to have fun by playing became by designing new levels and so on.
00:41:03 In order to prove these kind of interesting mathematical results that actually this game is really challenging.
00:41:09 And difficult.
00:41:15 So it's a bit of both Certainly I also just like playing games playing board games playing video games
00:41:22 and that's a lot of fun. Just as. Mediums to explore human experience I guess.
00:41:32 And I like the the role playing aspects I like the having fun with friends aspect
00:41:39 or exploring a world that's I mean these days.
00:41:42 Video games tell really powerful stories and so it becomes a new medium for storytelling.
00:41:47 So lots of more personal and just sort of fun aspects like that as I would be as a as a kid playing again.
00:41:54 And there's definitely a lot of nostalgia playing even playing old games as.
00:42:00 New Again they still hold up as being very exciting. But there's always even when I'm playing just for fun.
00:42:07 There's always in the back of my mind thinking I wonder if we can set this up as a clean mathematical problem
00:42:13 and analyze the complexity of this game
00:42:17 and some games are more amenable to this kind of mathematical analysis some of them require some adaptation to be a lot
00:42:24 of games have a lot of different elements it's really complicated mathematics is really good at getting at the core of
00:42:29 a problem. So it's a lot better when you have set up a simplified version.
00:42:33 Maybe you say oh let's just focus in on this one particular aspect of the game which if that's harder than the whole
00:42:40 thing is of course also even harder and so you can kind of isolate out the different parts
00:42:45 and tease out an interesting mathematical problem out of a real game or puzzle and then analyze that. So I mean.
00:42:52 It's it all fits together so as I'm playing a game. I'm always thinking about.
00:42:56 I wonder what I can tease out of this game and as I'm playing and having fun.
00:43:01 I'm also trying to think about that that mathematical formulation so.
00:43:05 It's good because then you get inspiration for new problems to solve just by having fun all day so.
00:43:17 Yeah I should get one.
00:43:19 But we made these wire take apart puzzles so each It's multiple pieces each piece is just made out of a piece of metal
00:43:28 wire that my dad would bend with pliers into shape and so one shade might be trouble clef
00:43:36 or some some recognizable shape or house I remember designing that one and then there be other pieces attached to it.
00:43:44 Everything's made out of wire.
00:43:45 Maybe some metal rings also and so these pieces appear to be interlocked and the challenge is to separate them.
00:43:52 And so while they look interlock there's actually some complicated procedure for pulling one piece at a.
00:44:00 Yeah there and you've solved the puzzle of that you have to put it back in and give it to someone else to solve.
00:44:04 So these are challenging the kind of a mix of geometry and apology in their design and.
00:44:14 Yeah there are a lot of fun you can be quite hard.
00:44:17 Some of them require hundreds of moves to solve some of them are easy if you know how but yeah.
00:44:27 So I think that the challenge of a human playing video games comes from different elements
00:44:34 and some parts are easy for computers to solve and other parts we sure are difficult for a computer to solve.
00:44:39 So if you imagine like solving a level of Super Mario Brothers there's there's kind of the physics of like the physical
00:44:48 aspect of pushing the buttons at the right time either pressing them really quickly
00:44:51 or exactly the right moment just before you fall off the ledge you jump
00:44:55 and land in the right place that sort of thing that computers are actually really good at doing
00:44:59 and there are people who exploit that in the tool assisted plays plays of games where they use computers to like slow
00:45:08 everything down and.
00:45:10 Time exactly the right moment to make a jump and things like that the computers can do some aspects really well
00:45:16 but there's kind of a there's a broader medal level in solving a puzzle
00:45:19 or solving a level in a video game where you need to plan out I should do this thing first
00:45:26 and then I'll go do this thing there's a time limit
00:45:28 and so it's really sensitive to how I should plan out the overall execution of the level executing it may be hard for
00:45:34 human easy for a computer but the planning part for a sufficiently complicated game is usually really difficult
00:45:41 and you can prove that that's computationally challenging now real world levels
00:45:46 and puzzles are usually designed to be right at the edge where you have to try several different options
00:45:51 but it's not impossible but in some sense
00:45:55 and that challenge comes out of this broader setting if you have a really large.
00:46:00 Well you can encode really hard problem inside that that puzzle and solving it.
00:46:05 You can show us how hard even for a computer to play.
00:46:09 So another example is like Tetris you have Tetris The usual the practical challenge is that you have this time limit.
00:46:16 You know the pieces falling you have to decide where to put it really fast computers are good at doing things really
00:46:21 fast but deciding where to put is actually really hard
00:46:26 and you can you can show that sort of long term planning of where you should put your pieces so that you won't run out
00:46:31 of space in your Tetris board.
00:46:33 That's actually competition intractable also so it's interesting I think real world games you have this interesting
00:46:40 mixture of making it hard for a human by giving time limits or physical execution can be challenging
00:46:45 and then you have this mastery aspect which very appealing to gamers.
00:46:50 But then usually there's this underlying computational difficulty that.
00:46:53 So you're solving this hard problem under time constraints that it's exciting for people. It's research for your site.
00:47:16 There definitely are some consequences I have a lot of games
00:47:21 or in some sense a like video games are often an abstraction of a real world problem.
00:47:26 Typical example is motion planning.
00:47:29 So you're either you have a bunch of robots
00:47:32 or you're a bunch of people trying to execute some goal you have a lot of objects you want to rearrange them into a
00:47:38 particular pattern
00:47:39 or maybe you're in a warehouse moving products around the every every product has a place it needs to go.
00:47:44 What's the optimal way for moving all these parts around.
00:47:48 That's those kinds of problems end up in a lot of video games also usually in a somewhat abstracted simplified form.
00:47:55 So proving those problems are hard shows also that.
00:48:00 These kinds of more real world problems are difficult as well maybe you can
00:48:04 or it helps you maybe try to isolate what are the what is special about the real world instances maybe your warehouse
00:48:11 is mostly two dimensional because you don't stack lots of things
00:48:14 or what are the it's speciality is of the real world instance that make them easier than the videogame So there's
00:48:22 definitely that kind of interplay
00:48:25 but I think a lot of people study the Myself included study the complexities of these games
00:48:31 and puzzles because it's fun and it's kind of a recreational pursuit.
00:48:35 So it's a little bit less serious than some areas of mathematics computer science but still we enjoy it
00:48:42 and it's kind of a fun.
00:48:43 I use it a lot as a way to get students excited about research because most people come in with their own background of
00:48:50 like what are fun games and puzzles that they grew up playing
00:48:54 and those inspired new mathematical problems either directly about those games
00:48:59 or about sort of the underlying principles
00:49:02 and these kinds of hardness personally call them to show these games are competition intractable are a nice way to get
00:49:09 started in research because you get to play with the game you get to use the expertise you have from having grown up
00:49:15 playing this game.
00:49:15 You probably spent way too many hours playing them
00:49:17 and that expertise is actually really helpful for solving the underlying math problem
00:49:21 and it can get people excited about. Oh this is this is computer science research I want to do more of this.
00:49:28 There's also the I think the broad appeal of you know there's some mathematical results that are hard for.
00:49:36 The general public to appreciate.
00:49:38 But you analyze a game or a puzzle that everyone has played or big segment the population is played
00:49:43 and they can appreciate like oh yeah I remember that being really hard.
00:49:46 Oh you can prove that mathematically Oh that's interesting.
00:49:49 I wonder how they do that and that can inspire people to enter the field or at least get a curiosity or
00:49:55 and learn about fields that they're not necessarily working in and appreciate that.
00:50:00 There's interesting things you can do about problems I happen to care about because most people like games
00:50:06 and so this isn't a nice kind of broad appeal connection where our years ten years.
00:50:21 It's hard to know exactly where my research will take me I definitely like MIT as a base because it's I mean there are
00:50:30 mazing students here amazing people doing all sorts of great and crazy things
00:50:34 and just a lot of flexibility to essentially do what we want and explore whatever we find interesting.
00:50:40 So what will be most interesting to us in ten years is hard to guess but this definitely is a nice.
00:50:49 Powerful base to do it from so different enjoying my time here.