1 00:00:04,38 --> 00:00:15,49 Right. Yeah well origami has a surprisingly rich mathematics and geometry to it. 2 00:00:16,78 --> 00:00:23,07 It's I originally got interested in origami because it just posed a lot of interesting mathematical questions you have 3 00:00:23,07 --> 00:00:27,64 this sheet of material and you have very simple rules you can't stretch it and you can't tear it 4 00:00:27,64 --> 00:00:35,65 and what can you do just by a reconfiguration just by folding and so it's very kind of a simple set up 5 00:00:35,65 --> 00:00:41,85 but the answers turn out to be surprisingly complicated and you need to use a lot of powerful geometry 6 00:00:41,85 --> 00:00:48,56 and algorithms to figure out what you can fault in many senses of you can really fold anything out of a sheet of paper 7 00:00:48,56 --> 00:00:52,42 and you can prove that mathematically. And that's sort of where we got started. 8 00:00:52,64 --> 00:00:53,52 It's very exciting 9 00:00:54,31 --> 00:01:00,82 and finding more interesting ways to make structure the fold between different shapes also has a lot of practical 10 00:01:00,82 --> 00:01:03,23 applications in science and medicine 11 00:01:03,23 --> 00:01:10,92 and engineering where you want to build some kind of structure that can change transform it shape from one thing to 12 00:01:10,92 --> 00:01:16,63 another so maybe you want to fold it down to some small size for storage or transportation. 13 00:01:17,00 --> 00:01:19,92 Like if you want to put something inside the body. 14 00:01:20,01 --> 00:01:25,18 Maybe you need to transport through small blood vessels and so you need to make it very compact 15 00:01:25,18 --> 00:01:27,18 or you want to deploy something into space. 16 00:01:27,3 --> 00:01:32,52 You want to fold it small so it fits inside your space shuttle and then going to unfold it when it gets there. 17 00:01:34,53 --> 00:01:40,16 I think it's even more exciting is you imagine like buildings or gadgets 18 00:01:40,16 --> 00:01:44,71 or things that can transform from one shape to another and serve different functions depending on what you need. 19 00:01:44,89 --> 00:01:51,11 Maybe your house a room in your house can transform from a kitchen to a bedroom and this kind of thing. 20 00:01:53,22 --> 00:02:00,53 One of a couple of the areas that we were exploring are things like printing. Now to robots. 21 00:02:00,85 --> 00:02:09,08 So there are a lot of rapid prototyping machines that are designed to make flat sheets of material. 22 00:02:09,1 --> 00:02:11,01 And how can you use them to make three D. 23 00:02:11,01 --> 00:02:12,27 Robots and other structures 24 00:02:13,7 --> 00:02:18,92 and folding is a good way to do that you can transform your two dimensional sheets into some cool three D. 25 00:02:18,92 --> 00:02:26,57 Structures so we one of our goals in this printable robot project is to make robots that can for like ten 26 00:02:26,57 --> 00:02:31,86 or twenty dollars of materials you can cut them and make them within a couple of hours. 27 00:02:32,01 --> 00:02:37,42 So everyone can make their own robot and customize their robot to do whatever they want. 28 00:02:37,43 --> 00:02:46,24 Another fun application is in making nano scale structures so we have out of the whole computer chip fabrication 29 00:02:46,24 --> 00:02:52,94 technology we have really good ways to pattern two dimensional surfaces at with nano scale features like nanometer 30 00:02:52,94 --> 00:02:59,9 resolution. But we're not so good at making three D. Structures at that scale and so folding offers another way. 31 00:02:59,95 --> 00:03:11,05 That's more in process and experimental but. An exciting possibility for folding is for you something that is. 32 00:03:11,07 --> 00:03:18,92 What makes your position as a professor sort of roses. Yeah. 33 00:03:19,23 --> 00:03:25,15 Yes I know lots of different players interested in different aspects of folding maybe more practical side I'm more on 34 00:03:25,15 --> 00:03:28,77 the theoretical side and developing new mathematics 35 00:03:28,77 --> 00:03:38,58 and tools to show to help those sort of kind of underlying technology for people to build on to make useful things. 36 00:03:39,62 --> 00:03:45,79 So we especially like to prove what we call universe ality results where we say in this kind of regime of origami 37 00:03:45,79 --> 00:03:47,2 design or folding design. 38 00:03:47,39 --> 00:03:51,27 You can make anything you want and we give you a computer algorithm to do that 39 00:03:51,27 --> 00:03:56,71 and so you can come in with your specifications like oh I'd like something that looks like this and it 40 00:03:56,71 --> 00:04:00,58 and the algorithm will give you how to fold exam. Actually that thing. 41 00:04:02,32 --> 00:04:09,56 And you know we get very general results they're not always the most practical because often we don't take into 42 00:04:09,56 --> 00:04:14,46 consideration things like the thickness of the material or other kind of structural issues 43 00:04:14,46 --> 00:04:21,02 and something we're trying to get to but by kind of simplifying looking at the core geometry we can get very general 44 00:04:21,02 --> 00:04:33,88 and powerful results and then that those can be adapted to more practical scenarios where you are going for something. 45 00:04:34,89 --> 00:04:38,27 You would think that there's a limitation but I don't know every year it. 46 00:04:38,3 --> 00:04:44,2 I'm amazed at what origami artists come up with there's new people with new ideas 47 00:04:44,2 --> 00:04:47,68 and it seems like almost limitless possibilities 48 00:04:48,57 --> 00:04:54,29 and especially if you start with a large enough sheet of paper you can really fold really really complicated things 49 00:04:55,5 --> 00:04:58,1 and there's still aspects we don't understand. 50 00:04:58,13 --> 00:05:05,54 For example area we look at a lot is curved crease folding so most are Grammies made with straight creases curved 51 00:05:05,54 --> 00:05:12,08 creases are a lot harder to understand and analyze and we're starting to make progress on the mathematics 52 00:05:12,08 --> 00:05:16,95 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 53 00:05:16,95 --> 00:05:19,97 that looks like this. Here's the curve creases you need to do that. 54 00:05:20,12 --> 00:05:26,18 So instead we've been experimenting a lot with just playing around trying different curve crease patterns 55 00:05:26,18 --> 00:05:30,39 and see what they produce and trying to be able to model that mathematically. 56 00:05:30,81 --> 00:05:32,99 And that led my father 57 00:05:32,99 --> 00:05:40,43 and I into the sculptural side of paper folding so most of the sculpture we made is make is around curved crease 58 00:05:40,43 --> 00:05:46,26 folding initially we're just experimenting trying to figure out what's possible and what what can be done 59 00:05:46,26 --> 00:05:53,27 but we kept making all these beautiful forms and so I started to embrace that as a purely sculptural. 60 00:05:53,33 --> 00:05:55,92 Endeavor as well but there's a lot of back and forth. 61 00:05:56,04 --> 00:05:59,26 I think that will do something sculpture really that will inspire new mathematics. 62 00:06:00,00 --> 00:06:04,18 We discuss we understand something better about curved creases mathematically that inspires new sculpture 63 00:06:04,18 --> 00:06:10,65 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. 64 00:06:12,21 --> 00:06:16,9 That's a big appeal to why people like to explore origami 65 00:06:16,9 --> 00:06:24,58 and mathematics together because you have this sort of scientific purpose maybe an engineering application 66 00:06:24,58 --> 00:06:30,64 or the beauty of the mathematics but then one of the applications is also to make sculpture. 67 00:06:32,00 --> 00:06:37,68 So it's really exciting to see these kinds of collaboration is a lot of engineering teams are bringing on origami 68 00:06:37,68 --> 00:06:45,75 artists at to help design new folding structures so artists have a lot of practical experience of how to make 69 00:06:45,75 --> 00:06:51,51 interesting folding structures and then they know the the literature which is a lot of people folding stuff 70 00:06:52,7 --> 00:07:03,1 and then that can inspire and inform new scientific discoveries. So your work your age. These are. 71 00:07:03,49 --> 00:07:08,63 Yeah that's where we like to live is right on the edge of knowledge where we we have a lot of tools 72 00:07:08,63 --> 00:07:10,91 but there's still something we don't understand. 73 00:07:10,92 --> 00:07:16,38 And so we try to push push that frontier of what's what's known on the scientific side 74 00:07:16,38 --> 00:07:24,49 and we use sculpture to kind of help explore that area more tentatively we can we can often make things that we don't 75 00:07:24,49 --> 00:07:25,69 yet fully understand. 76 00:07:25,71 --> 00:07:31,95 And so that lets us go a little beyond the frontier and sort of explore what's out there and see what's possible 77 00:07:31,95 --> 00:07:32,69 and then. 78 00:07:33,12 --> 00:07:40,7 Hopefully eventually understand that part mathematically where you where your science part formed you well what was it 79 00:07:40,7 --> 00:07:49,99 like for you just what was there. Yeah well in general we're looking at unsolved problems. 80 00:07:50,14 --> 00:07:59,31 I mean part of some sense one of the hardest parts is to figure out what the right question is. So you might want. 81 00:07:59,36 --> 00:07:59,69 There. 82 00:08:00,00 --> 00:08:04,36 Two types of questions about folding structures one is I give you a structure 83 00:08:04,36 --> 00:08:10,84 and I want to understand its properties and sort of analyze what it does how good it is what it folds into 84 00:08:10,84 --> 00:08:17,82 and the other side is the design side so you have some more high level specification of what you'd like to fold 85 00:08:17,82 --> 00:08:24,94 and then you want to automate the design of a structure that folds with those parameters designs maybe the more 86 00:08:24,94 --> 00:08:25,64 exciting side 87 00:08:25,64 --> 00:08:34,4 and there's many different ways you might formulate what you want to fold sort of the classic origami design problem is 88 00:08:34,4 --> 00:08:39,4 is shaped design. I say I give you a three dimensional shape. I want to fold that thing. 89 00:08:40,31 --> 00:08:41,74 What's a good way to fold that thing. 90 00:08:41,77 --> 00:08:47,48 And we're still we're still finding good algorithms for that we have some general procedures that work 91 00:08:47,48 --> 00:08:54,44 but they may not be so efficient as one of the standard measures of efficiency is if I have a square of a particular 92 00:08:54,44 --> 00:09:00,16 size material. How large of a version of that shape can I fold. 93 00:09:00,17 --> 00:09:05,55 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 94 00:09:05,55 --> 00:09:10,06 filled with little microscopic things not very efficient material usage. 95 00:09:10,39 --> 00:09:14,27 So how can we optimize that scale factor we still don't know the best way to do that. 96 00:09:15,39 --> 00:09:18,28 There's a sense in which we can't know exactly how good we can do that 97 00:09:18,28 --> 00:09:20,12 but we can hope to approximate the best solution. 98 00:09:21,63 --> 00:09:25,32 So that's something we're still actively working on for example our current. 99 00:09:25,66 --> 00:09:31,61 Favorite technique is called organizer and it's it's also free software 100 00:09:31,61 --> 00:09:37,39 and it's an algorithm we've been analyzing over the last several years to give an arbitrary three D. 101 00:09:37,39 --> 00:09:41,38 Shape that gives you a way to fold exactly that shape. 102 00:09:43,03 --> 00:09:45,7 It seems to be a good method but we don't know it's the best method 103 00:09:45,7 --> 00:09:52,31 and then there are many other questions based on other types of goals you might want like maybe you want to have a 104 00:09:52,31 --> 00:09:54,28 folding structure that can make two different shapes. 105 00:09:54,36 --> 00:09:59,83 We don't know much at all about that question or you want to make a folding that actually. 106 00:10:00,00 --> 00:10:02,64 Works with really thick material because you're making out of sheet metal 107 00:10:02,64 --> 00:10:07,54 or you want to make a practical mechanical structure. 108 00:10:07,56 --> 00:10:10,37 We're still understanding that we've made some progress on 109 00:10:10,37 --> 00:10:18,18 but there's still a lot of questions we don't know the best way to deal with with these kinds of practical issues 110 00:10:18,18 --> 00:10:23,23 and so that as becoming really relevant these days because a lot of people are trying to build these structures 111 00:10:23,23 --> 00:10:27,67 and sometimes it works sometimes it doesn't like to understand that threshold then 112 00:10:28,42 --> 00:10:31,63 and ideally automatically design structures that always work really well in practice. 113 00:10:42,29 --> 00:10:46,19 Yeah I mean I think we like to build objects and we. 114 00:10:46,25 --> 00:10:51,78 And it's even cooler when those objects can change shape so almost anywhere you imagine a gadget of some sort. 115 00:10:51,83 --> 00:10:58,3 I think folding could offer some interesting perspectives on on reconfigure ability. 116 00:10:59,04 --> 00:11:08,87 C one one area we haven't talked about is protein folding which is a kind of origami it's a little bit different 117 00:11:09,73 --> 00:11:15,04 but it's kind of essential to how just understanding how life works and also potentially drug design. 118 00:11:16,2 --> 00:11:22,59 So every living thing that we know of in this world is built up out of lots of little proteins kind of making life 119 00:11:22,59 --> 00:11:28,78 happen and proteins are centrally one dimensional pieces of paper that quite a lot into complicated three D. 120 00:11:28,78 --> 00:11:29,78 Structures in that three D. 121 00:11:29,78 --> 00:11:33,68 Structure kind of determines how it interacts with other proteins and what what its function is. 122 00:11:34,32 --> 00:11:41,59 And we don't really understand that process of folding kind of a one dimensional strip of paper into these three D. 123 00:11:41,59 --> 00:11:47,48 Structures how nature does it how we could do it how we could design proteins that fold into geometries that we want to 124 00:11:47,48 --> 00:11:51,46 like combat. You can imagine some disease comes along new disease. 125 00:11:51,61 --> 00:11:57,28 You could design a protein to fight specifically that disease but we don't know how to design. 126 00:11:58,04 --> 00:11:59,71 Proteins that folded the way we want to. 127 00:12:00,00 --> 00:12:06,94 And so we're trying to understand how proteins fold in order to sort of just understand how biology is functioning 128 00:12:06,94 --> 00:12:12,06 but also so that we can kind of control it in useful ways to kill viruses and things like that. 129 00:12:12,28 --> 00:12:15,83 So that's that's an exciting but difficult interaction. 130 00:12:17,28 --> 00:12:24,56 I would really like a sort of universal programmable gadget you know like we have lots of gadgets where you can 131 00:12:24,56 --> 00:12:29,65 download software updates like your smartphone you can download software updates and it does new things 132 00:12:30,63 --> 00:12:34,49 but we don't yet have a gadget where we can download new shapes 133 00:12:34,49 --> 00:12:43,33 or new geometries you can imagine a kind of universal gadget that can take on any shape I mean it has to preserve mass 134 00:12:43,33 --> 00:12:49,83 that you could imagine it unfolding and becoming a large thing at folding into a more compact. 135 00:12:50,2 --> 00:12:56,09 Structure changing shape maybe it's a chair or one one moment and it becomes a bicycle the next moment 136 00:12:56,09 --> 00:12:59,28 or I mean anything in principle is possible. 137 00:12:59,34 --> 00:13:01,95 It's we need to figure out what the practical regimes are 138 00:13:01,95 --> 00:13:06,89 but instead of having a separate gadget that does different functions 139 00:13:06,89 --> 00:13:12,46 or separate separate furniture that does different things you could imagine having fewer objects that are more 140 00:13:12,46 --> 00:13:17,37 reconfigurable so that that excites me like I really like gadgets. 141 00:13:17,39 --> 00:13:25,46 But I can have a gadget that can do more different things or be more customizable I think that's really exciting. 142 00:13:26,79 --> 00:13:28,92 I owe a lot of people in the field. 143 00:13:28,92 --> 00:13:32,58 Got into folding because they've been folding since they were kids and doing origami 144 00:13:32,58 --> 00:13:34,38 and then they learn about mathematics 145 00:13:34,38 --> 00:13:42,11 and think oh oh maybe we should combine these two I came from the other side so I was a beginning graduate student at 146 00:13:42,11 --> 00:13:48,84 University of Waterloo and I was just curious. I was looking for interesting problems to solve. 147 00:13:49,18 --> 00:13:59,45 I knew that I really like geometry and algorithms and. My father remembered an old. 148 00:14:00,00 --> 00:14:01,68 Unsolved problems that he had read about 149 00:14:01,68 --> 00:14:09,26 when he years ago from a column by Martin Gardner who used to write for Scientific American about mathematical games 150 00:14:10,08 --> 00:14:18,43 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 151 00:14:18,43 --> 00:14:22,22 and make one complete straight cut and then unfold the pieces 152 00:14:22,22 --> 00:14:29,04 and magicians like Houdini could produce a five pointed star lots of different simple shapes 153 00:14:29,75 --> 00:14:35,17 and Martin Gardner I was wondering you know what are the limits can you make anything by this process 154 00:14:35,17 --> 00:14:36,06 or what can you do 155 00:14:36,81 --> 00:14:44,19 and so that's the problem we started working on like OK I've got geometry in algorithms now seems like a cool unsolved 156 00:14:44,19 --> 00:14:48,95 problem to work on and it turned out to be fairly challenging took us a year or two to solve 157 00:14:50,05 --> 00:14:55,03 but it also was very exciting that we got our first universality result 158 00:14:55,03 --> 00:14:59,38 and we showed that you can make any poly gun any sheet metal straight sides 159 00:14:59,38 --> 00:15:06,01 or actually you can make several shapes all at once. Just by a one straight cut after folding. So those very exciting. 160 00:15:07,25 --> 00:15:09,64 It's fun problem motivated by magic. 161 00:15:09,81 --> 00:15:16,67 It turns out to have some practical applications also there are some designs for airbag folding collapsing airbags flat 162 00:15:16,67 --> 00:15:22,24 that are based on the same kind of algorithm that we didn't intend that at the time 163 00:15:23,42 --> 00:15:27,61 and it really got us excited about this world of folding where it seems to have very rich 164 00:15:27,61 --> 00:15:31,53 and complicated mathematics but also those kind of fun and visual 165 00:15:31,53 --> 00:15:37,94 and you can you can demonstrate these things you know you can fold a piece of paper make a kite and make a swan 166 00:15:37,94 --> 00:15:45,9 or whatever shape you want to so it has an attendee ability that everyone can kind of appreciate even if they're not a 167 00:15:45,9 --> 00:15:48,68 mathematician you can say hey look we solved this magic problem that's cool. 168 00:15:50,06 --> 00:16:07,99 You know something for you where it was well before right. Well. Yeah it's going to start. 169 00:16:08,89 --> 00:16:11,99 I guess my father became a single parent when I was two years old 170 00:16:13,00 --> 00:16:20,12 and so we've been close for a long time especially from when I was ages seven to eleven 171 00:16:20,12 --> 00:16:25,32 and we started traveling together and visited many different places. 172 00:16:25,57 --> 00:16:29,8 Mostly east coast of United States and just traveling for fun. 173 00:16:29,99 --> 00:16:34,24 There was no particular reason other than seeing different cultures within the United States 174 00:16:34,24 --> 00:16:42,46 and exploring which was really fun and throughout that time my dad treated me as a peer. So we would. 175 00:16:42,77 --> 00:16:48,87 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 176 00:16:48,87 --> 00:16:55,39 other places we'd stay for years and that was a really fun and bonding experience for us. 177 00:16:55,47 --> 00:16:57,79 Growing up and also because we're traveling a lot. 178 00:16:58,07 --> 00:17:02,74 We try to at home school and home school turned out to work really well for us. 179 00:17:04,37 --> 00:17:09,45 I would spend only like an hour a day doing sort of the breadth of regular school 180 00:17:09,45 --> 00:17:13,5 and so that I have many other hours during the day to explore things 181 00:17:13,5 --> 00:17:17,93 and very quickly for me exploring was computer programming. 182 00:17:17,97 --> 00:17:24,43 I got really excited about that essentially how to video games I played a lot of video games I was curious how they 183 00:17:24,43 --> 00:17:27,77 were made and my dad knew a little bit about computer programming to get us started 184 00:17:27,77 --> 00:17:30,31 and then we'd go to the library to learn more. 185 00:17:30,42 --> 00:17:37,05 This was all before the Internet and so I was sort of racially learning about computer programming 186 00:17:37,05 --> 00:17:41,19 and having a lot of fun there and then when school got out I would go and play with kids and things like that. 187 00:17:42,55 --> 00:17:48,47 So that was a really great time for me growing up and I went very fast in the computer science 188 00:17:48,47 --> 00:17:59,69 and eventually mathematics side of things right. So right. Yeah I asked over that when I was. 189 00:18:00,00 --> 00:18:07,35 Five or so and six years old my dad and I had our first collaboration we like to say with the Eric 190 00:18:07,35 --> 00:18:08,46 and dad puzzle company. 191 00:18:08,71 --> 00:18:16,72 So I helped design wire take apart puzzles and my dad would make them bending wire 192 00:18:17,5 --> 00:18:23,99 and then we sold to twenty stores across Canada and we split the income fifty fifty and it was a lot of fun. 193 00:18:25,22 --> 00:18:32,19 That was definitely the beginning of my interest in puzzles which is still to this day something I had like a lot 194 00:18:33,37 --> 00:18:37,17 and probably also the beginning of my interest in mathematics and geometry 195 00:18:37,17 --> 00:18:47,93 and things like that although that came much later as we were twelve. Yes yes. So after we ended this travel. 196 00:18:48,98 --> 00:18:54,18 I wanted to learn more about computing in computer science I learned was a thing 197 00:18:54,18 --> 00:18:56,14 and you have to go to university to learn about it. 198 00:18:56,19 --> 00:19:02,01 So there was some complication but I started undergraduate at twelve 199 00:19:02,83 --> 00:19:08,75 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 200 00:19:08,75 --> 00:19:14,32 when I was fourteen and then went to graduate school and got a master's and Ph D. 201 00:19:15,12 --> 00:19:31,39 By the time I was twenty and then went on the job market and became a professor here at MIT. You're right. Yes. 202 00:19:32,06 --> 00:19:39,01 Yeah it's really. We really value. Having fun and enjoying the work that we do. 203 00:19:39,85 --> 00:19:46,74 There's a very there's essentially no line between the work that we do and the things we do for pleasure. 204 00:19:46,95 --> 00:19:54,47 So it's all mixed together just with different kinds of outcomes maybe becomes a math paper maybe it becomes a 205 00:19:54,47 --> 00:19:59,37 sculpture maybe it's there's no outcome we're just doing it for fun but. 206 00:20:00,00 --> 00:20:06,13 It's all for fun and the philosophy is that if we do work that we enjoy 207 00:20:06,13 --> 00:20:13,04 and find pleasurable then we'll do it very well excel at it and that has been a useful guiding principle 208 00:20:15,18 --> 00:20:19,79 and I would encourage everyone to do the same it's definitely it may seem risky at times 209 00:20:19,79 --> 00:20:25,9 and certainly there was a worry that the work that we do is to recreational like you know we're studying the 210 00:20:25,9 --> 00:20:31,68 mathematics of a magic trick how could that be useful for anything but it turned out to be unexpectedly. 211 00:20:33,29 --> 00:20:40,09 But I think a lot of specially in mathematics there are just a lot of basic questions that are very curious 212 00:20:40,09 --> 00:20:41,44 and you want to know the answer to 213 00:20:42,26 --> 00:20:47,43 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 214 00:20:47,43 --> 00:20:54,26 about what's what you're allowed to do and yet it's very complicated to understand it's a nice context for. 215 00:20:55,03 --> 00:21:01,08 I think basic research tends to become useful eventually even though you may not see the applications ahead of time 216 00:21:01,08 --> 00:21:07,31 and so mathematicians tend to be attracted to like very simple questions that have complicated answers. 217 00:21:07,62 --> 00:21:12,73 Those tend to be also useful questions to answer always but if you solve enough of them. 218 00:21:12,83 --> 00:21:17,08 Many of them will become practical and so even though you do it for fun. 219 00:21:17,22 --> 00:21:24,74 It tends to have useful applications as well so that you might be worried by a lack of applications 220 00:21:24,74 --> 00:21:34,97 but turns out to be OK. It's for real life. It's really sweet. 221 00:21:35,15 --> 00:21:41,81 I mean we have pretty much ideal set ups where we can work on what we enjoy and get paid for it 222 00:21:41,81 --> 00:21:46,77 and have fun doing it and have all the resources to do it. We're very lucky. 223 00:21:52,47 --> 00:21:54,52 Yes So the glass blowing interest comes from. 224 00:21:55,73 --> 00:21:59,78 My dad's background which is more on the visual arts side so before I was born. 225 00:22:00,00 --> 00:22:04,26 In the late sixty's early seventy's he had the first glass studio in Canada. 226 00:22:04,31 --> 00:22:06,01 It's called the father of Canadian glass 227 00:22:07,59 --> 00:22:15,19 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 228 00:22:15,19 --> 00:22:16,89 blowing in North America 229 00:22:16,89 --> 00:22:23,66 and so he was experimenting exploring what's possible trying different recipes to make glasses and glass colors 230 00:22:23,66 --> 00:22:28,98 and things and then he didn't blow glass for many years until 231 00:22:30,19 --> 00:22:35,37 and I never really saw him blood last until we came to MIT fifteen years ago 232 00:22:35,37 --> 00:22:44,06 and we discovered he'd MIT has a glass blowing studio called The Glass lab and so my dad got curious to try 233 00:22:44,06 --> 00:22:45,24 and glass flying again. 234 00:22:45,5 --> 00:22:52,83 And so he started teaching there became one of the instructors and started blowing glass again 235 00:22:52,83 --> 00:22:58,7 and I got to see him blow glass and watched him make things and it's so beautiful and amazing to watch 236 00:22:58,7 --> 00:23:05,68 and then eventually like maybe maybe I should try clasp like that said Yeah you know you should at least see what it's 237 00:23:05,68 --> 00:23:07,69 like but be careful. It's addictive. 238 00:23:07,79 --> 00:23:22,92 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. 239 00:23:22,94 --> 00:23:28,5 It's a little more difficult because there's a lot of physics going on with glass blowing which is not exactly my forte 240 00:23:28,5 --> 00:23:35,85 but we're always looking for interesting math and connections between mathematics and glassblowing and we've found. 241 00:23:36,36 --> 00:23:40,6 We've found some interesting books there I think there's still a lot more to be explored. 242 00:23:40,67 --> 00:23:46,85 I would love to have algorithms to automatically design interesting because this sort of operations you can do are 243 00:23:46,85 --> 00:23:49,83 glassed in glass blowing a very simple. You know you can. 244 00:23:50,82 --> 00:23:56,16 You're turning your piece you can swing it around you can play with sort of gravity in this way you can heat different 245 00:23:56,16 --> 00:23:59,93 parts and cool other parts and that totally changes the shape that you produce. 246 00:24:00,25 --> 00:24:05,18 But it's a very complicated relationship and so it's hard to model all of that mathematically. 247 00:24:06,27 --> 00:24:12,51 But we've found some interesting regimes where it's simple enough that it's mostly geometric what's going on 248 00:24:13,6 --> 00:24:18,4 and so we can use computers to help design new patterns in glass. 249 00:24:18,54 --> 00:24:24,75 So we have some free software called virtual glass that we've been developing where you can design what are called 250 00:24:24,75 --> 00:24:27,1 Glass came patterns very simple. 251 00:24:29,22 --> 00:24:35,93 Conceptually simple but hard to visualize where you set up some essentially straight lines of color and glass 252 00:24:35,93 --> 00:24:36,78 and then twist them. 253 00:24:36,85 --> 00:24:45,55 And so you get some really cool twisty patterns they've been used in glass flying for for centuries. But. 254 00:24:45,57 --> 00:24:49,64 Pretty much everyone who makes glass cane follows one of standard set of patterns 255 00:24:50,51 --> 00:24:56,11 and so we were curious whether there were more patterns for Glass can that were possible in the software lets you 256 00:24:56,11 --> 00:25:00,19 explore those patterns and lets you try new things and sometimes you try a new thing 257 00:25:00,19 --> 00:25:02,15 and it looks kind of like an old thing. 258 00:25:02,2 --> 00:25:06,82 So it's not really interesting but other times you try a new pattern and it looks amazing in the software 259 00:25:06,82 --> 00:25:08,16 and that tells you here. 260 00:25:08,22 --> 00:25:13,53 This is something we should spend the time to actually learn how to make in real life software doesn't tell you exactly 261 00:25:13,53 --> 00:25:19,79 how to make it but it gives you a kind of schematic and then you have to do the glass blowing hard work 262 00:25:19,79 --> 00:25:26,21 but at least you know that the thing you're trying to make is really beautiful and so it's worth working towards. 263 00:25:26,46 --> 00:25:33,78 So you can rapidly try lots of different designs and software to find the one you want and then go physically make it. 264 00:25:33,79 --> 00:25:37,12 So it's really hard. 265 00:25:38,03 --> 00:25:44,76 Yeah I think it's I mean I think in general working on the boundary between two different fields you find interesting 266 00:25:44,76 --> 00:25:45,74 areas that. 267 00:25:46,33 --> 00:25:51,35 People tend to specialize in just one area and so they miss the things that the boundaries 268 00:25:52,09 --> 00:25:54,8 and so we've had a lot of fun exploring these boundaries 269 00:25:54,8 --> 00:25:59,39 and I think it comes partly from our different backgrounds my dad with the art background me with the more math 270 00:25:59,39 --> 00:26:06,03 and science. Background and we're always talking to each other and so we see we see the connections. 271 00:26:06,98 --> 00:26:12,78 When I started graduate school I was doing this sort of more theoretical mathematical work my dad's side 272 00:26:12,78 --> 00:26:14,4 and saying looks. That's interesting. 273 00:26:14,73 --> 00:26:16,96 This kind of creativity you're going through 274 00:26:16,96 --> 00:26:23,77 and solving unsolved mathematical problems is very much like the kind of thing that I go through in designing new 275 00:26:23,77 --> 00:26:26,4 sculptures or thinking about new art to build 276 00:26:27,19 --> 00:26:33,88 and so we started working together then he got he I taught him to become a mathematician. 277 00:26:33,9 --> 00:26:37,91 And he taught me to become an artist and so now we work on both together 278 00:26:37,91 --> 00:26:44,41 and it's really it's a lot of fun for us to collaborate in that way but also leads to really interesting questions 279 00:26:44,41 --> 00:26:50,36 and inspirations where instead of just thinking OK the math is the serious stuff 280 00:26:50,36 --> 00:26:55,84 and everything else is just you know side project we think of everything is like main projects 281 00:26:55,84 --> 00:27:15,44 and they inspire each other in ways that we couldn't predict. So I'm just working for years. We're definitely. 282 00:27:15,93 --> 00:27:20,28 Yeah I mean you could say frontiers of science and art maybe. 283 00:27:20,3 --> 00:27:26,95 Or that interplay but you know we're always as scientists we're always excited about the unknown 284 00:27:26,95 --> 00:27:33,77 and I mean that's as soon as we understand something fully it becomes almost boring 285 00:27:33,77 --> 00:27:37,79 and we want to move on to the next thing I mean we write down what we know and publish it 286 00:27:37,79 --> 00:27:40,9 and share it with the world so they can build on top of it 287 00:27:40,9 --> 00:27:48,67 but then we're always excited about the next question which we don't understand that's that's really what drives us is 288 00:27:48,67 --> 00:27:56,42 the price that we don't quite understand or like that seems a little strange. And we're curious about and. 289 00:27:57,58 --> 00:28:18,65 Yeah that's that's where we explore next. You know years at. Wells you might. Yeah it's a good question. 290 00:28:18,71 --> 00:28:25,1 I think in the in the folding regime. I work in many different areas but in the folding world. 291 00:28:26,79 --> 00:28:34,8 I think the biggest challenges right now are taking the nice mathematical geometric design algorithms that we have 292 00:28:34,8 --> 00:28:37,71 and adapting them to to real world materials. 293 00:28:38,03 --> 00:28:44,33 So we're starting to look at how does the thickness of the material affects what we can fold. 294 00:28:44,55 --> 00:28:49,99 How does the rigidity of material affect what we can fold off and you're making things out of plates and hinges. 295 00:28:50,36 --> 00:28:55,01 So you can really only fold at the creases whereas on paper it's more flexible. 296 00:28:55,03 --> 00:29:02,13 Between the creases So this is a world called rigid origami still trying to understand how to design within that space 297 00:29:02,13 --> 00:29:05,72 but it's very practical and exciting and for us it's nice 298 00:29:05,72 --> 00:29:09,31 and challenging because we don't know that's what that's what we don't know how to do 299 00:29:09,31 --> 00:29:14,69 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 300 00:29:14,69 --> 00:29:19,58 trying to take the rich and very general mathematics and adapting it 301 00:29:19,58 --> 00:29:29,57 or how to deal with the parameters of real world materials where you know other areas where you 302 00:29:29,57 --> 00:29:45,08 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 303 00:29:45,08 --> 00:29:51,51 square paper and all you can do is fold and it's really interesting to see what you can do just by folding 304 00:29:52,86 --> 00:29:59,93 but there are a lot of practical setups like in our printable robots project where it's. 305 00:30:00,00 --> 00:30:06,61 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. 306 00:30:06,61 --> 00:30:12,11 but We don't have to start from a square of material probably we're starting from some kind of rectangle of sheet 307 00:30:12,11 --> 00:30:16,87 material and why not also cut it in two dimensions before you fold 308 00:30:17,68 --> 00:30:24,99 and that's exciting because it can lead to much more efficient foldings potentially use all of the material now 309 00:30:24,99 --> 00:30:30,34 and you can make structures you couldn't make just by folding or you can you can make them much more efficiently 310 00:30:30,34 --> 00:30:36,87 and in different ways it's also a little it's tricky from a mathematical perspective because now we have so much more 311 00:30:36,87 --> 00:30:42,00 freedom we can cut and fold in some sense it's more freedom than we know what to do with 312 00:30:42,00 --> 00:30:48,12 and so that's that's kind of a new direction of folding where we also are cutting because why not. 313 00:30:48,27 --> 00:30:49,59 It's a practical thing you can do 314 00:30:51,11 --> 00:30:56,06 and maybe there are some settings where you want to add lots of cut some settings where you want to add fewer cuts we 315 00:30:56,06 --> 00:31:01,26 don't know the right balance between us and I think that's a new frontier we're still exploring 316 00:31:01,26 --> 00:31:07,96 and trying to understand but potentially leads to much better ways of folding structures. 317 00:31:07,98 --> 00:31:33,09 And going back to your you're very free for. Case don't have this space. If you go. 318 00:31:35,51 --> 00:31:37,96 I think it played a big role I mean it's hard to know exactly 319 00:31:38,68 --> 00:31:47,69 but I think growing up with so much free time unstructured time where I could just explore what interested me really 320 00:31:47,7 --> 00:31:56,94 gave me a big edge. Instead of sort of wasting time which a lot of schools do just filling that time. 321 00:31:56,99 --> 00:32:00,58 So as a kind of child care. It's set up. 322 00:32:01,58 --> 00:32:07,04 There's social aspects which are good too but a lot of time I feel like is wasted in school 323 00:32:07,04 --> 00:32:13,51 and so having the home school opened up this window where I could explore what interested me and 324 00:32:13,51 --> 00:32:18,98 and really dive in deeply and that let me go far ahead in the computer science world 325 00:32:18,98 --> 00:32:25,12 and I think in general could let students go really far ahead in the thing that excites them the most you still have to 326 00:32:25,12 --> 00:32:31,8 add in the breadth and socialize with other kids and so on but really 327 00:32:31,81 --> 00:32:39,82 and then going to university at a young age I think really gave me another edge whereas you can learn so much at a 328 00:32:39,82 --> 00:32:41,69 young age and so when you get to university. 329 00:32:41,69 --> 00:32:45,45 Suddenly there's really interesting things you're learning and it's really exciting 330 00:32:45,45 --> 00:32:48,92 and I still remember the things that I learned back then. 331 00:32:50,3 --> 00:32:57,77 So that's really powerful as a way to to get started and I think a lot of people could do it. 332 00:32:58,7 --> 00:33:01,36 There's also a more general sense of. 333 00:33:02,2 --> 00:33:10,07 Because we were improvising if we want a long travelling around we would talk to our neighbors learn about what they 334 00:33:10,07 --> 00:33:14,45 knew about and if they knew some interesting topic they would teach me and teach my dad. 335 00:33:15,57 --> 00:33:17,9 So I learned different aspects about the magic that way. 336 00:33:17,94 --> 00:33:20,32 I learned different kinds of cooking that way 337 00:33:21,58 --> 00:33:28,27 and that was a fun way to say it to appreciate different people of different backgrounds 338 00:33:28,27 --> 00:33:33,91 and different knowledge sets and I think in directly that influenced me 339 00:33:33,91 --> 00:33:37,71 and my dad to think a lot about collaboration 340 00:33:38,4 --> 00:33:43,18 and in current day we we collaborate with a lot of different mathematicians 341 00:33:43,18 --> 00:33:47,2 and different papers I've written papers I think over four hundred people at this point 342 00:33:48,63 --> 00:33:54,37 and on the art side we're also looking for collaborators interesting ways to combine different ideas from different 343 00:33:54,37 --> 00:33:59,93 minds we collaborate a lot with each other. Of course but also looking for outside inspiration. I thing. 344 00:34:00,00 --> 00:34:06,45 When you combine multiple people together you can really you can solve problems that could not be solved individually 345 00:34:07,33 --> 00:34:12,97 on the mathematical side this is because there's just so many areas of mathematics. You can't really know all of them. 346 00:34:13,63 --> 00:34:19,42 But some problems require lots of different tools to solve and so you can either go 347 00:34:19,42 --> 00:34:21,12 and learn about that tool it takes a long time 348 00:34:21,12 --> 00:34:24,04 or you could just collaborate with the person who ARE THE knows the tool 349 00:34:24,8 --> 00:34:29,06 and they can solve that piece of the problem really. Well you can solve your piece you combine the right people. 350 00:34:29,21 --> 00:34:31,01 You can solve big problems relatively easily 351 00:34:32,19 --> 00:34:39,18 and on the art side you get inspiration things that no one person could make because they have the creative voice from 352 00:34:39,18 --> 00:34:47,38 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 353 00:34:47,38 --> 00:34:52,71 and I came from this period where we're just kind of exploring together and being open to the people that we meet 354 00:34:52,71 --> 00:35:04,65 and learning from them. Not that I know of. And it's an interesting challenge to try to model. 355 00:35:06,13 --> 00:35:10,63 Fun or humor or surprise. Mathematically I've heard. 356 00:35:10,72 --> 00:35:19,85 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. 357 00:35:21,8 --> 00:35:36,6 You know it when you see it kind of definition. So it was like. Each Other. Large I see here. 358 00:35:37,89 --> 00:35:47,58 Yeah it's certainly a fascinating topic to think sort of at a high level of like mathematics for example has a kind of 359 00:35:48,9 --> 00:35:55,93 a branch mathematical logic where tries to understand where we try to understand mathematically what mathematics is 360 00:35:55,93 --> 00:36:00,94 and why it works or when it works when it doesn't work. But. 361 00:36:01,47 --> 00:36:07,19 Of course the mathematics we practice in real life is a kind of a social dynamic you know do you believe 362 00:36:08,23 --> 00:36:10,88 but someone claims they have a proof written down there 363 00:36:10,88 --> 00:36:16,28 but to really check the proof you have to check it very carefully and it's humans are perfect 364 00:36:16,28 --> 00:36:20,72 and so it's there's a social dynamic to the. 365 00:36:20,74 --> 00:36:27,09 The body of research we we create and in some ways it makes it more fascinating 366 00:36:27,09 --> 00:36:31,14 and colorful that that kind of mind share of what we know 367 00:36:31,14 --> 00:36:35,86 or what we think we know is always kind of changing usually we're adding things we think are true 368 00:36:36,69 --> 00:36:37,65 or that we claim are true. 369 00:36:37,73 --> 00:36:42,54 Sometimes we take them back away we look at an old theorem and people have been building on 370 00:36:42,54 --> 00:36:45,03 and realize oh actually that proof is wrong 371 00:36:45,03 --> 00:36:51,53 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 372 00:36:51,53 --> 00:36:56,13 it are the result may still be true but sometimes we need to find a new way to prove it. 373 00:36:56,2 --> 00:37:02,81 Sometimes the results and being false. That's that's more. It's occasionally scary but it's exciting. 374 00:37:04,85 --> 00:37:09,04 Always trying to discover new things but also make sure they're really correct. 375 00:37:09,75 --> 00:37:17,99 And definitely to me one of the appeals of mathematics is that you there is at least a sense of real truth of ultimate 376 00:37:17,99 --> 00:37:21,27 truth that in principle if you're doing it correctly 377 00:37:22,3 --> 00:37:25,44 and you prove something you really know that it is without a doubt true. 378 00:37:25,71 --> 00:37:30,99 There's no other area where you can be as certain but still even then 379 00:37:30,99 --> 00:37:36,88 or stuff like quite certain because humans make mistakes all the time. Yeah. 380 00:37:37,07 --> 00:37:43,92 So I mean certainly we can see a lot that we can kind of build up lots of evidence that something is true by 381 00:37:45,07 --> 00:37:50,34 constructing lots of examples and sculpture and and more practical engineering structures and so on 382 00:37:50,34 --> 00:37:59,37 but to know that it's always true is a little bit different to know that it's usually true. This start. 383 00:38:01,27 --> 00:38:03,28 Well you're right. 384 00:38:09,00 --> 00:38:11,45 You have puzzles of remained an active interest 385 00:38:11,45 --> 00:38:18,63 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 386 00:38:18,63 --> 00:38:22,57 say with paper folding are some other simple mathematical structure 387 00:38:22,57 --> 00:38:27,51 and the puzzle is you know what's possible what can you make these are kind of met a puzzle set sense 388 00:38:28,54 --> 00:38:35,56 but even puzzles themselves like the kind of board game puzzles you get or the like sliding blocks 389 00:38:35,56 --> 00:38:39,26 or these kinds of things are actually really interesting to study mathematically as well. 390 00:38:39,28 --> 00:38:46,96 And so my dad and I and many collaborators like to explore the mathematics of games and puzzles 391 00:38:47,73 --> 00:38:52,47 and we do it for video games like we studied Tetris and Super Mario Brothers 392 00:38:52,47 --> 00:38:57,54 and other Nintendo games that I grew up playing now I can study them mathematically 393 00:38:57,54 --> 00:39:03,87 and the sorts of things that we prove are that it's really hard to play these games perfectly. 394 00:39:03,89 --> 00:39:09,22 So if you if I give you a level of Super Mario Brothers and say can you get from start to finish. 395 00:39:09,43 --> 00:39:13,13 That's actually computationally difficult problem 396 00:39:13,14 --> 00:39:17,96 and you can prove that solving that problem is really hard for a computer to do 397 00:39:18,95 --> 00:39:22,49 and my philosophy is that humans are essentially a kind of computer 398 00:39:22,49 --> 00:39:27,91 and so that tells you that it's also really hard for humans to play these games perfectly 399 00:39:27,91 --> 00:39:31,41 or to solve these puzzles to play a Tetris game optimally 400 00:39:31,41 --> 00:39:37,36 or to slide blocks around to get one block out of the box all these problems are really really hard 401 00:39:37,36 --> 00:39:40,83 and I think it helps explain for humans. 402 00:39:40,88 --> 00:39:46,19 Why we enjoy them because humans like a challenge things should be challenging but not too difficult 403 00:39:47,38 --> 00:39:50,04 and proving these problems are computationally difficult. 404 00:39:50,15 --> 00:39:51,99 They're still solvable given enough time 405 00:39:51,99 --> 00:39:58,42 but in general you need an amount of time that grows exponentially with the size of the puzzle and so. 406 00:40:00,00 --> 00:40:05,95 It means it's beyond a certain size it really becomes intractable and even in a small size it's a challenge 407 00:40:05,95 --> 00:40:06,9 but still feasible. 408 00:40:07,17 --> 00:40:13,67 I think that's why it's fun to have this kind of mathematical justification for why we like playing games 409 00:40:13,67 --> 00:40:20,82 and puzzles and it's also a fun way to explore puzzles and games that I grew up with or know or love 410 00:40:20,82 --> 00:40:27,22 and be able to study studying them from a mathematical perspective lets me essentially play the game 411 00:40:27,22 --> 00:40:29,99 but in a more interesting way in some ways. 412 00:40:30,07 --> 00:40:38,05 Usually we have to design new levels new puzzles within a design space in order to show that. 413 00:40:38,16 --> 00:40:44,02 Oh we can build like logic gates and we can essentially build a computer within this game or puzzle. 414 00:40:44,55 --> 00:40:50,11 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 415 00:40:50,11 --> 00:40:51,55 to simulate a computer sexually. 416 00:40:53,08 --> 00:40:54,49 That's sort of the hardest thing that they can do 417 00:40:55,31 --> 00:41:03,6 and so we get to have fun by playing became by designing new levels and so on. 418 00:41:03,72 --> 00:41:09,1 In order to prove these kind of interesting mathematical results that actually this game is really challenging. 419 00:41:09,11 --> 00:41:14,55 And difficult. 420 00:41:15,54 --> 00:41:22,6 So it's a bit of both Certainly I also just like playing games playing board games playing video games 421 00:41:22,6 --> 00:41:31,62 and that's a lot of fun. Just as. Mediums to explore human experience I guess. 422 00:41:32,82 --> 00:41:39,47 And I like the the role playing aspects I like the having fun with friends aspect 423 00:41:39,47 --> 00:41:42,16 or exploring a world that's I mean these days. 424 00:41:42,22 --> 00:41:46,19 Video games tell really powerful stories and so it becomes a new medium for storytelling. 425 00:41:47,15 --> 00:41:54,59 So lots of more personal and just sort of fun aspects like that as I would be as a as a kid playing again. 426 00:41:54,68 --> 00:41:59,44 And there's definitely a lot of nostalgia playing even playing old games as. 427 00:42:00,00 --> 00:42:07,15 New Again they still hold up as being very exciting. But there's always even when I'm playing just for fun. 428 00:42:07,58 --> 00:42:13,68 There's always in the back of my mind thinking I wonder if we can set this up as a clean mathematical problem 429 00:42:13,68 --> 00:42:15,87 and analyze the complexity of this game 430 00:42:17,21 --> 00:42:24,24 and some games are more amenable to this kind of mathematical analysis some of them require some adaptation to be a lot 431 00:42:24,24 --> 00:42:29,17 of games have a lot of different elements it's really complicated mathematics is really good at getting at the core of 432 00:42:29,17 --> 00:42:32,8 a problem. So it's a lot better when you have set up a simplified version. 433 00:42:33,13 --> 00:42:40,17 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 434 00:42:40,17 --> 00:42:45,24 thing is of course also even harder and so you can kind of isolate out the different parts 435 00:42:45,24 --> 00:42:52,01 and tease out an interesting mathematical problem out of a real game or puzzle and then analyze that. So I mean. 436 00:42:52,52 --> 00:42:56,32 It's it all fits together so as I'm playing a game. I'm always thinking about. 437 00:42:56,51 --> 00:43:00,84 I wonder what I can tease out of this game and as I'm playing and having fun. 438 00:43:01,08 --> 00:43:05,13 I'm also trying to think about that that mathematical formulation so. 439 00:43:05,41 --> 00:43:17,6 It's good because then you get inspiration for new problems to solve just by having fun all day so. 440 00:43:17,61 --> 00:43:19,16 Yeah I should get one. 441 00:43:19,31 --> 00:43:28,35 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 442 00:43:28,35 --> 00:43:36,28 wire that my dad would bend with pliers into shape and so one shade might be trouble clef 443 00:43:36,28 --> 00:43:44,05 or some some recognizable shape or house I remember designing that one and then there be other pieces attached to it. 444 00:43:44,06 --> 00:43:45,09 Everything's made out of wire. 445 00:43:45,16 --> 00:43:52,62 Maybe some metal rings also and so these pieces appear to be interlocked and the challenge is to separate them. 446 00:43:52,63 --> 00:43:59,86 And so while they look interlock there's actually some complicated procedure for pulling one piece at a. 447 00:44:00,00 --> 00:44:04,6 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. 448 00:44:04,72 --> 00:44:13,16 So these are challenging the kind of a mix of geometry and apology in their design and. 449 00:44:14,28 --> 00:44:16,67 Yeah there are a lot of fun you can be quite hard. 450 00:44:17,56 --> 00:44:27,00 Some of them require hundreds of moves to solve some of them are easy if you know how but yeah. 451 00:44:27,2 --> 00:44:33,61 So I think that the challenge of a human playing video games comes from different elements 452 00:44:34,34 --> 00:44:39,83 and some parts are easy for computers to solve and other parts we sure are difficult for a computer to solve. 453 00:44:39,89 --> 00:44:48,32 So if you imagine like solving a level of Super Mario Brothers there's there's kind of the physics of like the physical 454 00:44:48,32 --> 00:44:51,73 aspect of pushing the buttons at the right time either pressing them really quickly 455 00:44:51,73 --> 00:44:55,18 or exactly the right moment just before you fall off the ledge you jump 456 00:44:55,18 --> 00:44:59,03 and land in the right place that sort of thing that computers are actually really good at doing 457 00:44:59,03 --> 00:45:08,65 and there are people who exploit that in the tool assisted plays plays of games where they use computers to like slow 458 00:45:08,65 --> 00:45:10,04 everything down and. 459 00:45:10,52 --> 00:45:16,3 Time exactly the right moment to make a jump and things like that the computers can do some aspects really well 460 00:45:16,3 --> 00:45:19,87 but there's kind of a there's a broader medal level in solving a puzzle 461 00:45:19,87 --> 00:45:26,26 or solving a level in a video game where you need to plan out I should do this thing first 462 00:45:26,26 --> 00:45:28,79 and then I'll go do this thing there's a time limit 463 00:45:28,79 --> 00:45:34,79 and so it's really sensitive to how I should plan out the overall execution of the level executing it may be hard for 464 00:45:34,79 --> 00:45:41,01 human easy for a computer but the planning part for a sufficiently complicated game is usually really difficult 465 00:45:41,95 --> 00:45:46,41 and you can prove that that's computationally challenging now real world levels 466 00:45:46,41 --> 00:45:51,37 and puzzles are usually designed to be right at the edge where you have to try several different options 467 00:45:51,37 --> 00:45:55,23 but it's not impossible but in some sense 468 00:45:55,23 --> 00:45:59,67 and that challenge comes out of this broader setting if you have a really large. 469 00:46:00,00 --> 00:46:05,46 Well you can encode really hard problem inside that that puzzle and solving it. 470 00:46:05,56 --> 00:46:08,61 You can show us how hard even for a computer to play. 471 00:46:09,72 --> 00:46:16,96 So another example is like Tetris you have Tetris The usual the practical challenge is that you have this time limit. 472 00:46:16,99 --> 00:46:21,85 You know the pieces falling you have to decide where to put it really fast computers are good at doing things really 473 00:46:21,85 --> 00:46:25,17 fast but deciding where to put is actually really hard 474 00:46:26,00 --> 00:46:31,86 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 475 00:46:31,86 --> 00:46:33,21 of space in your Tetris board. 476 00:46:33,38 --> 00:46:40,21 That's actually competition intractable also so it's interesting I think real world games you have this interesting 477 00:46:40,21 --> 00:46:45,43 mixture of making it hard for a human by giving time limits or physical execution can be challenging 478 00:46:45,43 --> 00:46:49,35 and then you have this mastery aspect which very appealing to gamers. 479 00:46:50,5 --> 00:46:53,91 But then usually there's this underlying computational difficulty that. 480 00:46:53,99 --> 00:47:15,79 So you're solving this hard problem under time constraints that it's exciting for people. It's research for your site. 481 00:47:16,66 --> 00:47:21,2 There definitely are some consequences I have a lot of games 482 00:47:21,21 --> 00:47:26,75 or in some sense a like video games are often an abstraction of a real world problem. 483 00:47:26,77 --> 00:47:29,15 Typical example is motion planning. 484 00:47:29,34 --> 00:47:32,17 So you're either you have a bunch of robots 485 00:47:32,17 --> 00:47:38,5 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 486 00:47:38,5 --> 00:47:39,16 particular pattern 487 00:47:39,16 --> 00:47:44,24 or maybe you're in a warehouse moving products around the every every product has a place it needs to go. 488 00:47:44,39 --> 00:47:47,72 What's the optimal way for moving all these parts around. 489 00:47:48,07 --> 00:47:55,54 That's those kinds of problems end up in a lot of video games also usually in a somewhat abstracted simplified form. 490 00:47:55,56 --> 00:47:59,83 So proving those problems are hard shows also that. 491 00:48:00,00 --> 00:48:04,27 These kinds of more real world problems are difficult as well maybe you can 492 00:48:04,27 --> 00:48:11,48 or it helps you maybe try to isolate what are the what is special about the real world instances maybe your warehouse 493 00:48:11,48 --> 00:48:14,36 is mostly two dimensional because you don't stack lots of things 494 00:48:14,36 --> 00:48:22,33 or what are the it's speciality is of the real world instance that make them easier than the videogame So there's 495 00:48:22,33 --> 00:48:24,07 definitely that kind of interplay 496 00:48:25,21 --> 00:48:31,65 but I think a lot of people study the Myself included study the complexities of these games 497 00:48:31,65 --> 00:48:35,47 and puzzles because it's fun and it's kind of a recreational pursuit. 498 00:48:35,61 --> 00:48:42,33 So it's a little bit less serious than some areas of mathematics computer science but still we enjoy it 499 00:48:42,33 --> 00:48:43,46 and it's kind of a fun. 500 00:48:43,57 --> 00:48:50,85 I use it a lot as a way to get students excited about research because most people come in with their own background of 501 00:48:50,85 --> 00:48:53,5 like what are fun games and puzzles that they grew up playing 502 00:48:54,41 --> 00:48:59,17 and those inspired new mathematical problems either directly about those games 503 00:48:59,17 --> 00:49:01,21 or about sort of the underlying principles 504 00:49:02,02 --> 00:49:09,61 and these kinds of hardness personally call them to show these games are competition intractable are a nice way to get 505 00:49:09,61 --> 00:49:15,09 started in research because you get to play with the game you get to use the expertise you have from having grown up 506 00:49:15,09 --> 00:49:15,73 playing this game. 507 00:49:15,9 --> 00:49:17,69 You probably spent way too many hours playing them 508 00:49:17,69 --> 00:49:21,69 and that expertise is actually really helpful for solving the underlying math problem 509 00:49:21,69 --> 00:49:26,99 and it can get people excited about. Oh this is this is computer science research I want to do more of this. 510 00:49:28,35 --> 00:49:35,86 There's also the I think the broad appeal of you know there's some mathematical results that are hard for. 511 00:49:36,23 --> 00:49:37,94 The general public to appreciate. 512 00:49:38,01 --> 00:49:43,86 But you analyze a game or a puzzle that everyone has played or big segment the population is played 513 00:49:43,86 --> 00:49:46,97 and they can appreciate like oh yeah I remember that being really hard. 514 00:49:46,99 --> 00:49:48,77 Oh you can prove that mathematically Oh that's interesting. 515 00:49:49,14 --> 00:49:55,08 I wonder how they do that and that can inspire people to enter the field or at least get a curiosity or 516 00:49:55,08 --> 00:49:59,7 and learn about fields that they're not necessarily working in and appreciate that. 517 00:50:00,00 --> 00:50:06,22 There's interesting things you can do about problems I happen to care about because most people like games 518 00:50:06,98 --> 00:50:21,91 and so this isn't a nice kind of broad appeal connection where our years ten years. 519 00:50:21,92 --> 00:50:30,33 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 520 00:50:30,33 --> 00:50:34,33 mazing students here amazing people doing all sorts of great and crazy things 521 00:50:34,33 --> 00:50:40,17 and just a lot of flexibility to essentially do what we want and explore whatever we find interesting. 522 00:50:40,5 --> 00:50:49,08 So what will be most interesting to us in ten years is hard to guess but this definitely is a nice. 523 00:50:49,1 --> 00:50:54,24 Powerful base to do it from so different enjoying my time here.