1 00:00:01,710 --> 00:00:04,200 Welcome, welcome back to the second week 2 00:00:04,200 --> 00:00:05,790 of Modeling Complex Systems. 3 00:00:05,790 --> 00:00:09,390 I made sure to have my black cat Virgil in this shot. 4 00:00:09,390 --> 00:00:11,460 Some of you saw Dawn, the white one, 5 00:00:11,460 --> 00:00:12,900 over the discussions this week. 6 00:00:12,900 --> 00:00:14,850 I thought the first week was great. 7 00:00:14,850 --> 00:00:18,180 I was impressed by all the amazing discussions we had. 8 00:00:18,180 --> 00:00:23,010 The first week was really meant to focus on models as nouns, 9 00:00:23,010 --> 00:00:24,600 what are models, 10 00:00:24,600 --> 00:00:27,270 what are different models we use in science 11 00:00:27,270 --> 00:00:28,683 and in everyday life. 12 00:00:29,758 --> 00:00:31,230 And I thought that the discussions really got to 13 00:00:31,230 --> 00:00:33,930 what I believe is important when we define models, 14 00:00:33,930 --> 00:00:36,547 which is the idea that there are no perfect models. 15 00:00:36,547 --> 00:00:40,364 One system can be represented in different ways. 16 00:00:40,364 --> 00:00:43,530 And you all did a great job of coming up 17 00:00:43,530 --> 00:00:45,240 with this idea of balance 18 00:00:45,240 --> 00:00:47,520 between the complexity of a model 19 00:00:47,520 --> 00:00:49,980 and the purpose of a model. 20 00:00:49,980 --> 00:00:52,602 So what questions are we trying to answer? 21 00:00:52,602 --> 00:00:56,280 In what way are we trying to look at the system? 22 00:00:56,280 --> 00:00:57,720 So for this second week, 23 00:00:57,720 --> 00:01:00,660 I thought it would be fun to focus on models as verbs. 24 00:01:00,660 --> 00:01:02,700 So how do we model? 25 00:01:02,700 --> 00:01:05,970 Because even though there are no perfect models, 26 00:01:05,970 --> 00:01:08,340 it's not the Wild West out there either. 27 00:01:08,340 --> 00:01:12,180 So the idea is, I want you to feel like you can come up 28 00:01:12,180 --> 00:01:14,850 with your own approaches to the problems we're gonna look. 29 00:01:14,850 --> 00:01:16,620 Feels like disease modeling right now. 30 00:01:16,620 --> 00:01:18,420 Definitely need new perspective. 31 00:01:18,420 --> 00:01:20,370 There are no perfect way to models, 32 00:01:20,370 --> 00:01:23,941 but there are people that think about the theory of modeling 33 00:01:23,941 --> 00:01:27,887 and what are the different approximations, idealizations, 34 00:01:27,887 --> 00:01:30,420 what is the thought process of most people 35 00:01:30,420 --> 00:01:32,550 when we go from a complex reality 36 00:01:32,550 --> 00:01:35,973 to a manageable computational or mathematical model? 37 00:01:38,010 --> 00:01:41,013 So let me just share my screen here for a second. 38 00:01:42,210 --> 00:01:44,100 So hopefully you can see my screen right now. 39 00:01:44,100 --> 00:01:45,840 I thought it would be fun to go over 40 00:01:45,840 --> 00:01:47,987 some of the types of models that are highlighted 41 00:01:47,987 --> 00:01:49,210 in the reading for this week, 42 00:01:49,210 --> 00:01:52,500 which is Models in Science, section one and two, 43 00:01:52,500 --> 00:01:57,500 and at the same time to go over some examples of models, 44 00:01:58,209 --> 00:02:02,070 the way we're going to use them in this class, really. 45 00:02:02,070 --> 00:02:07,070 So the first type of model that is discussed in the reading 46 00:02:08,280 --> 00:02:10,099 are scale models. 47 00:02:10,099 --> 00:02:13,173 And these already came up in the discussions. 48 00:02:15,330 --> 00:02:18,540 If we think about a maquette for an architect 49 00:02:18,540 --> 00:02:21,060 or a sculpture, so creating a model of the building 50 00:02:21,060 --> 00:02:22,710 or the statute that you want to build, 51 00:02:22,710 --> 00:02:24,150 that would be a scale model. 52 00:02:24,150 --> 00:02:26,640 You make it in a smaller size that's more manageable. 53 00:02:26,640 --> 00:02:29,130 Maybe you don't use the right material right away, 54 00:02:29,130 --> 00:02:31,320 but it gives you a 3D representation 55 00:02:31,320 --> 00:02:33,213 that is easier to work with 56 00:02:33,213 --> 00:02:36,210 than simply imagining your creation. 57 00:02:36,210 --> 00:02:37,590 And in the case of this course, 58 00:02:37,590 --> 00:02:39,780 we're still gonna use these scales models 59 00:02:39,780 --> 00:02:42,633 often to get around computational complexity. 60 00:02:43,860 --> 00:02:47,953 So we might wanna scale down a model, for example, 61 00:02:52,470 --> 00:02:54,180 of the human population. 62 00:02:54,180 --> 00:02:58,020 If we have this agent-based model with 7 billion nodes, 63 00:02:58,020 --> 00:03:02,010 7 billion individuals, individual agents interacting, 64 00:03:02,010 --> 00:03:04,020 that might be computationally extensive. 65 00:03:04,020 --> 00:03:07,720 So we might want to scale down the model 66 00:03:09,930 --> 00:03:14,133 for computational complexity. 67 00:03:19,500 --> 00:03:21,270 And really here the process is the same, 68 00:03:21,270 --> 00:03:22,770 just to make it more manageable, 69 00:03:22,770 --> 00:03:25,290 allow us to highlight certain features of the model. 70 00:03:25,290 --> 00:03:29,541 We might not need a full sized population. 71 00:03:29,541 --> 00:03:31,920 So that would be one use of the scale model. 72 00:03:31,920 --> 00:03:33,570 Most of what we're gonna do 73 00:03:33,570 --> 00:03:37,683 fall in the second family of models which are idealized. 74 00:03:42,540 --> 00:03:45,420 And really that's almost all mathematical models 75 00:03:45,420 --> 00:03:46,320 work this way. 76 00:03:46,320 --> 00:03:49,042 The idea is that we want to make simplifications 77 00:03:49,042 --> 00:03:53,670 to the real system to focus on what we believe is important. 78 00:03:53,670 --> 00:03:56,790 So if we're doing a forest fire model study, 79 00:03:56,790 --> 00:03:59,490 the robustness of the Amazon, 80 00:03:59,490 --> 00:04:01,830 then the smell of the trees might not matter. 81 00:04:01,830 --> 00:04:03,420 The colors of the tree might not matter. 82 00:04:03,420 --> 00:04:04,680 So we can scale that back, 83 00:04:04,680 --> 00:04:07,230 make the system more idealized in a way. 84 00:04:07,230 --> 00:04:09,810 So notice that idealized doesn't mean better here. 85 00:04:09,810 --> 00:04:13,196 It really just means more useful to the modeler. 86 00:04:13,196 --> 00:04:16,380 And that's how we're gonna allow ourselves 87 00:04:16,380 --> 00:04:20,010 to do mathematical model or computer programs 88 00:04:20,010 --> 00:04:23,040 that can follow reality in some way. 89 00:04:23,040 --> 00:04:26,130 And all of these approximations or idealizations 90 00:04:26,130 --> 00:04:27,030 fall in two families. 91 00:04:27,030 --> 00:04:28,683 So let me call them 2A and 2B. 92 00:04:30,270 --> 00:04:35,270 So we have Aristotelian idealizations or Galilean, 93 00:04:39,300 --> 00:04:42,330 and I don't want to go too deep in the details 94 00:04:42,330 --> 00:04:45,150 of the distinction between these two 95 00:04:45,150 --> 00:04:50,020 or the definition of Aristotelian versus Galilean 96 00:04:50,020 --> 00:04:52,290 idealizations, but I do think they're useful 97 00:04:52,290 --> 00:04:55,136 for modelers to keep in mind. 98 00:04:55,136 --> 00:04:57,787 So Aristotelian idealizations 99 00:04:57,787 --> 00:05:00,150 are when you simply remove something. 100 00:05:00,150 --> 00:05:02,091 So the previous examples I gave 101 00:05:02,091 --> 00:05:07,091 removing the smell or color 102 00:05:13,218 --> 00:05:14,551 of real systems, 103 00:05:18,210 --> 00:05:21,570 that data is definitely useful to ignore those features 104 00:05:21,570 --> 00:05:23,520 when modeling forest fire. 105 00:05:23,520 --> 00:05:24,600 But we have to keep in mind 106 00:05:24,600 --> 00:05:28,380 that now the model is not representative of any reality. 107 00:05:28,380 --> 00:05:32,280 There is no forest where there is no smell or color 108 00:05:32,280 --> 00:05:33,150 to the trees. 109 00:05:33,150 --> 00:05:35,700 That might not matter, but sometime it will, 110 00:05:35,700 --> 00:05:39,750 the idea that the idealizations we've made is such 111 00:05:39,750 --> 00:05:43,530 that our model does not correspond to any reality. 112 00:05:43,530 --> 00:05:45,480 It's just an approximation of it. 113 00:05:45,480 --> 00:05:48,240 Whereas Galilean are distortions, 114 00:05:48,240 --> 00:05:50,790 but we're still in the realm of the possible. 115 00:05:50,790 --> 00:05:53,660 So anytime a physicist, for example, 116 00:05:53,660 --> 00:05:58,660 make the approximation of frictionless movement 117 00:05:58,740 --> 00:06:01,583 or ignoring air resistance, 118 00:06:01,583 --> 00:06:05,250 it's convenient mathematically, but it also means 119 00:06:05,250 --> 00:06:07,300 that you could test the model in a vacuum 120 00:06:08,697 --> 00:06:09,530 and you should be able to predict the outcome 121 00:06:09,530 --> 00:06:10,752 of some experiments. 122 00:06:10,752 --> 00:06:14,880 So there is a world where those Galilean idealizations 123 00:06:14,880 --> 00:06:15,750 are still possible 124 00:06:15,750 --> 00:06:17,670 and the model still represents something. 125 00:06:17,670 --> 00:06:19,410 In the case of what we're gonna do, 126 00:06:19,410 --> 00:06:23,550 often Galilean approximations are gonna be the opposite 127 00:06:23,550 --> 00:06:25,710 of a scale model or are scaled up, 128 00:06:25,710 --> 00:06:26,910 which would be something 129 00:06:28,350 --> 00:06:31,263 like approximating very large populations. 130 00:06:32,340 --> 00:06:34,563 So all disease models, for example, 131 00:06:36,810 --> 00:06:39,090 will assume an almost infinite 132 00:06:39,090 --> 00:06:41,310 or literally an infinite population. 133 00:06:41,310 --> 00:06:44,310 So then we know that the models we're building for disease 134 00:06:44,310 --> 00:06:48,330 can't really be applied to households or small town, 135 00:06:48,330 --> 00:06:51,660 but work better for cities or large homogeneous country. 136 00:06:51,660 --> 00:06:53,490 So that's a Galilean approximation 137 00:06:53,490 --> 00:06:56,460 where we know that the larger the population, 138 00:06:56,460 --> 00:06:58,710 the better our model should fit reality. 139 00:06:58,710 --> 00:07:01,460 And then that's one way of validating what we're doing. 140 00:07:03,930 --> 00:07:05,780 One thing we're gonna use quite a bit 141 00:07:07,740 --> 00:07:11,100 are analogical models, 142 00:07:11,100 --> 00:07:13,143 which is the third family here, 143 00:07:16,290 --> 00:07:19,632 and a classic example, at least for me is, 144 00:07:19,632 --> 00:07:22,200 the mass spring system in physics 145 00:07:22,200 --> 00:07:24,270 is used to solve almost anything. 146 00:07:24,270 --> 00:07:29,270 So you can solve the sound that you would get by blowing 147 00:07:29,310 --> 00:07:32,160 in a half empty beer bottle using a mass spring system, 148 00:07:32,160 --> 00:07:35,100 the same way you could model to some extent 149 00:07:35,100 --> 00:07:37,840 electrons moving around with a mass spring system. 150 00:07:37,840 --> 00:07:42,300 So physicists use that idealized model often in analogies. 151 00:07:42,300 --> 00:07:44,520 So now it's not a clear model of mechanisms, 152 00:07:44,520 --> 00:07:46,950 but it still works in predicting some behavior. 153 00:07:46,950 --> 00:07:48,837 We're gonna do something similar. 154 00:07:48,837 --> 00:07:50,940 We're gonna have a lot of models that are gonna pop up 155 00:07:50,940 --> 00:07:52,509 time and time again. 156 00:07:52,509 --> 00:07:56,430 For example, we're gonna use 157 00:07:56,430 --> 00:07:58,923 a lot of rich get richer approximation. 158 00:08:02,100 --> 00:08:04,590 So the rich get richer mechanism will show up 159 00:08:04,590 --> 00:08:07,260 if we model scientific publications. 160 00:08:07,260 --> 00:08:10,380 Papers with a lot of citations are easier to find 161 00:08:10,380 --> 00:08:13,560 and therefore get more citations in the future. 162 00:08:13,560 --> 00:08:16,440 Similarly, wealth distribution in the US 163 00:08:16,440 --> 00:08:18,420 is a clear rich gets richer process. 164 00:08:18,420 --> 00:08:20,430 You gotta have money to make money. 165 00:08:20,430 --> 00:08:21,960 So these mechanisms, 166 00:08:21,960 --> 00:08:24,060 these general rich gets richer process, 167 00:08:24,060 --> 00:08:26,190 are gonna show up often as analogies 168 00:08:26,190 --> 00:08:29,730 and will allow us to translate intuition, 169 00:08:29,730 --> 00:08:31,803 learn from one system to another. 170 00:08:34,334 --> 00:08:35,580 And then the last family in the readings 171 00:08:37,590 --> 00:08:39,240 are these phenomenological model. 172 00:08:46,710 --> 00:08:49,424 I was just checking that I spelled that right. 173 00:08:49,424 --> 00:08:52,680 So phenomenological models, and as you can see, 174 00:08:52,680 --> 00:08:56,763 I have a harder time the more syllables there are in a word. 175 00:08:57,644 --> 00:09:00,300 But here, if you've been reading the textbook, 176 00:09:00,300 --> 00:09:03,870 you should be on chapter two right now. 177 00:09:03,870 --> 00:09:06,521 And this is what, here like you say, 178 00:09:06,521 --> 00:09:08,160 I would describe as these descriptive models. 179 00:09:08,160 --> 00:09:10,740 So they don't try and get to mechanisms 180 00:09:10,740 --> 00:09:13,740 behind a behavior or results, 181 00:09:13,740 --> 00:09:17,250 but they just try and reproduce its phenomenology 182 00:09:17,250 --> 00:09:20,127 or its behavior, the way it looks. 183 00:09:20,127 --> 00:09:21,510 So you could almost say 184 00:09:21,510 --> 00:09:24,720 that these models are independent of theories. 185 00:09:24,720 --> 00:09:27,060 They try to get to the data 186 00:09:27,060 --> 00:09:30,210 without necessarily assuming some prior knowledge 187 00:09:30,210 --> 00:09:32,760 or giving you any insights into the real systems. 188 00:09:32,760 --> 00:09:35,250 And we're mostly gonna steer away from that. 189 00:09:35,250 --> 00:09:37,953 That's what a lot of statistical models do. 190 00:09:38,910 --> 00:09:41,730 That being said, they're still an art to that. 191 00:09:41,730 --> 00:09:43,350 They require a choice of description. 192 00:09:43,350 --> 00:09:45,210 So there is insights that go into them. 193 00:09:45,210 --> 00:09:49,020 They're not completely agnostic of reality, 194 00:09:49,020 --> 00:09:50,790 but they don't necessarily tie 195 00:09:50,790 --> 00:09:53,640 in what we're aiming to do with this class. 196 00:09:53,640 --> 00:09:55,500 At the very end, we're still gonna do 197 00:09:55,500 --> 00:10:00,500 some model fitting and selection. 198 00:10:03,720 --> 00:10:06,510 So anytime you have a model and then you start fitting it 199 00:10:06,510 --> 00:10:10,020 to real data, there comes a point 200 00:10:10,020 --> 00:10:12,267 when you're comparing two models that are mechanistically 201 00:10:12,267 --> 00:10:14,940 the same and you're just trying to tune parameters 202 00:10:14,940 --> 00:10:18,090 or you're just basically building a phenomenological model 203 00:10:18,090 --> 00:10:18,933 at that point. 204 00:10:21,330 --> 00:10:26,250 So those categories are mo mainly useful to have in mind 205 00:10:26,250 --> 00:10:28,620 just to give us a common language. 206 00:10:28,620 --> 00:10:31,380 In the next video, I'll start giving you some recipes, 207 00:10:31,380 --> 00:10:33,235 how do we build model from scratch 208 00:10:33,235 --> 00:10:37,050 and having in mind when we're doing scale approximations 209 00:10:37,050 --> 00:10:39,300 or Aristotelian idealizations 210 00:10:39,300 --> 00:10:41,220 where we don't describe reality, 211 00:10:41,220 --> 00:10:43,620 Galilean approximations, where we do, 212 00:10:43,620 --> 00:10:44,880 just building analogies, 213 00:10:44,880 --> 00:10:48,060 so that the mechanisms might not be right, but are analogous 214 00:10:48,060 --> 00:10:51,660 to different systems or abandoning mechanisms altogether, 215 00:10:51,660 --> 00:10:54,210 and just trying to describe phenomenology. 216 00:10:54,210 --> 00:10:56,048 Those are the words we're gonna keep using 217 00:10:56,048 --> 00:10:57,510 over and over again. 218 00:10:57,510 --> 00:11:02,280 So this distinction from the Models in Science reading 219 00:11:02,280 --> 00:11:05,370 are really useful just in terms of setting a common language 220 00:11:05,370 --> 00:11:06,690 for the rest of the course. 221 00:11:06,690 --> 00:11:07,980 So I'll see you in the next one 222 00:11:07,980 --> 00:11:10,200 where we'll start building some recipes 223 00:11:10,200 --> 00:11:12,423 for how to build models from scratch.