WEBVTT 1 00:00:00.120 --> 00:00:02.720 Imagine you want to build a house, right, and your 2 00:00:02.759 --> 00:00:07.200 contractor just hands you a single atom and says good luck. 3 00:00:07.559 --> 00:00:09.320 Right, Yeah, that sounds like a nightmare. 4 00:00:09.439 --> 00:00:12.960 It is, but honestly, that is exactly what learning a 5 00:00:13.000 --> 00:00:16.039 traditional programming language often feels like. I mean, you open 6 00:00:16.079 --> 00:00:19.679 a textbook, you memorize this giant dictionary of syntacy. 7 00:00:19.760 --> 00:00:23.280 Oh, the semi collins forour loops, the brackets. 8 00:00:22.719 --> 00:00:24.960 Exactly, and then you sit down, you open a blank 9 00:00:25.000 --> 00:00:27.359 document and you're just staring at an empty void. 10 00:00:27.640 --> 00:00:30.600 Yeah, that blank screen is just it's the ultimate barrier 11 00:00:30.640 --> 00:00:32.119 to entry, you know, it really is. 12 00:00:32.399 --> 00:00:35.960 You literally have to teach the computer absolutely everything from 13 00:00:36.000 --> 00:00:38.719 scratch before you can even begin to build your house. 14 00:00:38.719 --> 00:00:41.640 Which is why that information overloads stops so many people 15 00:00:41.719 --> 00:00:44.000 dead in their tracks, like before they even get past 16 00:00:44.039 --> 00:00:47.200 the first chapter. Right, The mental overhead required to just 17 00:00:48.320 --> 00:00:51.640 set up a workspace, let alone execute an actual idea 18 00:00:51.840 --> 00:00:52.640 is staggering. 19 00:00:52.759 --> 00:00:56.600 Well, today we are completely bypassing that blank screen. We 20 00:00:56.679 --> 00:01:00.399 are doing a custom tailored deep dive specifically for you, 21 00:01:00.679 --> 00:01:01.119 the listener. 22 00:01:01.200 --> 00:01:03.679 Yeah, if you're someone who's just insanely curious, this is 23 00:01:03.719 --> 00:01:05.480 for you, exactly. 24 00:01:05.239 --> 00:01:08.560 If you want those brilliant aha moments of understanding how 25 00:01:08.640 --> 00:01:11.120 systems work. But you don't want to drown in the 26 00:01:11.159 --> 00:01:14.400 technical drudgery of computer science. Stick around. 27 00:01:14.560 --> 00:01:16.159 So what's our source material today? 28 00:01:16.599 --> 00:01:19.680 Right? So we are looking at a book called an 29 00:01:19.719 --> 00:01:23.640 Elementary Introduction to the Wolfram Language, written by Stephen Wolfrom 30 00:01:23.680 --> 00:01:24.879 back in twenty seventeen. 31 00:01:25.079 --> 00:01:27.680 You know, calling it a programming manual almost does it 32 00:01:27.680 --> 00:01:28.359 a disservice? 33 00:01:28.840 --> 00:01:30.719 Really? How so? Well? 34 00:01:31.000 --> 00:01:33.120 I mean it's really a ground up introduction to just 35 00:01:33.120 --> 00:01:35.439 a completely different paradigm of computation. 36 00:01:35.560 --> 00:01:38.560 Okay, that makes sense because our mission today is to 37 00:01:38.719 --> 00:01:44.319 explore the core principles of computational thinking, right, but through 38 00:01:44.359 --> 00:01:46.959 the lens of a language that was specifically designed to 39 00:01:47.079 --> 00:01:50.959 automate away the boring, repetitive parts of traditional coding. 40 00:01:51.120 --> 00:01:53.000 Yeah, the drudgery exactly. 41 00:01:53.040 --> 00:01:55.040 Okay, let's unpack this because we have to start with 42 00:01:55.040 --> 00:01:58.920 the fundamental philosophy here. It completely upends how we usually 43 00:01:58.920 --> 00:01:59.560 think about. 44 00:01:59.359 --> 00:02:02.319 Software, really does. We're moving away from the idea of programming, 45 00:02:02.359 --> 00:02:05.359 as you know, just giving blind instructions to a dumb. 46 00:02:05.079 --> 00:02:06.959 Machine, right, a machine that knows nothing. 47 00:02:06.920 --> 00:02:09.960 Exactly, and instead we're looking at programming as a collaboration 48 00:02:10.120 --> 00:02:12.039 with a highly knowledgeable system. 49 00:02:12.400 --> 00:02:16.800 Now, Stephen Wolfram spent what over thirty years developing. 50 00:02:16.319 --> 00:02:19.039 This architecture, Yeah, originating all the way back with a 51 00:02:19.080 --> 00:02:21.560 system called Mathematica in nineteen eighty eight. 52 00:02:21.840 --> 00:02:23.759 Wow, nineteen eighty eight. 53 00:02:24.039 --> 00:02:27.759 Yeah. And the defining characteristic of the wolf from language. 54 00:02:27.840 --> 00:02:31.479 The thing that makes it different from like C plus plus. 55 00:02:31.199 --> 00:02:35.120 Or Java exactly or Python. Yeah, the core trait is 56 00:02:35.120 --> 00:02:38.080 that it is intrinsically quote unquote knowledge based. 57 00:02:38.520 --> 00:02:43.759 Okay, knowledge based sounds a bit like like tech pro 58 00:02:43.960 --> 00:02:45.800 marketing jargon. Honestly it does. 59 00:02:46.080 --> 00:02:46.400 It does. 60 00:02:46.479 --> 00:02:48.560 Let's ground that in reality. What does that actually mean 61 00:02:48.599 --> 00:02:49.439 for the person. 62 00:02:49.159 --> 00:02:53.319 Typing well in a traditional language. The computer is incredibly fast, right, 63 00:02:53.520 --> 00:02:55.439 but it's born completely ignorant of the. 64 00:02:55.400 --> 00:02:57.479 Real world, like a super fast newborn. Yeah. 65 00:02:57.520 --> 00:02:58.960 I mean it knows how to add numbers, and it 66 00:02:59.000 --> 00:03:02.159 knows how to shuttle data back and forth in its memory. Okay, 67 00:03:02.199 --> 00:03:04.080 but if you want that computer to know what the 68 00:03:04.120 --> 00:03:08.360 population of London is, or what the color yellow. 69 00:03:08.000 --> 00:03:10.080 Looks like, or how to turn on a webcam. 70 00:03:09.879 --> 00:03:13.159 Exactly, you have to build that knowledge yourself. You have 71 00:03:13.199 --> 00:03:17.759 to write extensive code or import massive external libraries just 72 00:03:17.879 --> 00:03:20.000 to teach the machine those basic. 73 00:03:19.759 --> 00:03:21.919 Concepts and then you can finally manipulate them. 74 00:03:22.080 --> 00:03:25.479 Right. But the Wolf from Language flips that entirely. It 75 00:03:25.560 --> 00:03:30.479 has this vast encyclopedic amount of real world knowledge built 76 00:03:30.520 --> 00:03:31.800 directly into its. 77 00:03:31.639 --> 00:03:34.319 Core memory, like from the moment you boot it up, from. 78 00:03:34.159 --> 00:03:35.159 The second you boot it up. 79 00:03:35.240 --> 00:03:38.400 Yeah, which means the human sitting at the keyboard has 80 00:03:38.479 --> 00:03:42.879 to explain significantly less to actually get a result exactly. 81 00:03:42.919 --> 00:03:44.759 The computer already knows what you're talking about. 82 00:03:44.840 --> 00:03:46.879 But okay, if you're listening to this, you might be 83 00:03:46.879 --> 00:03:48.919 wondering about the obvious loophole. 84 00:03:48.520 --> 00:03:50.120 Here, the plain English question. 85 00:03:50.520 --> 00:03:54.919 Yeah, if the system already has so much built in knowledge, 86 00:03:55.159 --> 00:03:57.439 why can't I just talk to it in plain English forever? 87 00:03:57.840 --> 00:03:58.719 It's a fair question. 88 00:03:58.800 --> 00:04:00.560 I mean, we already have Wolf from out Alpha right now. 89 00:04:00.680 --> 00:04:02.759 You just type what is the distance to the moon 90 00:04:02.759 --> 00:04:04.680 into a search bar and it gives you the answer. 91 00:04:05.520 --> 00:04:08.960 Why force ourselves to learn as strict new syntax at all? 92 00:04:09.400 --> 00:04:13.960 So Wolf from Alpha is brilliant for quick, isolated queries. 93 00:04:14.680 --> 00:04:18.319 It parses human language incredibly well for those like single 94 00:04:18.360 --> 00:04:19.879 shot questions. 95 00:04:19.399 --> 00:04:21.040 Right, basic trivia or math. 96 00:04:21.279 --> 00:04:24.800 Yeah, but the limitation appears when you want to execute 97 00:04:24.959 --> 00:04:28.079 systematic multi step complexity what. 98 00:04:28.040 --> 00:04:29.560 Does that look like in practice? 99 00:04:29.600 --> 00:04:31.879 Well, imagine you want to take the data from your 100 00:04:31.920 --> 00:04:36.360 first question, feed it into a visual analyzer filter that 101 00:04:36.480 --> 00:04:40.199 visualization based on a live beta feed from a weather satellite. 102 00:04:40.319 --> 00:04:44.279 Oh wow, and then output and interactive dashboard. Plain English 103 00:04:44.360 --> 00:04:48.120 completely breaks down there because it's too messy exactly. Human 104 00:04:48.240 --> 00:04:51.839 language is simply too ambiguous and imprecise to carry an 105 00:04:51.879 --> 00:04:54.399 instruction through that many layers of logic. 106 00:04:54.639 --> 00:04:57.199 The computer would just make a fatal assumption at some point, right. 107 00:04:57.079 --> 00:04:58.720 It would guess what you meant and get it wrong. 108 00:04:58.920 --> 00:05:00.639 I look at it like walking in a restaurant. 109 00:05:01.000 --> 00:05:01.759 Okay, I like this. 110 00:05:02.160 --> 00:05:04.879 Using Plain English with Wolf from Alpha is like ordering 111 00:05:04.920 --> 00:05:07.319 off a menu. Yeah you can get a phenomenal meal, 112 00:05:07.439 --> 00:05:09.759 but you are entirely limited to what the chef has 113 00:05:09.800 --> 00:05:11.920 already decided to put on the menu for that day. 114 00:05:12.000 --> 00:05:14.680 Yeah, you can't ask for something entirely new exactly. 115 00:05:15.279 --> 00:05:18.560 But learning the wolfrom language is like getting the keys 116 00:05:18.879 --> 00:05:21.920 to a world class kitchen, and the computer is your 117 00:05:21.920 --> 00:05:23.199 Michelin star sous chef. 118 00:05:23.480 --> 00:05:25.120 Oh that's a great analogy. 119 00:05:24.839 --> 00:05:29.079 Right, This sious chef already knows the perfect knife techniques. 120 00:05:29.360 --> 00:05:32.920 They have the exact boiling point of every liquid memorized. 121 00:05:32.519 --> 00:05:34.600 But you still have to tell them what to make. 122 00:05:34.920 --> 00:05:38.920 Yes, you need a highly precise system, like a rigid 123 00:05:38.959 --> 00:05:42.279 shorthand to tell the chef exactly how to combine those 124 00:05:42.439 --> 00:05:46.879 raw ingredients to create your own, unique, completely original recipe. 125 00:05:46.959 --> 00:05:49.120 And the beauty of that kitchen scenario is how it 126 00:05:49.199 --> 00:05:51.720 shifts the technical burden. You don't have to worry about 127 00:05:51.720 --> 00:05:54.000 how the stove is wired or how the knife was 128 00:05:54.040 --> 00:05:57.000 forged exactly. You only need to formulate your recipe in 129 00:05:57.079 --> 00:05:58.680 computational terms. 130 00:05:58.399 --> 00:06:00.800 So you're just focusing on the idea, right. 131 00:06:01.079 --> 00:06:03.360 And the source points out that learning this is very 132 00:06:03.439 --> 00:06:06.800 much like learning a human language, just immensely more systematic. 133 00:06:06.839 --> 00:06:08.879 I mean, there are no weird exceptions. 134 00:06:08.399 --> 00:06:12.519 Absolutely none. There are absolutely no irregular verbs to memorize. 135 00:06:12.680 --> 00:06:16.439 Once you understand the core rules, those rules apply universally 136 00:06:16.480 --> 00:06:17.720 across the entire system. 137 00:06:17.959 --> 00:06:21.160 Okay, so how do we actually write this menu? Let's 138 00:06:21.199 --> 00:06:24.079 look at the foundational building blocks of this code. Let's 139 00:06:24.079 --> 00:06:27.160 do it in the wolf From language. Every single action 140 00:06:27.360 --> 00:06:31.519 operates via functions, and there is an unbreakable rule for 141 00:06:31.600 --> 00:06:32.360 these functions. 142 00:06:32.560 --> 00:06:34.319 They always start with a capital letter. 143 00:06:34.240 --> 00:06:39.360 Yes, capital letters, and the arguments the ingredients you are 144 00:06:39.360 --> 00:06:43.040 passing into the function are always enclosed in square brackets. 145 00:06:43.120 --> 00:06:45.439 That's the rigid shorthand you mentioned, right. 146 00:06:45.360 --> 00:06:46.519 So if you want to add two and two, you 147 00:06:46.519 --> 00:06:49.000 don't just use a plus sign. The engine under the 148 00:06:49.040 --> 00:06:52.800 hood is processing the word plus with the capital. 149 00:06:52.480 --> 00:06:54.600 P, then an open scare racket, then. 150 00:06:54.519 --> 00:06:57.240 The numbers two and two, separated by a comma and 151 00:06:57.279 --> 00:06:58.680 a close square bracket. Right. 152 00:06:58.959 --> 00:07:02.160 Or if you need a random number, you use random managure. 153 00:07:01.839 --> 00:07:03.439 With capital R and capital. 154 00:07:03.120 --> 00:07:06.480 I exactly followed by square brackets containing your parameters. 155 00:07:06.680 --> 00:07:10.199 So those functions are essentially the actions, right, they're the verbs, 156 00:07:10.360 --> 00:07:13.560 and they need materials to act upon. And the fundamental 157 00:07:13.560 --> 00:07:16.000 way to group materials in this language is a. 158 00:07:15.959 --> 00:07:19.199 List, right, And lists are enclosed in curly braces. 159 00:07:19.519 --> 00:07:23.279 Okay, curly braces. Something like open curly brace one, two, three, 160 00:07:23.480 --> 00:07:26.120 close curly brace is a fully formed. 161 00:07:25.879 --> 00:07:29.000 List, it is, And once you have items bundled in 162 00:07:29.000 --> 00:07:32.839 those curly braces, you can deploy your capital letter functions 163 00:07:32.839 --> 00:07:33.720 to manipulate them. 164 00:07:33.920 --> 00:07:36.839 So you can use a function like range to automatically 165 00:07:36.920 --> 00:07:39.319 generate a massive list of numbers. You don't have to 166 00:07:39.360 --> 00:07:40.439 type them by hand. 167 00:07:40.199 --> 00:07:41.120 Which is a life saver. 168 00:07:41.399 --> 00:07:44.160 Yeah, and you can deploy the reverse function to flip 169 00:07:44.160 --> 00:07:45.680 the entire list backward, or. 170 00:07:46.040 --> 00:07:49.279 Use join to snap two completely different lists together. 171 00:07:49.439 --> 00:07:51.480 And you can get surgical with it too. You can 172 00:07:51.519 --> 00:07:53.959 ask for just the first item the last item, or 173 00:07:54.079 --> 00:07:57.319 use the part function to extract the exact element sitting 174 00:07:57.399 --> 00:07:59.160 at say position number forty two. 175 00:07:59.319 --> 00:08:02.000 Yeah, you can even dismantle a single number, which I love. 176 00:08:02.120 --> 00:08:03.199 Wait, how does that work? 177 00:08:03.319 --> 00:08:06.839 You apply the integer digits function to let's say the 178 00:08:06.920 --> 00:08:09.639 year nineteen eighty eight, it shatters it into a list 179 00:08:09.639 --> 00:08:12.079 containing a one, A nine, and eight and an eight. 180 00:08:12.279 --> 00:08:14.279 Oh wow, why would you need to do that? 181 00:08:14.519 --> 00:08:18.079 Breaking integers down like that is a surprisingly powerful technique 182 00:08:18.079 --> 00:08:20.600 when you're hunting for hidden patterns and large data sets. 183 00:08:20.920 --> 00:08:23.480 That makes sense. But I have to challenge this swict 184 00:08:23.519 --> 00:08:24.600 syntax for a second though. 185 00:08:24.639 --> 00:08:24.920 Oh kay? 186 00:08:24.959 --> 00:08:28.639 Bringing on if I type plus with a lowercase P, 187 00:08:29.399 --> 00:08:32.279 or if I accidentally use parentheses instead of square brackets 188 00:08:32.320 --> 00:08:35.120 to contain my numbers. Yeah, the system just throws an 189 00:08:35.159 --> 00:08:35.480 air or. 190 00:08:35.600 --> 00:08:38.320 It does read text everywhere it stares. 191 00:08:38.000 --> 00:08:41.159 Back at me as red text. If the software is 192 00:08:41.200 --> 00:08:44.720 supposed to be so incredibly smart and knowledgeable, shouldn't be 193 00:08:44.759 --> 00:08:46.360 able to infer what I mean? 194 00:08:46.679 --> 00:08:50.320 It feels frustrating at first. I know, but that strictness 195 00:08:50.360 --> 00:08:54.840 exists for a critical architectural reason, which is think about 196 00:08:54.840 --> 00:08:58.720 how we use parentheses in standard mathematics. We use them 197 00:08:58.759 --> 00:09:00.159 strictly for grouping. 198 00:09:00.159 --> 00:09:02.519 Like writing out two plus three four to ensure the 199 00:09:02.559 --> 00:09:03.639 addition happens first. 200 00:09:03.799 --> 00:09:06.679 Exactly if the woolf From language allowed you to use 201 00:09:06.720 --> 00:09:10.519 parentheses for functions as well, the system would face massive 202 00:09:10.559 --> 00:09:12.720 ambiguity every time it read a line of code. 203 00:09:12.759 --> 00:09:14.799 Oh, I see, it wouldn't know if you were grouping 204 00:09:14.840 --> 00:09:17.200 a mathematical operation or trying to execute. 205 00:09:16.840 --> 00:09:22.200 A command precisely. By rigidly separating square brackets for functions, 206 00:09:22.639 --> 00:09:27.200 curly braces for lists, and parentheses for math, the language 207 00:09:27.200 --> 00:09:31.720 can process infantly complex nested structures without ever getting confused. 208 00:09:31.840 --> 00:09:34.080 That makes total sense. It's almost like a factory floor. 209 00:09:34.159 --> 00:09:35.240 A factory floor. 210 00:09:35.320 --> 00:09:38.639 Yeah, think about it. The functions those capital letter square 211 00:09:38.639 --> 00:09:42.919 bracket commands are highly specialized machines, okay, and the lists 212 00:09:43.120 --> 00:09:46.799 the curly brace structures are the conveyor belts transporting raw 213 00:09:46.840 --> 00:09:48.720 materials between those machines. Oh. 214 00:09:48.759 --> 00:09:49.240 I like that. 215 00:09:49.360 --> 00:09:52.399 The syntax has to be strict because the raw materials 216 00:09:52.480 --> 00:09:57.039 must be inserted into the machine in the exact correct orientation. 217 00:09:56.720 --> 00:10:00.360 Or the entire assembly line DRAMs exactly, that factory visualzation 218 00:10:00.480 --> 00:10:03.200 hits the nail on the head. But we need to 219 00:10:03.279 --> 00:10:07.240 explore the real genius of the materials on those conveyor belts. 220 00:10:07.279 --> 00:10:07.720 What do you mean? 221 00:10:07.879 --> 00:10:11.679 This is the core reason the entire architecture functions so seamlessly. 222 00:10:12.120 --> 00:10:14.879 The Wolf Firm language is fundamentally from the ground up, 223 00:10:14.919 --> 00:10:16.279 a symbolic language. 224 00:10:16.360 --> 00:10:19.320 A symbolic language. Let's break symbolic depth. What does that 225 00:10:19.399 --> 00:10:21.759 actually mean when you are sitting at the keyboard. 226 00:10:22.000 --> 00:10:25.559 So in a conventional coding language, you use arrays, which 227 00:10:25.559 --> 00:10:28.600 are basically their version of lists, but you generally have 228 00:10:28.679 --> 00:10:31.200 to declare what kind of data that array is allowed 229 00:10:31.240 --> 00:10:34.360 to hold. You have to explicitly warn the computer this 230 00:10:34.480 --> 00:10:37.360 array will only hold integers, or this array will only 231 00:10:37.399 --> 00:10:38.879 old text. 232 00:10:38.679 --> 00:10:41.120 So the computer can allocate the right amount of memory. 233 00:10:41.159 --> 00:10:44.639 Exactly, it allocates memory based on those strict data types. 234 00:10:45.159 --> 00:10:49.200 But in a symbolic language, a list can hold absolutely anything, 235 00:10:49.240 --> 00:10:52.360 anything at all. Anything. The system doesn't care about rigid 236 00:10:52.399 --> 00:10:55.440 data types because it treats everything simply as a symbol. 237 00:10:55.559 --> 00:10:56.679 Okay, give me an example. 238 00:10:56.799 --> 00:10:59.720 A list can hold numbers, It can hold text, It 239 00:10:59.759 --> 00:11:04.480 can hold completely undefined algebraic variables like just an A, 240 00:11:04.720 --> 00:11:07.240 B and a C without defining what A is, right, 241 00:11:07.320 --> 00:11:09.720 it just treats it as the symbol A. And it 242 00:11:09.759 --> 00:11:13.440 can even hold fully formed geometric graphs, three D spheres, 243 00:11:13.559 --> 00:11:14.519 and audio. 244 00:11:14.159 --> 00:11:16.080 Clips wait all mixed together, all. 245 00:11:15.960 --> 00:11:18.440 Mixed together in the exact same list at the same time. 246 00:11:18.679 --> 00:11:21.440 So my conveyor belt could literally be carrying a list 247 00:11:21.480 --> 00:11:24.480 that contains the number one, the color red, a photograph 248 00:11:24.480 --> 00:11:27.679 of a cat, and an interactive pie chart, all sitting 249 00:11:27.799 --> 00:11:28.799 right next to each other. 250 00:11:28.879 --> 00:11:32.600 Precisely to the Wolfram engine. They are all just symbolic 251 00:11:32.679 --> 00:11:34.519 expressions being passed along the belt. 252 00:11:34.600 --> 00:11:35.399 That is wild. 253 00:11:35.559 --> 00:11:39.200 It's a massive departure from traditional computer science, and it's 254 00:11:39.240 --> 00:11:42.960 the underlying secret that makes the language so deeply flexible. 255 00:11:43.200 --> 00:11:46.919 Okay, so we have a factory running smoothly moving abstract 256 00:11:46.919 --> 00:11:50.480 symbols along a belt. But computation is useless if human 257 00:11:50.519 --> 00:11:52.240 brains can't comprehend the output. 258 00:11:52.559 --> 00:11:54.879 Right, A massive list of one thousand numbers on a 259 00:11:54.919 --> 00:11:56.879 screen is just exhausting to look at. 260 00:11:57.000 --> 00:11:59.480 We need to see it. Well, how does the language 261 00:11:59.480 --> 00:12:02.840 turn raw awe abstract symbols into something visual. 262 00:12:03.000 --> 00:12:07.080 Well, the language is designed to make visualization almost comically effortless. 263 00:12:07.080 --> 00:12:09.120 Comical effortless, I'll be the judge of that. 264 00:12:09.200 --> 00:12:11.279 I mean it. If you have that massive list of numbers, 265 00:12:11.320 --> 00:12:13.600 you don't need to write a rendoing engine, Okay, you 266 00:12:13.639 --> 00:12:17.240 simply pass that list through a function called list line plot, 267 00:12:17.519 --> 00:12:20.600 and instantly you have a fully rendered chart just one word, 268 00:12:20.919 --> 00:12:23.879 one word. You can pass it through barchart or pie 269 00:12:23.960 --> 00:12:24.960 chart just as easily. 270 00:12:25.360 --> 00:12:28.639 Actually, the source notes a brilliant little detail about the 271 00:12:28.639 --> 00:12:32.039 pie chart function that really highlights the built in intelligence. 272 00:12:32.159 --> 00:12:33.559 Oh, the nine o'clock rule. 273 00:12:33.840 --> 00:12:38.279 Yes, when you execute that command, the language automatically knows 274 00:12:38.320 --> 00:12:41.639 to start the very first wedge of the pie exactly 275 00:12:41.639 --> 00:12:44.720 at the nine o'clock position and read clockwise. It's just a. 276 00:12:44.720 --> 00:12:46.759 Standard design principle, but it knows it by. 277 00:12:46.679 --> 00:12:50.519 Default, and it autonomously selects a highly readable sequence of 278 00:12:50.559 --> 00:12:53.159 colors for the wedges. You didn't have to code the 279 00:12:53.200 --> 00:12:56.600 geometry of a circle, calculate the angles of the wedges, 280 00:12:56.759 --> 00:12:59.159 or like define the hex codes for the colors. 281 00:12:59.279 --> 00:13:01.360 Right, the system is inherently knows what a good pie 282 00:13:01.399 --> 00:13:02.399 chart is supposed to look like. 283 00:13:02.440 --> 00:13:03.320 I save so much time. 284 00:13:03.440 --> 00:13:07.159 It does. And speaking of colors, they're treated as computational objects, 285 00:13:07.240 --> 00:13:08.399 not just text labels. 286 00:13:08.440 --> 00:13:11.000 So you don't type the word red as a string 287 00:13:11.039 --> 00:13:11.559 in quotes. 288 00:13:11.679 --> 00:13:13.919 No, you use it as a standalone symbol. You just 289 00:13:14.000 --> 00:13:16.120 evaluate red with a capital R. 290 00:13:16.399 --> 00:13:16.879 Wow. 291 00:13:17.000 --> 00:13:20.120 You can pass colors into a function like blend, handing 292 00:13:20.200 --> 00:13:23.159 it a list of yellow, pink, and green, and it 293 00:13:23.240 --> 00:13:26.039 mathematically computes the resulting mixture. 294 00:13:25.919 --> 00:13:27.639 So it blends the colors like actual paint. 295 00:13:27.720 --> 00:13:30.120 Exactly. You can run color negate on the symbol yellow 296 00:13:30.399 --> 00:13:33.039 and the system instantly outputs a blue square. 297 00:13:33.159 --> 00:13:36.679 Okay, But to really take advantage of visualization, you need 298 00:13:36.720 --> 00:13:39.320 a way to generate large amounts of structured data on 299 00:13:39.360 --> 00:13:41.600 the fly. Right. You don't want to type out one 300 00:13:41.600 --> 00:13:43.720 thousand numbers manually just to make a chart. 301 00:13:43.919 --> 00:13:47.279 No, nobody wants to do that. For that, the text 302 00:13:47.399 --> 00:13:49.279 introduces the table function. 303 00:13:49.559 --> 00:13:52.759 Okay. The table function uses something called an iterator, which 304 00:13:52.840 --> 00:13:55.559 honestly sounds incredibly intimidating to a newcomer. 305 00:13:55.679 --> 00:13:57.159 It sounds like math jargon. 306 00:13:57.399 --> 00:14:01.039 It does. If I type table open breads and squared, 307 00:14:01.440 --> 00:14:06.480 comma open curly brace and comma ten close curly brace, 308 00:14:06.679 --> 00:14:10.159 close bracket, what is actually happening inside the machine. 309 00:14:10.200 --> 00:14:12.799 Okay, an iterator is really just a set of instructions 310 00:14:12.799 --> 00:14:15.720 for counting discounting. Yeah, the system looks at the variable 311 00:14:15.759 --> 00:14:18.519 you've chosen, which is N. The iterator is the part 312 00:14:18.559 --> 00:14:22.000 inside the curly braces N Tenkay. It's basically telling the 313 00:14:22.039 --> 00:14:25.279 engine take this variable, end, start its value at one, 314 00:14:25.399 --> 00:14:28.159 and count up to ten. And for every single one 315 00:14:28.200 --> 00:14:30.919 of those ten steps, it executes the first part of 316 00:14:30.919 --> 00:14:34.320 your instruction. It calculates N squared, So. 317 00:14:34.360 --> 00:14:37.519 In a fraction of a second, it computes one, four, nine, sixteen, 318 00:14:37.720 --> 00:14:39.279 all the way to one hundred exactly. 319 00:14:39.519 --> 00:14:41.879 It bundles them into a neat list on your conveyor 320 00:14:41.879 --> 00:14:43.120 belt and hands them back to you. 321 00:14:43.279 --> 00:14:46.399 Generating data is great, and charting it is even better. 322 00:14:46.759 --> 00:14:49.159 But what if we want to physically interact with that data? 323 00:14:49.240 --> 00:14:50.360 This is my favorite part. 324 00:14:50.559 --> 00:14:53.919 The text introduces a function called manipulate, and this is 325 00:14:53.919 --> 00:14:55.559 where the entire paradigm shifts. 326 00:14:55.639 --> 00:14:56.399 It really does. 327 00:14:56.519 --> 00:14:58.639 If you take any piece of code, let's say a 328 00:14:58.679 --> 00:15:02.279 table generating a series of orange squares, and you wrap 329 00:15:02.320 --> 00:15:05.879 the manipulate function around it, you instantly magically have a 330 00:15:05.960 --> 00:15:06.720 user interface. 331 00:15:06.919 --> 00:15:10.360 Yeah, you pass it manipulate, then your code, then the 332 00:15:10.399 --> 00:15:12.039 parameters for a slider. 333 00:15:11.960 --> 00:15:15.399 And instead of spitting out a static, unchanging image of orange. 334 00:15:15.120 --> 00:15:18.679 Squares, the system outputs a graphical slider on your screen, 335 00:15:19.240 --> 00:15:21.519 and as you click and drag that slider back and 336 00:15:21.559 --> 00:15:24.120 forth from one to five, the number of orange squares 337 00:15:24.200 --> 00:15:27.039 drawn on your screen actively grows and shrinks in real time. 338 00:15:27.399 --> 00:15:31.639 It completely reframes the coding experience. I mean, traditional coding 339 00:15:31.720 --> 00:15:34.279 is like setting up a photograph. How so well you 340 00:15:34.360 --> 00:15:38.200 meticulously arrange your subjects, You calculate the lighting, you hit 341 00:15:38.240 --> 00:15:39.279 the shutter button. 342 00:15:39.120 --> 00:15:41.440 Which is the equivalent of compiling your code. 343 00:15:41.200 --> 00:15:45.919 Exactly, and you get a static, permanent picture. If you 344 00:15:46.000 --> 00:15:48.759 realize you want one subject move slightly to the left, 345 00:15:49.080 --> 00:15:52.759 you have to rearrange the entire physical scene, recompile the code, 346 00:15:52.879 --> 00:15:54.600 and take a whole new photograph. 347 00:15:54.639 --> 00:15:58.679 That's a really accurate description of traditional UI development, right. 348 00:15:58.799 --> 00:16:01.519 But wrapping your code in manipulate is like sculpting with 349 00:16:01.559 --> 00:16:02.159 wet clay. 350 00:16:02.320 --> 00:16:03.080 Oh I like that. 351 00:16:03.399 --> 00:16:06.879 You drag a slider and instantly watch how changing one 352 00:16:06.960 --> 00:16:10.240 single variable alters the slope of an entire. 353 00:16:10.000 --> 00:16:13.519 Bar chart, or modifies the hue of a three D sphere. 354 00:16:13.240 --> 00:16:15.240 Or adjusts the radius of a geometric cone. 355 00:16:15.399 --> 00:16:19.039 It's fluid, and the sheer amount of engineering automated away 356 00:16:19.120 --> 00:16:21.840 by that single command is staggering. I can imagine I mean, 357 00:16:21.879 --> 00:16:24.919 in almost any other widespread language, building a user interface 358 00:16:24.960 --> 00:16:28.559 with a functioning slider that dynamically updates a graphic that 359 00:16:28.679 --> 00:16:31.519 requires hundreds of lines of tdsuy code. 360 00:16:31.320 --> 00:16:32.039 Just for a slider. 361 00:16:32.240 --> 00:16:36.000 Oh yeah, you have to write event listeners to detect 362 00:16:36.000 --> 00:16:38.759 the mouse click. You have to manage state changes in 363 00:16:38.759 --> 00:16:42.039 the computer's memory. You have to build render loops to 364 00:16:42.159 --> 00:16:45.039 redraw the graphics sixty times a second so the animation 365 00:16:45.120 --> 00:16:45.799 looks smooth. 366 00:16:46.200 --> 00:16:47.200 And in this system. 367 00:16:47.279 --> 00:16:50.240 In this system, all of that infrastructure is handled invisibly. 368 00:16:50.799 --> 00:16:53.879 You are freed up to simply explore the parameter space 369 00:16:53.919 --> 00:16:57.399 of your problem interactively without ever breaking your train of thought. 370 00:16:57.559 --> 00:17:00.440 Okay, so we've built an incredible theoretical tool kid. So 371 00:17:00.480 --> 00:17:03.879 far we can generate numbers, plot them, and interact with 372 00:17:03.879 --> 00:17:07.440 geometric shapes the basics, but pure math can feel a 373 00:17:07.480 --> 00:17:11.079 bit sterile. Let's look at how this language handles the messy, 374 00:17:11.319 --> 00:17:15.559 unstructured reality of the physical world. Specifically, how does it 375 00:17:15.599 --> 00:17:17.960 compute images in human language. 376 00:17:18.359 --> 00:17:20.640 This is where the built in knowledge base really flexes 377 00:17:20.680 --> 00:17:23.799 its muscles. Let's look at image processing first. Okay, to 378 00:17:23.880 --> 00:17:26.759 this language, a photograph isn't just a static file sitting 379 00:17:26.759 --> 00:17:29.200 in a folder. It is an active data set ready 380 00:17:29.240 --> 00:17:30.039 to be computed. 381 00:17:30.160 --> 00:17:32.640 So you can open your notebook and type current image 382 00:17:32.680 --> 00:17:34.519 with empty square brackets and it. 383 00:17:34.480 --> 00:17:37.759 Will instantly pull a live frame from your computer's webcam 384 00:17:38.079 --> 00:17:38.480 just like that. 385 00:17:38.680 --> 00:17:41.480 Yeah, and because we were in a symbolic system, you 386 00:17:41.480 --> 00:17:44.640 can apply math like functions directly to the pixels of 387 00:17:44.640 --> 00:17:45.119 your face. 388 00:17:45.440 --> 00:17:48.960 Exactly. You can pass the image through pellernegate to get 389 00:17:49.000 --> 00:17:51.039 this eerie inverted picture. 390 00:17:51.839 --> 00:17:54.200 But wait, how does the computer actually know how to 391 00:17:54.200 --> 00:17:57.920 do something like blur or edge detect? I mean, it's 392 00:17:57.920 --> 00:18:00.839 not a human eye, So what does haveing? Mathematically? 393 00:18:00.880 --> 00:18:03.720 That's a great question. The system views your photograph as 394 00:18:03.759 --> 00:18:07.559 a massive grid, a matrix of numbers, okay, a grid 395 00:18:07.559 --> 00:18:11.119 of numbers, right, where each number represents the color value 396 00:18:11.160 --> 00:18:14.480 of a specific pixel. When you pass that matrix into 397 00:18:14.480 --> 00:18:17.440 the blur function, the system looks at the numerical value 398 00:18:17.440 --> 00:18:20.119 of a single pixel, then looks at the numbers of 399 00:18:20.200 --> 00:18:24.319 all the pixels immediately surrounding it, and mathematically averages them together. 400 00:18:24.559 --> 00:18:27.480 Oh wow, and it does this for every single pixel 401 00:18:27.519 --> 00:18:31.319