1 00:00:00,533 --> 00:00:02,133 Dimensionality reduction strike of the three-body theory 2 00:00:02,166 --> 00:00:03,900 What did you knock out? 3 00:00:04,100 --> 00:00:05,766 In Liu Cixin's three-body 4 00:00:05,766 --> 00:00:08,900 The Singer Civilization threw a piece of binary foil into the solar system 5 00:00:09,700 --> 00:00:12,133 This thing is only the size of a palm, 8.5. 6 00:00:12,166 --> 00:00:13,500 Centimeters long, 5.2. 7 00:00:13,500 --> 00:00:14,333 centimeter width 8 00:00:14,366 --> 00:00:14,866 No thickness. 9 00:00:15,400 --> 00:00:17,200 But it's just such a small piece of paper 10 00:00:17,200 --> 00:00:19,133 The moment you come into contact with three-dimensional space 11 00:00:19,166 --> 00:00:20,700 Flattened the entire solar system 12 00:00:21,766 --> 00:00:23,000 3D to 2D 13 00:00:23,000 --> 00:00:26,066 All planets, spaceships, and humans 14 00:00:26,066 --> 00:00:28,233 It all becomes a painting that is too thin to have any thickness 15 00:00:29,100 --> 00:00:30,933 This image shocked countless readers 16 00:00:31,466 --> 00:00:34,333 The four words dimensionality reduction and strike also became popular all over the Internet 17 00:00:34,366 --> 00:00:35,733 Becomes a catch-all adjective 18 00:00:36,666 --> 00:00:37,933 Use it commercially 19 00:00:37,933 --> 00:00:40,366 Say one company hits another company with dimensionality reduction 20 00:00:41,333 --> 00:00:42,533 Cognitively use it. 21 00:00:42,533 --> 00:00:44,266 Say that the master strikes the novice with dimensionality reduction 22 00:00:45,066 --> 00:00:46,866 But I want to ask you a serious question today 23 00:00:47,766 --> 00:00:48,766 dimensionality reduction strike 24 00:00:48,766 --> 00:00:50,133 What did you knock out? 25 00:00:50,833 --> 00:00:51,866 It's not life. 26 00:00:51,900 --> 00:00:52,400 Not matter 27 00:00:53,066 --> 00:00:53,600 Is a dimension 28 00:00:54,566 --> 00:00:56,233 What is that dimension? 29 00:00:56,366 --> 00:00:58,033 Why lose a dimension? 30 00:00:58,066 --> 00:00:59,533 Is equivalent to destruction 31 00:00:59,600 --> 00:01:00,300 Hello 32 00:01:00,333 --> 00:01:01,166 Hello. 33 00:01:01,166 --> 00:01:01,733 I am Wang Lijie 34 00:01:02,600 --> 00:01:04,166 We're not going to talk about investing today 35 00:01:04,166 --> 00:01:05,300 Don't talk about practice 36 00:01:05,333 --> 00:01:07,966 Let's talk about dimensionality. It's deceptively simple. 37 00:01:08,533 --> 00:01:09,933 It's a bottomless concept. 38 00:01:10,766 --> 00:01:11,633 I promise. 39 00:01:11,633 --> 00:01:14,866 After the chat, your understanding of dimensionality reduction strikes will be completely upgraded 40 00:01:15,666 --> 00:01:17,000 And you will find 41 00:01:17,000 --> 00:01:18,233 The concept of dimension 42 00:01:18,233 --> 00:01:20,633 It may be to understand AI and physics 43 00:01:21,266 --> 00:01:23,800 Even a central key to understanding consciousness 44 00:01:24,533 --> 00:01:25,000 OK 45 00:01:25,000 --> 00:01:26,300 We start with the basics. 46 00:01:27,300 --> 00:01:28,433 What is one-dimensional? 47 00:01:28,533 --> 00:01:28,933 A thread. 48 00:01:29,866 --> 00:01:30,933 Length only 49 00:01:30,933 --> 00:01:31,933 No width 50 00:01:31,933 --> 00:01:32,400 No height 51 00:01:33,433 --> 00:01:37,233 You can imagine an ant trapped on an infinitely long wire. 52 00:01:37,233 --> 00:01:39,166 It can only go forward or backward. 53 00:01:40,066 --> 00:01:42,100 Its entire universe is this wire. 54 00:01:43,066 --> 00:01:44,466 Front and rear directions 55 00:01:44,500 --> 00:01:45,166 That's one dimension. 56 00:01:46,366 --> 00:01:47,600 What is two-dimensional? 57 00:01:47,766 --> 00:01:48,066 One face 58 00:01:49,066 --> 00:01:49,933 There is length 59 00:01:49,966 --> 00:01:50,766 Have width 60 00:01:50,800 --> 00:01:51,533 But no height 61 00:01:52,466 --> 00:01:54,566 Imagine that you are a little person drawn on a piece of paper 62 00:01:54,566 --> 00:01:56,566 You can move back and forth, left and right. 63 00:01:56,566 --> 00:01:58,666 But you can never leave the surface of this paper 64 00:01:59,533 --> 00:02:01,933 You don't even know the concept of up and down 65 00:02:01,933 --> 00:02:03,333 Because in your world 66 00:02:03,366 --> 00:02:04,900 There is no third way. 67 00:02:05,300 --> 00:02:06,566 What is 3D? 68 00:02:06,866 --> 00:02:08,400 It's the space that we live in every day. 69 00:02:09,300 --> 00:02:11,000 Length, width and height 70 00:02:11,666 --> 00:02:13,100 You can go backwards and forwards. 71 00:02:13,100 --> 00:02:14,500 You can go left and right. 72 00:02:14,533 --> 00:02:15,466 You can go up and down. 73 00:02:16,366 --> 00:02:17,433 Three directions 74 00:02:17,466 --> 00:02:18,666 Three dimensions 75 00:02:18,666 --> 00:02:20,766 It makes up everything you can see and touch 76 00:02:21,533 --> 00:02:22,266 Go here. 77 00:02:22,300 --> 00:02:23,433 Most people are fine 78 00:02:24,233 --> 00:02:25,566 And then someone tells you 79 00:02:25,566 --> 00:02:26,366 The fourth dimension is time. 80 00:02:27,233 --> 00:02:27,933 That's acceptable. 81 00:02:29,166 --> 00:02:30,666 Einstein told us that 82 00:02:30,666 --> 00:02:32,433 Space and time are not separate 83 00:02:32,866 --> 00:02:34,166 They are a whole 84 00:02:34,200 --> 00:02:34,733 It's called spacetime. 85 00:02:35,566 --> 00:02:37,566 You live in a three-dimensional space. 86 00:02:37,566 --> 00:02:40,600 But you have no choice in one direction at the same time 87 00:02:40,633 --> 00:02:41,233 It's time. 88 00:02:42,033 --> 00:02:44,300 You can only move from the past to the future 89 00:02:44,300 --> 00:02:44,966 Can't look back 90 00:02:46,000 --> 00:02:48,000 Time is a one-way street. 91 00:02:48,000 --> 00:02:49,200 It is your fourth dimension 92 00:02:50,200 --> 00:02:50,866 OK 93 00:02:50,866 --> 00:02:51,933 End here 94 00:02:51,966 --> 00:02:53,800 And most people's cognitive map just stops. 95 00:02:54,666 --> 00:02:56,466 one-dimensional two-dimensional three-dimensional four-dimensional 96 00:02:56,466 --> 00:02:56,933 clearly 97 00:02:57,833 --> 00:02:59,266 But I want to interject here first 98 00:03:00,300 --> 00:03:02,833 Now, four dimensions has a hidden trap. 99 00:03:03,666 --> 00:03:06,866 Many people believe that time is the fourth spatial dimension 100 00:03:06,900 --> 00:03:08,500 As if you could move in the direction of time 101 00:03:09,300 --> 00:03:09,666 No. 102 00:03:10,566 --> 00:03:14,300 There is an essential difference between the time dimension and the space dimension 103 00:03:14,300 --> 00:03:17,600 It's a space where you can go backwards or forwards. 104 00:03:17,600 --> 00:03:19,500 But time is a one-way street. 105 00:03:20,366 --> 00:03:22,233 You can only move from the past to the future 106 00:03:23,233 --> 00:03:26,466 They call this the Lorentz metric in physics. 107 00:03:26,466 --> 00:03:29,800 The mathematical notation of the time dimension is reversed from the spatial dimension 108 00:03:31,400 --> 00:03:33,833 So Einstein's four-dimensional spacetime 109 00:03:33,866 --> 00:03:37,066 It doesn't just add a direction to the three dimensions. 110 00:03:37,100 --> 00:03:41,166 It's about stitching together space and time in a very particular way. 111 00:03:42,066 --> 00:03:43,133 Figure this out 112 00:03:43,166 --> 00:03:44,933 You can understand a deeper truth 113 00:03:45,600 --> 00:03:48,600 Dimensions and dimensions are not necessarily equivalent 114 00:03:48,633 --> 00:03:50,066 They can have different properties 115 00:03:50,933 --> 00:03:53,200 There are dimensions you can go back and forth in. 116 00:03:53,200 --> 00:03:55,100 Some dimensions you can only travel one way 117 00:03:56,033 --> 00:03:57,833 This distinction will be very important later 118 00:03:59,033 --> 00:03:59,700 OK 119 00:03:59,700 --> 00:04:00,300 Back to Main Line 120 00:04:00,966 --> 00:04:02,066 If I were to ask you 121 00:04:02,066 --> 00:04:03,133 What is the fifth dimension? 122 00:04:03,233 --> 00:04:04,100 What about six dimensions? 123 00:04:04,266 --> 00:04:05,300 What about seven dimensions? 124 00:04:05,433 --> 00:04:08,966 And even string theory says the universe has 10 or 11 dimensions. 125 00:04:08,966 --> 00:04:10,100 What are these dimensions? 126 00:04:10,500 --> 00:04:12,100 Most people's reaction is 127 00:04:12,100 --> 00:04:13,000 no. 128 00:04:13,000 --> 00:04:14,000 Can't think of it 129 00:04:14,000 --> 00:04:14,900 Can't draw it in my head 130 00:04:15,733 --> 00:04:16,266 It's normal. 131 00:04:17,100 --> 00:04:20,233 Because our brains evolved in three dimensions. 132 00:04:20,866 --> 00:04:23,866 Our sense of sight, hearing, touch 133 00:04:23,866 --> 00:04:26,333 They're all customized senses in three dimensions. 134 00:04:27,300 --> 00:04:29,733 Let you imagine space beyond four dimensions 135 00:04:29,766 --> 00:04:32,866 It's like asking ants on a piece of paper to imagine heights. 136 00:04:33,733 --> 00:04:35,766 It simply doesn't have the hardware to process this information. 137 00:04:36,666 --> 00:04:37,100 But 138 00:04:37,366 --> 00:04:39,366 Can't think of it doesn't mean it doesn't exist 139 00:04:40,000 --> 00:04:42,400 And this is the single most important cognitive upgrade point of the day. 140 00:04:43,333 --> 00:04:44,933 The way humans understand dimensions 141 00:04:45,100 --> 00:04:46,266 It's not imaginary. 142 00:04:46,700 --> 00:04:48,233 It's about logic and mathematics. 143 00:04:49,500 --> 00:04:51,166 Let me explain dimensions differently. 144 00:04:52,100 --> 00:04:53,400 What is the essence of dimensions? 145 00:04:53,800 --> 00:04:54,566 Is the degree of freedom 146 00:04:55,166 --> 00:04:59,000 Is the minimum number of numbers you need to describe the position of something 147 00:04:59,933 --> 00:05:01,766 Positioning an ant on a piece of wire. 148 00:05:02,333 --> 00:05:03,466 All you need is a number. 149 00:05:04,033 --> 00:05:05,866 For example, 3 cm away from the starting point 150 00:05:06,600 --> 00:05:07,633 A number. 151 00:05:07,633 --> 00:05:08,100 one-dimensional 152 00:05:08,833 --> 00:05:10,300 Locate a point on a piece of paper 153 00:05:10,800 --> 00:05:12,233 You need two numbers. 154 00:05:12,233 --> 00:05:13,833 For example, abscissa 3 155 00:05:13,866 --> 00:05:14,566 Vertical coordinate 5 156 00:05:15,466 --> 00:05:16,266 Two numbers 157 00:05:16,533 --> 00:05:16,966 two-dimensional 158 00:05:17,800 --> 00:05:19,533 Locating a fly in a room 159 00:05:20,066 --> 00:05:21,033 You need three numbers. 160 00:05:21,366 --> 00:05:24,100 One coordinate each for length, width and height 161 00:05:24,633 --> 00:05:25,700 Three numbers. 162 00:05:25,766 --> 00:05:26,300 3D 163 00:05:27,733 --> 00:05:30,933 If you still want to know when the fly was in that position 164 00:05:31,366 --> 00:05:33,166 You also need to add a time coordinate. 165 00:05:33,833 --> 00:05:34,666 Four numbers. 166 00:05:34,900 --> 00:05:35,333 4D 167 00:05:36,100 --> 00:05:36,700 Did you see it? 168 00:05:37,400 --> 00:05:39,333 Dimension is not a mysterious concept of space 169 00:05:40,166 --> 00:05:43,500 Dimension is how many independent numbers are required to describe something 170 00:05:44,433 --> 00:05:46,233 Each additional independent information axis 171 00:05:46,533 --> 00:05:47,366 Just one more dimension 172 00:05:48,233 --> 00:05:49,766 Once this understanding is established 173 00:05:50,133 --> 00:05:51,800 Gao Wei is no longer incredible 174 00:05:52,533 --> 00:05:53,633 What is the fifth dimension? 175 00:05:53,800 --> 00:05:55,266 Here I want to explain first 176 00:05:56,133 --> 00:05:59,733 The explanation of more than five dimensions is not completely settled in the field of physics 177 00:06:00,233 --> 00:06:02,533 But there is a widely discussed way of understanding it 178 00:06:03,400 --> 00:06:06,533 If four-dimensional space-time describes our universe 179 00:06:06,533 --> 00:06:09,266 The complete historical trajectory from birth to the present 180 00:06:09,766 --> 00:06:12,033 Then the fifth dimension refers to possibility 181 00:06:12,966 --> 00:06:14,833 It is at a certain historical juncture 182 00:06:14,866 --> 00:06:16,733 If a different choice occurs 183 00:06:16,733 --> 00:06:18,366 Will fork off into another universe 184 00:06:18,933 --> 00:06:21,366 The initial conditions of the two universes are the same 185 00:06:21,400 --> 00:06:22,800 But the follow-up development is different 186 00:06:23,266 --> 00:06:24,400 The Fifth Dimension 187 00:06:24,400 --> 00:06:26,600 Is to connect these if the original axis 188 00:06:27,866 --> 00:06:28,933 What about six dimensions? 189 00:06:29,066 --> 00:06:33,066 If the fifth dimension is forked from the same starting point, it is different. 190 00:06:33,066 --> 00:06:35,666 The sixth dimension is to get everything out of the same starting point 191 00:06:35,700 --> 00:06:38,266 All the possibilities of sending are folded together. 192 00:06:38,700 --> 00:06:39,900 You can imagine 193 00:06:39,900 --> 00:06:42,366 Five dimensions are the different branches of a tree. 194 00:06:42,400 --> 00:06:47,266 The sixth dimension is to see the whole tree from the root to the top as a point 195 00:06:47,600 --> 00:06:49,300 Seven-dimensional is even more powerful 196 00:06:49,566 --> 00:06:52,533 Seven dimensions means different initial conditions. 197 00:06:53,066 --> 00:06:56,333 Not different branches of the same Big Bang. 198 00:06:56,333 --> 00:06:58,566 But from a completely different Big Bang 199 00:06:58,566 --> 00:07:00,100 Different physical constants 200 00:07:00,133 --> 00:07:02,533 Worlds from different cosmic beginnings 201 00:07:03,033 --> 00:07:08,000 Each of these initial conditions produces a completely different tree of possibilities. 202 00:07:08,533 --> 00:07:09,233 seven-dimensional 203 00:07:09,233 --> 00:07:12,166 It's the dimension that connects the roots of these different trees. 204 00:07:12,666 --> 00:07:15,466 Eight-dimensional, nine-dimensional, ten-dimensional. 205 00:07:15,500 --> 00:07:16,600 And so on. 206 00:07:16,600 --> 00:07:17,800 More and more abstract 207 00:07:18,133 --> 00:07:20,533 All the way down to the ten dimensions described by string theory 208 00:07:20,566 --> 00:07:22,366 Or the eleven dimensions of M-theory 209 00:07:22,966 --> 00:07:24,400 On that scale 210 00:07:24,400 --> 00:07:27,633 All possible universes, all possible laws of physics 211 00:07:27,766 --> 00:07:29,900 All possible timelines 212 00:07:29,933 --> 00:07:32,000 It's all put together in a mathematical framework. 213 00:07:32,433 --> 00:07:33,800 I know that's it. 214 00:07:33,833 --> 00:07:36,133 Your brain may have started to smoke 215 00:07:36,466 --> 00:07:37,600 It's so normal. 216 00:07:38,133 --> 00:07:41,300 But you don't have to draw a mental picture of what these dimensions look like. 217 00:07:41,733 --> 00:07:43,866 You only need to remember one core concept 218 00:07:43,866 --> 00:07:45,266 Each additional dimension 219 00:07:45,266 --> 00:07:47,666 Is to add an independent description axis 220 00:07:47,933 --> 00:07:51,600 Adds a layer of information that you can't even see in the lower dimensions 221 00:07:51,833 --> 00:07:54,300 Now we're back to the three-body dimensionality reduction strike 222 00:07:54,600 --> 00:07:59,233 When the singer civilization used two-dimensional foil to compress three-dimensional space into two dimensions 223 00:07:59,266 --> 00:08:00,800 What does it do? 224 00:08:00,966 --> 00:08:02,733 It destroys a degree of freedom 225 00:08:03,033 --> 00:08:04,733 It puts the height dimension 226 00:08:04,766 --> 00:08:06,466 Erased from the universe 227 00:08:06,733 --> 00:08:08,000 What does that mean? 228 00:08:08,066 --> 00:08:11,100 That means all structures that depend on height to exist. 229 00:08:11,133 --> 00:08:12,466 Instant collapse 230 00:08:12,900 --> 00:08:15,633 Your body needs three dimensions to function. 231 00:08:15,666 --> 00:08:20,266 Your organs are arranged up, down, back, left, right in three dimensions. 232 00:08:20,566 --> 00:08:22,500 Blood vessels need to pass through tissue 233 00:08:22,533 --> 00:08:25,633 Nerves are layered to transmit signals, DNA 234 00:08:25,633 --> 00:08:28,766 The double helix needs three dimensions to fold 235 00:08:29,733 --> 00:08:31,400 When the third dimension disappears 236 00:08:31,433 --> 00:08:34,966 And all of these structures are forced to slap flat. 237 00:08:34,966 --> 00:08:39,133 It's like turning a precision mechanical watch into a discus with a steamroller. 238 00:08:40,000 --> 00:08:41,933 All the parts are still there 239 00:08:41,966 --> 00:08:45,266 But the spatial relationship between them was completely destroyed 240 00:08:45,600 --> 00:08:47,700 What the dimensionality reduction strike knocks down is not matter 241 00:08:47,700 --> 00:08:48,700 Is relationship 242 00:08:48,966 --> 00:08:53,566 They're structures and functions that can only exist in a certain number of dimensions. 243 00:08:53,833 --> 00:08:55,000 Think again 244 00:08:55,000 --> 00:08:58,866 This actually explains a phenomenon that we observe in our daily lives 245 00:08:59,233 --> 00:09:02,833 Why a photo can never compare to the scenery seen with your own eyes 246 00:09:02,900 --> 00:09:04,866 Because photographs are two-dimensional. 247 00:09:04,866 --> 00:09:07,700 It loses a dimension of the three-dimensional world 248 00:09:08,066 --> 00:09:09,333 In-depth information is gone 249 00:09:09,366 --> 00:09:12,433 The kind of depth you can feel when you stand on the edge of a cliff 250 00:09:12,433 --> 00:09:14,066 I can't give you the photo. 251 00:09:14,433 --> 00:09:18,800 Why do I always feel that the voice I hear on the phone is not as real as chatting in person? 252 00:09:18,866 --> 00:09:22,900 Because telephony compresses many of the frequency dimensions of sound. 253 00:09:22,933 --> 00:09:25,966 What you're receiving is a dimensionality reduced sound. 254 00:09:26,233 --> 00:09:28,533 Dimension is not an ornament of space 255 00:09:28,700 --> 00:09:30,766 Dimension is the carrier of information 256 00:09:31,733 --> 00:09:35,233 Each dimension carries an independent network of relationships 257 00:09:35,366 --> 00:09:36,333 One less dimension 258 00:09:36,366 --> 00:09:38,066 A whole layer of relationships is missing 259 00:09:38,466 --> 00:09:41,833 And those complex structures that depend on this relationship to exist 260 00:09:41,866 --> 00:09:42,933 Zero All 261 00:09:43,066 --> 00:09:43,700 OK 262 00:09:43,700 --> 00:09:48,133 Now let's take the concept of dimensionality to a more exciting place, AI. 263 00:09:48,433 --> 00:09:50,733 I said it in a previous video. 264 00:09:50,733 --> 00:09:53,966 The parameters of the big language model don't store knowledge. 265 00:09:53,966 --> 00:09:56,433 It's geometry that stores knowledge. 266 00:09:56,733 --> 00:09:59,966 The geometry exists in a high-dimensional vector space. 267 00:10:00,400 --> 00:10:02,600 So how many dimensions does space have? 268 00:10:02,733 --> 00:10:04,266 Take GPT-4 as an example 269 00:10:04,266 --> 00:10:07,233 And the embedding dimensions are about 12,000 plus dimensions. 270 00:10:07,733 --> 00:10:10,433 This means that every word, every concept 271 00:10:10,466 --> 00:10:14,833 In the world of AI, it is a coordinate point that exists in more than 10,000 dimensions of space 272 00:10:15,200 --> 00:10:16,166 more than 10,000 dimensions 273 00:10:16,866 --> 00:10:19,166 You can't even imagine five dimensions, AI. 274 00:10:19,166 --> 00:10:21,400 Thinking in more than 10,000 dimensions 275 00:10:21,766 --> 00:10:23,466 But that's not the craziest part. 276 00:10:23,766 --> 00:10:26,300 Ten thousand dimensions is just the representation space of individual words. 277 00:10:26,766 --> 00:10:29,366 If you add up the parameter space of the entire model 278 00:10:29,400 --> 00:10:31,433 That's trillions of parameters. 279 00:10:31,433 --> 00:10:33,733 It's a trillion-dimensional surface. 280 00:10:34,266 --> 00:10:36,666 Language data for thousands of years of human civilization 281 00:10:36,666 --> 00:10:40,300 Compressed into a precise shape in this ultra-high-dimensional space 282 00:10:40,766 --> 00:10:43,000 Why does AI need so many dimensions? 283 00:10:43,066 --> 00:10:45,466 Because language is incredibly complex. 284 00:10:45,900 --> 00:10:47,300 In three dimensions. 285 00:10:47,300 --> 00:10:50,133 Cats and dogs can only approach or stay away 286 00:10:50,166 --> 00:10:53,366 The best you can say is that they are similar or they are different. 287 00:10:53,866 --> 00:10:55,766 But in 10,000 dimensions 288 00:10:55,800 --> 00:10:59,800 Cats and dogs can be very close in the dimension of pet attributes 289 00:10:59,800 --> 00:11:02,766 They go a long way in terms of independence. 290 00:11:02,766 --> 00:11:06,700 There's a subtle distance in the number of years we've been domesticated. 291 00:11:06,733 --> 00:11:09,733 It almost coincides in the dimension of Internet popularity 292 00:11:10,066 --> 00:11:11,166 Ten thousand dimensions 293 00:11:11,166 --> 00:11:13,266 It's 10,000 individual relationship axes. 294 00:11:13,733 --> 00:11:16,366 This means that the relationship between any two concepts 295 00:11:16,366 --> 00:11:20,400 Can be broken down into 10,000 independent components to describe precisely 296 00:11:20,666 --> 00:11:23,200 This is why AI can understand language 297 00:11:23,433 --> 00:11:24,966 It's not memory. 298 00:11:25,000 --> 00:11:28,833 It's in a very high-dimensional space beyond the imagination of the human brain 299 00:11:28,833 --> 00:11:31,300 Encoding meaning in geometry. 300 00:11:31,566 --> 00:11:32,800 And here's what's interesting. 301 00:11:32,833 --> 00:11:36,333 This high-dimensional representation and the way the human brain works 302 00:11:36,366 --> 00:11:38,100 It's mathematically isomorphic. 303 00:11:38,466 --> 00:11:40,800 The human brain has about 100 billion nerve cells 304 00:11:41,000 --> 00:11:42,800 One hundred trillion synaptic connections. 305 00:11:43,266 --> 00:11:45,100 The strength of each synaptic connection 306 00:11:45,100 --> 00:11:46,400 Is a parameter 307 00:11:46,933 --> 00:11:48,700 When you learn to recognize your mother's face 308 00:11:48,700 --> 00:11:51,366 It's not because you have a picture in your head. 309 00:11:51,366 --> 00:11:55,800 It's that certain synapses in your visual cortex are tuned to specific patterns. 310 00:11:56,266 --> 00:11:58,166 The space formed by these patterns 311 00:11:58,166 --> 00:11:59,733 And AI's parameter space 312 00:11:59,766 --> 00:12:02,066 It's mathematically the same thing. 313 00:12:02,433 --> 00:12:03,566 So you see 314 00:12:03,566 --> 00:12:08,000 Dimensions are not an abstract concept that only exists in physics textbooks 315 00:12:08,266 --> 00:12:10,233 Dimensions are the skeleton of information. 316 00:12:11,166 --> 00:12:14,200 The information that can be carried in one dimension is extremely limited 317 00:12:14,200 --> 00:12:16,533 It's the distance on a thread. 318 00:12:16,866 --> 00:12:18,666 2D can carry more 319 00:12:18,666 --> 00:12:20,266 Positional relationship on the plane 320 00:12:20,766 --> 00:12:22,466 One more layer in 3D 321 00:12:22,500 --> 00:12:23,533 three-dimensional structure 322 00:12:24,000 --> 00:12:25,500 Each additional dimension 323 00:12:25,500 --> 00:12:29,000 The complexity of the relationship that can be accommodated increases exponentially 324 00:12:29,466 --> 00:12:32,600 This is why dimensionality reduction strikes in the Trisolaran are so deadly 325 00:12:33,000 --> 00:12:34,800 It's not because you got thinner. 326 00:12:34,800 --> 00:12:38,666 It's because your information carrying capacity has been taken away. 327 00:12:39,033 --> 00:12:41,433 A three-dimensional creature is photographed in two dimensions. 328 00:12:41,466 --> 00:12:44,566 It was as if 10,000 lines of code had been deleted to one line. 329 00:12:45,133 --> 00:12:47,533 The characters of the code may still be there. 330 00:12:47,566 --> 00:12:50,066 But the program doesn't run anymore 331 00:12:50,466 --> 00:12:51,600 And the other way around. 332 00:12:51,633 --> 00:12:54,133 What does ascension mean? 333 00:12:54,233 --> 00:12:56,566 It means you have a whole new level of freedom 334 00:12:56,566 --> 00:12:58,400 More relationships can be encoded 335 00:12:58,433 --> 00:13:00,333 More complex structures can be built 336 00:13:00,733 --> 00:13:03,466 There's a key concept here called the curse of dimensions. 337 00:13:03,900 --> 00:13:05,766 In mathematics and computer science 338 00:13:05,800 --> 00:13:07,466 This is a famous puzzle. 339 00:13:07,766 --> 00:13:09,400 When the dimensions increase 340 00:13:09,433 --> 00:13:11,633 The volume of space exponentially expands. 341 00:13:11,966 --> 00:13:15,166 In three-dimensional space, if there are 10 grids in each direction 342 00:13:15,200 --> 00:13:16,700 You have a thousand grids. 343 00:13:17,100 --> 00:13:18,633 But in one hundred dimensions 344 00:13:18,666 --> 00:13:20,800 Again, 10 squares in each direction. 345 00:13:20,800 --> 00:13:23,066 You need 10 ^ 100 squares. 346 00:13:23,066 --> 00:13:26,233 That's bigger than all the atoms in the universe. 347 00:13:26,766 --> 00:13:28,633 This means that in high-dimensional space 348 00:13:28,633 --> 00:13:30,466 Data can become extremely sparse 349 00:13:30,733 --> 00:13:34,166 You need an astronomical amount of data to fill the space 350 00:13:34,633 --> 00:13:37,166 This is why training a large language model 351 00:13:37,200 --> 00:13:39,966 We need to feed them texts that have been written by almost all of humanity. 352 00:13:39,966 --> 00:13:44,566 Because it needs to build dense enough coordinate points in more than 10,000 dimensions of space 353 00:13:44,600 --> 00:13:46,733 To draw the geometry of language 354 00:13:47,333 --> 00:13:49,166 But AI overcame the curse 355 00:13:49,600 --> 00:13:51,600 It uses a very clever method 356 00:13:51,600 --> 00:13:53,066 It's called the manifold hypothesis. 357 00:13:53,366 --> 00:13:56,533 It means that although the entire space is more than 10,000 dimensions 358 00:13:56,566 --> 00:14:00,500 But meaningful data is not evenly distributed throughout space 359 00:14:00,900 --> 00:14:04,766 The really meaningful points are spread over a low-dimensional surface. 360 00:14:04,800 --> 00:14:08,100 Like the surface of the earth although embedded in three dimensions 361 00:14:08,100 --> 00:14:11,333 But to walk on Earth, you only need two coordinates. 362 00:14:11,366 --> 00:14:12,366 longitude and latitude 363 00:14:13,100 --> 00:14:16,166 What AI needs to do is not to fill the entire high-dimensional space 364 00:14:16,200 --> 00:14:19,133 It's about finding that low-dimensional surface hidden in high-dimensional space. 365 00:14:19,833 --> 00:14:24,266 This is the essence of AI's transition from a three-dimensional physical world to a multi-dimensional parametric space 366 00:14:25,266 --> 00:14:27,400 It's not bearing the curse of the dimension 367 00:14:27,433 --> 00:14:30,066 It's a skeleton that finds information in high-dimensional space. 368 00:14:30,900 --> 00:14:32,966 This also answers a question that many people are confused about 369 00:14:33,766 --> 00:14:38,166 Why can AI sometimes see patterns that humans cannot? 370 00:14:38,266 --> 00:14:40,100 It's not because AI is smarter 371 00:14:40,100 --> 00:14:42,566 It's because AI sees the world in more dimensions than we do 372 00:14:43,433 --> 00:14:46,500 It's like a three-dimensional creature looking down on a two-dimensional plane. 373 00:14:46,500 --> 00:14:49,966 It can see things that flat creatures would never see 374 00:14:49,966 --> 00:14:50,933 Like the whole picture of the labyrinth 375 00:14:51,633 --> 00:14:54,633 AI looks down on human language in the world of space 376 00:14:54,666 --> 00:14:58,366 It can see semantic correlations that we would never notice in three-dimensional cognition 377 00:14:59,200 --> 00:14:59,866 And finally. 378 00:14:59,900 --> 00:15:01,633 And I want to leave you with an open question. 379 00:15:02,300 --> 00:15:04,566 If dimensions are the skeleton of information 380 00:15:04,600 --> 00:15:10,100 And we humans are stuck in a four-dimensional spacetime with three dimensions of space plus one dimension of time. 381 00:15:10,100 --> 00:15:11,333 Then our consciousness 382 00:15:11,366 --> 00:15:14,833 Is it also locked in some kind of four-dimensional prison? 383 00:15:15,000 --> 00:15:17,700 If there was a way to raise consciousness 384 00:15:17,700 --> 00:15:19,433 Even if it only rises one dimension 385 00:15:19,433 --> 00:15:22,100 What will the world we see look like? 386 00:15:22,200 --> 00:15:23,466 Have you ever considered 387 00:15:23,500 --> 00:15:25,133 Enlightenment in Buddhism 388 00:15:25,166 --> 00:15:27,733 Could it be some kind of ascension of consciousness? 389 00:15:27,933 --> 00:15:30,533 The experience of All That Is in meditation. 390 00:15:30,566 --> 00:15:34,200 Could it be that consciousness has temporarily broken through the three-dimensional limit? 391 00:15:34,233 --> 00:15:36,666 A glimpse of a higher-dimensional network of relationships 392 00:15:36,766 --> 00:15:37,633 I'm really not sure. 393 00:15:38,366 --> 00:15:42,000 But I think it's a question worth thinking about when you lie in bed tonight 394 00:15:42,533 --> 00:15:44,533 Do you think consciousness can be ascended? 395 00:15:44,966 --> 00:15:45,966 If you can 396 00:15:46,000 --> 00:15:48,833 What do you think the world that five-dimensional consciousness sees is like? 397 00:15:48,900 --> 00:15:49,933 I am Wang Lijie 398 00:15:49,933 --> 00:15:50,600 See you next time.