1 00:00:00,000 --> 00:00:02,279 Welcome to the Deep Dive, where we take a stack 2 00:00:02,279 --> 00:00:04,500 of dense sources and extract the knowledge nuggets 3 00:00:04,500 --> 00:00:07,480 you need to be perfectly informed. Today, we 4 00:00:07,480 --> 00:00:09,339 are wading into what our sources universally 5 00:00:09,339 --> 00:00:12,900 describe as, well, probably the most contentious 6 00:00:12,900 --> 00:00:15,599 debate in cognitive science. Yeah, it's been 7 00:00:15,599 --> 00:00:18,760 called ferocious, even tear -filled, which gives 8 00:00:18,760 --> 00:00:20,480 you a sense of the stakes. We're talking about 9 00:00:20,480 --> 00:00:23,820 the poverty of the stimulus, or POS. Right, POS. 10 00:00:24,120 --> 00:00:26,750 It sounds technical. But it hits right at the 11 00:00:26,750 --> 00:00:29,350 heart of how we become human, doesn't it? Linguistics, 12 00:00:29,589 --> 00:00:32,070 psychology, philosophy, they all clash here. 13 00:00:32,189 --> 00:00:35,109 Absolutely. And our mission today for you listening 14 00:00:35,109 --> 00:00:37,850 is to really clarify this. We want to break down 15 00:00:37,850 --> 00:00:40,609 what POS actually is, why it sparked decades 16 00:00:40,609 --> 00:00:43,429 of debate, and crucially, how it shapes our understanding 17 00:00:43,429 --> 00:00:45,549 of language development. And specifically, the 18 00:00:45,549 --> 00:00:47,590 arguments for and against it. We're going deep 19 00:00:47,590 --> 00:00:50,070 on the evidence today. Exactly. So let's start 20 00:00:50,070 --> 00:00:53,369 with the core idea. At its heart, Kios is a developmental 21 00:00:53,369 --> 00:00:55,770 claim. It's about the information, the data, 22 00:00:55,810 --> 00:00:57,770 that's available to a child learning language. 23 00:00:57,909 --> 00:01:00,609 It basically says that sometimes the language 24 00:01:00,609 --> 00:01:04,370 a child hears, the stimulus, has this unresolvable 25 00:01:04,370 --> 00:01:07,659 ambiguity. meaning the input, the sentences they 26 00:01:07,659 --> 00:01:10,280 hear, could logically support more than one grammatical 27 00:01:10,280 --> 00:01:13,519 rule or structure. The stimulus is insufficient 28 00:01:13,519 --> 00:01:16,599 on its own, as the sources put it. It's a classic 29 00:01:16,599 --> 00:01:19,900 induction problem, going from examples to rules. 30 00:01:20,260 --> 00:01:23,260 So the kid hears stuff, but that stuff is compatible 31 00:01:23,260 --> 00:01:26,620 with, say, grammar A and grammar B, and the input 32 00:01:26,620 --> 00:01:29,180 doesn't tell them which one is right. Precisely. 33 00:01:29,180 --> 00:01:31,359 And the reason this is such a big deal isn't 34 00:01:31,359 --> 00:01:34,239 just the ambiguity itself. It's that kids solve 35 00:01:34,239 --> 00:01:37,299 it. they reliably end up with the correct grammar. 36 00:01:37,519 --> 00:01:39,980 Ah, okay. That's the kicker. That's the picker. 37 00:01:40,019 --> 00:01:42,459 This is the phenomenon our sources call constrained 38 00:01:42,459 --> 00:01:45,659 generalization. Children somehow figure out the 39 00:01:45,659 --> 00:01:48,140 right, very specific linguistic knowledge, even 40 00:01:48,140 --> 00:01:50,340 though the data they got was, well, technically 41 00:01:50,340 --> 00:01:52,579 compatible with wrong answers to. They don't 42 00:01:52,579 --> 00:01:54,319 make the errors you'd expect if the data was 43 00:01:54,319 --> 00:01:57,379 truly ambiguous. Exactly. How do they avoid those 44 00:01:57,379 --> 00:02:00,760 tempting, logical, but wrong paths? That's the 45 00:02:00,760 --> 00:02:03,680 mystery POS forces us to confront. Okay, let's 46 00:02:03,680 --> 00:02:06,019 really unpack the logic here then. Because the 47 00:02:06,019 --> 00:02:09,599 argument for needing some kind of innate knowledge, 48 00:02:09,639 --> 00:02:12,199 or at least some internal guidance, it flows 49 00:02:12,199 --> 00:02:14,780 directly from this logical structure. It's quite 50 00:02:14,780 --> 00:02:17,180 a neat four -step argument. It really is. Step 51 00:02:17,180 --> 00:02:20,849 one is simple. Data. Everyone agrees children 52 00:02:20,849 --> 00:02:23,710 get external data. They hear language being spoken 53 00:02:23,710 --> 00:02:26,509 around them. This data is what they use to learn 54 00:02:26,509 --> 00:02:29,810 the underlying representation, the grammar. Straightforward 55 00:02:29,810 --> 00:02:33,259 enough. No arguments there. Step two is the controversial 56 00:02:33,259 --> 00:02:37,500 bit, the claim of poverty of the stimulus. This 57 00:02:37,500 --> 00:02:40,599 external data, the sentences they hear, are compatible 58 00:02:40,599 --> 00:02:43,120 with more than one hypothesis about the underlying 59 00:02:43,120 --> 00:02:46,479 grammar. Crucially, the data don't uniquely point 60 00:02:46,479 --> 00:02:48,960 to the correct hypothesis. That's the unresolvable 61 00:02:48,960 --> 00:02:51,080 ambiguity we talked about. Exactly. Then step 62 00:02:51,080 --> 00:02:53,659 three is the empirical observation, constrained 63 00:02:53,659 --> 00:02:56,680 generalization. Despite the ambiguity in the 64 00:02:56,680 --> 00:02:58,860 data, children consistently figure out the correct, 65 00:02:58,960 --> 00:03:01,740 specific grammar. They avoid the other possibilities 66 00:03:01,740 --> 00:03:03,879 the data were compatible with. They land on the 67 00:03:03,879 --> 00:03:06,520 right answer. They do. Which leads inevitably 68 00:03:06,520 --> 00:03:10,539 to step four, the conclusion. Prior knowledge 69 00:03:10,539 --> 00:03:13,460 or abilities. Since the external data wasn't 70 00:03:13,460 --> 00:03:15,699 enough to single out the right answer, the child 71 00:03:15,699 --> 00:03:18,750 must have something internal. some prior knowledge, 72 00:03:18,810 --> 00:03:21,469 some built -in inductive bias that pushes them 73 00:03:21,469 --> 00:03:23,650 towards the correct generalization and away from 74 00:03:23,650 --> 00:03:26,150 the errors. So if you can prove steps one, two, 75 00:03:26,349 --> 00:03:29,689 and three, step four just follows logically. 76 00:03:30,199 --> 00:03:31,979 That's the power of the argument, and it's why 77 00:03:31,979 --> 00:03:34,620 establishing that POS, step two, actually happens 78 00:03:34,620 --> 00:03:37,360 in real language learning is so critical. That's 79 00:03:37,360 --> 00:03:39,560 where the fight is. Right. To make this ambiguity 80 00:03:39,560 --> 00:03:42,500 really clear, let's use that visual analogy mentioned 81 00:03:42,500 --> 00:03:44,759 in the sources, the figure one idea. It really 82 00:03:44,759 --> 00:03:47,000 helps visualize the problem. It does. Imagine 83 00:03:47,000 --> 00:03:49,599 a space representing all possible grammatical 84 00:03:49,599 --> 00:03:52,300 rules for some aspect of language. The actual 85 00:03:52,300 --> 00:03:54,740 sentences a child hears are like beta points, 86 00:03:54,939 --> 00:03:57,020 let's call them Xs, scattered in this space. 87 00:03:57,280 --> 00:03:59,740 Okay, I'm picturing points on a map. Good. Now 88 00:03:59,740 --> 00:04:02,000 imagine several different hypotheses, different 89 00:04:02,000 --> 00:04:04,300 possible rules that could explain these X's. 90 00:04:04,439 --> 00:04:08,400 Let's call them hypothesis A, B, C, D, E, and 91 00:04:08,400 --> 00:04:10,659 F. These are like different shapes drawn on the 92 00:04:10,659 --> 00:04:13,620 map. And the X's fall inside these shapes. Exactly. 93 00:04:13,840 --> 00:04:16,610 And here's the crucial part. All the observed 94 00:04:16,610 --> 00:04:19,230 X's fall within the boundaries of all these hypotheses 95 00:04:19,230 --> 00:04:22,990 A, B, C, D, and F. Hearing the X's doesn't help 96 00:04:22,990 --> 00:04:25,410 the child choose between A, B, C, D, E, or F. 97 00:04:25,629 --> 00:04:28,550 They all fit the data perfectly. Precisely. Now 98 00:04:28,550 --> 00:04:31,709 let's say hypothesis C is the narrow correct 99 00:04:31,709 --> 00:04:35,269 rule for English. And hypothesis F is a much 100 00:04:35,269 --> 00:04:38,449 broader incorrect rule. Maybe one that allows 101 00:04:38,449 --> 00:04:41,029 sentences English speakers never actually say. 102 00:04:41,230 --> 00:04:43,310 Like an overgeneralization. Right. Since every 103 00:04:43,310 --> 00:04:45,990 X the child hears is compatible with both C and 104 00:04:45,990 --> 00:04:48,790 F, there's no single data point that tells the 105 00:04:48,790 --> 00:04:51,949 child, hey, rule F is wrong. So if a child just 106 00:04:51,949 --> 00:04:53,730 learned from the data, they could easily pick 107 00:04:53,730 --> 00:04:56,620 F. And they might never realize it's too broad. 108 00:04:56,759 --> 00:04:58,620 That's the logical problem. Why would they ever 109 00:04:58,620 --> 00:05:00,660 narrow it down from F to C if the data never 110 00:05:00,660 --> 00:05:02,959 forces them to? If they stuck with F, they'd 111 00:05:02,959 --> 00:05:05,120 make mistakes, produce ungrammatical sentences. 112 00:05:05,360 --> 00:05:07,279 But they don't. That's the constrained generalization. 113 00:05:07,689 --> 00:05:10,829 Exactly. They converge on C. They avoid the tempting 114 00:05:10,829 --> 00:05:14,149 error of F. And that convergence that needs an 115 00:05:14,149 --> 00:05:16,589 explanation beyond just the input data. It points 116 00:05:16,589 --> 00:05:19,149 to something internal, something prior. So the 117 00:05:19,149 --> 00:05:22,250 whole debate really hinges on showing this ambiguity 118 00:05:22,250 --> 00:05:25,949 isn't just theoretical. It's real. OK, so let's 119 00:05:25,949 --> 00:05:28,329 dig into what insufficient data really means 120 00:05:28,329 --> 00:05:30,310 in practice, because, you know, people argue 121 00:05:30,310 --> 00:05:32,490 about this constantly. The traditional argument 122 00:05:32,490 --> 00:05:35,120 is about data just literally being missing. Right. 123 00:05:35,180 --> 00:05:37,160 That's what we can call type 1. The data just 124 00:05:37,160 --> 00:05:39,560 aren't there. This aligns perfectly with that 125 00:05:39,560 --> 00:05:41,459 core definition we started with. It means the 126 00:05:41,459 --> 00:05:43,620 specific examples, the data points that would 127 00:05:43,620 --> 00:05:46,540 uniquely pick out the correct hypothesis, they're 128 00:05:46,540 --> 00:05:48,519 just absent from what the child typically hears. 129 00:05:48,720 --> 00:05:51,019 And the classic example of this is the subset 130 00:05:51,019 --> 00:05:52,879 problem. Can you walk us through that? Sure. 131 00:05:52,959 --> 00:05:55,600 The subset problem occurs when the correct hypothesis, 132 00:05:55,959 --> 00:05:58,639 let's call it C again, is a subset of a bigger, 133 00:05:58,759 --> 00:06:02,060 incorrect, overgeneralized hypothesis. FC is 134 00:06:02,060 --> 00:06:05,240 nested inside F. So everything allowed by C is 135 00:06:05,240 --> 00:06:08,220 also allowed by F, but F allows extra stuff too. 136 00:06:08,540 --> 00:06:11,660 Exactly. Think about Y word questions in English. 137 00:06:12,040 --> 00:06:15,459 The correct role, hypothesis C, says Y words 138 00:06:15,459 --> 00:06:17,300 generally need to be at the front of the clause. 139 00:06:17,439 --> 00:06:20,420 Like, what did the penguin see? Or... I know 140 00:06:20,420 --> 00:06:22,360 what the penguins saw. Okay, standard English. 141 00:06:22,600 --> 00:06:25,620 But imagine an incorrect, broader hypothesis, 142 00:06:26,079 --> 00:06:28,920 F, that says why words can be at the front or 143 00:06:28,920 --> 00:06:32,019 they can stay in situ, meaning where they'd be 144 00:06:32,019 --> 00:06:35,319 in a statement, like the penguins saw what, used 145 00:06:35,319 --> 00:06:37,540 as a regular statement, not an echo question. 146 00:06:37,839 --> 00:06:40,100 Which sounds wrong in English, yeah, ungrammatical. 147 00:06:40,199 --> 00:06:43,199 Right. Now, every single correct sentence the 148 00:06:43,199 --> 00:06:46,399 child hears that follows rule C. each word at 149 00:06:46,399 --> 00:06:48,800 the front, is also perfectly compatible with 150 00:06:48,800 --> 00:06:51,220 the broader incorrect rule F, which allows both 151 00:06:51,220 --> 00:06:54,399 fronted and in situ. Ah, I see. So there are 152 00:06:54,399 --> 00:06:56,920 no sentences that are okay by C but forbidden 153 00:06:56,920 --> 00:07:00,800 by F. Precisely. There are no C but not F examples 154 00:07:00,800 --> 00:07:03,579 in the input. So if a child somehow started with 155 00:07:03,579 --> 00:07:06,040 the broader hypothesis F, nothing they hear would 156 00:07:06,040 --> 00:07:08,819 ever contradict it. They'd have no positive evidence 157 00:07:08,819 --> 00:07:10,860 forcing them to shrink their hypothesis down 158 00:07:10,860 --> 00:07:14,379 to the correct, narrower rule C. That creates 159 00:07:14,379 --> 00:07:16,920 the unresolvable ambiguity. Logically, they could 160 00:07:16,920 --> 00:07:19,079 just stick with F forever. That's the classic 161 00:07:19,079 --> 00:07:21,360 POS argument from the subset problem. It seems 162 00:07:21,360 --> 00:07:25,329 logically airtight. But modern approaches, especially 163 00:07:25,329 --> 00:07:28,370 from people who aren't keen on innate language 164 00:07:28,370 --> 00:07:31,379 rules. They have ways around this, don't they, 165 00:07:31,459 --> 00:07:33,899 using statistics? They do. This is where things 166 00:07:33,899 --> 00:07:36,579 like the size principle come into play. The idea 167 00:07:36,579 --> 00:07:38,959 proposed by people like Tenenbaum and Griffiths 168 00:07:38,959 --> 00:07:41,279 is that children might be doing sophisticated 169 00:07:41,279 --> 00:07:44,720 probabilistic reasoning. They might use the ambiguous 170 00:07:44,720 --> 00:07:47,560 data itself as indirect evidence against the 171 00:07:47,560 --> 00:07:50,620 broader hypothesis F. How does that work if the 172 00:07:50,620 --> 00:07:53,550 data fits both? Think about it this way. Hypothesis 173 00:07:53,550 --> 00:07:56,829 F, the big, broad rule, predicts a huge range 174 00:07:56,829 --> 00:07:59,170 of possible sentences, including lots of weird, 175 00:07:59,250 --> 00:08:02,069 ungrammatical ones. Hypothesis C, the narrow 176 00:08:02,069 --> 00:08:05,129 rule, predicts only a small, specific set. If 177 00:08:05,129 --> 00:08:07,250 the child only ever hears sentences from that 178 00:08:07,250 --> 00:08:10,189 small, specific set predicted by C, even though 179 00:08:10,189 --> 00:08:12,449 those sentences are also compatible with F, a 180 00:08:12,449 --> 00:08:14,980 smart statistical learner might reason. Hmm. 181 00:08:15,160 --> 00:08:17,319 If the rule is really the big F, I should be 182 00:08:17,319 --> 00:08:19,319 hearing a much wider variety of sentences by 183 00:08:19,319 --> 00:08:21,399 now. Since I'm only hearing this very restricted 184 00:08:21,399 --> 00:08:23,600 set, it's much more probable that the true rule 185 00:08:23,600 --> 00:08:26,660 is the narrow one, C. So the very lack of hearing 186 00:08:26,660 --> 00:08:29,379 the broader examples becomes evidence against 187 00:08:29,379 --> 00:08:32,210 the broader rule. That's clever. It is clever. 188 00:08:32,309 --> 00:08:34,429 It uses the absence of evidence as a form of 189 00:08:34,429 --> 00:08:37,289 evidence. But, and this is crucial, it doesn't 190 00:08:37,289 --> 00:08:39,570 eliminate the need for prior knowledge. It just 191 00:08:39,570 --> 00:08:42,129 changes what kind of knowledge is needed. Right. 192 00:08:42,210 --> 00:08:44,529 Instead of needing an innate rule about words, 193 00:08:44,769 --> 00:08:47,169 the child needs an innate ability for complex 194 00:08:47,169 --> 00:08:49,730 Bayesian inference, applying something like the 195 00:08:49,730 --> 00:08:52,330 size principle. Exactly. The prior knowledge 196 00:08:52,330 --> 00:08:54,690 shifts from being language -specific content 197 00:08:54,690 --> 00:08:58,129 to being a powerful, possibly domain -general 198 00:08:58,129 --> 00:09:00,549 learning mechanism. Okay, so that covers the 199 00:09:00,549 --> 00:09:02,350 lack of direct positive evidence. What about 200 00:09:02,350 --> 00:09:04,679 other kinds of evidence? like negative evidence, 201 00:09:04,840 --> 00:09:07,399 parents correcting kids. Right. So direct positive 202 00:09:07,399 --> 00:09:09,879 evidence are the Xs, the examples of correct 203 00:09:09,879 --> 00:09:13,059 sentences. Negative evidence is information about 204 00:09:13,059 --> 00:09:15,799 what's wrong. Now, explicit correction, a parent 205 00:09:15,799 --> 00:09:17,879 saying, no, don't say it like that, is actually 206 00:09:17,879 --> 00:09:20,159 pretty rare for grammar. And famously, kids often 207 00:09:20,159 --> 00:09:23,059 ignore it anyway. Classic work by Brown and Hanlon 208 00:09:23,059 --> 00:09:24,659 showed that. Yeah, I remember reading that. Kids 209 00:09:24,659 --> 00:09:27,320 care more about truth than grammar. Often, yes. 210 00:09:27,899 --> 00:09:31,139 So the focus shifted to indirect evidence. This 211 00:09:31,139 --> 00:09:33,419 is data that requires the child to make an inference. 212 00:09:33,779 --> 00:09:36,559 A common example is recasts. That's when the 213 00:09:36,559 --> 00:09:38,679 parent repeats the child's sentence, but correctly. 214 00:09:38,820 --> 00:09:41,679 Yeah. Child says, her eat cookie. Parent says, 215 00:09:41,899 --> 00:09:44,559 yes, she is eating the cookie. For this to work 216 00:09:44,559 --> 00:09:46,519 as negative evidence, the child has to notice 217 00:09:46,519 --> 00:09:48,840 the difference, infer that their version was 218 00:09:48,840 --> 00:09:51,259 wrong, and figure out the rule from the correction. 219 00:09:51,559 --> 00:09:53,440 That sounds like it requires pretty sophisticated 220 00:09:53,440 --> 00:09:56,179 processing. It absolutely does. Which brings 221 00:09:56,179 --> 00:09:59,440 us to another key reason why POS can occur, even 222 00:09:59,440 --> 00:10:02,360 if the data is technically out there. The usability 223 00:10:02,360 --> 00:10:05,100 of data. Meaning the child just can't process 224 00:10:05,100 --> 00:10:07,500 it yet. Exactly. Think about the language adults 225 00:10:07,500 --> 00:10:10,279 use. Some sentences are really complex, maybe 226 00:10:10,279 --> 00:10:13,080 with multiple embedded clauses like, ah, the 227 00:10:13,080 --> 00:10:15,799 cat that the dog chased climbed the tree that, 228 00:10:15,860 --> 00:10:18,159 you know, it gets complicated. Let's call these 229 00:10:18,159 --> 00:10:21,200 complex bits the H points for hard to use. A 230 00:10:21,200 --> 00:10:23,840 young child's developing brain, their working 231 00:10:23,840 --> 00:10:26,620 memory, their ability to parse syntax might just 232 00:10:26,620 --> 00:10:29,200 not be able to handle those H points yet. Even 233 00:10:29,200 --> 00:10:31,399 if those sentences are in the input stream, they 234 00:10:31,399 --> 00:10:33,440 fly right past the child. They're effectively 235 00:10:33,440 --> 00:10:36,139 invisible. So the child is only learning from 236 00:10:36,139 --> 00:10:38,519 the simpler sentences they can process. the S 237 00:10:38,519 --> 00:10:41,700 points. Right. And if that smaller set of usable 238 00:10:41,700 --> 00:10:45,039 data, the S points, is still ambiguous, if it 239 00:10:45,039 --> 00:10:47,139 doesn't contain the crucial examples needed to 240 00:10:47,139 --> 00:10:49,879 rule out incorrect hypotheses, then the child 241 00:10:49,879 --> 00:10:53,159 experiences POS. It's poverty caused not by the 242 00:10:53,159 --> 00:10:55,320 environment, but by the limits of the child's 243 00:10:55,320 --> 00:10:57,960 own processing system at that stage. That makes 244 00:10:57,960 --> 00:10:59,860 a lot of sense. The effective input is smaller 245 00:10:59,860 --> 00:11:02,389 than the total input. Definitely. Now, the sources 246 00:11:02,389 --> 00:11:04,950 also mention two other kinds of problematic data, 247 00:11:05,090 --> 00:11:07,490 often lumped in with POS, but they're a bit different. 248 00:11:07,809 --> 00:11:10,809 Noisy data and misleading data. How are they 249 00:11:10,809 --> 00:11:13,330 different from the core type 1 ambiguity? The 250 00:11:13,330 --> 00:11:15,309 key difference is how they affect the correct 251 00:11:15,309 --> 00:11:19,029 hypothesis, C. Remember, type 1 POS is about 252 00:11:19,029 --> 00:11:22,210 ambiguity. The data fits both C and the wrong 253 00:11:22,210 --> 00:11:25,970 hypothesis, F. Types 2 and 3 are more about data 254 00:11:25,970 --> 00:11:28,090 that might actively make the child think C is 255 00:11:28,090 --> 00:11:30,789 wrong. Okay, give me an example of type 2 noisy 256 00:11:30,789 --> 00:11:34,990 data. Noisy data endpoints are just errors. Maybe 257 00:11:34,990 --> 00:11:38,289 a parent misspeaks, hesitates, or maybe the child 258 00:11:38,289 --> 00:11:40,529 hears a non -native speaker making systematic 259 00:11:40,529 --> 00:11:43,570 errors, like transferring a grammar rule from 260 00:11:43,570 --> 00:11:46,009 their first language. Like hearing someone consistently 261 00:11:46,009 --> 00:11:49,750 put who words in situ in English. Exactly. If 262 00:11:49,750 --> 00:11:52,149 a child hears enough of that noise, endpoints 263 00:11:52,149 --> 00:11:54,889 it might actively contradict the correct rule 264 00:11:54,889 --> 00:11:58,309 c it doesn't just create ambiguity it might push 265 00:11:58,309 --> 00:12:00,830 the child towards the wrong rule f or make them 266 00:12:00,830 --> 00:12:03,590 discard c altogether it distorts the picture 267 00:12:03,590 --> 00:12:06,549 okay so noise actively misleads what about type 268 00:12:06,549 --> 00:12:10,909 3 misleading data misleading data m points are 269 00:12:10,909 --> 00:12:12,929 utterances that are actually grammatical in the 270 00:12:12,929 --> 00:12:15,389 language, but the child misinterprets them. The 271 00:12:15,389 --> 00:12:17,809 classic example is echo questions. Like you did 272 00:12:17,809 --> 00:12:20,250 what? Right. That's perfectly fine English, but 273 00:12:20,250 --> 00:12:22,549 its grammar is exceptional and it depends heavily 274 00:12:22,549 --> 00:12:25,549 on the intonation, the prosody. If a child misses 275 00:12:25,549 --> 00:12:27,570 that special prosody, they might take that end 276 00:12:27,570 --> 00:12:29,950 point as general evidence that, hey, putting 277 00:12:29,950 --> 00:12:32,669 what at the end is okay sometimes. And that again 278 00:12:32,669 --> 00:12:35,470 contradicts the narrow correct rule C for standard 279 00:12:35,470 --> 00:12:39,330 questions. Exactly. So both noisy data and misleading 280 00:12:39,330 --> 00:12:42,470 data can confuse the learner, potentially leading 281 00:12:42,470 --> 00:12:45,070 them away from the correct hypothesis. While 282 00:12:45,070 --> 00:12:47,629 they can contribute to ambiguity, their main 283 00:12:47,629 --> 00:12:49,730 danger is actively pointing the child in the 284 00:12:49,730 --> 00:12:52,759 wrong direction. The core POS argument, though, 285 00:12:52,840 --> 00:12:55,360 the one that logically forces us to assume prior 286 00:12:55,360 --> 00:12:57,879 knowledge, is still that type one ambiguity, 287 00:12:58,100 --> 00:13:01,399 especially the subset problem combined with usability 288 00:13:01,399 --> 00:13:03,519 limits. Right. Because that's where the data 289 00:13:03,519 --> 00:13:06,299 truly underdetermines the grammar. So if we accept 290 00:13:06,299 --> 00:13:09,379 that POS exists, that the input is ambiguous 291 00:13:09,379 --> 00:13:11,720 and that kids still get it right, constrained 292 00:13:11,720 --> 00:13:14,679 generalization, we're forced to conclude they 293 00:13:14,679 --> 00:13:16,840 have some kind of prior knowledge or ability 294 00:13:16,840 --> 00:13:18,940 guiding them. The internal bias. The internal 295 00:13:18,940 --> 00:13:21,789 bias. Now the huge debate, the one causing all 296 00:13:21,789 --> 00:13:24,210 the tears, is about the nature of this prior 297 00:13:24,210 --> 00:13:27,009 knowledge. Is it innate? And if so, what kind 298 00:13:27,009 --> 00:13:28,929 of innate? Because prior could just mean learned 299 00:13:28,929 --> 00:13:31,669 earlier, right? Like maybe kids learn basic statistics 300 00:13:31,669 --> 00:13:34,330 first and then apply that to language. That's 301 00:13:34,330 --> 00:13:36,870 a fair point. You can have derived prior knowledge. 302 00:13:37,129 --> 00:13:39,809 But the argument... famously pushed by Chomsky 303 00:13:39,809 --> 00:13:42,190 and others, is that if you trace any derived 304 00:13:42,190 --> 00:13:44,809 knowledge back far enough, you eventually hit 305 00:13:44,809 --> 00:13:47,269 rock bottom. You hit something that wasn't derived 306 00:13:47,269 --> 00:13:49,190 from earlier experience. The starting point. 307 00:13:49,289 --> 00:13:51,149 The starting point. The biological endowment. 308 00:13:51,480 --> 00:13:54,639 Everyone agrees humans have some innate biological 309 00:13:54,639 --> 00:13:57,320 endowment for language. After all, you can expose 310 00:13:57,320 --> 00:13:59,480 kittens or rocks to language all day long and 311 00:13:59,480 --> 00:14:01,860 they won't learn it. Children do. So something 312 00:14:01,860 --> 00:14:04,559 innate is required. OK, so innateness isn't really 313 00:14:04,559 --> 00:14:07,139 the question. It's what is innate. Exactly. That's 314 00:14:07,139 --> 00:14:10,200 the core split. On one side, you have linguistic 315 00:14:10,200 --> 00:14:13,379 nativism. This is the view most strongly associated 316 00:14:13,379 --> 00:14:16,639 with universal grammar, UG. People like Chomsky, 317 00:14:16,799 --> 00:14:20,330 Hornstein, Lightfoot. They argue that at least 318 00:14:20,330 --> 00:14:22,529 some of the innate knowledge required to solve 319 00:14:22,529 --> 00:14:25,169 POS is language -specific. Meaning its knowledge 320 00:14:25,169 --> 00:14:27,330 or abilities only useful for learning language, 321 00:14:27,490 --> 00:14:30,129 not for anything else, like a dedicated language 322 00:14:30,129 --> 00:14:33,909 module in the brain. Precisely. UG, in this sense, 323 00:14:34,009 --> 00:14:36,950 refers to those specific built -in linguistic 324 00:14:36,950 --> 00:14:39,830 principles or structures. And for the linguistic 325 00:14:39,830 --> 00:14:42,789 nativists, the burden of proof is, in a way, 326 00:14:42,909 --> 00:14:46,389 lower. They just need to find one piece of necessary 327 00:14:46,389 --> 00:14:49,470 innate knowledge that can't be explained by general 328 00:14:49,470 --> 00:14:52,509 learning mechanisms. If they find one specifically 329 00:14:52,509 --> 00:14:54,769 linguistic thing, they win the argument against 330 00:14:54,769 --> 00:14:56,830 pure empiricism. Okay, so what's the other side? 331 00:14:56,990 --> 00:14:59,409 The other side is non -linguistic nativism, which 332 00:14:59,409 --> 00:15:01,370 often travels under the banner of empiricism, 333 00:15:01,490 --> 00:15:03,899 though it's a sophisticated empiricism. Thinkers 334 00:15:03,899 --> 00:15:06,759 like Clark, Lappin, Chater, and others, they 335 00:15:06,759 --> 00:15:08,500 absolutely agree there are innate abilities. 336 00:15:08,639 --> 00:15:11,059 They have to. Right. The up -to -his -neck innate 337 00:15:11,059 --> 00:15:14,379 mechanisms idea from Quine. Exactly. They accept 338 00:15:14,379 --> 00:15:17,720 innate biases. But they argue that all the necessary 339 00:15:17,720 --> 00:15:20,230 innate abilities are domain general. These are 340 00:15:20,230 --> 00:15:22,509 things like powerful statistical learning mechanisms, 341 00:15:22,750 --> 00:15:25,750 pattern recognition, memory capacity, maybe a 342 00:15:25,750 --> 00:15:27,830 general preference for simplicity or efficiency. 343 00:15:28,070 --> 00:15:30,149 Things useful for learning lots of different 344 00:15:30,149 --> 00:15:33,190 things, not just language. So they believe language 345 00:15:33,190 --> 00:15:35,450 is learned using the brain's general purpose 346 00:15:35,450 --> 00:15:38,059 toolkit, which happens to be innate. That's the 347 00:15:38,059 --> 00:15:40,240 idea. Their challenge is much bigger though. 348 00:15:40,419 --> 00:15:43,200 They have to show that every single instance 349 00:15:43,200 --> 00:15:46,399 of constrained generalization in language, every 350 00:15:46,399 --> 00:15:50,419 POS problem, can be solved using only the input 351 00:15:50,419 --> 00:15:53,039 data combined with these non -linguistic innate 352 00:15:53,039 --> 00:15:55,960 abilities. They can't allow even one little piece 353 00:15:55,960 --> 00:15:58,580 of language -specific innate knowledge. That 354 00:15:58,580 --> 00:16:01,399 sets up the battle lines pretty clearly. Specific 355 00:16:01,399 --> 00:16:03,840 linguistic instincts versus powerful general 356 00:16:03,840 --> 00:16:05,940 learning tools. It does, and it leads to some 357 00:16:05,940 --> 00:16:08,100 really interesting ideas about how POS might 358 00:16:08,100 --> 00:16:10,980 interact with language evolution itself. Simon 359 00:16:10,980 --> 00:16:13,299 Kirby's work is fascinating here. How does evolution 360 00:16:13,299 --> 00:16:16,600 fit in? Does it favor one side? Kirby's model 361 00:16:16,600 --> 00:16:19,419 suggests something really cool. POS might actually 362 00:16:19,419 --> 00:16:21,940 cause children to have the right innate biases 363 00:16:21,940 --> 00:16:24,360 over evolutionary time. It's a feedback loop. 364 00:16:24,519 --> 00:16:27,049 Yeah, explain that. Imagine parents produce language 365 00:16:27,049 --> 00:16:29,669 that's ambiguous. That's the POS situation. Their 366 00:16:29,669 --> 00:16:32,210 kids facing this ambiguity are forced to rely 367 00:16:32,210 --> 00:16:34,389 on whatever internal biases they happen to have. 368 00:16:34,470 --> 00:16:36,330 Let's call the bias the purple ellipse, like 369 00:16:36,330 --> 00:16:38,809 in the sources figure five analogy. So the ambiguous 370 00:16:38,809 --> 00:16:42,190 data forces them to use their bias. Right. The 371 00:16:42,190 --> 00:16:44,830 bias then guides them to settle on a specific 372 00:16:44,830 --> 00:16:47,750 underlying grammar, the purple one. Now, here's 373 00:16:47,750 --> 00:16:50,309 the twist. When these children grow up and have 374 00:16:50,309 --> 00:16:53,129 their own kids. They produce language based on 375 00:16:53,129 --> 00:16:56,049 the grammar their bias led them to adopt. So 376 00:16:56,049 --> 00:16:58,190 they produce ambiguous data consistent with the 377 00:16:58,190 --> 00:17:01,350 purple grammar. Exactly. And the next generation 378 00:17:01,350 --> 00:17:04,609 of kids who inherit the same purple bias, encounter 379 00:17:04,609 --> 00:17:07,549 the same ambiguous data, rely on their bias, 380 00:17:07,589 --> 00:17:09,849 and converge on the same purple grammar again. 381 00:17:10,109 --> 00:17:12,769 Wow. So the language itself gets shaped, generation 382 00:17:12,769 --> 00:17:15,549 after generation, to fit the learner's biases. 383 00:17:15,890 --> 00:17:18,730 Precisely. The bias doesn't just help learn the 384 00:17:18,730 --> 00:17:20,849 language. It helps create the structure of the 385 00:17:20,849 --> 00:17:24,529 language over time. The amiguity, POS, forces 386 00:17:24,529 --> 00:17:27,109 reliance on the bias, and the bias then ensures 387 00:17:27,109 --> 00:17:29,289 the language stays stable in a form that the 388 00:17:29,289 --> 00:17:31,210 bias can handle. That kind of turns the problem 389 00:17:31,210 --> 00:17:33,710 on its head. The bias works because the language 390 00:17:33,710 --> 00:17:36,109 has evolved to match it, driven by the constant 391 00:17:36,109 --> 00:17:38,990 pressure of POS. It's a really elegant evolutionary 392 00:17:38,990 --> 00:17:42,049 perspective on why our innate predispositions 393 00:17:42,049 --> 00:17:44,150 and language structures might be so well suited 394 00:17:44,150 --> 00:17:46,829 to each other. Okay. Now let's pivot to the arguments 395 00:17:46,829 --> 00:17:50,130 against POS, or at least arguments that say maybe 396 00:17:50,130 --> 00:17:53,710 the stimulus isn't so poor after all. If we just 397 00:17:53,710 --> 00:17:55,769 look closely enough or assume smarter learners, 398 00:17:56,009 --> 00:17:59,049 this often gets quantitative, right? Trying to 399 00:17:59,049 --> 00:18:02,450 figure out how much data is really enough. Exactly. 400 00:18:02,529 --> 00:18:05,130 The earliest attempts at this were these formal 401 00:18:05,130 --> 00:18:07,789 learnability approaches, famously starting with 402 00:18:07,789 --> 00:18:11,309 Gold's work in 1967. Ah, yes. Gold's theorem. 403 00:18:11,450 --> 00:18:14,299 That caused a huge stir, didn't it? often cited 404 00:18:14,299 --> 00:18:16,700 as proof POS was real for language learning. 405 00:18:16,819 --> 00:18:20,039 It was, but often misinterpreted. Gold showed 406 00:18:20,039 --> 00:18:22,660 that certain formal classes of languages couldn't 407 00:18:22,660 --> 00:18:24,940 be learned in principle just from positive examples 408 00:18:24,940 --> 00:18:27,440 without negative evidence. People jumped from 409 00:18:27,440 --> 00:18:30,259 that mathematical result to saying, see, human 410 00:18:30,259 --> 00:18:33,279 language needs innate rules. But the assumptions 411 00:18:33,279 --> 00:18:36,500 were key. Hugely key. Gold's setup required the 412 00:18:36,500 --> 00:18:38,680 learner to succeed on any possible sequence of 413 00:18:38,680 --> 00:18:41,519 input data, even deliberately tricky adversarial 414 00:18:41,519 --> 00:18:43,960 sequences designed to fool the learner. That's 415 00:18:43,960 --> 00:18:46,059 not realistic. Right. Kids learn from typical 416 00:18:46,059 --> 00:18:48,240 input, not from someone trying to trick them. 417 00:18:48,420 --> 00:18:51,319 Exactly. The takeaway from Gold isn't that language 418 00:18:51,319 --> 00:18:53,400 is unlearnable, but that learnability results 419 00:18:53,400 --> 00:18:56,500 depend heavily on the assumptions. If you make 420 00:18:56,500 --> 00:18:58,960 the learning problem unrealistically hard with 421 00:18:58,960 --> 00:19:02,079 false idealizations and the learner fails, it 422 00:19:02,079 --> 00:19:04,519 doesn't tell you much about real learning. Conversely, 423 00:19:04,539 --> 00:19:06,519 if you make it harder and the learner succeeds, 424 00:19:06,900 --> 00:19:09,500 then you know the easier real problem is definitely 425 00:19:09,500 --> 00:19:12,880 solvable. OK, so gold was maybe a red herring. 426 00:19:13,000 --> 00:19:16,500 What about more recent formal approaches? They've 427 00:19:16,500 --> 00:19:18,740 become much more sophisticated. For instance, 428 00:19:19,039 --> 00:19:21,160 Clark and Lappin later argued that learners could 429 00:19:21,160 --> 00:19:24,000 potentially solve many POS problems, even subset 430 00:19:24,000 --> 00:19:26,160 problems, if they employed a powerful strategy. 431 00:19:26,940 --> 00:19:29,720 Basically, treating things they don't hear as 432 00:19:29,720 --> 00:19:31,740 evidence that those things are ungrammatical. 433 00:19:32,230 --> 00:19:34,529 So using indirect negative evidence based on 434 00:19:34,529 --> 00:19:36,990 frequency. Essentially, yes. Interpreting low 435 00:19:36,990 --> 00:19:39,970 probability as ungrammatical. If a certain sentence 436 00:19:39,970 --> 00:19:42,369 type compatible with the broader hypothesis F 437 00:19:42,369 --> 00:19:44,390 is logically possible but just never seems to 438 00:19:44,390 --> 00:19:46,329 occur in the input after hearing tons of data, 439 00:19:46,529 --> 00:19:48,849 the learner might implicitly conclude it's not 440 00:19:48,849 --> 00:19:50,829 allowed. That sounds like the size principle 441 00:19:50,829 --> 00:19:53,789 again. Almost. It's very related. It again shifts 442 00:19:53,789 --> 00:19:56,180 the burden. You might not need innate linguistic 443 00:19:56,180 --> 00:19:59,180 rules, but you do need a potentially innate learning 444 00:19:59,180 --> 00:20:01,940 strategy, this ability to use statistical absence 445 00:20:01,940 --> 00:20:05,779 as negative evidence. It solves POS, but still 446 00:20:05,779 --> 00:20:08,140 requires a specific kind of built -in learning 447 00:20:08,140 --> 00:20:11,740 ability. Okay, moving from formal proofs to actual 448 00:20:11,740 --> 00:20:14,579 child development. How do researchers use the 449 00:20:14,579 --> 00:20:17,859 timing of learning as evidence? This is the developmental 450 00:20:17,859 --> 00:20:20,720 benchmarking approach, really pushed by Leggett 451 00:20:20,720 --> 00:20:23,319 and Yang. The core idea is pretty intuitive. 452 00:20:23,829 --> 00:20:25,589 things that are harder to learn from the input 453 00:20:25,589 --> 00:20:28,589 should take longer makes sense so the hypothesis 454 00:20:28,589 --> 00:20:30,789 is that the age at which a child masters some 455 00:20:30,789 --> 00:20:33,670 piece of grammar should correlate with how often 456 00:20:33,670 --> 00:20:36,529 they get clear unambiguous positive evidence 457 00:20:36,529 --> 00:20:38,970 for it in their input The challenge there must 458 00:20:38,970 --> 00:20:41,490 be defining unambiguous evidence. Oh, absolutely. 459 00:20:41,710 --> 00:20:44,289 It's painstaking work. Researchers have to carefully 460 00:20:44,289 --> 00:20:46,569 define exactly what sentence structures would 461 00:20:46,569 --> 00:20:49,529 count as clear proof for a specific rule. Then 462 00:20:49,529 --> 00:20:51,910 they analyze child language corpora, like childies, 463 00:20:51,930 --> 00:20:54,049 to estimate the frequency of those structures. 464 00:20:54,049 --> 00:20:57,289 Maybe it's, say, 1 .2 % of the input. And then 465 00:20:57,289 --> 00:20:59,829 they see when kids typically master that rule, 466 00:20:59,990 --> 00:21:02,390 maybe age three. Right. That gives you a baseline. 467 00:21:02,650 --> 00:21:06,089 1 .2 % frequency leads to mastery around age 468 00:21:06,089 --> 00:21:09,150 three. Now, the crucial test is when you find 469 00:21:09,150 --> 00:21:11,609 another piece of knowledge, let's call it K -Less, 470 00:21:11,690 --> 00:21:14,250 which has much lower frequency of unambiguous 471 00:21:14,250 --> 00:21:16,450 evidence in the input, maybe only 0 .1%. Okay. 472 00:21:16,490 --> 00:21:18,650 But you find that children master K -Less just 473 00:21:18,650 --> 00:21:21,490 as early, also around age 3, as the rule K -More, 474 00:21:21,609 --> 00:21:24,430 which had much more frequent evidence. Ah, so 475 00:21:24,430 --> 00:21:26,650 the warning speed for K -Less is faster than 476 00:21:26,650 --> 00:21:28,890 the data frequency alone would predict. Exactly. 477 00:21:29,589 --> 00:21:32,069 That discrepancy is the evidence for POS regarding 478 00:21:32,069 --> 00:21:34,869 K -Less. The child must be using something other 479 00:21:34,869 --> 00:21:37,069 than just the frequency of unambiguous data, 480 00:21:37,130 --> 00:21:39,569 some internal bias, to speed up the learning 481 00:21:39,569 --> 00:21:42,009 of K -Less and acquire it so early despite the 482 00:21:42,009 --> 00:21:44,869 sparse input. That's a clever empirical way to 483 00:21:44,869 --> 00:21:47,029 detect the influence of bias. But what about 484 00:21:47,029 --> 00:21:49,950 cases where unambiguous data is essentially zero, 485 00:21:50,049 --> 00:21:53,390 like maybe the word subset problem? Right. Benchmarking 486 00:21:53,390 --> 00:21:56,539 relies on some unambiguous data. For true subset 487 00:21:56,539 --> 00:21:59,099 problems, we need something else. This brings 488 00:21:59,099 --> 00:22:01,460 us to arguably the most powerful quantitative 489 00:22:01,460 --> 00:22:04,559 tools used today. Information theoretic approaches, 490 00:22:04,920 --> 00:22:08,019 often using the minimum description length MDL 491 00:22:08,019 --> 00:22:11,259 principle. MDL sounds complex, but the core idea 492 00:22:11,259 --> 00:22:14,319 is about simplicity. Exactly. MDL comes from 493 00:22:14,319 --> 00:22:16,380 information theory and basically says that the 494 00:22:16,380 --> 00:22:18,500 best hypothesis is the one that provides the 495 00:22:18,500 --> 00:22:21,480 most compact description or encoding of both 496 00:22:21,480 --> 00:22:23,880 the hypothesis itself and the data observed so 497 00:22:23,880 --> 00:22:26,660 far. It assumes learners have an innate bias 498 00:22:26,660 --> 00:22:29,619 towards simplicity or efficiency. A domain general 499 00:22:29,619 --> 00:22:31,940 preference for compact explanations. Precisely. 500 00:22:31,940 --> 00:22:34,200 Imagine again you have two hypotheses. C, the 501 00:22:34,200 --> 00:22:36,980 complex but correct one, and E, a simpler but 502 00:22:36,980 --> 00:22:39,099 incorrect one. Like maybe E is move the first 503 00:22:39,099 --> 00:22:41,059 auxiliary and C is the complex move the main 504 00:22:41,059 --> 00:22:43,680 clause auxiliary. Good example. Initially, storing 505 00:22:43,680 --> 00:22:46,640 rule E is cheaper. It's simple. Storing the complex 506 00:22:46,640 --> 00:22:49,460 rule C costs more mental storage space up front. 507 00:22:49,579 --> 00:22:51,859 But now the child starts hearing sentences, the 508 00:22:51,859 --> 00:22:55,740 data, the X's. The correct, complex rule C might 509 00:22:55,740 --> 00:22:57,819 allow you to encode or predict this incoming 510 00:22:57,819 --> 00:23:00,980 data very efficiently. The simple but wrong rule 511 00:23:00,980 --> 00:23:03,359 E, however, will keep running into sentences 512 00:23:03,359 --> 00:23:05,599 it can't explain easily. It has to keep adding 513 00:23:05,599 --> 00:23:08,119 exceptions or patches. So the total cost of using 514 00:23:08,119 --> 00:23:10,799 E, the simple rule plus all its messy exceptions, 515 00:23:11,059 --> 00:23:14,349 starts to grow rapidly. Exactly. While the cost 516 00:23:14,349 --> 00:23:16,109 of C, the complex rule, plus the efficiently 517 00:23:16,109 --> 00:23:19,569 encoded data grows more slowly, MDL calculates 518 00:23:19,569 --> 00:23:21,710 the break -even point, which the source has called 519 00:23:21,710 --> 00:23:23,829 de -break -even. That's the amount of data you 520 00:23:23,829 --> 00:23:26,029 need to observe before the total cost of the 521 00:23:26,029 --> 00:23:29,069 complex but correct hypothesis C becomes less 522 00:23:29,069 --> 00:23:31,390 than the total cost of the simple but incorrect 523 00:23:31,390 --> 00:23:34,289 hypothesis E. The point where complexity pays 524 00:23:34,289 --> 00:23:36,490 off because it handles the data better. Precisely. 525 00:23:36,569 --> 00:23:38,769 After you've seen amount of beta, The rational 526 00:23:38,769 --> 00:23:40,930 efficiency -seeking learner should switch to 527 00:23:40,930 --> 00:23:43,849 hypothesis C. So how does this test for POS? 528 00:23:44,430 --> 00:23:46,809 Researchers calculate this data how much data 529 00:23:46,809 --> 00:23:48,950 is needed for the MDL learner to pick the right 530 00:23:48,950 --> 00:23:52,009 rule. Then, crucially, they translate that amount 531 00:23:52,009 --> 00:23:54,950 of data into an age. How do they do that translation? 532 00:23:55,420 --> 00:23:57,420 They use estimates of how much language children 533 00:23:57,420 --> 00:24:00,539 hear per day or per hour, drawing on studies 534 00:24:00,539 --> 00:24:02,759 like Hart and Risley's work on word exposure, 535 00:24:03,059 --> 00:24:06,099 combined with estimates of waking hours. This 536 00:24:06,099 --> 00:24:08,420 gives an expected age by which a child should 537 00:24:08,420 --> 00:24:10,859 have encountered DEFL data points. Okay, so the 538 00:24:10,859 --> 00:24:13,480 model predicts an age of acquisition based purely 539 00:24:13,480 --> 00:24:16,339 on data and the simplicity bias. Right. Now, 540 00:24:16,420 --> 00:24:19,490 if that predicted age from the MDL model is way 541 00:24:19,490 --> 00:24:21,529 later than the age children actually acquire 542 00:24:21,529 --> 00:24:23,690 the rule. Like, the model says it should take 543 00:24:23,690 --> 00:24:26,230 500 years to figure out wanna contraction based 544 00:24:26,230 --> 00:24:28,750 on data and simplicity alone, but kids get it 545 00:24:28,750 --> 00:24:31,369 by age five, then you've found POS. Because the 546 00:24:31,369 --> 00:24:34,029 simplicity bias alone wasn't enough to explain 547 00:24:34,029 --> 00:24:37,609 the speed. Exactly. It means the child must have 548 00:24:37,609 --> 00:24:40,390 additional biases beyond just preferring compact 549 00:24:40,390 --> 00:24:43,650 descriptions that are helping them converge on 550 00:24:43,650 --> 00:24:46,410 the right answer much, much faster than the data 551 00:24:46,410 --> 00:24:48,990 alone would allow. These quantitative methods 552 00:24:48,990 --> 00:24:51,529 really force the debate onto empirical ground. 553 00:24:52,240 --> 00:24:54,619 Alright, so moving from the methods to the actual 554 00:24:54,619 --> 00:24:57,339 battleground. Specific linguistic phenomena. 555 00:24:57,960 --> 00:25:00,420 Case studies are absolutely vital because they 556 00:25:00,420 --> 00:25:03,039 force everyone to get really concrete. You can't 557 00:25:03,039 --> 00:25:05,220 just vaguely talk about language. You have to 558 00:25:05,220 --> 00:25:07,539 define the specific rule, the competing hypotheses, 559 00:25:07,880 --> 00:25:10,619 the actual data available, and what abilities 560 00:25:10,619 --> 00:25:12,380 you're assuming the child brings to the table. 561 00:25:12,650 --> 00:25:14,309 This is where we see if these quantitative methods 562 00:25:14,309 --> 00:25:17,109 actually work and what kinds of biases seem necessary. 563 00:25:17,430 --> 00:25:19,690 Let's start with the big one, the classic, syntax 564 00:25:19,690 --> 00:25:22,349 structure dependence. Right. This is often seen 565 00:25:22,349 --> 00:25:24,410 as the bedrock argument for linguistic nativism. 566 00:25:24,470 --> 00:25:26,829 The problem, as we touched on, is how kids learn 567 00:25:26,829 --> 00:25:29,390 to form complex yes -no questions. They need 568 00:25:29,390 --> 00:25:31,490 to learn the rule isn't linear. It's not move 569 00:25:31,490 --> 00:25:34,750 the first is or can you find. It's move the auxiliary 570 00:25:34,750 --> 00:25:37,809 verb that belongs to the main clause, which requires 571 00:25:37,809 --> 00:25:39,950 understanding hierarchical sentence structure. 572 00:25:40,509 --> 00:25:43,230 Exactly. Like in, is the dog that is chasing 573 00:25:43,230 --> 00:25:46,130 the squirrel happy? You move the first is, but 574 00:25:46,130 --> 00:25:47,930 in the dog that is chasing the squirrel is happy, 575 00:25:48,069 --> 00:25:50,269 the is you'd move to make a question is the second 576 00:25:50,269 --> 00:25:52,650 one. It depends on the structure. And the initial 577 00:25:52,650 --> 00:25:55,849 POS argument was that the simple linear rules, 578 00:25:56,049 --> 00:25:59,309 move the first O, would work for most simple 579 00:25:59,309 --> 00:26:01,809 sentences kids hear, making them seem like the 580 00:26:01,809 --> 00:26:05,109 obvious choice based on frequency. Yet kids somehow 581 00:26:05,109 --> 00:26:07,470 learn the complex, structure -dependent rule 582 00:26:07,470 --> 00:26:10,799 very early, around age three. Correct. It looked 583 00:26:10,799 --> 00:26:13,539 like a slam dunk for POS needing innate structural 584 00:26:13,539 --> 00:26:16,519 knowledge. So naturally, researchers tried to 585 00:26:16,519 --> 00:26:18,680 knock it down by arguing the data was sufficient. 586 00:26:19,019 --> 00:26:22,119 Tell us about that first major attempt, Reale 587 00:26:22,119 --> 00:26:24,720 and Christensen, back in 2005. What was their 588 00:26:24,720 --> 00:26:27,160 idea? They argued that kids could figure it out 589 00:26:27,160 --> 00:26:29,660 using simple statistics specifically. the frequency 590 00:26:29,660 --> 00:26:32,859 of word pairs, big grams, and triplets, tritograms, 591 00:26:32,859 --> 00:26:35,319 across all the language they hear, not just questions. 592 00:26:35,480 --> 00:26:38,000 They claim that the statistical patterns in everyday 593 00:26:38,000 --> 00:26:40,940 sentences implicitly favor structure -dependent 594 00:26:40,940 --> 00:26:42,980 interpretations, even if the child doesn't consciously 595 00:26:42,980 --> 00:26:47,640 know the rule. So no innate syntax needed, just 596 00:26:47,640 --> 00:26:51,140 a powerful statistical learner tallying word 597 00:26:51,140 --> 00:26:54,279 sequences. Sounds domain general. It did, but 598 00:26:54,279 --> 00:26:56,859 that claim didn't hold up for long. Later work 599 00:26:56,859 --> 00:26:59,940 by Kamm and others showed that Reale and Christensen's 600 00:26:59,940 --> 00:27:02,680 result was likely a statistical artifact of the 601 00:27:02,680 --> 00:27:06,000 specific data set they used. When tested on larger, 602 00:27:06,079 --> 00:27:08,839 more representative language samples, those simple 603 00:27:08,839 --> 00:27:11,559 word statistics weren't reliable enough to distinguish 604 00:27:11,559 --> 00:27:14,220 the structure -dependent rule. So the ambiguity 605 00:27:14,220 --> 00:27:17,390 remained. The simple stats weren't enough. It 606 00:27:17,390 --> 00:27:20,630 seemed not. The purely statistical solution didn't 607 00:27:20,630 --> 00:27:23,069 quite work. This pushed researchers back towards 608 00:27:23,069 --> 00:27:25,029 needing some kind of bias, but maybe still a 609 00:27:25,029 --> 00:27:27,559 domain general one. That led to the work by Perforce, 610 00:27:27,839 --> 00:27:29,940 Tenenbaum, and Regeer. What did they propose? 611 00:27:30,240 --> 00:27:32,460 They took a broader view. Instead of just looking 612 00:27:32,460 --> 00:27:34,359 at yes -no questions, they treated structure 613 00:27:34,359 --> 00:27:36,680 dependence as an over -hypothesis, a general 614 00:27:36,680 --> 00:27:38,799 property likely true of the entire grammatical 615 00:27:38,799 --> 00:27:41,220 system. They used Bayesian modeling and found 616 00:27:41,220 --> 00:27:43,440 that yes, POS still exists for this problem, 617 00:27:43,579 --> 00:27:45,759 but it could be solved by a domain -general simplicity 618 00:27:45,759 --> 00:27:49,640 bias. The MDL idea again. Essentially, yes. A 619 00:27:49,640 --> 00:27:51,240 preference for the grammar that provides the 620 00:27:51,240 --> 00:27:53,660 simplest, most compact overall explanation for 621 00:27:53,660 --> 00:27:56,440 all the language data. A system built on structure 622 00:27:56,440 --> 00:27:59,799 dependence, while complex locally, might be simpler 623 00:27:59,799 --> 00:28:02,180 overall than a system relying on lots of linear 624 00:28:02,180 --> 00:28:05,460 rules and exceptions. So domain general simplicity 625 00:28:05,460 --> 00:28:08,400 could still win? Potentially. But then the pendulum 626 00:28:08,400 --> 00:28:10,380 swung back again with Ebbend and colleagues. 627 00:28:10,640 --> 00:28:12,980 It did. They took an even broader perspective, 628 00:28:13,160 --> 00:28:15,460 trying to learn not just syntax, but also how 629 00:28:15,460 --> 00:28:18,059 syntax relates to logical meaning using context. 630 00:28:18,619 --> 00:28:21,740 Their model succeeded, but the bias it needed 631 00:28:21,740 --> 00:28:25,059 was interesting. A preference for rational rules. 632 00:28:25,279 --> 00:28:27,900 Rational rules. Meaning? Rules that are not only 633 00:28:27,900 --> 00:28:30,640 simple or compact, but also tend to reuse common 634 00:28:30,640 --> 00:28:33,339 building blocks or operations. Efficiency through 635 00:28:33,339 --> 00:28:36,410 reuse. Now, the bias itself, prefer simple reusable 636 00:28:36,410 --> 00:28:39,009 rules, sounds pretty domain general. But the 637 00:28:39,009 --> 00:28:41,150 kinds of building blocks their system needed 638 00:28:41,150 --> 00:28:43,390 to reuse to successfully learn structure dependence 639 00:28:43,390 --> 00:28:46,769 look suspiciously like abstract linguistic primitives, 640 00:28:46,769 --> 00:28:49,329 things related to thematic roles, argument structure, 641 00:28:49,650 --> 00:28:52,609 the link between syntax and meaning. Ah, so the 642 00:28:52,609 --> 00:28:55,289 learning engine might be general rationality 643 00:28:55,289 --> 00:28:58,289 reuse, but the parts it needs to operate on might 644 00:28:58,289 --> 00:29:01,160 be language -specific innate knowledge. That's 645 00:29:01,160 --> 00:29:03,380 the interpretation that supports linguistic nativism. 646 00:29:03,480 --> 00:29:06,519 It's a subtle point. Is the crucial innate part 647 00:29:06,519 --> 00:29:08,920 the general learning strategy or the specific 648 00:29:08,920 --> 00:29:11,460 representational units it works with? The debate 649 00:29:11,460 --> 00:29:14,259 continues there. And finally, the neural network 650 00:29:14,259 --> 00:29:17,240 approach by McCoy and others. What did that show? 651 00:29:17,519 --> 00:29:19,640 They showed that certain types of neural networks 652 00:29:19,640 --> 00:29:21,900 could learn the structure -dependent rule without 653 00:29:21,900 --> 00:29:24,660 being explicitly programmed with hierarchical 654 00:29:24,660 --> 00:29:27,700 syntax, which sounds like a win for the anti 655 00:29:27,700 --> 00:29:30,140 -innate crowd. But it's not that simple. It's 656 00:29:30,140 --> 00:29:32,589 not. Because the network architecture itself, 657 00:29:32,869 --> 00:29:35,410 how the nodes and layers are connected, the learning 658 00:29:35,410 --> 00:29:38,450 algorithms used contains implicit biases. The 659 00:29:38,450 --> 00:29:40,369 success of the network doesn't mean no bias is 660 00:29:40,369 --> 00:29:42,869 needed. It just means the necessary bias might 661 00:29:42,869 --> 00:29:44,549 be embedded in the structure of the learning 662 00:29:44,549 --> 00:29:47,210 mechanism rather than explicit rules. It still 663 00:29:47,210 --> 00:29:50,829 reinforces the core POS conclusion. You need 664 00:29:50,829 --> 00:29:52,789 some internal constraint to get structure dependence 665 00:29:52,789 --> 00:29:56,190 right. The debate just shifts to where that constraint 666 00:29:56,190 --> 00:29:59,269 lives. Okay, so syntax remains a complex battleground. 667 00:29:59,640 --> 00:30:02,710 Let's shift gears. What about a case that seems 668 00:30:02,710 --> 00:30:06,890 to lean away from linguistic nativism, like learning 669 00:30:06,890 --> 00:30:09,430 number words? Right, lexical semantics, learning 670 00:30:09,430 --> 00:30:12,190 the meaning of exact cardinal number words like 671 00:30:12,190 --> 00:30:16,609 1, 2, 11, 97. The learning target here is the 672 00:30:16,609 --> 00:30:18,509 cardinality principle, or really the successor 673 00:30:18,509 --> 00:30:20,829 function, knowing that the next word in the count 674 00:30:20,829 --> 00:30:23,670 list means exactly one more. And the POS argument 675 00:30:23,670 --> 00:30:27,650 here is? The input is incredibly skewed. Kids 676 00:30:27,650 --> 00:30:30,910 hear one, two, three constantly, but higher numbers 677 00:30:30,910 --> 00:30:33,690 are much rarer. It follows a power law distribution. 678 00:30:34,089 --> 00:30:37,230 So the data is arguably insufficient to robustly 679 00:30:37,230 --> 00:30:39,809 teach the infinite, perfectly regular plus one 680 00:30:39,809 --> 00:30:42,470 system, especially distinguishing it from alternatives 681 00:30:42,470 --> 00:30:44,609 like maybe it's base 10 or maybe there are weird 682 00:30:44,609 --> 00:30:47,069 exceptions for large numbers. Yet kids do learn 683 00:30:47,069 --> 00:30:49,099 it. But it's a staged process, right? They go 684 00:30:49,099 --> 00:30:50,880 through being a one -knower, then a two -knower. 685 00:30:51,059 --> 00:30:53,259 Exactly. They learn the meanings individually 686 00:30:53,259 --> 00:30:55,339 for small numbers, and then suddenly, usually 687 00:30:55,339 --> 00:30:57,700 around age four or five, they make this inductive 688 00:30:57,700 --> 00:31:00,460 leap and understand the whole system. They become 689 00:31:00,460 --> 00:31:03,259 cardinal principal knowers. So how was this modeled? 690 00:31:03,359 --> 00:31:05,539 Did it require language -specific knowledge? 691 00:31:05,940 --> 00:31:08,240 This is where Pianidosi and colleagues' work 692 00:31:08,240 --> 00:31:11,240 comes in. They built an ideal learner model that 693 00:31:11,240 --> 00:31:14,039 remarkably reproduced that exact staged learning 694 00:31:14,039 --> 00:31:17,200 trajectory. And the key finding was that it did 695 00:31:17,200 --> 00:31:20,279 so using only assumed domain general building 696 00:31:20,279 --> 00:31:22,900 blocks. Like what? Things like basic comparison, 697 00:31:23,259 --> 00:31:25,960 is this set bigger than that set, combinatorial 698 00:31:25,960 --> 00:31:29,099 abilities, can it combine concepts, and crucially, 699 00:31:29,140 --> 00:31:32,500 recursion. Can I apply a rule repeatedly? These 700 00:31:32,500 --> 00:31:35,339 feel more like general logical or mathematical 701 00:31:35,339 --> 00:31:38,359 primitives. Not specifically linguistic units. 702 00:31:38,680 --> 00:31:41,140 Correct. And the driving force was again that 703 00:31:41,140 --> 00:31:43,519 rational rules bias preferred the simplest, most 704 00:31:43,519 --> 00:31:46,619 compact system that reuses components. In this 705 00:31:46,619 --> 00:31:48,940 case, the successor function plus one is a beautifully 706 00:31:48,940 --> 00:31:51,759 simple recursive rule. Because both the building 707 00:31:51,759 --> 00:31:53,960 blocks and the simplicity bias seem domain general, 708 00:31:54,180 --> 00:31:56,720 this case study is often cited as strong evidence 709 00:31:56,720 --> 00:31:59,500 for the non -linguistic nativist view. It shows 710 00:31:59,500 --> 00:32:01,660 general cognitive abilities might be enough for 711 00:32:01,660 --> 00:32:03,980 some complex learning. Interesting. Okay, one 712 00:32:03,980 --> 00:32:06,480 last case study. Phonology word final, obstruent, 713 00:32:06,480 --> 00:32:08,799 devoicing. Like in Dutch, hand, sounding like 714 00:32:08,799 --> 00:32:11,619 hunt. Right. The rule is basically if a consonant 715 00:32:11,619 --> 00:32:15,200 that blocks airflow, an obstruent like BDGVZ, 716 00:32:15,240 --> 00:32:17,680 occurs at the very end of a word, pronounce it 717 00:32:17,680 --> 00:32:21,259 as its voiceless counterpart, PTKFS. So hand, 718 00:32:21,380 --> 00:32:24,579 dog, with a D sound gets pronounced with a T 719 00:32:24,579 --> 00:32:28,769 sound. Where's the potential POS here? The ambiguity, 720 00:32:28,950 --> 00:32:30,970 as it's already pointed out, lies in the scope 721 00:32:30,970 --> 00:32:33,130 of the rule. Does the child learn the precise 722 00:32:33,130 --> 00:32:36,269 rule to voice substituents only when word final? 723 00:32:36,650 --> 00:32:39,049 Or do they learn a simpler but wrong rule, like 724 00:32:39,049 --> 00:32:41,470 always devoice D at the end of a word, or maybe 725 00:32:41,470 --> 00:32:44,390 even devoice all consonants at the end of words? 726 00:32:44,529 --> 00:32:45,950 How would they tell the difference? They need 727 00:32:45,950 --> 00:32:48,109 evidence where the sound isn't word final but 728 00:32:48,109 --> 00:32:50,970 might seem like it, or where a final sound that 729 00:32:50,970 --> 00:32:53,430 isn't an obstruent stays voiced. For example, 730 00:32:53,690 --> 00:32:56,269 hearing the plural honden, where the D is followed 731 00:32:56,269 --> 00:32:59,309 by a vowel and stays voiced, is crucial evidence 732 00:32:59,309 --> 00:33:01,630 against the rule being just always devoice final 733 00:33:01,630 --> 00:33:04,809 D. Okay, so does the input reliably contain enough 734 00:33:04,809 --> 00:33:07,230 of that contrasting evidence? That's the open 735 00:33:07,230 --> 00:33:10,210 question. Whether POS actually exists here depends 736 00:33:10,210 --> 00:33:13,230 entirely on detailed analysis of Dutch child 737 00:33:13,230 --> 00:33:15,750 -directed speech corpora, which, according to 738 00:33:15,750 --> 00:33:18,230 our sources, hasn't definitively resolved the 739 00:33:18,230 --> 00:33:21,170 issue yet. We know adults generalize the rule 740 00:33:21,170 --> 00:33:24,150 correctly to new words, so children do reach 741 00:33:24,150 --> 00:33:26,869 the constrained generalization. So this is a 742 00:33:26,869 --> 00:33:28,890 prime candidate for those quantitative methods 743 00:33:28,890 --> 00:33:31,250 we discussed earlier. Absolutely. You could apply 744 00:33:31,250 --> 00:33:33,750 the developmental benchmarking approach. See 745 00:33:33,750 --> 00:33:35,789 if the age of acquisition matches the frequency 746 00:33:35,789 --> 00:33:39,289 of unambiguous evidence like Honden. Or you could 747 00:33:39,289 --> 00:33:42,289 use the MDL rational rules approach. Calculate 748 00:33:42,289 --> 00:33:44,450 the Dorbank point for learning the precise rule 749 00:33:44,450 --> 00:33:47,390 versus simpler alternatives based on corpus data. 750 00:33:47,670 --> 00:33:49,809 And the result would provide more evidence in 751 00:33:49,809 --> 00:33:53,019 this ongoing nativist debate. If general simplicity 752 00:33:53,019 --> 00:33:55,519 works, it's a point for non -linguistic nativism. 753 00:33:55,660 --> 00:33:58,420 If it requires assuming innate phonological features, 754 00:33:58,660 --> 00:34:01,279 it's a point for linguistic nativism. Exactly. 755 00:34:01,420 --> 00:34:04,299 It shows how these specific, concrete case studies 756 00:34:04,299 --> 00:34:07,119 are where the real progress is made. Hashtag 757 00:34:07,119 --> 00:34:10,320 tag outro. So, wrapping this all up, what's the 758 00:34:10,320 --> 00:34:13,440 big mixture? I think the real value of the poverty 759 00:34:13,440 --> 00:34:15,639 of the stimulus concept honestly goes beyond 760 00:34:15,639 --> 00:34:18,039 just settling the nativist debate, as important 761 00:34:18,039 --> 00:34:20,199 as that is. How so? It highlights a fundamental 762 00:34:20,199 --> 00:34:23,019 truth about learning, especially language learning. 763 00:34:23,139 --> 00:34:26,099 It's a hard problem. The input children get is 764 00:34:26,099 --> 00:34:30,289 often noisy, ambiguous, and incomplete. POS isn't 765 00:34:30,289 --> 00:34:33,110 some rare edge case. It's likely a frequent challenge 766 00:34:33,110 --> 00:34:36,269 children overcome constantly. It forces us to 767 00:34:36,269 --> 00:34:38,949 appreciate the sheer power and sophistication 768 00:34:38,949 --> 00:34:41,730 of the child's learning mechanisms. That constrained 769 00:34:41,730 --> 00:34:44,070 generalization is kind of miraculous when you 770 00:34:44,070 --> 00:34:45,849 think about the messy data they start with. It 771 00:34:45,849 --> 00:34:47,510 really is. And the way forward in understanding 772 00:34:47,510 --> 00:34:50,070 it seems clear now. It requires rigor and quantification. 773 00:34:50,349 --> 00:34:52,809 No more hand -wavy arguments. Right. You need 774 00:34:52,809 --> 00:34:55,530 to, as the sources stress, one, precisely define 775 00:34:55,530 --> 00:34:58,059 the specific learning problem. What's the target 776 00:34:58,059 --> 00:34:59,880 rule? What are the plausible alternatives? What 777 00:34:59,880 --> 00:35:03,500 data is actually available? Then two, quantitatively 778 00:35:03,500 --> 00:35:05,920 measure if POS is actually occurring for that 779 00:35:05,920 --> 00:35:09,159 specific problem. Use tools like developmental 780 00:35:09,159 --> 00:35:12,519 benchmarking or calculate that Devin point with 781 00:35:12,519 --> 00:35:15,539 MDL. Is the data mathematically sufficient given 782 00:35:15,539 --> 00:35:18,309 reasonable learning assumptions? and third if 783 00:35:18,309 --> 00:35:20,670 pos is confirmed you need an existence proof 784 00:35:20,670 --> 00:35:24,309 show exactly how a specific proposed learning 785 00:35:24,309 --> 00:35:27,750 mechanism with its specific biases can provably 786 00:35:27,750 --> 00:35:30,969 solve that specific instance of pos using the 787 00:35:30,969 --> 00:35:33,510 available data exactly being explicit about the 788 00:35:33,510 --> 00:35:36,130 hypotheses the data the learners abilities and 789 00:35:36,130 --> 00:35:38,389 the biases that's how we move beyond the shouting 790 00:35:38,389 --> 00:35:41,000 matches Looking at the solutions we've discussed, 791 00:35:41,239 --> 00:35:42,860 particularly from the quantitative modeling, 792 00:35:43,099 --> 00:35:45,440 it's striking how often these domain general 793 00:35:45,440 --> 00:35:48,840 biases like simplicity or MDL or rational rules 794 00:35:48,840 --> 00:35:50,800 seem to play a key role. They definitely do. 795 00:35:50,860 --> 00:35:53,360 They're powerful explanatory tools. Yet, as we 796 00:35:53,360 --> 00:35:55,500 saw with the structure dependence case, even 797 00:35:55,500 --> 00:35:57,900 those general biases might need to operate on 798 00:35:57,900 --> 00:36:00,139 some kind of pre -existing, perhaps language 799 00:36:00,139 --> 00:36:02,360 -specific representational structure to work 800 00:36:02,360 --> 00:36:04,840 properly for syntax. That seems to be the cutting 801 00:36:04,840 --> 00:36:06,920 edge right now, understanding that interplay 802 00:36:06,920 --> 00:36:09,440 between general learning mechanisms and potentially 803 00:36:09,440 --> 00:36:12,320 specific representational formats. Which leaves 804 00:36:12,320 --> 00:36:14,219 us with a really provocative final thought for 805 00:36:14,219 --> 00:36:17,159 you, the listener, to chew on. We've framed the 806 00:36:17,159 --> 00:36:20,760 debate as linguistic nativism versus non -linguistic 807 00:36:20,760 --> 00:36:24,500 nativism. Linguistic nativism wins if even one 808 00:36:24,500 --> 00:36:27,139 crucial piece of the innate toolkit is language 809 00:36:27,139 --> 00:36:29,989 specific. Right. But what if we push the non 810 00:36:29,989 --> 00:36:32,869 -linguistic idea even further? Could it be that 811 00:36:32,869 --> 00:36:35,369 all the seemingly language -specific structures 812 00:36:35,369 --> 00:36:38,230 or biases, like the innate expectation that syntax 813 00:36:38,230 --> 00:36:41,210 connects systematically to meaning, or the preference 814 00:36:41,210 --> 00:36:43,530 for hierarchical structure itself, could themselves 815 00:36:43,530 --> 00:36:46,760 be derived from One single, even more fundamental, 816 00:36:47,000 --> 00:36:49,940 non -linguistic bias. Like what kind of bias? 817 00:36:50,199 --> 00:36:52,559 What if the brain's most basic drive is simply 818 00:36:52,559 --> 00:36:55,139 a preference for maximal similarity across all 819 00:36:55,139 --> 00:36:57,639 its different representational systems? Imagine 820 00:36:57,639 --> 00:36:59,440 the brain wants the way it represents visual 821 00:36:59,440 --> 00:37:01,599 scenes, the way it represents concepts, and the 822 00:37:01,599 --> 00:37:03,820 way it represents linguistic utterances to all 823 00:37:03,820 --> 00:37:06,199 use similar structural principles, hierarchy, 824 00:37:06,539 --> 00:37:09,079 compositionality, recursion, because that's maximally 825 00:37:09,079 --> 00:37:11,949 efficient overall. Ah, so the pressure for syntax 826 00:37:11,949 --> 00:37:14,389 to be hierarchical wouldn't come from an innate 827 00:37:14,389 --> 00:37:17,329 syntax module, but from a deep -seated drive 828 00:37:17,329 --> 00:37:19,730 for syntax to look like vision and conceptual 829 00:37:19,730 --> 00:37:22,989 structure. Exactly. Could that single, ultra 830 00:37:22,989 --> 00:37:25,949 -general bias for cross -system similarity be 831 00:37:25,949 --> 00:37:28,210 powerful enough to bootstrap all the specific 832 00:37:28,210 --> 00:37:30,969 structures we observe in language without needing 833 00:37:30,969 --> 00:37:33,289 any of them to be explicitly innate linguistic 834 00:37:33,289 --> 00:37:35,489 knowledge? That's something to think about. A 835 00:37:35,489 --> 00:37:37,969 potential grand unification theory for cognition. 836 00:37:38,650 --> 00:37:40,730 Definitely something to explore further. Thanks 837 00:37:40,730 --> 00:37:42,110 for joining us for the deep dive.