WEBVTT 00:00:00.000 --> 00:00:04.080 You know, back in 1956, a machine didn't just 00:00:04.080 --> 00:00:07.000 solve a complicated math problem faster than 00:00:07.000 --> 00:00:10.339 a human. Right. It actually found a more beautiful, 00:00:10.960 --> 00:00:14.300 more elegant path to the truth than two of the 00:00:14.300 --> 00:00:17.260 greatest mathematical minds of the 20th century. 00:00:17.440 --> 00:00:19.839 Welcome to Deep Dive. It really is an incredible 00:00:19.839 --> 00:00:22.100 story. I mean, we're looking at a field that 00:00:22.100 --> 00:00:24.879 sits right at this crazy intersection of pure 00:00:24.879 --> 00:00:28.839 mathematics, philosophy, and artificial intelligence. 00:00:29.199 --> 00:00:31.859 Exactly. And our mission today is to give you, 00:00:31.879 --> 00:00:34.920 the listener, the ultimate shortcut to understanding 00:00:34.920 --> 00:00:37.079 this foundational, almost science fiction level 00:00:37.079 --> 00:00:39.539 concept in computer science, which is automated 00:00:39.539 --> 00:00:41.590 reasoning. Yeah, it's a heavy topic, but we're 00:00:41.590 --> 00:00:43.729 going to break it down. We really are. And just 00:00:43.729 --> 00:00:45.789 to give you a sense of our roadmap, we are pulling 00:00:45.789 --> 00:00:48.329 from a really comprehensive Wikipedia article 00:00:48.329 --> 00:00:51.570 on automated reasoning today, along with several 00:00:51.570 --> 00:00:53.549 of its deep -cut reference materials. Some really 00:00:53.549 --> 00:00:55.789 fascinating sources in there. Oh, for sure. And 00:00:55.789 --> 00:00:57.750 for you listening, here is exactly why you need 00:00:57.750 --> 00:00:59.770 to care about this. We are living in a moment 00:00:59.770 --> 00:01:02.549 right now where everyone is using these AI chatbots. 00:01:02.789 --> 00:01:04.250 And well, we all know they hallucinate, right? 00:01:04.489 --> 00:01:07.150 Oh, constantly. Yeah, they just constantly make 00:01:07.150 --> 00:01:09.739 things up. Right. So understanding automa - reasoning 00:01:09.739 --> 00:01:12.599 is the key to knowing how we are actually teaching 00:01:12.599 --> 00:01:15.159 machines not just to guess the next word in a 00:01:15.159 --> 00:01:19.200 sentence but to you know actually think deduce 00:01:19.200 --> 00:01:22.620 and verify truths with absolute certainty it's 00:01:22.620 --> 00:01:25.319 the antidote to the hallucination problem exactly 00:01:25.319 --> 00:01:28.280 okay so Let's unpack this. We need to set the 00:01:28.280 --> 00:01:31.519 foundation first. What exactly is this field 00:01:31.519 --> 00:01:34.299 even trying to achieve? Well, the primary goal 00:01:34.299 --> 00:01:37.180 of automated reasoning is to basically build 00:01:37.180 --> 00:01:39.579 computer programs that allow machines to reason 00:01:39.579 --> 00:01:41.659 completely automatically, or I mean, at least 00:01:41.659 --> 00:01:44.200 as close to completely as mechanically possible. 00:01:44.280 --> 00:01:45.739 So we're not just talking about a chatbot that 00:01:45.739 --> 00:01:48.019 sounds smart. No, no, not at all. We are talking 00:01:48.019 --> 00:01:50.879 about a machine that deduces what is mathematically 00:01:50.879 --> 00:01:54.120 and logically true. The most developed areas 00:01:54.120 --> 00:01:56.340 here are automated theorem, proving where the 00:01:56.340 --> 00:01:58.500 machine actually discovers a proof on its own, 00:01:58.819 --> 00:02:00.760 and automated proof checking. And proof checking 00:02:00.760 --> 00:02:03.159 is where the human does the work first. Exactly. 00:02:03.579 --> 00:02:05.719 A human provides the reasoning, and the machine 00:02:05.719 --> 00:02:08.460 rigorously verifies that absolutely no logical 00:02:08.460 --> 00:02:11.500 laws were broken. OK, so to do that, to actually 00:02:11.500 --> 00:02:14.240 automate reasoning, we have to define what perfect 00:02:14.240 --> 00:02:17.039 reasoning looks like, right? Which means we have 00:02:17.039 --> 00:02:20.150 to step completely away from how the human brain 00:02:20.150 --> 00:02:22.169 actually operates. Right, because human reasoning 00:02:22.169 --> 00:02:25.069 is just incredibly messy. I mean, it relies heavily 00:02:25.069 --> 00:02:28.250 on intuition. Yeah. A human mathematician will 00:02:28.250 --> 00:02:31.590 just, you know, skip a dozen minor logical steps 00:02:31.590 --> 00:02:33.770 and a proof because a connection just feels right 00:02:33.770 --> 00:02:36.650 or it looks obvious based on their past experience. 00:02:36.969 --> 00:02:38.590 You know, when I was reading the sources for 00:02:38.590 --> 00:02:40.610 this, it made me think of walking across a frozen 00:02:40.610 --> 00:02:44.039 lake. Oh, interesting. How so? Well, human intuition 00:02:44.039 --> 00:02:46.340 is like looking at the ice, seeing it look solid 00:02:46.340 --> 00:02:48.919 enough and just walk it across. You take a few 00:02:48.919 --> 00:02:50.599 steps. You don't fall in. So you just assume 00:02:50.599 --> 00:02:52.960 the whole lake is safe. Right. You extrapolate. 00:02:53.039 --> 00:02:57.479 Yeah. But formal logic, on the other hand, is 00:02:57.479 --> 00:03:00.259 like pausing to check the structural integrity 00:03:00.259 --> 00:03:03.479 of every single individual ice crystal before 00:03:03.479 --> 00:03:06.050 you are willing to move even an inch. That is 00:03:06.050 --> 00:03:08.430 a great analogy. And what's fascinating here 00:03:08.430 --> 00:03:11.689 is that a formal proof requires exactly that 00:03:11.689 --> 00:03:13.870 microscopic level of scrutiny. Is relentless. 00:03:14.229 --> 00:03:17.370 It really is. In a formal proof, every single 00:03:17.370 --> 00:03:19.669 logical inference has to be traced all the way 00:03:19.669 --> 00:03:21.710 back to the fundamental axioms of mathematics. 00:03:22.150 --> 00:03:24.590 You absolutely cannot skip steps. No intuitive 00:03:24.590 --> 00:03:27.849 leaps allowed. Zero. you cannot appeal to intuition. 00:03:28.110 --> 00:03:31.169 Even if translating a specific, you know, intuitive 00:03:31.169 --> 00:03:33.509 leap into formal logic would be totally routine 00:03:33.509 --> 00:03:36.590 and boring for a human mathematician, the machine 00:03:36.590 --> 00:03:39.330 demands the intermediate steps. It forces you 00:03:39.330 --> 00:03:41.810 to show your work. Exactly. Because by removing 00:03:41.810 --> 00:03:44.569 human intuition entirely, a formal proof strips 00:03:44.569 --> 00:03:47.150 away the exact places where logical errors like 00:03:47.150 --> 00:03:50.509 to hide. That makes total sense. Yeah. But logic 00:03:50.509 --> 00:03:52.490 isn't always just proving that two plus two is 00:03:52.490 --> 00:03:55.310 four, right? Like life and human thought involve 00:03:55.180 --> 00:03:57.659 a lot of gray areas. Does automated reasoning 00:03:57.659 --> 00:04:00.460 only deal with rigid black and white math? No, 00:04:00.460 --> 00:04:02.479 it goes much deeper than that, actually. The 00:04:02.479 --> 00:04:05.020 field also tackles how to reason by analogy. 00:04:05.219 --> 00:04:06.939 For instance, it works with induction, which 00:04:06.939 --> 00:04:10.379 is drawing a general rule from specific examples. 00:04:10.379 --> 00:04:13.219 OK. And also abduction. Abduction, like an alien 00:04:13.219 --> 00:04:17.019 abduction. Ha, no, logical abduction. It's essentially 00:04:17.019 --> 00:04:19.819 forming the most likely explanation for a set 00:04:19.819 --> 00:04:23.060 of observations, like a doctor diagnosing a patient 00:04:23.060 --> 00:04:25.750 based on a list of symptoms. Oh, I see. Yeah. 00:04:26.089 --> 00:04:28.129 And the sources also highlight something called 00:04:28.129 --> 00:04:31.129 non -monotonic reasoning. Okay, non -monotonic. 00:04:31.269 --> 00:04:32.689 I'm going to need you to break that down for 00:04:32.689 --> 00:04:35.250 me. Sure. So in classical logic, once you prove 00:04:35.250 --> 00:04:38.149 something is true, it stays true forever. Adding 00:04:38.149 --> 00:04:40.990 new information doesn't change it. That's monotonic. 00:04:41.410 --> 00:04:43.529 Right. Non -monotonic reasoning is closer to 00:04:43.529 --> 00:04:46.470 real life. It's when you might draw a logical 00:04:46.470 --> 00:04:48.889 conclusion, but then you learn a new piece of 00:04:48.889 --> 00:04:51.709 information that actually forces you to retract 00:04:51.709 --> 00:04:54.230 that earlier conclusion. So you basically change 00:04:54.230 --> 00:04:56.730 your mind based on new evidence. Right. Exactly. 00:04:56.850 --> 00:04:59.089 And a brilliant example of this from the reference 00:04:59.089 --> 00:05:02.040 materials is John Paul. Oscar system. Oscar? 00:05:02.220 --> 00:05:04.779 Yeah, Oscar is an automated argumentation system. 00:05:05.120 --> 00:05:07.519 So instead of just proving a rigid math theorem, 00:05:08.040 --> 00:05:10.740 it applies constraints of minimality and consistency 00:05:10.740 --> 00:05:14.180 to literally argue with itself. Wait, it argues 00:05:14.180 --> 00:05:17.079 with itself? Yeah, it builds what's called a 00:05:17.079 --> 00:05:19.930 defeasible argument. Defeasible meaning, you 00:05:19.930 --> 00:05:22.430 know, an argument that can be defeated. The system 00:05:22.430 --> 00:05:24.589 generates a claim and then it systematically 00:05:24.589 --> 00:05:27.149 searches its own database for a counter example 00:05:27.149 --> 00:05:30.649 to destroy its own claim. That's wild. It acts 00:05:30.649 --> 00:05:33.129 as both the prosecution and the defense, weighing 00:05:33.129 --> 00:05:35.910 evidence under uncertain conditions. Honestly, 00:05:35.930 --> 00:05:38.589 that sounds computationally exhausting. I mean, 00:05:38.589 --> 00:05:41.470 checking every single mathematical ice crystal 00:05:41.470 --> 00:05:44.269 or having a machine constantly prosecute and 00:05:44.269 --> 00:05:46.170 defend its own thoughts. What's a massive amount 00:05:46.170 --> 00:05:48.439 of processing? It really makes me wonder. what 00:05:48.439 --> 00:05:51.060 forced early computer scientists to even attempt 00:05:51.060 --> 00:05:54.120 this. Did they just like get tired of doing manual 00:05:54.120 --> 00:05:57.319 math? Well, sort of, yeah. The sheer physical 00:05:57.319 --> 00:05:59.620 limitation of the human brain to hold massive 00:05:59.620 --> 00:06:02.079 logical structures without making a single mistake 00:06:02.079 --> 00:06:04.439 was a huge driver. That makes sense. But the 00:06:04.439 --> 00:06:06.680 actual birth of the field is heavily debated. 00:06:07.300 --> 00:06:09.319 Some historians point back to Martin Davis in 00:06:09.319 --> 00:06:12.839 1954. He implemented a concept called Pressberger's 00:06:12.839 --> 00:06:15.500 Decision Procedure, and his program successfully 00:06:15.500 --> 00:06:18.439 proved that the sum of two even numbers is even. 00:06:18.639 --> 00:06:22.170 Okay, 1954. Right. But others argue the field 00:06:22.170 --> 00:06:24.730 really crystallized a few years later at this 00:06:24.730 --> 00:06:28.009 really famous Cornell summer meeting in 1957 00:06:28.009 --> 00:06:30.709 that gathered logicians and computer scientists 00:06:30.709 --> 00:06:32.529 together. You know, the project that really caught 00:06:32.529 --> 00:06:35.490 my eye right in that same window was the logic 00:06:35.490 --> 00:06:38.810 theorist program from 1956. Oh, yes. A classic. 00:06:39.110 --> 00:06:42.529 The creators, Alan Newell, Cliff Shaw and Herbert 00:06:42.529 --> 00:06:45.689 Simon, they pointed their machine at this massive 00:06:45.689 --> 00:06:48.589 book called the Principia Mathematica. What was 00:06:48.589 --> 00:06:51.470 the deal with that specific book? Well, the Principia 00:06:51.470 --> 00:06:55.069 Mathematica was a monumental multi -volume masterwork 00:06:55.069 --> 00:06:58.550 written between 1910 and 1913 by Alfred North 00:06:58.550 --> 00:07:01.029 Whitehead and Bertrand Russell. OK. Their whole 00:07:01.029 --> 00:07:03.930 goal was to derive all mathematical truths purely 00:07:03.930 --> 00:07:07.170 in terms of symbolic logic. It was widely considered 00:07:07.170 --> 00:07:09.970 the absolute Mount Everest of formal logic. So 00:07:09.970 --> 00:07:11.910 naturally, you point the new computer Mount Everest. 00:07:12.129 --> 00:07:15.350 Exactly. So Newell, Shaw, and Simon fed 52 theorems 00:07:15.350 --> 00:07:17.370 from chapter two of this absolute beast of a 00:07:17.370 --> 00:07:19.689 book into their logic theorist program. And the 00:07:19.689 --> 00:07:22.300 machine? proved 38 of them. It did. But here's 00:07:22.300 --> 00:07:25.379 the part that I just couldn't believe. The logic 00:07:25.379 --> 00:07:28.000 theorist didn't just mimic the human proofs that 00:07:28.000 --> 00:07:30.560 Whitehead and Russell had published. For one 00:07:30.560 --> 00:07:33.120 of those theorems, the machine actually found 00:07:33.120 --> 00:07:35.980 a proof that was more elegant. Yeah, that's the 00:07:35.980 --> 00:07:38.959 real kicker. Like it required fewer steps and 00:07:38.959 --> 00:07:41.420 was more logically beautiful than the proof provided 00:07:41.420 --> 00:07:43.740 by two of the greatest minds of the 20th century. 00:07:43.930 --> 00:07:47.449 It totally outlogist its human masters. It found 00:07:47.449 --> 00:07:50.209 a cleaner, purely mechanical path to the truth. 00:07:50.529 --> 00:07:52.449 And the funny thing is, the creators actually 00:07:52.449 --> 00:07:54.589 had trouble getting those results published in 00:07:54.589 --> 00:07:56.629 human mathematics journals at first. You were 00:07:56.629 --> 00:07:59.269 probably defensive. Oh, almost certainly. But 00:07:59.269 --> 00:08:01.970 that success deeply impacted how those scientists 00:08:01.970 --> 00:08:06.009 viewed the future. I mean, by 1958, Newell, Shaw, 00:08:06.069 --> 00:08:08.250 and Simon published a paper containing a quote 00:08:08.250 --> 00:08:11.089 that is just dripping with audacity. Let's hear 00:08:11.089 --> 00:08:14.339 it. They wrote, and I quote, There are now in 00:08:14.339 --> 00:08:16.939 the world machines that think, that learn, and 00:08:16.939 --> 00:08:20.060 that create. Moreover, their ability to do these 00:08:20.060 --> 00:08:22.519 things is going to increase rapidly until the 00:08:22.519 --> 00:08:25.060 range of problems they can handle will be coextensive 00:08:25.060 --> 00:08:27.360 with the range to which the human mind has been 00:08:27.360 --> 00:08:30.220 applied. Wow. They were essentially calling their 00:08:30.220 --> 00:08:33.820 shot in 1958, predicting the entire future of 00:08:33.820 --> 00:08:36.879 AI based on this one breakthrough. They completely 00:08:36.879 --> 00:08:39.539 saw the horizon. But you know, here's where it 00:08:39.539 --> 00:08:41.200 gets really interesting for me though. I have 00:08:41.200 --> 00:08:43.320 to push back a little on what this machine is 00:08:43.320 --> 00:08:45.529 actually doing. Okay, go for it. Aren't these 00:08:45.529 --> 00:08:48.070 early programs, and I mean even the modern ones, 00:08:48.330 --> 00:08:51.149 aren't they just glorified calculators? Like, 00:08:51.149 --> 00:08:54.230 how does a program actually prove a philosophical 00:08:54.230 --> 00:08:56.970 or mathematical concept without just crunching 00:08:56.970 --> 00:08:58.970 numbers really fast? That's a great question. 00:08:59.129 --> 00:09:01.149 And the distinction really lies in the difference 00:09:01.149 --> 00:09:04.389 between arithmetic and formal logic. A calculator 00:09:04.389 --> 00:09:06.690 takes numerical inputs and runs them through 00:09:06.690 --> 00:09:09.590 a hard -wired arithmetic operation. It just computes. 00:09:09.710 --> 00:09:12.190 Right. Numbers in, numbers out. Exactly. But 00:09:12.190 --> 00:09:15.580 automated reasoning systems manipulate They take 00:09:15.580 --> 00:09:18.440 abstract logical concepts and apply a strict 00:09:18.440 --> 00:09:20.679 set of rules to transform those symbols into 00:09:20.679 --> 00:09:23.480 a verified truth. They don't just calculate a 00:09:23.480 --> 00:09:25.879 result, they generate the actual chain of reasoning. 00:09:26.279 --> 00:09:28.460 OK, so if I am a computer scientist trying to 00:09:28.460 --> 00:09:31.559 build one of these logic engines, what kind of 00:09:31.559 --> 00:09:33.500 programming language am I even using to talk 00:09:33.500 --> 00:09:35.480 to the machine? Like, it can't just be standard 00:09:35.480 --> 00:09:38.860 code. No. You are using highly specialized languages 00:09:38.860 --> 00:09:41.419 designed specifically for symbolic manipulation. 00:09:42.259 --> 00:09:44.200 Let's look at a major system from the sources. 00:09:44.730 --> 00:09:47.970 the Boyer -Moore theorem prover, also known as 00:09:47.970 --> 00:09:53.110 NQTHM. NQTHM. Got it. This started in 1971 in 00:09:53.110 --> 00:09:55.549 Edinburgh, and it was built entirely in Pure 00:09:55.549 --> 00:09:58.730 Lisp, which is a very unique, highly recursive 00:09:58.730 --> 00:10:02.190 programming language. Good. And NQTHM had this 00:10:02.190 --> 00:10:05.009 fascinating mechanism for learning. It utilized 00:10:05.009 --> 00:10:07.429 an induction heuristic based entirely on the 00:10:07.429 --> 00:10:09.809 failure of its own symbolic evaluations. How 00:10:09.809 --> 00:10:12.029 does a machine logically learn from a failure? 00:10:12.240 --> 00:10:14.240 Well, imagine the system is trying to prove a 00:10:14.240 --> 00:10:16.240 rule that applies to all number. It tries to 00:10:16.240 --> 00:10:18.440 calculate the steps normally, but it hits a wall 00:10:18.440 --> 00:10:20.559 where a variable is unknown and it just can't 00:10:20.559 --> 00:10:22.879 proceed. Look at dead end. Right. Now a normal 00:10:22.879 --> 00:10:25.240 program would just crash or throw an error, but 00:10:25.240 --> 00:10:27.659 Enki THM was designed to analyze the shape of 00:10:27.659 --> 00:10:30.059 that dead end. The shape of it. Yeah, it looked 00:10:30.059 --> 00:10:32.559 at the exact point where the evaluation failed, 00:10:32.960 --> 00:10:35.399 and it used the structure of that failure to 00:10:35.399 --> 00:10:38.399 guess the underlying mathematical pattern, formulating 00:10:38.399 --> 00:10:41.059 a totally new logical step to bypass the wall. 00:10:41.320 --> 00:10:43.539 Oh, wow. So it literally mapped its own dead 00:10:43.539 --> 00:10:46.220 ends to find the open door. Exactly. That is 00:10:46.220 --> 00:10:47.659 brilliant. But let's bring this into the real 00:10:47.659 --> 00:10:49.820 world for a second, because if we're talking 00:10:49.820 --> 00:10:52.559 about trusting software to, I don't know, fly 00:10:52.559 --> 00:10:54.779 a commercial airplane or manage a national power 00:10:54.779 --> 00:10:57.000 grid, we can't just have a system making good 00:10:57.000 --> 00:10:59.440 guesses. We need Absolute certainty. Which is 00:10:59.440 --> 00:11:02.399 exactly where a system like ROCK comes in. ROCK, 00:11:02.620 --> 00:11:05.139 spelled R -O -Z -Q. Right. Yes, formerly known 00:11:05.139 --> 00:11:07.759 as COCK. This system was developed in France 00:11:07.759 --> 00:11:10.779 and represents just a massive leap forward. ROCK 00:11:10.779 --> 00:11:12.659 operates on something called the Calculus of 00:11:12.659 --> 00:11:16.159 Inductive Constructions, or CIC. Okay, CIC. In 00:11:16.159 --> 00:11:19.019 the CIC framework, a mathematical proof and a 00:11:19.019 --> 00:11:21.440 computer program are treated as the exact same 00:11:21.440 --> 00:11:23.759 mathematical object. Wait, hold on. A proof and 00:11:23.759 --> 00:11:26.269 a program are the same thing. In this specific 00:11:26.269 --> 00:11:29.090 architecture, yes. And because of this, Rock 00:11:29.090 --> 00:11:31.970 can do something incredible. Let's say you write 00:11:31.970 --> 00:11:34.289 a logical specification proving mathematically 00:11:34.289 --> 00:11:36.929 that a specific sorting algorithm is flawless. 00:11:37.090 --> 00:11:39.389 Okay. Rock doesn't just give you a checkmark 00:11:39.389 --> 00:11:42.470 saying your math is right. It mechanically extracts 00:11:42.470 --> 00:11:45.269 that theoretical proof and translates it directly 00:11:45.269 --> 00:11:48.750 into actual executable source code like OCaml 00:11:48.750 --> 00:11:51.649 or Haskell. Are you serious? So you do the pure 00:11:51.649 --> 00:11:53.909 math and the system literally spits out the working 00:11:53.909 --> 00:11:56.799 software? Yes. And because the software was extracted 00:11:56.799 --> 00:11:59.620 mechanically from a formal logical proof, it 00:11:59.620 --> 00:12:01.940 is physically impossible for that resulting code 00:12:01.940 --> 00:12:04.840 to have a logical bug. It is strictly guaranteed 00:12:04.840 --> 00:12:07.419 to behave exactly as specified. That completely 00:12:07.419 --> 00:12:09.860 blows my mind. What is the limit to this? How 00:12:09.860 --> 00:12:12.399 complex of a problem can these systems actually 00:12:12.399 --> 00:12:15.269 handle? The milestones are pretty staggering, 00:12:15.850 --> 00:12:19.029 honestly. Back in 1986, a researcher named Natarajan 00:12:19.029 --> 00:12:21.190 Shankar used the Boyer -Moor system we talked 00:12:21.190 --> 00:12:24.230 about to formalize Gödel's first incompleteness 00:12:24.230 --> 00:12:27.230 theorem. Which is huge. Massive. And by 2004, 00:12:27.490 --> 00:12:29.830 the rock system was used to verify the four -color 00:12:29.830 --> 00:12:32.970 theorem. But one of the most wild examples from 00:12:32.970 --> 00:12:36.570 the sources happened in 2016 regarding the Boolean 00:12:36.570 --> 00:12:40.110 Pythagorean triples problem. Researchers formalized 00:12:40.110 --> 00:12:42.929 this as a Boolean Satisfiability Problem, or 00:12:42.929 --> 00:12:45.769 a SAT problem. I saw the term SAT problem in 00:12:45.769 --> 00:12:48.000 the reading. What actually is that? Basically, 00:12:48.259 --> 00:12:51.019 a SAT problem asks if there is any possible way 00:12:51.019 --> 00:12:53.799 to assign true or false to a massive set of variables 00:12:53.799 --> 00:12:56.820 so that the entire overall equation evaluates 00:12:56.820 --> 00:12:59.500 to true. OK. True or false logic dates. Right. 00:12:59.639 --> 00:13:01.639 For the Pythagorean problem, imagine you have 00:13:01.639 --> 00:13:04.340 to color every whole number either red or blue. 00:13:04.820 --> 00:13:07.340 The rule is that no three numbers that satisfy 00:13:07.340 --> 00:13:09.460 the Pythagorean theorem, like three, four, and 00:13:09.460 --> 00:13:12.259 five, can all be the same color. OK. False. So 00:13:12.259 --> 00:13:13.919 mathematicians wanted to know if you could color 00:13:13.919 --> 00:13:16.000 numbers this way forever without breaking the 00:13:16.000 --> 00:13:18.399 rule. And how did the automated reasoner tackle 00:13:18.399 --> 00:13:21.460 that? By using pure brute force logic combined 00:13:21.460 --> 00:13:23.600 with some really smart pruning techniques, the 00:13:23.600 --> 00:13:25.519 system checked combinations all the way up to 00:13:25.519 --> 00:13:29.379 the number 7 ,824 and proved that, yes, you can 00:13:29.379 --> 00:13:31.580 color them without breaking the rule. But at 00:13:31.580 --> 00:13:34.720 the number 7 ,825, it becomes mathematically 00:13:34.720 --> 00:13:37.320 impossible. And to prove this, the system generated 00:13:37.320 --> 00:13:40.100 a proof file that was 200 terabytes in size. 00:13:40.320 --> 00:13:43.460 200 terabytes. Yeah. No human being could ever 00:13:43.460 --> 00:13:45.820 read that proof in a single lifetime. Not even. 00:13:45.769 --> 00:13:48.330 close, but we trust the result because we mathematically 00:13:48.330 --> 00:13:50.470 trust the logic engine that generated it. But 00:13:50.470 --> 00:13:52.970 wait, if we had the logic theorists outperforming 00:13:52.970 --> 00:13:56.490 humans back in 1956, and we are generating 200 00:13:56.490 --> 00:14:00.210 terabyte proofs today, why hasn't automated reasoning 00:14:00.210 --> 00:14:02.490 just been the dominant force in tech for the 00:14:02.490 --> 00:14:06.090 last 70 years? I mean, the reality of technological 00:14:06.090 --> 00:14:08.590 progress is rarely a straight line. What happened 00:14:08.590 --> 00:14:10.779 in between? Yeah, it definitely wasn't a straight 00:14:10.779 --> 00:14:13.580 line. The field actually hit a massive wall in 00:14:13.580 --> 00:14:16.559 the 1980s and early 1990s. This period is widely 00:14:16.559 --> 00:14:19.179 known as the AI winter. Right, the AI winter. 00:14:19.379 --> 00:14:21.740 The theoretical math was totally sound, but the 00:14:21.740 --> 00:14:24.120 hardware simply couldn't handle the combinatorial 00:14:24.120 --> 00:14:26.440 explosion of data required to run these proofs 00:14:26.440 --> 00:14:28.980 at scale. Funding dried up. So they just got 00:14:28.980 --> 00:14:31.250 stuck waiting for better computers. Pretty much. 00:14:31.710 --> 00:14:33.830 But the researchers didn't stop. They basically 00:14:33.830 --> 00:14:36.269 went into hibernation and optimized their logic 00:14:36.269 --> 00:14:39.529 engines. And the rebound became highly visible 00:14:39.529 --> 00:14:42.889 by 2005. That's when Microsoft started integrating 00:14:42.889 --> 00:14:45.830 automated verification technology directly into 00:14:45.830 --> 00:14:48.389 their internal projects. Oh, interesting. Yeah, 00:14:48.389 --> 00:14:50.669 they even incorporated logical checking into 00:14:50.669 --> 00:14:54.110 the 2012 version of Visual C. So the technology 00:14:54.110 --> 00:14:56.950 moved out of academic labs and straight into 00:14:56.950 --> 00:14:59.509 the software compiling tools used by millions 00:14:59.509 --> 00:15:02.110 of regular developers. So what does this all 00:15:02.110 --> 00:15:04.470 mean for us today right in the middle of this 00:15:04.470 --> 00:15:08.529 massive boom in generative AI? Well in the 2020s 00:15:08.529 --> 00:15:11.210 the focus has violently shifted back to automated 00:15:11.210 --> 00:15:14.190 reasoning as the ultimate cure for the AI hallucination 00:15:14.190 --> 00:15:15.710 problem we talked about at the start. Bringing 00:15:15.710 --> 00:15:18.549 it full circle. Exactly. Large language models 00:15:18.549 --> 00:15:20.750 guess the next word based on statistical patterns. 00:15:20.850 --> 00:15:23.159 They don't actually understand truth. So to fix 00:15:23.159 --> 00:15:25.220 this, researchers are building reasoning language 00:15:25.220 --> 00:15:28.039 models like DeepSeq R1, which are designed to 00:15:28.039 --> 00:15:30.519 literally spend additional computational time 00:15:30.519 --> 00:15:32.840 pondering a problem before they generate a single 00:15:32.840 --> 00:15:35.460 word of output. But how does spending more time 00:15:35.460 --> 00:15:39.500 pondering actually fix the hallucination fundamentally? 00:15:40.259 --> 00:15:42.080 Like, isn't it just thinking about a wrong answer 00:15:42.080 --> 00:15:44.899 longer? If we connect this to the bigger picture, 00:15:45.220 --> 00:15:47.320 it leads us to the absolute bleeding edge of 00:15:47.320 --> 00:15:50.639 the field. Neuro -symbolic architectures. This 00:15:50.639 --> 00:15:52.919 is the marriage of two completely different eras 00:15:52.919 --> 00:15:56.480 of computer science. Okay, neuro -symbolic. So 00:15:56.480 --> 00:15:58.440 the neuro part being the modern neural networks 00:15:58.440 --> 00:16:01.120 and the symbolic part being the formal logic 00:16:01.120 --> 00:16:03.440 engines like rock that we just discussed. You 00:16:03.440 --> 00:16:06.000 nailed it! It sounds kind of like pairing a wildly 00:16:06.000 --> 00:16:09.539 creative architect who dreams up impossible gravity 00:16:09.539 --> 00:16:12.659 -defying buildings with a ruthless safety inspector 00:16:12.659 --> 00:16:15.120 who checks the math on every single load -bearing 00:16:15.120 --> 00:16:17.620 beam before a single brick is laid. That is a 00:16:17.620 --> 00:16:19.480 perfect way to look at it. The neural network 00:16:19.480 --> 00:16:22.019 provides the intuition, the pattern recognition, 00:16:22.299 --> 00:16:24.960 and those creative leaps. It drafts the blueprint. 00:16:25.179 --> 00:16:27.259 Right. But before that answer is ever shown to 00:16:27.259 --> 00:16:30.320 you, the symbolic logic engine takes over. It 00:16:30.320 --> 00:16:32.559 attempts to formally prove the neural network's 00:16:32.559 --> 00:16:35.120 generated answer using strict mathematical axiom. 00:16:35.139 --> 00:16:37.639 And if it fails? If the safety inspector finds 00:16:37.639 --> 00:16:41.259 a logical flaw, it rejects the answer and forces 00:16:41.259 --> 00:16:44.309 the neural network to try again. The entire goal 00:16:44.309 --> 00:16:47.590 is to give AI a built -in, mathematically flawless 00:16:47.590 --> 00:16:51.090 lie detector. Man, it really is the invisible 00:16:51.090 --> 00:16:53.269 safety net for our modern digital infrastructure. 00:16:53.409 --> 00:16:56.250 Yeah. Because as we discussed, we are handing 00:16:56.250 --> 00:16:59.230 over control of power grids, financial markets, 00:16:59.330 --> 00:17:02.250 and aviation software to machines. If there is 00:17:02.250 --> 00:17:04.630 a logical bug in those systems, the consequences 00:17:04.630 --> 00:17:07.349 are just catastrophic. Absolutely. And to keep 00:17:07.349 --> 00:17:09.609 improving that safety net, the community maintains 00:17:09.609 --> 00:17:12.589 this massive, constantly updated library called 00:17:12.589 --> 00:17:16.289 the TPTP, the Thousands of Problems for Theorem 00:17:16.289 --> 00:17:18.480 Provers. Library of problems. Yeah. It provides 00:17:18.480 --> 00:17:20.500 a standardized battleground for these systems. 00:17:20.980 --> 00:17:22.859 There are even regular competitions held at the 00:17:22.859 --> 00:17:25.220 KD conference where different automated theorem 00:17:25.220 --> 00:17:27.019 provers from all around the world compete to 00:17:27.019 --> 00:17:29.640 see which system can solve the most complex logic 00:17:29.640 --> 00:17:33.000 puzzles from the TPTP library. It is literally 00:17:33.000 --> 00:17:35.299 the Olympics for artificial logic. It really 00:17:35.299 --> 00:17:38.380 is. I love that so much. An international competition 00:17:38.380 --> 00:17:42.039 to build a sharper, faster truth machine. As 00:17:42.039 --> 00:17:44.220 we wrap up this deep dive, want to turn it over 00:17:44.220 --> 00:17:46.900 to you for the final word, looking at this entire 00:17:46.900 --> 00:17:50.200 journey from the 1950s to today. What is the 00:17:50.200 --> 00:17:51.839 biggest takeaway the listener should be chewing 00:17:51.839 --> 00:17:54.500 on? You know, I keep going back to that initial 00:17:54.500 --> 00:17:57.279 shock in 1956 with the logic theorist. Yeah, 00:17:57.279 --> 00:18:00.200 that was wild. The machine found a more elegant 00:18:00.200 --> 00:18:02.400 mathematical proof than Whitehead and Russell, 00:18:02.759 --> 00:18:05.339 and it did it by mechanically applying logical 00:18:05.339 --> 00:18:08.339 rules without using a single drop of human intuition. 00:18:08.559 --> 00:18:10.960 Right. If a machine can create a more elegant 00:18:10.960 --> 00:18:14.019 truth through sheer mechanical deduction, it 00:18:14.019 --> 00:18:16.220 really forces us to ask a rather uncomfortable 00:18:16.220 --> 00:18:18.920 question. Which is? Is human intuition actually 00:18:18.920 --> 00:18:21.319 the magical, irreplaceable source of creativity 00:18:21.319 --> 00:18:24.549 we think? it is? Or is intuition just a biological 00:18:24.549 --> 00:18:27.450 shortcut, a messy adaptation our brains use simply 00:18:27.450 --> 00:18:29.430 because we lack the processing power to run the 00:18:29.430 --> 00:18:32.789 formal logic? Our greatest aha moments just workarounds 00:18:32.789 --> 00:18:37.089 for our biological hardware limits. That is a 00:18:37.089 --> 00:18:39.309 wild thought to leave on. Thank you so much for 00:18:39.309 --> 00:18:40.890 joining us on this journey into the invisible 00:18:40.890 --> 00:18:43.529 logic running our world. Keep questioning your 00:18:43.529 --> 00:18:45.690 own assumptions. Keep checking those ice crystals. 00:18:45.970 --> 00:18:48.089 We will catch you on the next Deep Dive.