WEBVTT 00:00:00.000 --> 00:00:02.439 Imagine you're sitting in a command bunker, right? 00:00:02.799 --> 00:00:05.040 You're staring at a radar screen and you have 00:00:05.040 --> 00:00:07.259 exactly three minutes to decide if you were going 00:00:07.259 --> 00:00:09.439 to launch a nuclear counter -strike. Yeah. The 00:00:09.439 --> 00:00:11.699 alarm is blaring. And you just don't know for 00:00:11.699 --> 00:00:13.919 sure if the blips on the screen are incoming 00:00:13.919 --> 00:00:18.379 enemy missiles or just a really poorly timed 00:00:18.379 --> 00:00:20.539 computer glitch. Right. How do you make that 00:00:20.539 --> 00:00:23.410 choice? You can't know the truth. So you basically 00:00:23.410 --> 00:00:26.170 assume the absolute worst. Yeah, it is the ultimate 00:00:26.170 --> 00:00:28.309 high stakes gamble. I mean, you are forced to 00:00:28.309 --> 00:00:31.170 act against a potentially hostile universe where 00:00:31.170 --> 00:00:34.340 guessing wrong literally means game over. Exactly. 00:00:34.719 --> 00:00:36.759 Welcome to this deep dive, everyone. I'm so glad 00:00:36.759 --> 00:00:40.140 you could join us today. We are exploring a dense 00:00:40.140 --> 00:00:43.200 but honestly highly consequential Wikipedia article 00:00:43.200 --> 00:00:45.600 on a mathematical decision rule called Minimax. 00:00:45.840 --> 00:00:48.359 It's quite the topic. It really is. Our mission 00:00:48.359 --> 00:00:50.920 for you today is to demystify this seemingly 00:00:50.920 --> 00:00:53.420 abstract math concept. Yeah. We're going to reveal 00:00:53.420 --> 00:00:55.939 how it secretly governs everything from, well, 00:00:56.079 --> 00:00:58.600 the way artificial intelligence plays chess to 00:00:58.600 --> 00:01:01.479 how we vote in our democracies and even how philosophers 00:01:01.479 --> 00:01:04.739 define a completely just society. It is quite 00:01:04.739 --> 00:01:07.840 the journey. And fittingly, our visual backdrop 00:01:07.840 --> 00:01:12.599 today is this shifting conceptual array of complex 00:01:12.599 --> 00:01:15.959 game trees and branching timelines. Yeah, representing 00:01:15.959 --> 00:01:18.019 the endless exploration of all those possible 00:01:18.019 --> 00:01:20.900 futures. Okay, let's unpack this. Before we can 00:01:20.900 --> 00:01:23.099 talk about supercomputers or the philosophy of 00:01:23.099 --> 00:01:25.500 justice, we really have to establish the basic 00:01:25.500 --> 00:01:28.060 mechanics of navigating a worst -case scenario. 00:01:28.859 --> 00:01:30.980 What exactly are we looking at here? Well, at 00:01:30.980 --> 00:01:34.500 its core, MiniMax is a decision rule used for 00:01:34.500 --> 00:01:36.780 minimizing the possible loss in a worst -case 00:01:36.780 --> 00:01:39.739 scenario. It was originally formulated for game 00:01:39.739 --> 00:01:42.700 theory, specifically for games with multiple 00:01:42.700 --> 00:01:45.019 players where, you know, one person's win is 00:01:45.019 --> 00:01:47.560 exactly another person's loss. A zero -sum situation. 00:01:47.879 --> 00:01:50.420 Exactly. Now, when you are dealing with gains 00:01:50.420 --> 00:01:52.700 rather than losses, the rule is flipped and is 00:01:52.700 --> 00:01:55.500 referred to as Maximin. Praximin. Right. That 00:01:55.500 --> 00:01:57.819 means you are trying to maximize your minimum 00:01:57.819 --> 00:02:00.439 gain. Maximize the minimum gain. I'll be honest, 00:02:00.700 --> 00:02:02.400 that sounds like a riddle you'd have to solve 00:02:02.400 --> 00:02:05.040 to cross a troll's bridge. I know, I know. It 00:02:05.040 --> 00:02:06.980 is a bit counterintuitive until you break down 00:02:06.980 --> 00:02:09.919 the mechanics. The critical difference between 00:02:09.919 --> 00:02:12.460 the two really comes down to the order of operations. 00:02:13.189 --> 00:02:16.590 Think of it sequentially. OK. In Maximin, the 00:02:16.590 --> 00:02:19.490 maximization comes after the minimization. You 00:02:19.490 --> 00:02:21.770 try to maximize your value before knowing what 00:02:21.770 --> 00:02:24.409 the other players will do. You are assuming the 00:02:24.409 --> 00:02:26.330 worst and just making the best of it. Right. 00:02:26.530 --> 00:02:28.669 But in Minimax, you are actually in a much better 00:02:28.669 --> 00:02:30.909 position. You maximize your value knowing what 00:02:30.909 --> 00:02:33.590 the others did. Oh, OK. Let me try to put this 00:02:33.590 --> 00:02:35.530 into the real world. Yeah. Let's say you are 00:02:35.530 --> 00:02:37.509 deciding whether to pack an umbrella for a trip. 00:02:37.680 --> 00:02:41.020 Packing that umbrella just in case is a classic 00:02:41.020 --> 00:02:43.219 maximum strategy, right? Too precisely. You are 00:02:43.219 --> 00:02:45.900 maximizing your comfort in the absolute worst 00:02:45.900 --> 00:02:48.400 -case scenario, which is a massive downpour, 00:02:48.900 --> 00:02:50.400 before you actually know what the weather will 00:02:50.400 --> 00:02:52.879 do. You secure your baseline of comfort first. 00:02:53.080 --> 00:02:56.560 That is a perfect everyday application. You are 00:02:56.560 --> 00:02:59.379 looking at the worst possible outcomes for every 00:02:59.379 --> 00:03:01.139 choice you could make, and you are selecting 00:03:01.139 --> 00:03:03.039 the choice where that worst -case outcome is 00:03:03.039 --> 00:03:05.629 the least damaging. Okay, got it. And the source 00:03:05.629 --> 00:03:08.250 text gives a very specific pure math example 00:03:08.250 --> 00:03:11.270 of this using a grid, or a payoff matrix, with 00:03:11.270 --> 00:03:13.030 two players. They call them a row player and 00:03:13.030 --> 00:03:15.550 a column player. Right. And in the text, it's 00:03:15.550 --> 00:03:18.310 just this dry grid of numbers. If the row player 00:03:18.310 --> 00:03:20.870 chooses the top row, it's this number. If they 00:03:20.870 --> 00:03:23.849 choose the bottom row, it's that number. It's 00:03:23.849 --> 00:03:25.590 a bit hard to visualize. It can be dry, yeah. 00:03:25.629 --> 00:03:28.090 So let's make it visceral. Let's imagine those 00:03:28.090 --> 00:03:31.830 choices, top, middle, and bottom, as three actual 00:03:31.830 --> 00:03:33.870 physical doors you have to walk through. Oh, 00:03:33.870 --> 00:03:36.610 I like that. Let's look at the row player's options, 00:03:36.689 --> 00:03:39.210 assuming they are only using pure strategies. 00:03:39.289 --> 00:03:41.930 Meaning? That simply means they pick one door 00:03:41.930 --> 00:03:44.169 and stick to it. There's no trickery or flipping 00:03:44.169 --> 00:03:46.689 coins. If the row player walks through the top 00:03:46.689 --> 00:03:48.969 door, the text tells us their payoff will be 00:03:48.969 --> 00:03:52.229 either a 3 or a 2. OK, not bad. If they walk 00:03:52.229 --> 00:03:54.789 through the middle door, it will be a 5 or a 00:03:54.789 --> 00:03:57.729 painful penalty of negative 10. And if they choose 00:03:57.729 --> 00:04:00.729 the bottom door, the payoffs are either a 4 or 00:04:00.729 --> 00:04:03.090 a devastating trap door, dropping them to negative 00:04:03.090 --> 00:04:05.479 100. See, when you phrase it like that, looking 00:04:05.479 --> 00:04:08.139 at that bottom door is terrifying. I mean, I 00:04:08.139 --> 00:04:10.060 could get a solid four, but it could also fall 00:04:10.060 --> 00:04:12.659 into a pit of negative 100. That's a massive 00:04:12.659 --> 00:04:15.219 game -ending penalty. Absolutely. And the middle 00:04:15.219 --> 00:04:17.019 door isn't great either, with a risk of losing 00:04:17.019 --> 00:04:20.339 10. Right. So following the Maximum Rule, the 00:04:20.339 --> 00:04:22.480 row player doesn't even look at the potential 00:04:22.480 --> 00:04:25.279 rewards. They strictly look at the worst possible 00:04:25.279 --> 00:04:27.819 outcome for each choice. So they just focus on 00:04:27.819 --> 00:04:30.920 the floors, not the ceilings. Exactly. Top door's 00:04:30.920 --> 00:04:33.860 worst case is a gain of 2. Middle door's worst 00:04:33.860 --> 00:04:36.860 case is losing 10. Bottom door's worst case is 00:04:36.860 --> 00:04:41.240 losing 100. The highest or, I guess, most survivable 00:04:41.240 --> 00:04:44.259 of those minimums is 2. Therefore, the row player 00:04:44.259 --> 00:04:47.139 chooses the top door. guaranteeing a payoff of 00:04:47.139 --> 00:04:49.420 at least two. So it's not about winning big, 00:04:49.600 --> 00:04:52.180 it's about not losing everything. They are playing 00:04:52.180 --> 00:04:55.120 it incredibly safe. And I assume the column player, 00:04:55.379 --> 00:04:57.160 choosing between their own left and right options, 00:04:57.420 --> 00:05:00.480 does the exact same defensive calculus. Yes, 00:05:00.480 --> 00:05:02.920 they do. The column player evaluates left and 00:05:02.920 --> 00:05:04.720 right. If they play left, their absolute worst 00:05:04.720 --> 00:05:07.279 payoff is zero. If they play right, their worst 00:05:07.279 --> 00:05:09.620 payoff is negative 20. So they go left. Right. 00:05:09.720 --> 00:05:12.540 They choose left to secure a baseline of at least 00:05:12.540 --> 00:05:14.779 zero, stepping right around that negative 20 00:05:14.779 --> 00:05:16.879 trap. OK. That makes sense when the board is 00:05:16.879 --> 00:05:19.540 static. You look at the trap doors. You calculate 00:05:19.540 --> 00:05:21.620 the depth of the spike. and you choose the safest 00:05:21.620 --> 00:05:25.399 path. But a static grid is one thing. What happens 00:05:25.399 --> 00:05:28.259 when we step into active competition? Yeah, that's 00:05:28.259 --> 00:05:30.019 where it gets messy. Like what happens when we 00:05:30.019 --> 00:05:33.779 look at a pure two -player zero -sum game? The 00:05:33.779 --> 00:05:36.920 dynamic completely fractures because in a zero 00:05:36.920 --> 00:05:40.060 -sum game, the environment isn't neutral. Your 00:05:40.060 --> 00:05:42.480 opponent is actively trying to minimize your 00:05:42.480 --> 00:05:44.819 score in order to maximize their own. Right. 00:05:44.920 --> 00:05:46.819 If you win a slice of pizza, they physically 00:05:46.819 --> 00:05:49.600 lose a slice of pizza. There is no mutual benefit. 00:05:49.720 --> 00:05:51.639 And the source mentions that in these zero -sum 00:05:51.639 --> 00:05:53.980 games, the minimax solution is the same as the 00:05:53.980 --> 00:05:56.680 Nash equilibrium. But walk me through the how. 00:05:57.019 --> 00:05:59.600 How does the math hold up when someone is actively 00:05:59.600 --> 00:06:01.839 hunting you? Well, the source material illustrates 00:06:01.839 --> 00:06:05.339 this with a complex 3x3 matrix involving player 00:06:05.339 --> 00:06:08.939 A and player B. Player A has choices A1, A2, 00:06:09.000 --> 00:06:12.459 and A3. Player B has B1, B2, and B3. Because 00:06:12.459 --> 00:06:14.839 it's zero -sum, whatever the payoff is for player 00:06:14.839 --> 00:06:17.639 A, the payoff for player B is the exact same 00:06:17.639 --> 00:06:20.500 number, just with the sign reversed. So if player 00:06:20.500 --> 00:06:24.079 A wins 5, player B inherently loses 5. Okay, 00:06:24.079 --> 00:06:26.879 so it's a direct tactical duel. Exactly. So let's 00:06:26.879 --> 00:06:29.839 look at player A's simple maximum choice. If 00:06:29.839 --> 00:06:32.879 we evaluate all the rows, the math tells us choice 00:06:32.879 --> 00:06:36.600 A2 is the safest. The absolute worst possible 00:06:36.600 --> 00:06:39.439 result if player A chooses A2 is having to pay 00:06:39.439 --> 00:06:42.360 one to player B. Okay, not a huge loss. For player 00:06:42.360 --> 00:06:44.439 B doing the same defensive analysis on their 00:06:44.439 --> 00:06:47.379 options, their simple maximum choice is B2, because 00:06:47.379 --> 00:06:50.980 the worst possible result is A0 payment, no loss, 00:06:51.040 --> 00:06:53.170 no gain. But wait, let me push back on this. 00:06:53.209 --> 00:06:55.370 Go for it. If we are playing this game and you 00:06:55.370 --> 00:06:57.410 are player B and you believe that I'm going to 00:06:57.410 --> 00:07:00.029 play it safe and choose A2, you aren't going 00:07:00.029 --> 00:07:02.470 to just sit there and choose B2 for a zero payout. 00:07:02.730 --> 00:07:04.470 You're going to adapt. You are going to switch 00:07:04.470 --> 00:07:07.050 your move to B1 because the matrix shows that 00:07:07.050 --> 00:07:10.129 against my A2, your B1 gives you a gain of one. 00:07:10.370 --> 00:07:12.350 Right. And you've spotted the foundational flaw 00:07:12.350 --> 00:07:15.209 of applying static rules to dynamic human behavior. 00:07:15.550 --> 00:07:18.720 But the flaw doesn't stop there. Because if I 00:07:18.720 --> 00:07:21.480 realize that you are going to switch to B1 to 00:07:21.480 --> 00:07:24.399 try and snatch that one point, I'm going to abandon 00:07:24.399 --> 00:07:27.279 my safe A2 strategy. I'm going to switch to A1 00:07:27.279 --> 00:07:31.019 because the grid says A1 against your B1 gives 00:07:31.019 --> 00:07:33.939 me a massive gain of three. Yep. It's an endless 00:07:33.939 --> 00:07:36.720 exhausting loop of second guessing. I know that 00:07:36.720 --> 00:07:38.930 you know that. I know that you know. It never 00:07:38.930 --> 00:07:41.850 stops. What's fascinating here is that game theorists 00:07:41.850 --> 00:07:44.610 mathematically recognize this exact paranoia. 00:07:45.009 --> 00:07:48.149 The simple pure strategy completely breaks down 00:07:48.149 --> 00:07:50.910 here. It is inherently unstable. So how do they 00:07:50.910 --> 00:07:53.470 solve it? Through two mechanical steps. First, 00:07:53.670 --> 00:07:56.009 you trim the fat. you eliminate what they call 00:07:56.009 --> 00:07:58.410 dominated choices. Dominated choices. Let's translate 00:07:58.410 --> 00:08:00.730 that. That just means moves that are mathematically 00:08:00.730 --> 00:08:02.750 embarrassing to make, right? Moves that fail 00:08:02.750 --> 00:08:04.589 no matter what the opponent does. Precisely. 00:08:04.810 --> 00:08:07.889 In the text matrix, player A will never, under 00:08:07.889 --> 00:08:11.129 any circumstance, choose A3, because their other 00:08:11.129 --> 00:08:13.750 options always yield better results against any 00:08:13.750 --> 00:08:15.730 of V's moves. You just snip that branch off the 00:08:15.730 --> 00:08:18.089 tree completely. Makes sense. But, as you pointed 00:08:18.089 --> 00:08:20.129 out, even with a smaller tree, we still have 00:08:20.129 --> 00:08:22.269 that endless loop of second guessing. Right. 00:08:22.290 --> 00:08:24.459 So how do you actually break the loop? You introduce 00:08:24.459 --> 00:08:27.139 the concept of mixed strategies. This means, 00:08:27.300 --> 00:08:29.660 instead of picking one move 100 % of the time, 00:08:29.899 --> 00:08:32.759 you use probabilities. You randomize your choices 00:08:32.759 --> 00:08:35.159 based on specific mathematical weights. Wait, 00:08:35.159 --> 00:08:37.120 really? You stop trying to outsmart the opponent 00:08:37.120 --> 00:08:38.940 and you turn yourself into a random number generator? 00:08:39.200 --> 00:08:42.440 Essentially, yes. In a zero -sum game, being 00:08:42.440 --> 00:08:45.419 predictable is the same as being dead. In this 00:08:45.419 --> 00:08:48.559 specific matrix from the source, player A can 00:08:48.559 --> 00:08:51.240 guarantee stability by choosing A1 with a one 00:08:51.240 --> 00:08:53.679 in six probability and A2 with a five in six 00:08:53.679 --> 00:08:56.740 probability. On the other side, player B secures 00:08:56.740 --> 00:08:58.960 their defensive position by choosing B1 with 00:08:58.960 --> 00:09:01.840 a one third probability and B2 with a two thirds 00:09:01.840 --> 00:09:04.220 probability. But what does that actually do? 00:09:04.340 --> 00:09:06.320 I'm rolling a die now instead of making a choice. 00:09:06.700 --> 00:09:09.559 By adopting those specific rigid probabilities, 00:09:10.059 --> 00:09:12.299 both players mathematically secure an expected 00:09:12.299 --> 00:09:15.820 payoff. or an expected gain of exactly one third. 00:09:16.039 --> 00:09:18.600 Meaning, if you play this game a thousand times, 00:09:18.860 --> 00:09:21.360 no matter what psychological mind games the other 00:09:21.360 --> 00:09:23.899 person tries to play, the math dictates that 00:09:23.899 --> 00:09:26.700 the value settles at one third. They've created 00:09:26.700 --> 00:09:30.620 concrete mathematical stability out of pure chaotic 00:09:30.620 --> 00:09:33.240 second -guessing. Here's where it gets really 00:09:33.240 --> 00:09:36.350 interesting for me. Because humans might try 00:09:36.350 --> 00:09:38.830 to use mixed strategies by flipping a coin or 00:09:38.830 --> 00:09:41.629 trying to be erratic, but computers, computers 00:09:41.629 --> 00:09:44.809 don't guess. They have the processing power to 00:09:44.809 --> 00:09:48.019 map out these possibilities explicitly. This 00:09:48.019 --> 00:09:50.639 bridges the abstract mathematical theory straight 00:09:50.639 --> 00:09:53.500 into real -world technology. Yes. This is the 00:09:53.500 --> 00:09:56.000 realm of combinatorial game theory. This is where 00:09:56.000 --> 00:09:58.379 the minimax algorithm becomes the literal brain 00:09:58.379 --> 00:10:00.559 of artificial intelligence for games like tic 00:10:00.559 --> 00:10:03.379 -tac -toe, checkers, or chess. And it does this 00:10:03.379 --> 00:10:05.639 by working backwards. I love the visual of this. 00:10:05.759 --> 00:10:08.159 It's like the AI is a paranoid mental time traveler. 00:10:08.600 --> 00:10:10.899 The computer looks into every possible future 00:10:10.899 --> 00:10:13.190 timeline of the chess game. It assumes that you, 00:10:13.509 --> 00:10:16.169 its human opponent, will always make the absolute 00:10:16.169 --> 00:10:19.289 best, most punishing counter move in every single 00:10:19.289 --> 00:10:22.870 timeline. And then, knowing how every timeline 00:10:22.870 --> 00:10:26.090 inevitably ends, it travels back to the present 00:10:26.090 --> 00:10:28.950 moment on the board and chooses the single path 00:10:28.950 --> 00:10:31.309 that guarantees the least amount of destruction. 00:10:31.480 --> 00:10:34.240 That is a highly accurate way to conceptualize 00:10:34.240 --> 00:10:37.059 the code. The AI treats itself as the maximizing 00:10:37.059 --> 00:10:39.299 player and its opponent as the minimizing player. 00:10:39.759 --> 00:10:42.200 The algorithm assigns a concrete numerical value 00:10:42.200 --> 00:10:45.059 to the end of the game. If the AI wins, that 00:10:45.059 --> 00:10:47.820 game state gets a value of plus one or sometimes 00:10:47.820 --> 00:10:51.259 positive infinity. If the opponent wins, that 00:10:51.259 --> 00:10:54.059 timeline gets a value of negative one or negative 00:10:54.059 --> 00:10:56.259 infinity. Layer after layer, it's just calculating, 00:10:56.620 --> 00:10:59.019 if I do this, they do that to minimize my score, 00:10:59.120 --> 00:11:01.360 then I do this to maximize it. Yes. And the text 00:11:01.360 --> 00:11:03.299 brings up the most famous historical example 00:11:03.299 --> 00:11:06.659 of this. The IBM chess computer Deep Blue beating 00:11:06.659 --> 00:11:09.299 the reigning human world champion, Garry Kasparov, 00:11:09.559 --> 00:11:12.879 in 1997. The source notes, Deep Blue looked ahead 00:11:12.879 --> 00:11:16.059 at least 12 plies. A ply being just one turn 00:11:16.059 --> 00:11:19.019 taken by one player. 12 moves deep into the future. 00:11:19.259 --> 00:11:21.059 Which sounds incredibly deep, but chess is a 00:11:21.059 --> 00:11:23.840 massive game. Even a supercomputer can't actually 00:11:23.840 --> 00:11:25.960 map every single timeline in chess all the way 00:11:25.960 --> 00:11:29.529 to a checkmate, can it? It cannot. No. And this 00:11:29.529 --> 00:11:33.049 is the great limitation of a naive minimax algorithm. 00:11:33.649 --> 00:11:35.690 The source material refers to this limitation 00:11:35.690 --> 00:11:38.350 as the effective branching factor. Let's define 00:11:38.350 --> 00:11:41.169 that. In a game like chess, every single turn 00:11:41.169 --> 00:11:44.929 offers dozens of possible legal moves. For every 00:11:44.929 --> 00:11:47.450 one of those moves, the opponent has dozens of 00:11:47.450 --> 00:11:50.250 responses. The number of possible game states 00:11:50.250 --> 00:11:53.470 doesn't just grow, it explodes exponentially. 00:11:53.549 --> 00:11:55.289 Right. It gets out of hand fast. Within a few 00:11:55.289 --> 00:11:57.850 moves, you are looking at billions of timelines. 00:11:58.509 --> 00:12:01.350 It is computationally impossible for any machine 00:12:01.350 --> 00:12:03.730 to map the entire game of chess from the first 00:12:03.730 --> 00:12:05.730 move to the last. So the time machine breaks 00:12:05.730 --> 00:12:07.889 down because there are simply too many alternate 00:12:07.889 --> 00:12:10.700 dimensions to visit. The clock is ticking. So 00:12:10.700 --> 00:12:13.820 how did Deep Blue actually beat Kasparov if it 00:12:13.820 --> 00:12:15.700 couldn't see to the end of the game? By using 00:12:15.700 --> 00:12:18.259 two critical mathematical workarounds. First, 00:12:18.399 --> 00:12:20.440 they used a technique called alpha -beta pruning. 00:12:20.820 --> 00:12:23.080 This dramatically improves performance without 00:12:23.080 --> 00:12:25.320 changing the final decision. Explain the how 00:12:25.320 --> 00:12:27.779 of that. How do you skip calculating a timeline 00:12:27.779 --> 00:12:30.309 without missing something important? Think of 00:12:30.309 --> 00:12:33.330 the algorithm searching down a massive branching 00:12:33.330 --> 00:12:36.629 tree of possibilities. Let's say it's evaluating 00:12:36.629 --> 00:12:39.549 a specific sequence of moves, and three steps 00:12:39.549 --> 00:12:42.509 down this timeline, it sees that the human opponent 00:12:42.509 --> 00:12:45.830 has a move that captures the AI's queen for absolutely 00:12:45.830 --> 00:12:49.490 free. A catastrophic loss. Right. The AI doesn't 00:12:49.490 --> 00:12:52.509 need to calculate the next 20 moves of that specific 00:12:52.509 --> 00:12:55.950 timeline to know it's a terrible path. The math 00:12:55.950 --> 00:12:58.409 proves that the maximum possible score of this 00:12:58.409 --> 00:13:00.730 branch is already lower than a safer branch it 00:13:00.730 --> 00:13:03.169 found earlier. So it simply stops searching. 00:13:03.309 --> 00:13:05.350 Oh, wow. Yeah, it takes a pair of mathematical 00:13:05.350 --> 00:13:08.129 shears and prunes that dead branch off the tree. 00:13:08.490 --> 00:13:10.690 It doesn't waste processing power calculating 00:13:10.690 --> 00:13:13.490 exactly how badly it will lose. It just knows 00:13:13.490 --> 00:13:15.409 never to go down that path. It cuts the dead 00:13:15.409 --> 00:13:17.429 weight. That's brilliant. But even with a pruned 00:13:17.429 --> 00:13:20.250 tree, you still can't see the final check made. 00:13:20.590 --> 00:13:22.669 At some point, the computer just has to guess, 00:13:22.809 --> 00:13:25.500 right? Exactly, and that brings us to the second 00:13:25.500 --> 00:13:28.580 workaround heuristic evaluation functions. Since 00:13:28.580 --> 00:13:31.379 the computer can't reach the absolute final winning 00:13:31.379 --> 00:13:34.399 or losing state of the game, it has to forcefully 00:13:34.399 --> 00:13:38.200 stop calculating at a certain depth, say 12 plies. 00:13:38.820 --> 00:13:41.259 At that exact point, it uses a heuristic which 00:13:41.259 --> 00:13:43.519 is essentially an educated mathematical guess. 00:13:43.879 --> 00:13:46.620 But how does a machine guess? How does it evaluate 00:13:46.620 --> 00:13:49.960 a board without a clear winner? It translates 00:13:49.960 --> 00:13:53.080 abstract concepts into rigid numbers. It evaluates 00:13:53.080 --> 00:13:55.039 the current board state by looking at material. 00:13:55.279 --> 00:13:57.480 Maybe a pawn is worth one point, a knight is 00:13:57.480 --> 00:14:00.539 three. It looks at board control, assigning fractional 00:14:00.539 --> 00:14:02.740 points for every square a piece threatens. Okay, 00:14:02.840 --> 00:14:05.340 I see. It tallies all these microadvantages up 00:14:05.340 --> 00:14:08.039 and assigns a finite numerical value to that 00:14:08.039 --> 00:14:10.519 timeline. It's a mathematically programmed intuition 00:14:10.519 --> 00:14:12.899 representing the belief that this path will eventually 00:14:12.899 --> 00:14:16.159 lead to a win. So it's forced to rely on a programmed 00:14:16.159 --> 00:14:18.419 gut feeling because the perfect information of 00:14:18.419 --> 00:14:21.259 the endgame is out of reach. But Deep Blue's 00:14:21.259 --> 00:14:23.600 universe, even with billions of branches, is 00:14:23.600 --> 00:14:26.340 still perfect. The chessboard has edges. It has 00:14:26.340 --> 00:14:29.179 strict rules. Real life doesn't. So how does 00:14:29.179 --> 00:14:31.720 this math survive when we step out of the computer 00:14:31.720 --> 00:14:34.639 and into the chaos of human society where we 00:14:34.639 --> 00:14:37.159 don't even know all the rules? How do we use 00:14:37.159 --> 00:14:40.080 MiniMax when there is no clearly defined opponent 00:14:40.080 --> 00:14:42.799 sitting across from us? It translates surprisingly 00:14:42.799 --> 00:14:46.120 well, particularly into individual decision -making 00:14:46.120 --> 00:14:49.580 under severe real -world uncertainty. The source 00:14:49.580 --> 00:14:51.960 gives a great example, prospecting for minerals. 00:14:52.779 --> 00:14:55.679 This is an incredibly expensive endeavor. If 00:14:55.679 --> 00:14:58.080 a mining company drills and finds nothing, they 00:14:58.080 --> 00:15:00.559 waste a fortune. If they find minerals, the rewards 00:15:00.559 --> 00:15:02.960 are astronomical. But the Earth isn't playing 00:15:02.960 --> 00:15:05.870 a game against you. The dirt doesn't have a strategy 00:15:05.870 --> 00:15:09.070 to hide the gold. It's just dirt. True. But the 00:15:09.070 --> 00:15:11.549 decision theory treats this uncertainty as a 00:15:11.549 --> 00:15:14.070 game against nature. It adopts a mindset very 00:15:14.070 --> 00:15:16.190 similar to Murphy's Law. Anything that can go 00:15:16.190 --> 00:15:18.590 wrong will go wrong. What's crucial here is that 00:15:18.590 --> 00:15:21.470 it's a non -probabilistic decision theory. Non 00:15:21.470 --> 00:15:24.009 -probabilistic. Right. Meaning it explicitly 00:15:24.009 --> 00:15:27.080 does not care about the odds. Exactly. It does 00:15:27.080 --> 00:15:29.759 not rely on the exact mathematical probabilities 00:15:29.759 --> 00:15:31.820 of outcomes. It doesn't care if a geologist says 00:15:31.820 --> 00:15:34.059 there's a 10 % chance or 80 % chance of finding 00:15:34.059 --> 00:15:37.740 gold. It relies strictly on scenario analysis. 00:15:38.299 --> 00:15:41.340 What is the absolute worst possible outcome of 00:15:41.340 --> 00:15:44.320 this decision? You simply rank the outcomes. 00:15:44.440 --> 00:15:46.919 You don't measure the exact statistical distances 00:15:46.919 --> 00:15:49.580 between them. And you choose the path where that 00:15:49.580 --> 00:15:52.379 worst case scenario doesn't bankrupt you. That's 00:15:52.379 --> 00:15:54.120 entirely different from how we are taught to 00:15:54.120 --> 00:15:57.049 think. You aren't calculating your odds of success. 00:15:57.169 --> 00:15:59.649 You are just building the strongest bunker possible, 00:16:00.110 --> 00:16:02.409 which brings up an incredibly interesting and 00:16:02.409 --> 00:16:04.789 frankly exhausting application from the text, 00:16:05.690 --> 00:16:08.809 democracy and voting. Ah, yes. The Wikipedia 00:16:08.809 --> 00:16:12.490 article discusses lesser evil voting, or LEV. 00:16:13.029 --> 00:16:14.549 And just to be perfectly clear to you listening, 00:16:14.669 --> 00:16:16.669 we are discussing this purely and partially. 00:16:16.889 --> 00:16:19.070 as an acrobic application of the theory from 00:16:19.070 --> 00:16:21.409 the source material. Yes, absolutely. The text 00:16:21.409 --> 00:16:23.629 quotes political thinkers Norrin Chomsky and 00:16:23.629 --> 00:16:26.269 John Halley, who argue that voting in a system 00:16:26.269 --> 00:16:28.850 with two major choices can be viewed purely through 00:16:28.850 --> 00:16:31.450 the lens of a minimax strategy. And as someone 00:16:31.450 --> 00:16:34.090 who gets deeply fatigued by election seasons, 00:16:34.850 --> 00:16:37.539 the logic here is fascinating. The quote from 00:16:37.539 --> 00:16:39.519 the source states that voting should not be viewed 00:16:39.519 --> 00:16:42.659 as a form of personal self -expression. It shouldn't 00:16:42.659 --> 00:16:45.120 be about moral retaliation against candidates 00:16:45.120 --> 00:16:47.960 who fail to perfectly reflect your values, and 00:16:47.960 --> 00:16:51.159 it's not about judging a corrupt system. Instead, 00:16:51.259 --> 00:16:53.639 they argue, it is simply a mechanical opportunity 00:16:53.639 --> 00:16:57.100 to reduce harm. It is the ultimate real world 00:16:57.100 --> 00:17:00.320 application of minimizing the maximum possible 00:17:00.320 --> 00:17:03.580 loss. In this framework, you evaluate the candidates, 00:17:03.820 --> 00:17:05.900 determine which one represents the absolute worst 00:17:05.900 --> 00:17:08.220 case scenario for your interests or the country's 00:17:08.220 --> 00:17:10.380 interests, and you vote for the other one. Wow. 00:17:10.460 --> 00:17:12.500 You aren't trying to maximize your ideal gain 00:17:12.500 --> 00:17:15.240 or achieve a utopian vision. You are strictly 00:17:15.240 --> 00:17:17.680 minimizing the worst case damage. It certainly 00:17:17.680 --> 00:17:20.220 strips all the romance and idealism out of democracy, 00:17:20.220 --> 00:17:23.200 but the mathematical logic of it is undeniable. 00:17:23.519 --> 00:17:25.910 You are pruning the darkest branch of the tree. 00:17:26.130 --> 00:17:28.289 If we connect this to the bigger picture, this 00:17:28.289 --> 00:17:31.529 exact logic scales up from individual votes to 00:17:31.529 --> 00:17:33.670 the very foundation of how we define a moral 00:17:33.670 --> 00:17:37.220 society. In philosophy, the term Maximin is deeply 00:17:37.220 --> 00:17:39.799 associated with John Rawls and his monumental 00:17:39.799 --> 00:17:43.140 work, A Theory of Justice. Wait, how does a political 00:17:43.140 --> 00:17:46.160 philosopher use game theory math? Rawls used 00:17:46.160 --> 00:17:48.839 Maximin logic to formulate what he called the 00:17:48.839 --> 00:17:51.599 Difference Principle. He created a famous thought 00:17:51.599 --> 00:17:54.779 experiment called the Veil of Ignorance. He argued 00:17:54.779 --> 00:17:57.160 that if you were designing a society from scratch, 00:17:57.319 --> 00:17:58.900 you should do it without knowing where you would 00:17:58.900 --> 00:18:01.000 personally end up in that society. Because you 00:18:01.000 --> 00:18:03.099 could be anyone. Right. You don't know if you 00:18:03.099 --> 00:18:05.799 will be born rich. or poor, healthy or sick, 00:18:06.059 --> 00:18:08.359 part of a majority, or a marginalized minority. 00:18:08.660 --> 00:18:10.359 Because if you don't know where you will land, 00:18:10.460 --> 00:18:13.180 you are forced to protect yourself against the 00:18:13.180 --> 00:18:15.740 absolute worst -case scenario. You assume you 00:18:15.740 --> 00:18:18.420 will be born in the very bottom. Precisely. Because 00:18:18.420 --> 00:18:20.920 of that uncertainty, a rational person using 00:18:20.920 --> 00:18:23.700 maximin logic would demand that a just society 00:18:23.700 --> 00:18:26.440 is one where social and economic inequalities 00:18:26.440 --> 00:18:28.880 are specifically arranged to provide the greatest 00:18:28.880 --> 00:18:31.460 benefit to the least advantaged members of society. 00:18:31.839 --> 00:18:35.009 Wow. He took the logic of avoiding a negative 00:18:35.009 --> 00:18:38.450 100 payoff in a simple grid game and used it 00:18:38.450 --> 00:18:40.890 to argue that a society is only mathematically 00:18:40.890 --> 00:18:43.950 fair if the absolute bottom rung of the ladder 00:18:43.950 --> 00:18:46.130 is raised as high off the ground as possible. 00:18:46.130 --> 00:18:48.269 Yeah. Because you never know if you're the one 00:18:48.269 --> 00:18:50.430 who is going to be standing on it. You maximize 00:18:50.430 --> 00:18:53.750 the minimum position in society. It's an incredibly 00:18:53.750 --> 00:18:56.750 powerful philosophical framework built entirely 00:18:56.750 --> 00:18:59.630 on the bones of risk aversion and game theory. 00:18:59.829 --> 00:19:01.609 So what does this all mean for you listening 00:19:01.609 --> 00:19:03.950 right now? It means that whether you are agonizing 00:19:03.950 --> 00:19:06.269 over a career change, whether you are casting 00:19:06.269 --> 00:19:09.069 a pragmatic ballot in an election, or, going 00:19:09.069 --> 00:19:10.910 all the way back to our first example, whether 00:19:10.910 --> 00:19:12.769 you are just packing an umbrella for a weekend 00:19:12.769 --> 00:19:15.869 trip, you are very likely intuitively applying 00:19:15.869 --> 00:19:18.450 minimax logic. You really are. You are ignoring 00:19:18.450 --> 00:19:20.930 the exact percentages, looking at the darkest 00:19:20.930 --> 00:19:23.690 cloud on the horizon, and simply protecting yourself 00:19:23.690 --> 00:19:25.789 against the worst possible timeline. It is a 00:19:25.789 --> 00:19:28.549 fundamental human survival mechanism, formalized 00:19:28.549 --> 00:19:31.089 into strict mathematics. We've covered an incredible 00:19:31.089 --> 00:19:33.500 amount of ground - today. We started with the 00:19:33.500 --> 00:19:36.460 strict, unyielding math of row and column matrices. 00:19:37.079 --> 00:19:39.440 We saw how Deep Blue harnessed that paranoid 00:19:39.440 --> 00:19:42.900 logic, pruning dead branches and using mathematical 00:19:42.900 --> 00:19:45.599 intuition to calculate twelve plies into the 00:19:45.599 --> 00:19:48.440 future and defeat Garry Kasparov. And we traced 00:19:48.440 --> 00:19:51.180 that exact same logic all the way to John Rawls, 00:19:51.519 --> 00:19:54.460 designing a vision for a just society by rigorously 00:19:54.460 --> 00:19:56.359 looking out for the most disadvantaged among 00:19:56.359 --> 00:19:59.529 us. It really highlights how interconnected mathematics, 00:19:59.890 --> 00:20:02.890 technology, and human philosophy truly are. But 00:20:02.890 --> 00:20:04.769 it also leaves us with a lingering question. 00:20:05.160 --> 00:20:07.319 Something I've been thinking about as we unpack 00:20:07.319 --> 00:20:09.460 all of these worst -case scenarios. Okay, lay 00:20:09.460 --> 00:20:11.440 it on us. We've learned today that the minimax 00:20:11.440 --> 00:20:13.920 algorithm trains artificial intelligence to always 00:20:13.920 --> 00:20:16.220 assume the opponent will make the most punishing 00:20:16.220 --> 00:20:19.059 worst -case counter move. It literally programs 00:20:19.059 --> 00:20:21.420 the AI to expect the worst from the world in 00:20:21.420 --> 00:20:24.140 order to survive. So what happens in the near 00:20:24.140 --> 00:20:28.839 future when two incredibly powerful AIs, both 00:20:28.839 --> 00:20:32.160 running minimax -style logic, are forced to interact 00:20:32.160 --> 00:20:35.029 in the real world outside the strict confines 00:20:35.029 --> 00:20:37.829 and perfect rolls of a chessboard. Will their 00:20:37.829 --> 00:20:40.109 mutual assumption of the worst -case scenario 00:20:40.109 --> 00:20:43.829 trap them in an endless cycle of extreme defensive 00:20:43.829 --> 00:20:46.960 paranoia? Oh, that is chilling. If both sides 00:20:46.960 --> 00:20:49.240 assume the others out to destroy them, they might 00:20:49.240 --> 00:20:51.740 accidentally create the very conflict that you're 00:20:51.740 --> 00:20:53.819 both mathematically trying to avoid. Exactly. 00:20:54.059 --> 00:20:56.359 A self -fulfilling prophecy of destruction born 00:20:56.359 --> 00:20:58.740 entirely out of perfect defensive mathematics. 00:20:59.180 --> 00:21:00.579 Something to think about the next time you try 00:21:00.579 --> 00:21:02.640 to outsmart a machine. Or the next time you are 00:21:02.640 --> 00:21:04.420 sitting in a bunker staring at a radar screen 00:21:04.420 --> 00:21:06.160 wondering if the universe is out to get you. 00:21:06.640 --> 00:21:08.220 Thank you so much for joining us on this deep 00:21:08.220 --> 00:21:09.420 dive. We will see you next time.