WEBVTT 00:00:00.000 --> 00:00:03.480 Have you ever found yourself in this incredibly 00:00:03.480 --> 00:00:06.480 frustrating but completely universal modern scenario? 00:00:07.059 --> 00:00:10.480 You're staring down a long, complicated mathematical 00:00:10.480 --> 00:00:13.019 equation. Oh, yeah. We've all been there. Right. 00:00:13.119 --> 00:00:15.779 And you've got your calculator. Maybe it's the 00:00:15.779 --> 00:00:19.300 app on your phone or maybe just a cheap solar 00:00:19.300 --> 00:00:23.000 powered one sitting on your desk. And you painstakingly 00:00:23.000 --> 00:00:25.420 start typing the whole thing out. Punching in 00:00:25.420 --> 00:00:28.359 every single digit. Exactly. You're carefully 00:00:28.359 --> 00:00:30.320 hitting the numbers, hitting the plus sign, the 00:00:30.320 --> 00:00:32.560 multiply sign, trying desperately to keep track 00:00:32.560 --> 00:00:35.140 of the parentheses. You're opening brackets inside 00:00:35.140 --> 00:00:36.899 of brackets, just hoping you remember to close 00:00:36.899 --> 00:00:38.560 them all at the end. Which is always a gamble. 00:00:38.909 --> 00:00:41.250 It really is. And you finally hit that satisfying 00:00:41.250 --> 00:00:44.130 equals button, and the number that pops up is 00:00:44.130 --> 00:00:47.270 so wildly incorrect that you just know deep down 00:00:47.270 --> 00:00:50.170 in your bones the machine completely butchered 00:00:50.170 --> 00:00:52.090 the order of operations. It happens all the time. 00:00:52.189 --> 00:00:55.590 You usually end up grabbing a scrap of paper 00:00:55.590 --> 00:00:57.670 to write down the intermediate steps, or you 00:00:57.670 --> 00:00:59.450 just type the entire string of numbers in like 00:00:59.450 --> 00:01:01.549 three more times, crossing your fingers that 00:01:01.549 --> 00:01:03.979 you get the same answer twice. Which completely 00:01:03.979 --> 00:01:06.319 defeats the whole purpose of using a machine 00:01:06.319 --> 00:01:08.480 to save time in the first place. It really does. 00:01:08.579 --> 00:01:10.760 It's a massive workflow killer. Which brings 00:01:10.760 --> 00:01:13.659 us to today's deep dive. We are pulling from 00:01:13.659 --> 00:01:16.840 an incredibly detailed Wikipedia article on a 00:01:16.840 --> 00:01:19.739 mathematical and computing concept known as reverse 00:01:19.739 --> 00:01:24.260 Polish notation, or RPN for short. A very intimidating 00:01:24.260 --> 00:01:28.159 name for a very elegant concept. Seriously. Because 00:01:28.159 --> 00:01:30.180 what if I told you there is an entirely different 00:01:30.180 --> 00:01:33.120 way to do math? a way that looks at first glance 00:01:33.120 --> 00:01:35.920 completely backward, but is actually so deeply 00:01:35.920 --> 00:01:38.739 elegant that it eliminates the need for parentheses 00:01:38.739 --> 00:01:41.540 entirely. To really understand why this matters, 00:01:41.680 --> 00:01:43.620 we have to pull ourselves out of this modern 00:01:43.620 --> 00:01:46.439 era of iPhones and infinite cloud storage. We 00:01:46.439 --> 00:01:49.159 need to go back to a time of giant, room -filling 00:01:49.159 --> 00:01:52.319 computer mainframes, scattered engineering blueprints, 00:01:52.420 --> 00:01:55.019 and the sleek angular lines of the very first 00:01:55.019 --> 00:01:57.140 pocket calculators. Which is such a great visual. 00:01:57.340 --> 00:02:00.409 It's essential to set the stage. We want to frame 00:02:00.409 --> 00:02:03.469 the core value of this topic for you today. Understanding 00:02:03.469 --> 00:02:06.310 RPN isn't just about learning a quirky way to 00:02:06.310 --> 00:02:09.229 punch numbers into a keypad. It is about learning 00:02:09.229 --> 00:02:11.969 a radically more efficient way to process information 00:02:11.969 --> 00:02:14.569 and interact with technology, all without getting 00:02:14.569 --> 00:02:17.289 overwhelmed by rules and syntax. That is the 00:02:17.289 --> 00:02:19.960 exact mission for this deep dive. We're going 00:02:19.960 --> 00:02:22.580 to demystify this seemingly backward way of doing 00:02:22.580 --> 00:02:26.419 math, uncover exactly why it's maintained a diehard, 00:02:26.560 --> 00:02:29.280 almost fanatical cult following among engineers 00:02:29.280 --> 00:02:31.979 and programmers for decades. Oh, they are definitely 00:02:31.979 --> 00:02:34.280 fanatical about it. They really are. And we'll 00:02:34.280 --> 00:02:36.979 explore how this single brilliant concept shaped 00:02:36.979 --> 00:02:39.560 the very early days of computing. It's a journey 00:02:39.560 --> 00:02:42.340 that takes us from theoretical logic in the 1920s 00:02:42.340 --> 00:02:44.819 through the bombing raids of World War II and 00:02:44.819 --> 00:02:46.939 right into the fierce high stakes calculator 00:02:46.939 --> 00:02:50.060 wars of the 1970s and 80s. 80s. Okay, let's unpack 00:02:50.060 --> 00:02:52.219 this, starting with the absolute basics. What 00:02:52.219 --> 00:02:54.939 even is reverse Polish notation? Right. To understand 00:02:54.939 --> 00:02:56.580 it, we first have to look at how we normally 00:02:56.580 --> 00:02:59.860 write math. Which is called infix notation. If 00:02:59.860 --> 00:03:02.120 you want to add 3 and 4, you just write it as 00:03:02.120 --> 00:03:05.419 3 plus 4. The operator, the plus sign, goes directly 00:03:05.419 --> 00:03:07.520 in between the numbers. And those numbers are 00:03:07.520 --> 00:03:10.300 called the operands. That structure makes perfect 00:03:10.300 --> 00:03:12.300 sense to our human brains when we read it out 00:03:12.300 --> 00:03:15.680 loud left to right. We say 3 plus 4. We announce 00:03:15.680 --> 00:03:17.500 the first ingredient, we announce the action 00:03:17.500 --> 00:03:19.159 we want to take, and then we announce the second 00:03:19.159 --> 00:03:21.460 ingredient. Exactly. It's built for spoken language. 00:03:21.740 --> 00:03:24.419 But in reverse Polish notation, the operators 00:03:24.419 --> 00:03:27.219 follow the operands. So that simple 3 plus 4 00:03:27.219 --> 00:03:30.060 equation becomes 3 4 plus. You're essentially 00:03:30.060 --> 00:03:32.280 giving the machine all the ingredients first, 00:03:32.419 --> 00:03:34.879 and only then do you tell it what to do with 00:03:34.879 --> 00:03:37.900 them. To really grasp how a machine processes 00:03:37.900 --> 00:03:40.659 this, you need to understand the concept of a 00:03:40.659 --> 00:03:43.599 stack. It is the fundamental architecture behind 00:03:43.599 --> 00:03:47.000 RPN. Stack is everything. Think of a stack just 00:03:47.000 --> 00:03:49.400 like one of those spring -loaded stacks of plates 00:03:49.400 --> 00:03:52.259 you see at a cafeteria buffet. It's a last -in, 00:03:52.280 --> 00:03:54.340 first -out system. Right. If you put a fresh 00:03:54.340 --> 00:03:56.979 plate on top of the stack... That exact plate 00:03:56.979 --> 00:03:59.340 is the very first one the next person in line 00:03:59.340 --> 00:04:01.419 is going to grab. In computer science terms, 00:04:01.719 --> 00:04:04.819 when we add a number to that mental pile, we 00:04:04.819 --> 00:04:07.599 call it pushing to the stack. And when a mathematical 00:04:07.599 --> 00:04:10.199 operation needs to use a number, it removes it 00:04:10.199 --> 00:04:12.060 from the very top of the pile, which we call 00:04:12.060 --> 00:04:15.280 popping it off the stack. Push and pop. Simple 00:04:15.280 --> 00:04:17.420 enough. So let's walk you through a slightly 00:04:17.420 --> 00:04:19.899 more complex equation to see this in action. 00:04:20.379 --> 00:04:22.540 Let's step away from simple addition and take 00:04:22.540 --> 00:04:26.060 the standard math problem. 3 minus 4 plus 5. 00:04:26.319 --> 00:04:29.000 Okay, let's trace the physical workflow on an 00:04:29.000 --> 00:04:31.920 RPN calculator. First, you type the number 3 00:04:31.920 --> 00:04:35.180 and hit the Enter key. That pushes the 3 onto 00:04:35.180 --> 00:04:36.959 your empty stack. Your first plate is loaded. 00:04:37.220 --> 00:04:40.910 Then you type 4 and hit Enter. Now the 4 is sitting 00:04:40.910 --> 00:04:43.170 directly on top of the 3 in your mental plate 00:04:43.170 --> 00:04:46.230 dispenser. Next, you hit the minus key. The calculator 00:04:46.230 --> 00:04:48.709 sees that minus key, so it immediately pops the 00:04:48.709 --> 00:04:50.730 top two numbers off the stack, the 4 and the 00:04:50.730 --> 00:04:54.410 3. Right. It subtracts 4 from 3, gets a result 00:04:54.410 --> 00:04:57.089 of negative 1, and pushes that negative 1 right 00:04:57.089 --> 00:04:59.149 back onto the top of the stack. So the original 00:04:59.149 --> 00:05:01.129 numbers are totally gone, and you just have a 00:05:01.129 --> 00:05:03.110 negative 1 sitting there waiting. Waiting for 00:05:03.110 --> 00:05:06.069 the next instruction. Exactly. Then you move 00:05:06.069 --> 00:05:08.129 to the next part of the problem. You type 5. 00:05:08.370 --> 00:05:10.990 You push that onto the stack on top of the negative 00:05:10.990 --> 00:05:13.810 1. Finally, you hit the plus key. The calculator 00:05:13.810 --> 00:05:16.649 pops the 5 and the negative 1, adds them together, 00:05:16.810 --> 00:05:20.149 and pushes the final answer, 4, onto the stack. 00:05:20.610 --> 00:05:23.029 And you're done. What's fascinating here is when 00:05:23.029 --> 00:05:25.209 you use this system, you completely eliminate 00:05:25.209 --> 00:05:27.470 the need for the order of operations. That's 00:05:27.470 --> 00:05:30.149 the real magic. You don't need to remember, please 00:05:30.149 --> 00:05:32.870 excuse my dear Aunt Sally or PEMDAS or any of 00:05:32.870 --> 00:05:34.829 that. You never have to worry about whether multiplication 00:05:34.829 --> 00:05:36.990 should happen before addition because you are 00:05:36.990 --> 00:05:39.689 actively dictating the exact flow of the math 00:05:39.689 --> 00:05:41.930 as you input it. And crucially, you completely 00:05:41.930 --> 00:05:45.129 eliminate the need for parentheses. Every single 00:05:45.129 --> 00:05:47.670 equation, no matter how monstrously complex, 00:05:48.069 --> 00:05:50.610 can just be evaluated linearly. left to right 00:05:50.610 --> 00:05:53.230 that is the massive aha moment for most people 00:05:53.230 --> 00:05:55.290 let's look at an equation that normally requires 00:05:55.290 --> 00:05:58.129 parentheses like open bracket three plus four 00:05:58.129 --> 00:06:00.529 close bracket multiplied by open bracket five 00:06:00.529 --> 00:06:03.329 plus six close bracket in standard notation you 00:06:03.329 --> 00:06:06.509 absolutely need those brackets to force the calculator 00:06:06.509 --> 00:06:09.370 to do the addition blocks first before it tackles 00:06:09.370 --> 00:06:10.990 a multiplication in the middle but let's look 00:06:10.990 --> 00:06:13.149 at how beautifully simple this is with an rpn 00:06:13.149 --> 00:06:16.069 stack walk us through the exact stack progression 00:06:16.069 --> 00:06:18.810 for that one sure you push your three then push 00:06:18.810 --> 00:06:21.579 your four You hit the plus key, the calculator 00:06:21.579 --> 00:06:25.879 pops them, adds them, and pushes a 7 to the stack. 00:06:26.079 --> 00:06:28.300 You just leave it sitting there. Okay, so a 7 00:06:28.300 --> 00:06:30.839 is on plate 1. Right. Next, you push your 5 and 00:06:30.839 --> 00:06:33.680 push your 6. You hit the plus key again. The 00:06:33.680 --> 00:06:35.839 calculator pops the 5 and 6, adds them, and pushes 00:06:35.839 --> 00:06:38.399 an 11. So now, if you look at your stack, you 00:06:38.399 --> 00:06:40.980 have an 11 sitting right on top of that 7 from 00:06:40.980 --> 00:06:43.000 the first part of the problem. Exactly. Finally, 00:06:43.040 --> 00:06:45.100 you hit the multiply key. The calculator grabs 00:06:45.100 --> 00:06:47.860 the top two plates, the 11 and the 7, multiplies 00:06:47.860 --> 00:06:50.519 them, and gives you 77. The machine never needed 00:06:50.519 --> 00:06:53.100 to know about brackets or priorities. It just 00:06:53.100 --> 00:06:56.120 followed your precise step -by -step logic. Getting 00:06:56.120 --> 00:06:58.740 a machine to operate with that level of unbroken 00:06:58.740 --> 00:07:01.439 flow took some serious intellectual leaps in 00:07:01.439 --> 00:07:03.540 history. Which brings up a question I'm still 00:07:03.540 --> 00:07:06.600 hung up on. The name. Reverse Polish notation 00:07:06.600 --> 00:07:09.680 sounds like a very specific origin story. Who 00:07:09.680 --> 00:07:12.259 exactly was Polish and what were they reversing? 00:07:12.300 --> 00:07:14.879 The name traces back to a logician named John 00:07:14.879 --> 00:07:18.100 Łukasiewicz. He was a brilliant Polish mathematician 00:07:18.100 --> 00:07:22.060 who, back in 1924, invented the prefix version 00:07:22.060 --> 00:07:24.060 of this system. Which was just called Polish 00:07:24.060 --> 00:07:26.680 notation, right? Correct. In his version, the 00:07:26.680 --> 00:07:29.759 operators came before the operands. So that addition 00:07:29.759 --> 00:07:32.360 equation would be written as plus 3, 4. It was 00:07:32.360 --> 00:07:34.399 a massive breakthrough in formal logic because 00:07:34.399 --> 00:07:36.459 it completely removed ambiguity from written 00:07:36.459 --> 00:07:39.040 mathematical expressions. But it was the reverse 00:07:39.040 --> 00:07:41.759 of that concept, putting the operator at the 00:07:41.759 --> 00:07:44.680 very end, that really caught fire decades later 00:07:44.680 --> 00:07:46.639 when people started trying to build the first 00:07:46.639 --> 00:07:48.720 computing machines. Yes, the postfix version. 00:07:48.860 --> 00:07:51.720 That takes us to the very first computer to actually 00:07:51.720 --> 00:07:53.879 implement this reverse notation in its hardware. 00:07:54.279 --> 00:07:57.620 Conrad Zuse's Z3 computer, built in Germany way 00:07:57.620 --> 00:08:00.519 back in 1941. The sources say that in dialogue 00:08:00.519 --> 00:08:03.079 mode, the Z3 allowed an operator to enter two 00:08:03.079 --> 00:08:05.240 operands, followed by the desired operation. 00:08:05.579 --> 00:08:07.379 It's basically functioning like a giant room 00:08:07.379 --> 00:08:10.110 -sized RPM calculator. But the history of the 00:08:10.110 --> 00:08:13.490 Z3 adds a layer of real -world drama to this 00:08:13.490 --> 00:08:16.230 timeline. The machine was completely destroyed 00:08:16.230 --> 00:08:18.930 in an Allied bombing raid on Berlin in December 00:08:18.930 --> 00:08:23.050 1943. Which is a huge historical tragedy for 00:08:23.050 --> 00:08:26.370 computer science. Because of the war, Zuse's 00:08:26.370 --> 00:08:28.470 brilliant implementation remained essentially 00:08:28.470 --> 00:08:31.620 unknown outside of Germany. for a very long time. 00:08:31.660 --> 00:08:33.399 They actually had to build a working replica 00:08:33.399 --> 00:08:37.279 of it much later in 1961 just to prove it existed 00:08:37.279 --> 00:08:39.580 and functioned the way he claimed. Right. So 00:08:39.580 --> 00:08:41.559 because that initial breakthrough was lost to 00:08:41.559 --> 00:08:43.779 the world during the war, the concept of reverse 00:08:43.779 --> 00:08:46.919 Polish notation had to be reborn. The sources 00:08:46.919 --> 00:08:49.700 paint this incredible narrative of convergent 00:08:49.700 --> 00:08:52.450 evolution. The problem of how to make a machine 00:08:52.450 --> 00:08:55.370 process complex math efficiently was so universal 00:08:55.370 --> 00:08:57.990 that brilliant minds across the globe just kept 00:08:57.990 --> 00:09:00.129 independently arriving at the exact same logical 00:09:00.129 --> 00:09:02.289 conclusion. It wasn't just a handful of people 00:09:02.289 --> 00:09:05.669 in one lab. In 1954, the reverse Polish scheme 00:09:05.669 --> 00:09:07.490 was proposed independently in the United States 00:09:07.490 --> 00:09:09.549 by Arthur Birx, Don Warren, and Jesse Wright. 00:09:09.899 --> 00:09:12.159 And then, just a few years later, a philosopher 00:09:12.159 --> 00:09:14.139 and computer scientist named Charles Hamblin 00:09:14.139 --> 00:09:17.000 in Australia was staring down these massive early 00:09:17.000 --> 00:09:20.399 computers and realized the fatal flaw in how 00:09:20.399 --> 00:09:23.220 they processed logic. He extended the algorithms 00:09:23.220 --> 00:09:25.620 and notation for a programming language called 00:09:25.620 --> 00:09:28.620 George. Hamblin realized early computers were 00:09:28.620 --> 00:09:31.000 wasting an enormous amount of their limited processing 00:09:31.000 --> 00:09:34.960 power trying to assign a specific named memory 00:09:34.960 --> 00:09:37.620 address to every single intermediate step of 00:09:37.620 --> 00:09:39.740 a calculation. But if you used a stack, you didn't 00:09:39.740 --> 00:09:41.559 need to name the memory slots. You just pushed 00:09:41.559 --> 00:09:45.000 and popped. Exactly. Then, in the early 60s, 00:09:45.059 --> 00:09:47.580 it gets reinvented yet again by Friedrich L. 00:09:47.659 --> 00:09:51.330 Bauer and Edgar W. Dijkstra. Dykstra is an absolute 00:09:51.330 --> 00:09:53.970 legend in computer science. He created something 00:09:53.970 --> 00:09:56.330 called the shunting yard algorithm to automatically 00:09:56.330 --> 00:09:59.049 convert normal, human -readable, infixed math 00:09:59.049 --> 00:10:01.909 into reverse Polish notation so that the computer 00:10:01.909 --> 00:10:04.190 could actually digest it. The name of that algorithm 00:10:04.190 --> 00:10:07.289 is so evocative. Let's visualize a physical train 00:10:07.289 --> 00:10:09.009 yard for a second to understand how Dykstra's 00:10:09.009 --> 00:10:12.669 mind worked. I love this analogy. Imagine a mathematical 00:10:12.669 --> 00:10:15.129 equation coming down the railroad tracks like 00:10:15.129 --> 00:10:18.149 a mixed -up freight train. You have number cars 00:10:18.149 --> 00:10:21.090 and operator cars all coupled together. The algorithm 00:10:21.090 --> 00:10:23.789 acts like the switch operator in the locomotive. 00:10:23.870 --> 00:10:27.090 Right. As the train arrives, the locomotive pushes 00:10:27.090 --> 00:10:29.230 the number car straight through onto the main 00:10:29.230 --> 00:10:32.070 output track. But when it hits an operator car, 00:10:32.230 --> 00:10:35.090 like a plus or minus sign, it shunts it off onto 00:10:35.090 --> 00:10:37.970 a side track, temporarily holding it there. It 00:10:37.970 --> 00:10:40.570 keeps pushing numbers to the main track and only 00:10:40.570 --> 00:10:43.169 pulls the operators off the siding and attaches 00:10:43.169 --> 00:10:45.370 them to the back of the train when the order 00:10:45.370 --> 00:10:47.549 of operations dictates it. By the time the train 00:10:47.549 --> 00:10:49.450 leaves the yard, the cars have been completely 00:10:49.450 --> 00:10:52.629 reorganized into perfect reverse Polish notation. 00:10:52.929 --> 00:10:55.370 If we connect this to the bigger picture, you 00:10:55.370 --> 00:10:57.370 really have to understand why all these different 00:10:57.370 --> 00:10:59.990 scientists, from an Australian philosopher to 00:10:59.990 --> 00:11:02.230 American hardware engineers like Robert S. Barton, 00:11:02.309 --> 00:11:05.289 were converging on this one idea. Barton developed 00:11:05.289 --> 00:11:07.629 an RPN architecture for the massive Burroughs 00:11:07.629 --> 00:11:12.009 B5000 computer in 1958, right? Yes. And the reason 00:11:12.009 --> 00:11:14.269 they all kept finding this solution was hardware 00:11:14.269 --> 00:11:17.169 limitations. Early computers had virtually no 00:11:17.169 --> 00:11:20.529 memory. Magnetic core memory was incredibly expensive, 00:11:20.929 --> 00:11:24.289 physically huge, and generated a ton of heat. 00:11:24.509 --> 00:11:26.590 Every single time a computer had to store an 00:11:26.590 --> 00:11:29.350 intermediate number, log its location, and then 00:11:29.350 --> 00:11:32.389 retrieve it later, it cost precious time and 00:11:32.389 --> 00:11:35.509 physical resources. RPN drastically reduced memory 00:11:35.509 --> 00:11:38.710 access. By using that simple spring -loaded stack, 00:11:39.029 --> 00:11:41.750 early machines could evaluate wildly complex 00:11:41.750 --> 00:11:45.139 equations with... absolute minimal hardware overhead 00:11:45.139 --> 00:11:47.759 it was the ultimate life hack for a machine with 00:11:47.759 --> 00:11:50.559 limited brain power and as computing technology 00:11:50.559 --> 00:11:53.259 slowly began to shrink down from the size of 00:11:53.259 --> 00:11:55.919 a room to the size of desk that incredible efficiency 00:11:55.919 --> 00:11:58.340 became the killer feature for the next frontier 00:11:58.340 --> 00:12:00.879 of tech the desktop era Here's where it gets 00:12:00.879 --> 00:12:02.820 really interesting, because we are entering the 00:12:02.820 --> 00:12:05.580 golden age of the calculator wars. The transition 00:12:05.580 --> 00:12:08.080 to desktop machines meant every ounce of efficiency 00:12:08.080 --> 00:12:10.620 mattered even more. You were no longer dealing 00:12:10.620 --> 00:12:13.019 with massive cooling systems and unlimited power 00:12:13.019 --> 00:12:16.299 supplies. In June 1963, a company called Freyden 00:12:16.299 --> 00:12:19.159 introduced RPN to the commercial desktop calculator 00:12:19.159 --> 00:12:22.000 market with a machine called the EC -130. This 00:12:22.000 --> 00:12:24.340 thing was an absolute beauty of mid -century 00:12:24.340 --> 00:12:27.139 engineering. It didn't have an LCD screen. It 00:12:27.139 --> 00:12:30.970 had a cathode ray tube display. like a tiny glowing 00:12:30.970 --> 00:12:33.990 green television screen that showed a four -level 00:12:33.990 --> 00:12:36.909 stack. But here's the wild part. It showed the 00:12:36.909 --> 00:12:40.529 stack upside down. The last in -first -out working 00:12:40.529 --> 00:12:42.570 register was sitting at the very bottom of the 00:12:42.570 --> 00:12:45.149 screen, and the older numbers were rising up 00:12:45.149 --> 00:12:47.269 to the top. It was a revolutionary moment for 00:12:47.269 --> 00:12:49.230 an engineer to be able to physically see the 00:12:49.230 --> 00:12:51.409 contents of the computer's memory stack right 00:12:51.409 --> 00:12:53.769 in front of them glowing on a screen. It completely 00:12:53.769 --> 00:12:56.559 changed how they interacted with the data. But 00:12:56.559 --> 00:12:58.600 while Fryden was early to the game, it was another 00:12:58.600 --> 00:13:01.179 company that would take RPN, refine it, and turn 00:13:01.179 --> 00:13:03.340 it into a global phenomenon. Hewlett Packard. 00:13:03.440 --> 00:13:06.460 HP absolutely dominated the space for decades. 00:13:06.840 --> 00:13:10.220 Total domination. In 1968, HP engineers designed 00:13:10.220 --> 00:13:13.779 the 9100A desktop calculator. It used a three 00:13:13.779 --> 00:13:15.799 -level stack. They called the working registers 00:13:15.799 --> 00:13:18.429 X for the keyboard input. Y to accumulate the 00:13:18.429 --> 00:13:21.350 data, and Z for temporary storage. That machine 00:13:21.350 --> 00:13:23.850 popularized RPN among the scientific community, 00:13:24.129 --> 00:13:26.950 but the real earth -shattering game -changer 00:13:26.950 --> 00:13:30.210 came four years later. 1972, the release of the 00:13:30.210 --> 00:13:33.750 HP -35, the world's first handheld, pocket -sized 00:13:33.750 --> 00:13:36.679 scientific calculator. This is the device that 00:13:36.679 --> 00:13:39.120 essentially killed the physical wooden slide 00:13:39.120 --> 00:13:42.080 rule overnight. You had engineers out on surveying 00:13:42.080 --> 00:13:44.700 sites or working in Apollo -era aerospace labs 00:13:44.700 --> 00:13:46.960 throwing away the tools they had used for their 00:13:46.960 --> 00:13:49.379 entire careers because this little plastic brick 00:13:49.379 --> 00:13:51.600 could do it better. It introduced the classical 00:13:51.600 --> 00:13:55.659 four -level RPM stag, labeled X, Y, Z, and T 00:13:55.659 --> 00:13:59.070 for top. HP established a very specific, rigid 00:13:59.070 --> 00:14:01.929 rule set for that stack that became absolute 00:14:01.929 --> 00:14:04.750 gospel for engineers. For instance, it had an 00:14:04.750 --> 00:14:06.909 automatic stack lift feature. When you dropped 00:14:06.909 --> 00:14:09.789 numbers off the stack during a calculation, the 00:14:09.789 --> 00:14:11.990 machine would automatically duplicate the top 00:14:11.990 --> 00:14:14.850 register to save you keystrokes in certain repetitive 00:14:14.850 --> 00:14:17.529 calculations. It was meticulously designed for 00:14:17.529 --> 00:14:19.769 power users who needed to work fast in the field. 00:14:19.889 --> 00:14:22.309 And those power users absolutely worshipped it. 00:14:22.350 --> 00:14:24.950 RPN achieved total cult status in the engineering 00:14:24.950 --> 00:14:28.009 world. used reverse Polish notation on every 00:14:28.009 --> 00:14:30.529 single handheld calculator it sold, scientific, 00:14:30.610 --> 00:14:33.169 financial, programmable models, all the way until 00:14:33.169 --> 00:14:36.850 1977. Our source mentions this incredible, highly 00:14:36.850 --> 00:14:39.590 memorable detail about that corporate pride. 00:14:40.169 --> 00:14:43.649 In the 1980s, HP actually produced a promotional 00:14:43.649 --> 00:14:47.149 baseball hat for its employees and fans that 00:14:47.149 --> 00:14:50.470 simply said, No equals. That is a brilliant piece 00:14:50.470 --> 00:14:52.529 of marketing with a double meaning. It was a 00:14:52.529 --> 00:14:55.370 boast, obviously, saying that HP calculators 00:14:55.370 --> 00:14:57.429 had no equals in the marketplace in terms of 00:14:57.429 --> 00:14:59.990 quality and precision. But it was also a literal 00:14:59.990 --> 00:15:03.309 nerdy inside joke. RPN calculators physically 00:15:03.309 --> 00:15:05.330 do not have an equals button on the keyboard. 00:15:05.570 --> 00:15:07.409 You just hit the enter key to push things to 00:15:07.409 --> 00:15:09.889 the stack, and the operators themselves instantly 00:15:09.889 --> 00:15:12.490 execute the math. There is no need to ask the 00:15:12.490 --> 00:15:14.750 machine to evaluate an entire string at the very 00:15:14.750 --> 00:15:17.259 end. HP's commitment to the stack format didn't 00:15:17.259 --> 00:15:19.759 stop with basic arithmetic, though. By 1986, 00:15:20.159 --> 00:15:22.419 they evolved the fundamental concept into something 00:15:22.419 --> 00:15:25.639 much broader called RPL, or reverse Polish language. 00:15:25.919 --> 00:15:28.100 The paradigm shift from the classic RPN to this 00:15:28.100 --> 00:15:31.240 new RPL was huge. The classic RPN on those early 00:15:31.240 --> 00:15:33.360 calculators had a fixed stack, usually three 00:15:33.360 --> 00:15:37.419 or four levels, like X, Y, Z, and T. If you pushed 00:15:37.419 --> 00:15:39.659 too many numbers onto that mental plate dispenser, 00:15:39.799 --> 00:15:41.960 the ones at the very bottom just fell off the 00:15:41.960 --> 00:15:43.860 bottom of the machine and were lost to the void 00:15:43.860 --> 00:15:47.059 forever. RPL introduced an unlimited dynamic 00:15:47.059 --> 00:15:49.799 stack. It was only limited by the calculator's 00:15:49.799 --> 00:15:52.500 total available system memory. But more importantly, 00:15:52.740 --> 00:15:55.779 RPL was object -oriented. Instead of just holding 00:15:55.779 --> 00:16:00.259 a single, simple number like 4 or 72, the stack 00:16:00.259 --> 00:16:03.159 could now hold complex data. You could push entire 00:16:03.159 --> 00:16:05.679 paragraphs of text strings. You could push complex 00:16:05.679 --> 00:16:08.100 matrices, which are basically massive grids of 00:16:08.100 --> 00:16:10.759 numbers. You could push algebraic symbols or 00:16:10.759 --> 00:16:13.240 even entire software programs onto the stack. 00:16:13.419 --> 00:16:15.559 It fundamentally changed how users interacted 00:16:15.559 --> 00:16:18.000 with the machine, turning calculators from simple 00:16:18.000 --> 00:16:21.440 math tools into incredibly powerful, programmable 00:16:21.440 --> 00:16:24.659 pocket computers. Hearing all this history, you 00:16:24.659 --> 00:16:26.539 might be asking yourself a very reasonable question. 00:16:26.970 --> 00:16:29.110 if this system requires learning a whole new 00:16:29.110 --> 00:16:31.990 way of thinking about math and completely rewiring 00:16:31.990 --> 00:16:34.669 how you process numbers why did it have such 00:16:34.669 --> 00:16:36.970 a passionate following did it actually make a 00:16:36.970 --> 00:16:38.590 difference in the day -to -day work of an engineer 00:16:38.590 --> 00:16:41.649 it ultimately comes down to ergonomics and speed 00:16:42.169 --> 00:16:44.190 Researchers actually studied this extensively 00:16:44.190 --> 00:16:46.710 during the calculator wars. Ergonomic testing 00:16:46.710 --> 00:16:49.629 comparing traditional algebraic notation to reverse 00:16:49.629 --> 00:16:53.230 Polish notation found that RPN leads to significantly 00:16:53.230 --> 00:16:55.809 faster calculations. Because you aren't constantly 00:16:55.809 --> 00:16:58.750 hunting around the keypad for the open and close 00:16:58.750 --> 00:17:01.190 parentheses keys. Precisely. You never have to 00:17:01.190 --> 00:17:04.210 type parentheses, which means fewer total keystrokes 00:17:04.210 --> 00:17:07.369 to enter a typical complex calculation. If a 00:17:07.369 --> 00:17:10.109 problem takes 30 keystrokes on a standard calculator, 00:17:10.390 --> 00:17:13.230 it might only take 20 on an RPN machine. Over 00:17:13.230 --> 00:17:15.730 the course of an eight -hour workday, that efficiency 00:17:15.730 --> 00:17:18.890 compounds massively. Furthermore, the studies 00:17:18.890 --> 00:17:21.710 found that users of RPN calculators made fewer 00:17:21.710 --> 00:17:24.490 overall mistakes. The workflow forces you to 00:17:24.490 --> 00:17:26.730 break a complex problem down into its logical 00:17:26.730 --> 00:17:29.799 steps, evaluating from the inside out. It was 00:17:29.799 --> 00:17:31.980 highly intuitive for engineers because it closely 00:17:31.980 --> 00:17:34.059 mirrored how they used to physically work through 00:17:34.059 --> 00:17:36.619 problems on a traditional slide rule. You calculate 00:17:36.619 --> 00:17:38.680 a small piece of the problem, you physically 00:17:38.680 --> 00:17:41.019 hold that result, you calculate the next small 00:17:41.019 --> 00:17:43.119 piece, and then you combine them. To balance 00:17:43.119 --> 00:17:46.259 that out, the sources also note some strong anecdotal 00:17:46.259 --> 00:17:49.500 evidence from the other side of the aisle. RPN 00:17:49.500 --> 00:17:51.960 is notoriously difficult to learn if you were 00:17:51.960 --> 00:17:54.440 already raised on algebraic notation in grade 00:17:54.440 --> 00:17:57.579 school. Your brain is hardwired to hear 3 plus 00:17:57.579 --> 00:18:01.059 4. So retraining it to think 3 and or 4 plus 00:18:01.059 --> 00:18:03.519 feels a lot like trying to write a letter with 00:18:03.519 --> 00:18:05.940 your non -dominant hand. It is an undeniably 00:18:05.940 --> 00:18:09.539 steep learning curve. The friction is real. But 00:18:09.539 --> 00:18:11.900 once that workflow clicks in your brain, many 00:18:11.900 --> 00:18:14.039 people claim they can never go back to a standard 00:18:14.039 --> 00:18:16.539 calculator. So what does this all mean for us 00:18:16.539 --> 00:18:19.559 today? Is RPN just a museum piece for vintage 00:18:19.559 --> 00:18:22.279 calculator collectors and tech historians? Not 00:18:22.279 --> 00:18:24.559 at all. Its footprint in modern software is actually 00:18:24.559 --> 00:18:27.319 quite vast. even if it's hidden deeply under 00:18:27.319 --> 00:18:29.720 the hood where most consumers never see it. For 00:18:29.720 --> 00:18:31.859 example, it is still the underlying logic used 00:18:31.859 --> 00:18:34.160 in stack -oriented programming languages like 00:18:34.160 --> 00:18:36.400 Forth. And if you ever open up a standard Unix 00:18:36.400 --> 00:18:38.680 operating system and use the command line calculator 00:18:38.680 --> 00:18:41.299 program, which is called DC, you are interacting 00:18:41.299 --> 00:18:43.940 directly with RPN. The application that I found 00:18:43.940 --> 00:18:46.079 most surprising today actually has nothing to 00:18:46.079 --> 00:18:49.359 do with calculators or typing numbers into a 00:18:49.359 --> 00:18:51.640 terminal. It's PostScript. For anyone unfamiliar, 00:18:51.980 --> 00:18:54.140 this is the page description language that tells 00:18:54.140 --> 00:18:56.519 modern printers exactly how to print documents. 00:18:56.900 --> 00:19:00.299 All those beautiful, complex graphics, the varied 00:19:00.299 --> 00:19:03.480 typography, the intricate layouts that your computer 00:19:03.480 --> 00:19:06.420 sends over to a laser printer, that data is often 00:19:06.420 --> 00:19:09.000 being processed using reverse Polish notation. 00:19:09.609 --> 00:19:11.609 Let's provide a bit of context on why that is. 00:19:12.109 --> 00:19:15.089 Printers historically have had incredibly limited 00:19:15.089 --> 00:19:17.569 internal memory compared to the computer sending 00:19:17.569 --> 00:19:20.670 them files. Right. When a computer sends a massive 00:19:20.670 --> 00:19:23.930 high resolution image file to a printer, the 00:19:23.930 --> 00:19:26.349 printer can't always hold the entire page layout 00:19:26.349 --> 00:19:28.849 in its memory all at once before figuring out 00:19:28.849 --> 00:19:31.609 how to print it. RPN allows the printer to process 00:19:31.609 --> 00:19:34.509 the document piece by piece linearly as it reads 00:19:34.509 --> 00:19:36.869 the incoming data. Popping instructions off the 00:19:36.869 --> 00:19:38.809 stack and executing them immediately without 00:19:38.809 --> 00:19:40.690 needing to buffer the whole file is brilliant. 00:19:40.890 --> 00:19:43.970 The global footprint of this logic is also staggering. 00:19:44.250 --> 00:19:47.329 It wasn't just confined to American tech giants 00:19:47.329 --> 00:19:50.930 like HP or Burroughs. In Britain. Clive Sinclair's 00:19:50.930 --> 00:19:53.970 famous ultra -thin calculators in the mid -70s 00:19:53.970 --> 00:19:56.490 used it. Commodore implemented versions of it. 00:19:56.589 --> 00:19:58.789 And it was absolutely huge in the Soviet Union. 00:19:58.930 --> 00:20:01.529 The legendary Soviet programmable calculators 00:20:01.529 --> 00:20:05.470 like the MK -52 and MK -61 used RPN for both 00:20:05.470 --> 00:20:07.849 their manual modes and for complex programming. 00:20:08.170 --> 00:20:10.329 These were the highly robust calculators physically 00:20:10.329 --> 00:20:12.849 taken into space by Soviet cosmonauts on the 00:20:12.849 --> 00:20:15.049 Soyuz missions. It just goes to show that the 00:20:15.049 --> 00:20:17.390 underlying logic of a stack -based architecture 00:20:17.390 --> 00:20:20.640 transcends borders. languages, and politics. 00:20:20.940 --> 00:20:24.539 It is just pure, unadulterated mathematical efficiency. 00:20:24.980 --> 00:20:28.390 And that legacy actively lives on today. Enthusiast 00:20:28.390 --> 00:20:30.930 hardware companies like Swiss Micros are currently 00:20:30.930 --> 00:20:33.890 manufacturing high -end, modern calculators that 00:20:33.890 --> 00:20:37.170 faithfully recreate the classic HP RPN experience. 00:20:37.549 --> 00:20:39.890 For a brand new generation of engineers and financial 00:20:39.890 --> 00:20:42.349 analysts who want that tactile, hyper -efficient 00:20:42.349 --> 00:20:44.750 workflow right on their desk. Which is just so 00:20:44.750 --> 00:20:47.369 cool. It proves that a genuinely great idea doesn't 00:20:47.369 --> 00:20:49.890 truly die just because the mainstream consumer 00:20:49.890 --> 00:20:52.170 market moves on to something shinier. This raises 00:20:52.170 --> 00:20:53.950 an important question as we look back at the 00:20:53.950 --> 00:20:57.259 entire history we've discussed today. a quirky 00:20:57.259 --> 00:20:59.819 historical artifact or a neat parlor trick for 00:20:59.819 --> 00:21:03.420 math nerds. It is an incredibly elegant, mathematically 00:21:03.420 --> 00:21:07.420 pure way of processing logic. It completely removes 00:21:07.420 --> 00:21:10.420 ambiguity from written equations. It perfectly 00:21:10.420 --> 00:21:12.940 aligns human input with the way machine processing 00:21:12.940 --> 00:21:15.380 actually works at a fundamental hardware level. 00:21:15.480 --> 00:21:18.019 Yeah. It is a bridge between the messy human 00:21:18.019 --> 00:21:21.319 mind and the rigid logic of a silicon chip. Which 00:21:21.319 --> 00:21:23.940 brings me to a final lingering thought I want 00:21:23.940 --> 00:21:26.220 you to mull over after we wrap up today's deep 00:21:26.220 --> 00:21:28.900 dive. The ergonomic research we talked about 00:21:28.900 --> 00:21:31.279 showed pretty conclusively that RPN is fundamentally 00:21:31.279 --> 00:21:35.140 faster. It requires fewer keystrokes. It is demonstrably 00:21:35.140 --> 00:21:37.960 less prone to user error when doing complex math. 00:21:38.349 --> 00:21:40.869 Yet society largely abandoned it in consumer 00:21:40.869 --> 00:21:43.210 electronics. The mass market rejected it simply 00:21:43.210 --> 00:21:45.509 because the initial learning curve felt too alien 00:21:45.509 --> 00:21:47.329 to people who are used to writing things down 00:21:47.329 --> 00:21:50.230 on paper in the traditional algebraic way. We 00:21:50.230 --> 00:21:52.289 collectively traded peak efficiency and accuracy 00:21:52.289 --> 00:21:54.869 for the warm comfort of familiarity. We chose 00:21:54.869 --> 00:21:58.099 what was easy over what was best. Exactly. So 00:21:58.099 --> 00:21:59.980 if we are willing to make that trade -off with 00:21:59.980 --> 00:22:02.420 the calculators in our pockets, sacrificing the 00:22:02.420 --> 00:22:04.960 absolute best, most efficient method just because 00:22:04.960 --> 00:22:07.700 we're afraid of a steep learning curve, what 00:22:07.700 --> 00:22:10.220 other modern software tools, workplace workflows, 00:22:10.480 --> 00:22:12.619 or daily life systems are we currently using 00:22:12.619 --> 00:22:15.640 that are vastly less productive simply because 00:22:15.640 --> 00:22:17.779 we prefer the devil we know? That is a great 00:22:17.779 --> 00:22:20.420 question to leave on. Thank you so much for joining 00:22:20.420 --> 00:22:22.920 us for this deep dive into the fascinating upside 00:22:22.920 --> 00:22:25.720 down world of reverse Polish notation. Stay curious 00:22:25.720 --> 00:22:28.559 out there. And hey, maybe go download an RPN 00:22:28.559 --> 00:22:30.799 calculator emulator on your phone today. Try 00:22:30.799 --> 00:22:32.940 it out. Give it a solid week of use. See if it 00:22:32.940 --> 00:22:34.539 changes the way you think about breaking down 00:22:34.539 --> 00:22:35.319 and solving problems.