WEBVTT 00:00:00.000 --> 00:00:04.059 Welcome to today's deep dive. We are really thrilled 00:00:04.059 --> 00:00:06.179 to have you with us because today we are talking 00:00:06.179 --> 00:00:09.660 about a very specific, highly relatable, kind 00:00:09.660 --> 00:00:12.720 of everyday frustration. Oh yeah, a very universal 00:00:12.720 --> 00:00:15.519 one. Right. So picture this. You are sitting 00:00:15.519 --> 00:00:18.859 at your desk. trying to type a massively long, 00:00:18.960 --> 00:00:22.559 complicated mathematical equation into your standard 00:00:22.559 --> 00:00:24.539 calculator. Maybe you're doing your taxes or 00:00:24.539 --> 00:00:26.559 something. Exactly, doing your taxes or trying 00:00:26.559 --> 00:00:28.320 to figure out a messy split bill with friends. 00:00:28.559 --> 00:00:30.760 You are opening parentheses, you're closing parentheses. 00:00:30.800 --> 00:00:33.799 You are hoping you remembered the order of operations 00:00:33.799 --> 00:00:36.740 from, you know, middle school algebra. Please 00:00:36.740 --> 00:00:39.890 excuse my dear Aunt Sally. Yes, but... You get 00:00:39.890 --> 00:00:42.170 paranoid. So you hit the clear button just to 00:00:42.170 --> 00:00:44.649 be safe, completely losing 10 minutes of tedious 00:00:44.649 --> 00:00:47.170 work. You start over, you finally hit the equal 00:00:47.170 --> 00:00:49.689 sign, and what do you get? Syntax error. Syntax 00:00:49.689 --> 00:00:52.890 error. You are lost in a sea of brackets. But 00:00:52.890 --> 00:00:54.649 what if there was an entirely different way to 00:00:54.649 --> 00:00:57.049 do math, a way where there are zero parentheses, 00:00:57.369 --> 00:00:59.710 and where you literally never have to worry about 00:00:59.710 --> 00:01:01.810 the order of operations ever again? I mean, it 00:01:01.810 --> 00:01:04.650 sounds almost like magic when you phrase it that 00:01:04.650 --> 00:01:07.730 way, but it's actually a highly logical, deeply 00:01:07.730 --> 00:01:10.840 practical system. And it isn't just a quirk of 00:01:10.840 --> 00:01:13.340 calculator history either. No, it's not. It's 00:01:13.340 --> 00:01:15.920 a fascinating study in how humans interact with 00:01:15.920 --> 00:01:19.159 machines and how sometimes the way we are traditionally 00:01:19.159 --> 00:01:21.700 taught to think isn't actually the most efficient 00:01:21.700 --> 00:01:24.079 way to get things done. Today, we're exploring 00:01:24.079 --> 00:01:27.120 the topic of reverse Polish notation, which is 00:01:27.120 --> 00:01:29.719 widely known as RPN. We've pulled together a 00:01:29.719 --> 00:01:32.219 really comprehensive Wikipedia article detailing 00:01:32.219 --> 00:01:34.700 the history, the mechanics, and the practical 00:01:34.700 --> 00:01:37.459 implications of RPN. It's a great source. It 00:01:37.459 --> 00:01:39.980 really is. Our mission for this Deep Dives is 00:01:39.980 --> 00:01:42.180 to understand how a purely theoretical logic 00:01:42.180 --> 00:01:45.620 concept from 1924 became a hidden powerhouse 00:01:45.620 --> 00:01:48.439 of early computing and eventually a cult favorite 00:01:48.439 --> 00:01:50.739 among engineers and Wall Street bankers. Wall 00:01:50.739 --> 00:01:53.219 Street loved this stuff. They really did. We 00:01:53.219 --> 00:01:55.180 are going to look at what this whole system teaches 00:01:55.180 --> 00:01:57.920 us about pure efficiency. And to help me synthesize 00:01:57.920 --> 00:02:00.200 this incredibly dense, globe -spanning history, 00:02:00.420 --> 00:02:03.030 I've got our resident expert here. I am very 00:02:03.030 --> 00:02:04.790 glad to be here. The story of reverse Polish 00:02:04.790 --> 00:02:07.609 notation is it's one of those great technological 00:02:07.609 --> 00:02:11.289 narratives. It spans from European logicians 00:02:11.289 --> 00:02:14.569 to wartime computer pioneers right down to the 00:02:14.569 --> 00:02:16.969 device sitting in your pocket today. Ultimately, 00:02:17.129 --> 00:02:19.590 it's a story about the relentless pursuit of 00:02:19.590 --> 00:02:22.129 absolute optimization. OK, let's unpack this. 00:02:22.210 --> 00:02:25.250 What actually is reverse Polish notation? If 00:02:25.250 --> 00:02:27.110 you have a standard calculator in front of you 00:02:27.110 --> 00:02:29.569 right now, you use what is called infix notation. 00:02:29.889 --> 00:02:32.250 Right. That just means the operator. the plus 00:02:32.250 --> 00:02:34.650 or minus sign goes in between the numbers, three 00:02:34.650 --> 00:02:37.469 plus four. But in reverse Polish notation, the 00:02:37.469 --> 00:02:40.090 operators follow the operands. So instead of 00:02:40.090 --> 00:02:42.569 three plus four, you'd enter three, then four, 00:02:42.650 --> 00:02:44.949 and then the plus sign. Right. And to understand 00:02:44.949 --> 00:02:46.509 the name itself, we kind of have to look at the 00:02:46.509 --> 00:02:48.370 Polish part first. Yeah. Where does that come 00:02:48.370 --> 00:02:50.789 from? It refers to the nationality of the brilliant 00:02:50.789 --> 00:02:55.069 logician Jan Ukasiewicz. Back in 1924, he invented 00:02:55.069 --> 00:02:58.419 standard Polish notation. In his system, which 00:02:58.419 --> 00:03:01.060 is also known as prefix notation, the operators 00:03:01.060 --> 00:03:03.340 precede the operands. So the plus sign comes 00:03:03.340 --> 00:03:05.780 first. Exactly. You'd put the plus sign first, 00:03:05.979 --> 00:03:09.819 then the 3, then the 4. RPN, or postfix notation, 00:03:10.300 --> 00:03:13.319 is quite literally the reverse of Ukasiewicz's 00:03:13.319 --> 00:03:16.719 invention. Entering 3 or 4 plus feels incredibly 00:03:16.719 --> 00:03:19.539 abstract until you understand how the machine 00:03:19.539 --> 00:03:22.550 is actually processing it. To do that, we really 00:03:22.550 --> 00:03:25.169 need to talk about the stack. The stack is everything. 00:03:25.590 --> 00:03:27.810 It is. Think of the stack like one of those spring 00:03:27.810 --> 00:03:29.689 -loaded plate dispensers you see at a buffet 00:03:29.689 --> 00:03:32.189 restaurant. It's last in, first out construct. 00:03:32.569 --> 00:03:34.590 You push a plate onto the top, and when you need 00:03:34.590 --> 00:03:36.590 one, you pop the top plate off. That's a great 00:03:36.590 --> 00:03:39.009 mental model. Thanks. Let's walk through a slightly 00:03:39.009 --> 00:03:41.090 longer example from our sources to make it clear. 00:03:41.330 --> 00:03:45.150 Say you want to calculate 3 minus 4 plus 5. In 00:03:45.150 --> 00:03:49.449 RPN, you would punch in 3, enter 4 minus 5 plus. 00:03:49.810 --> 00:03:52.139 Exactly. Exactly. And to visualize the physical 00:03:52.139 --> 00:03:53.900 mechanics of what you just described, the pushing 00:03:53.900 --> 00:03:56.240 and topping, we can look at it step by step. 00:03:56.520 --> 00:03:58.520 First, the number three is pushed onto the stack. 00:03:58.659 --> 00:04:01.020 The number four is pushed on top of it. At this 00:04:01.020 --> 00:04:03.479 moment, the four is on top and the three is sitting 00:04:03.479 --> 00:04:05.719 below it. OK, wait, let's hold there for a second. 00:04:05.939 --> 00:04:08.099 So I've pushed the three and I've pushed the 00:04:08.099 --> 00:04:10.419 four. They're sitting on my mental string loaded 00:04:10.419 --> 00:04:13.620 plate dispenser. The four is the top plate. What 00:04:13.620 --> 00:04:15.939 happens the exact millisecond I hit the minus 00:04:15.939 --> 00:04:18.639 button? What's fascinating here is that the calculator 00:04:18.639 --> 00:04:22.920 automatically removes or pops those top two items 00:04:22.920 --> 00:04:25.620 from the stack. It performs the calculation of 00:04:25.620 --> 00:04:28.860 3 minus 4, and then it puts the result, which 00:04:28.860 --> 00:04:31.680 is negative 1, right back onto the top of the 00:04:31.680 --> 00:04:33.540 stack. Oh, I see. Yeah, then you enter the 5, 00:04:33.720 --> 00:04:35.480 pushing it onto the stack above your negative 00:04:35.480 --> 00:04:38.019 1. You hit the plus sign, it pops them both off, 00:04:38.079 --> 00:04:40.139 adds them, and leaves you with your final answer 00:04:40.139 --> 00:04:43.100 of 4. I hear you saying it is elegant, but... 00:04:43.470 --> 00:04:46.410 If I'm being totally honest, writing 3, 4 plus 00:04:46.410 --> 00:04:49.670 feels incredibly counterintuitive. Does it actually 00:04:49.670 --> 00:04:52.050 save that much time, or is it just a flex for 00:04:52.050 --> 00:04:53.970 engineers who want to look smart? No, it saves 00:04:53.970 --> 00:04:56.589 a massive amount of time, and to see why, we 00:04:56.589 --> 00:04:59.250 have to look at a more complex equation. Think 00:04:59.250 --> 00:05:01.290 about the headache of a bulky equation like this. 00:05:01.610 --> 00:05:04.540 Open parenthesis, 3 plus 4. Close parenthesis, 00:05:04.560 --> 00:05:07.500 multiplied by, open parenthesis, 5 plus 6, close 00:05:07.500 --> 00:05:10.040 parenthesis. That's exhausting just to say out 00:05:10.040 --> 00:05:12.199 loud. Right. Think of how many keystrokes that 00:05:12.199 --> 00:05:15.579 takes. In RPN, that whole messy bracket -filled 00:05:15.579 --> 00:05:18.339 equation gracefully flattens out into a linear 00:05:18.339 --> 00:05:21.920 left -to -right sequence. 3, enter 4, plus 5, 00:05:22.120 --> 00:05:25.660 enter 6, plus multiply. Wow. No brackets, no 00:05:25.660 --> 00:05:27.660 holding numbers in your head. Here's where it 00:05:27.660 --> 00:05:29.759 gets really interesting. If this was invented 00:05:29.759 --> 00:05:32.879 as a theoretical logic concept in the 1920s, 00:05:32.899 --> 00:05:35.459 how did it actually make the jump into computers? 00:05:35.660 --> 00:05:39.120 Who was the first person to try coding a parenthesis 00:05:39.120 --> 00:05:42.120 -free system into a machine? The very first computer 00:05:42.120 --> 00:05:45.079 to use post -fix notation wasn't some sleek consumer 00:05:45.079 --> 00:05:48.879 gadget. It was Konrad Zuse's Z3 computer in Germany 00:05:48.879 --> 00:05:53.079 way back in 1941, followed by a Z4 in 1945. 1941, 00:05:53.420 --> 00:05:55.360 so right in the middle of the war. Yes, and Zuse's 00:05:55.360 --> 00:05:58.000 Z3 allowed operators in dialogue mode to enter 00:05:58.000 --> 00:06:00.120 two operands followed by the desired operation. 00:06:00.500 --> 00:06:02.600 But there is a tragic historical detail here, 00:06:02.699 --> 00:06:05.180 that pioneering Z3 machine was completely destroyed 00:06:05.180 --> 00:06:08.759 in a bombing raid on December 21st, 1943. Wow, 00:06:08.819 --> 00:06:10.839 so his breakthrough was just lost. to history 00:06:10.839 --> 00:06:13.879 in the rubble? Essentially, yes. It remained 00:06:13.879 --> 00:06:16.740 unknown outside of Germany for a long time, though 00:06:16.740 --> 00:06:19.360 a replica was eventually built with Zuse's help 00:06:19.360 --> 00:06:23.399 much later, in 1961. But that isolation during 00:06:23.399 --> 00:06:26.040 the wartime and post -war period set the stage 00:06:26.040 --> 00:06:28.139 for one of the most common phenomenons in the 00:06:28.139 --> 00:06:30.639 history of science. Parallel reinvention. Exactly, 00:06:30.899 --> 00:06:33.100 parallel reinvention. Right, where a bunch of 00:06:33.100 --> 00:06:35.160 different people... independently invent the 00:06:35.160 --> 00:06:37.839 exact same thing without ever talking to each 00:06:37.839 --> 00:06:40.180 other. Precisely. And the reason they were all 00:06:40.180 --> 00:06:42.819 inventing RPN at the same time comes down to 00:06:42.819 --> 00:06:44.879 what we could call the war for memory. If you 00:06:44.879 --> 00:06:46.819 are listening to this on a smartphone right now, 00:06:46.980 --> 00:06:50.160 you have billions of bytes of memory in your 00:06:50.160 --> 00:06:52.579 pocket. Basically unlimited. Right. But in the 00:06:52.579 --> 00:06:55.879 1950s, computer memory was physical, massive 00:06:55.879 --> 00:06:58.899 and incredibly expensive. It relied on vacuum 00:06:58.899 --> 00:07:01.759 tubes and delay lines. Storing a parenthesis 00:07:01.759 --> 00:07:04.160 in a computer's memory cost. precious hardware 00:07:04.160 --> 00:07:06.519 space. Literally wasting physical space on a 00:07:06.519 --> 00:07:10.079 bracket. Yes. So scientists were desperate to 00:07:10.079 --> 00:07:13.060 optimize. The reverse Polish scheme was proposed 00:07:13.060 --> 00:07:17.220 again in 1954 by Arthur Birx, Don Warren, and 00:07:17.220 --> 00:07:20.839 Jesse Wright. Then it was independently reinvented 00:07:20.839 --> 00:07:23.980 again in the early 1960s by Friedrich Bauer and 00:07:23.980 --> 00:07:26.879 Edsger Dijkstra to reduce computer memory access 00:07:26.879 --> 00:07:29.220 times. I want to highlight Dijkstra for a moment 00:07:29.220 --> 00:07:31.579 because the sources give a really great visual 00:07:31.579 --> 00:07:34.220 detail about his work. When he was figuring out 00:07:34.220 --> 00:07:36.740 how to mechanically convert standard math into 00:07:36.740 --> 00:07:39.839 this post -fix notation. He invented something 00:07:39.839 --> 00:07:42.279 called the shunting yard algorithm. That's a 00:07:42.279 --> 00:07:44.459 classic algorithm. Yeah. And he named it that 00:07:44.459 --> 00:07:46.720 because he envisioned the numbers as train cars 00:07:46.720 --> 00:07:49.199 rolling down a track and the mathematical operators 00:07:49.199 --> 00:07:51.860 pluses and minuses being temporarily held on 00:07:51.860 --> 00:07:53.899 a side rail, just like the sorting of trains 00:07:53.899 --> 00:07:56.300 in a railroad shunting yard. That train analogy 00:07:56.300 --> 00:07:58.680 is vital because it highlights a massive conceptual 00:07:58.680 --> 00:08:01.449 shift. Dijkstra wasn't trying to build a machine 00:08:01.449 --> 00:08:03.389 that could read math like a grammatical sentence. 00:08:03.670 --> 00:08:06.069 He was trying to turn math into a set of actionable 00:08:06.069 --> 00:08:08.350 instructions. An active recipe rather than a 00:08:08.350 --> 00:08:10.850 static statement. Exactly. And he wasn't alone 00:08:10.850 --> 00:08:14.389 in this realization. In the mid -1950s in Australia, 00:08:14.689 --> 00:08:17.550 a philosopher and computer scientist named Charles 00:08:17.550 --> 00:08:20.490 Hamlin created a high -level programming language 00:08:20.490 --> 00:08:22.970 called George, which utilized these concepts. 00:08:23.290 --> 00:08:26.050 His work was largely driven by the sheer memory 00:08:26.050 --> 00:08:28.670 overhead required to process mathematical brackets. 00:08:29.009 --> 00:08:32.029 So we have Germany, the UK, Australia. What about 00:08:32.029 --> 00:08:34.740 the United States? Over in the U .S., around 00:08:34.740 --> 00:08:38.539 1958, a designer named Robert Barton was independently 00:08:38.539 --> 00:08:41.879 developing RPN for the massive Burroughs B5000 00:08:41.879 --> 00:08:45.159 computer. And how did he stumble onto it? Was 00:08:45.159 --> 00:08:48.210 he reading Hamblin's work from Australia? Not 00:08:48.210 --> 00:08:51.149 at all. He happened to read a 1954 textbook on 00:08:51.149 --> 00:08:54.210 symbolic logic by Irving Kopi. Barton found a 00:08:54.210 --> 00:08:56.590 brief reference to Polish notation in the text, 00:08:56.690 --> 00:08:59.830 went down a massive rabbit hole reading Jan Jukasiewicz's 00:08:59.830 --> 00:09:02.289 original works, and applied it to computer architecture 00:09:02.289 --> 00:09:04.389 before he even knew about the innovations happening 00:09:04.389 --> 00:09:06.809 in Australia. That's incredible. It really highlights 00:09:06.809 --> 00:09:09.090 how this concept was a fundamental puzzle piece 00:09:09.090 --> 00:09:10.950 waiting to be found by the hardware designers 00:09:10.950 --> 00:09:13.539 of the era. But it didn't stay locked away in 00:09:13.539 --> 00:09:15.720 those massive room -sized mainframes forever. 00:09:16.279 --> 00:09:18.580 Eventually, it had to make the jump to the calculators 00:09:18.580 --> 00:09:20.559 sitting on people's desks. The transition really 00:09:20.559 --> 00:09:23.919 kicked off in June 1963 with the Fryden EC130 00:09:23.919 --> 00:09:27.120 desktop calculator. This device was designed 00:09:27.120 --> 00:09:29.980 by Bob Reagan. And it featured a four level stack 00:09:29.980 --> 00:09:32.440 that was actually displayed on a tiny cathode 00:09:32.440 --> 00:09:35.159 ray tube screen. A CRT screen on a calculator. 00:09:35.360 --> 00:09:37.220 Yeah. And they showed the stack upside down. 00:09:37.259 --> 00:09:39.659 So the last in first out register was visibly 00:09:39.659 --> 00:09:41.820 sitting at the bottom of the screen. Following 00:09:41.820 --> 00:09:45.139 that, you had the Monroe Epic around 1966 supporting 00:09:45.139 --> 00:09:48.000 a similar input scheme. But the company that 00:09:48.000 --> 00:09:50.919 truly turned RPN into a religion. Was Hewlett 00:09:50.919 --> 00:09:52.980 Packard. Was absolutely Hewlett Packard. Hewlett 00:09:52.980 --> 00:09:55.879 Packard totally dominated this space. Their engineers 00:09:55.879 --> 00:09:58.679 designed the 9100A desktop. top calculator in 00:09:58.679 --> 00:10:02.039 1968, utilizing a three -level stack. They had 00:10:02.039 --> 00:10:04.500 working registers named X for the keyboard, Y 00:10:04.500 --> 00:10:07.179 to accumulate data, and a visible storage register 00:10:07.179 --> 00:10:10.419 Z for temporary holds. A very solid design. It 00:10:10.419 --> 00:10:13.500 was. This calculator was a massive hit and popularized 00:10:13.500 --> 00:10:15.759 RPN among the scientific and engineering communities. 00:10:16.080 --> 00:10:18.759 But in 1972, they fundamentally changed the game. 00:10:18.899 --> 00:10:22.190 That was the year they released the HP -35. It 00:10:22.190 --> 00:10:25.490 was the world's first handheld scientific calculator. 00:10:25.789 --> 00:10:27.750 If you are listening to this and trying to visualize 00:10:27.750 --> 00:10:31.149 that era, imagine you were an engineer in 1972 00:10:31.149 --> 00:10:35.070 holding this HP -35. This wasn't just a calculator. 00:10:35.190 --> 00:10:37.470 This was a supercomputer that could suddenly 00:10:37.470 --> 00:10:39.870 fit inside your pocket. And it introduced what 00:10:39.870 --> 00:10:42.750 is now known as the classical four -level RPN 00:10:42.750 --> 00:10:46.210 stack. Instead of three levels, you had the XYZ 00:10:46.210 --> 00:10:50.080 and T -registers T standing for top. This specific 00:10:50.080 --> 00:10:52.940 architecture had very distinct, highly optimized 00:10:52.940 --> 00:10:55.779 rules. How so? Well, for instance, the enter 00:10:55.779 --> 00:10:57.860 key, which was mandatory since you didn't have 00:10:57.860 --> 00:11:00.919 an equals sign, uniquely duplicated values into 00:11:00.919 --> 00:11:03.299 the Y register under certain conditions. And 00:11:03.299 --> 00:11:04.820 when you popped a number off the stack, that 00:11:04.820 --> 00:11:07.200 top T register would duplicate itself on drops. 00:11:07.379 --> 00:11:09.679 They called it top stack level repetition. So 00:11:09.679 --> 00:11:11.580 it was just copying that top value down as you 00:11:11.580 --> 00:11:13.899 worked. Right. The entire purpose was to ease 00:11:13.899 --> 00:11:16.480 complex calculations and save the user precious 00:11:16.480 --> 00:11:19.580 keystrokes. HP lean. into this identity hard. 00:11:19.799 --> 00:11:21.840 In the 1980s, they even handed out promotional 00:11:21.840 --> 00:11:24.980 hats that just said no equals. I love that. It 00:11:24.980 --> 00:11:27.179 is such an incredibly nerdy piece of marketing, 00:11:27.299 --> 00:11:29.580 but it was brilliant. It was a boast about the 00:11:29.580 --> 00:11:32.019 quality of their engineering and a literal reference 00:11:32.019 --> 00:11:34.700 to the fact that their RPM calculators didn't 00:11:34.700 --> 00:11:38.080 have an equals key. They used RPN on every handheld 00:11:38.080 --> 00:11:41.000 calculator they sold, scientific, financial, 00:11:41.120 --> 00:11:44.419 programmable, until about 1977. But it didn't 00:11:44.419 --> 00:11:46.480 stop there. Right. The sources note that the 00:11:46.480 --> 00:11:48.379 evolution didn't stop with that four -level stack. 00:11:48.639 --> 00:11:53.740 In 1986, HP introduced RPL. The shift to RPL 00:11:53.740 --> 00:11:56.480 was incredibly significant. It moved away from 00:11:56.480 --> 00:11:59.240 that fixed, rigid four -level stack and introduced 00:11:59.240 --> 00:12:02.460 a dynamic stack. This new stack was only limited 00:12:02.460 --> 00:12:04.559 by the amount of available memory on the physical 00:12:04.559 --> 00:12:07.539 device. Wait, the sources also call RPL an object 00:12:07.539 --> 00:12:10.500 -oriented successor to RPN. I'm used to my calculator 00:12:10.500 --> 00:12:12.600 just handling flat numbers. What does it actually 00:12:12.600 --> 00:12:15.179 mean for a calculator to treat something as an 00:12:15.179 --> 00:12:17.460 object on a stack? That is a great clarification 00:12:17.460 --> 00:12:21.320 to make. In the older traditional RPN calculators, 00:12:21.360 --> 00:12:24.320 the stack could only hold numbers, a three, a 00:12:24.320 --> 00:12:27.940 four, a decimal. But a dynamic object -oriented 00:12:27.940 --> 00:12:30.879 stack can hold entirely different kinds of data. 00:12:31.039 --> 00:12:33.080 You could push a text string onto the stack. 00:12:33.240 --> 00:12:35.500 You could push a complex mathematical matrix 00:12:35.500 --> 00:12:38.980 or an entire list of variables. So it's not just 00:12:38.980 --> 00:12:41.559 basic arithmetic anymore. Not at all. You could 00:12:41.559 --> 00:12:44.299 even push a graphic image onto the stack, and 00:12:44.299 --> 00:12:46.379 the calculator's programming would know how to 00:12:46.379 --> 00:12:49.220 handle that specific object. That drastically 00:12:49.220 --> 00:12:51.059 changes the behavior of the machine, doesn't 00:12:51.059 --> 00:12:53.539 it? Because if you have an unlimited stack holding 00:12:53.539 --> 00:12:55.899 all these different objects, there is no top 00:12:55.899 --> 00:12:57.879 register to automatically duplicate when you 00:12:57.879 --> 00:13:00.350 drop a value anymore. Correct. Plus, instead 00:13:00.350 --> 00:13:02.529 of just silently dropping values off the stack 00:13:02.529 --> 00:13:04.450 when it overflowed like the older models did, 00:13:04.590 --> 00:13:06.789 the RPL system would actually display an error 00:13:06.789 --> 00:13:09.350 message if you ran out of physical memory. But 00:13:09.350 --> 00:13:11.009 we should be careful to point out that while 00:13:11.009 --> 00:13:13.929 HP gets the lion's share of the historical credit, 00:13:14.389 --> 00:13:17.070 RPN was definitely not just an HP phenomenon. 00:13:17.590 --> 00:13:19.509 Right. The sources list a surprising number of 00:13:19.509 --> 00:13:22.470 fascinating implementations globally. In Britain, 00:13:22.649 --> 00:13:24.950 Clive Sinclair released the Sinclair Scientific 00:13:24.950 --> 00:13:29.490 in 1974 using RPN. Commodore produced their Minuteman 00:13:29.490 --> 00:13:32.009 models. The Soviets used it too. Yes. In the 00:13:32.009 --> 00:13:34.129 Soviet Union, programmable calculators like the 00:13:34.129 --> 00:13:38.509 MK -52 and MK -61 utilized RPN for both automatic 00:13:38.509 --> 00:13:41.950 mode and programming. It is amazing how enduring 00:13:41.950 --> 00:13:44.450 those designs are. Modern Russian calculators 00:13:44.450 --> 00:13:46.850 designed in Novosibirsk since 2007 are actually 00:13:46.850 --> 00:13:49.190 still backwards compatible with those Soviet 00:13:49.190 --> 00:13:51.990 models. That's wild. And there is a huge community 00:13:51.990 --> 00:13:54.250 today building modern hardware, like the Swiss 00:13:54.250 --> 00:13:57.509 Micro's replicas of classic HP devices. You also 00:13:57.509 --> 00:14:00.110 see RPN living on in software languages. The 00:14:00.110 --> 00:14:02.529 PostScript page description language uses it, 00:14:02.590 --> 00:14:04.889 as does the stack -oriented programming language 00:14:04.889 --> 00:14:07.500 for it. So what does this all mean? We have traced 00:14:07.500 --> 00:14:09.500 this from wartime mainframes to modern software, 00:14:09.759 --> 00:14:11.559 but the lingering question for anyone listening 00:14:11.559 --> 00:14:14.659 is, why? If I already spent years in school learning 00:14:14.659 --> 00:14:17.320 how to write 3 plus 4, why should I retrain my 00:14:17.320 --> 00:14:19.799 adult brain to write 3, 4 plus? The answer comes 00:14:19.799 --> 00:14:22.940 down to two highly measurable metrics, speed 00:14:22.940 --> 00:14:26.929 and accuracy. Testing comparing RPN with standard 00:14:26.929 --> 00:14:29.929 algebraic notation consistently found that RPN 00:14:29.929 --> 00:14:33.289 led to much faster calculations. Now, initially, 00:14:33.409 --> 00:14:35.549 people assumed this was because the system placed 00:14:35.549 --> 00:14:38.649 a lower cognitive load on the brain, but later 00:14:38.649 --> 00:14:40.769 research clarified the nuance. It wasn't that 00:14:40.769 --> 00:14:42.710 the brain was working less, right? It was purely 00:14:42.710 --> 00:14:45.549 physical. Exactly. The increased speed simply 00:14:45.549 --> 00:14:47.669 came down to the fact that the user had to press 00:14:47.669 --> 00:14:50.850 far fewer keys. Without the need to open and 00:14:50.850 --> 00:14:53.409 close parentheses, you are physically doing less 00:14:53.409 --> 00:14:56.169 work. to input a complex formula. Furthermore, 00:14:56.370 --> 00:14:58.470 the testing showed that users of reverse Polish 00:14:58.470 --> 00:15:01.009 calculators actually make fewer mistakes than 00:15:01.009 --> 00:15:03.330 users of standard calculators. I really like 00:15:03.330 --> 00:15:05.990 the comparison from the text that likened using 00:15:05.990 --> 00:15:08.750 an RPN calculator to the workflow of using a 00:15:08.750 --> 00:15:11.070 traditional analog slide rule. Yes, that's the 00:15:11.070 --> 00:15:14.129 perfect analogy. With a slide rule, you are constantly 00:15:14.129 --> 00:15:16.590 feeding intermediate results right back into 00:15:16.590 --> 00:15:18.690 the next step of the problem without needing 00:15:18.690 --> 00:15:20.450 to write anything down on a piece of scratch 00:15:20.450 --> 00:15:23.509 paper or hit an equals key to finalize a thought. 00:15:24.469 --> 00:15:27.309 RPN operates the exact same way. You aren't stopping 00:15:27.309 --> 00:15:29.250 and starting. You're just flowing through the 00:15:29.250 --> 00:15:31.350 math. If we connect this to the bigger picture, 00:15:31.409 --> 00:15:33.169 though, we do have to acknowledge the catch. 00:15:33.929 --> 00:15:36.009 The sources provide a very balanced view here. 00:15:36.549 --> 00:15:39.330 Anecdotal evidence strongly suggests that RPN 00:15:39.330 --> 00:15:41.809 is, in fact, more difficult for users who have 00:15:41.809 --> 00:15:45.570 already had standard algebraic notation hardwired 00:15:45.570 --> 00:15:48.289 into their brains. It demands a totally different 00:15:48.289 --> 00:15:50.590 way of parsing a problem. That makes total sense. 00:15:50.789 --> 00:15:52.850 If you spend your whole life reading sentences 00:15:52.850 --> 00:15:55.610 formatted as subject -verb -object, suddenly 00:15:55.610 --> 00:15:57.610 switching to subject -object -verb is going to 00:15:57.610 --> 00:16:00.009 trip you up, even if it technically uses fewer 00:16:00.009 --> 00:16:03.169 letters. Exactly. So it represents a classic... 00:16:03.309 --> 00:16:05.769 human -computer interaction trade -off. You are 00:16:05.769 --> 00:16:08.330 trading a steep initial learning curve for a 00:16:08.330 --> 00:16:10.970 lifetime of long -term efficiency. Let's recap 00:16:10.970 --> 00:16:13.809 this incredible journey. We started with a Polish 00:16:13.809 --> 00:16:17.889 logician, Jan Jukasiewicz, in the 1920s, who 00:16:17.889 --> 00:16:20.370 just wanted a cleaner way to write logic equations. 00:16:21.580 --> 00:16:24.460 purely theoretical concept, was grabbed by Conrad 00:16:24.460 --> 00:16:26.580 Zuse for the earliest computers to save precious 00:16:26.580 --> 00:16:29.600 memory, and then mathematically refined by computer 00:16:29.600 --> 00:16:32.100 scientists all over the globe, from Australia 00:16:32.100 --> 00:16:34.639 to the United States. A truly global effort. 00:16:34.940 --> 00:16:37.940 It revolutionized the calculator industry, largely 00:16:37.940 --> 00:16:40.440 thanks to HP putting an incredibly powerful four 00:16:40.440 --> 00:16:42.960 -level stack right into the pockets of engineers 00:16:42.960 --> 00:16:45.639 and scientists. And ultimately, it proved that 00:16:45.639 --> 00:16:48.139 the way we are taught math in grade school isn't 00:16:48.139 --> 00:16:50.159 the only way for humans and machines to communicate. 00:16:50.620 --> 00:16:53.320 I think that is the most enduring lesson of reverse 00:16:53.320 --> 00:16:55.399 Polish notation. We touched on this earlier with 00:16:55.399 --> 00:16:57.539 Dijkstra's train yard analogy. But RPN forces 00:16:57.539 --> 00:16:59.879 us to look at an equation not as a static sentence 00:16:59.879 --> 00:17:02.580 to be passively read, but as an active sequence 00:17:02.580 --> 00:17:05.039 of events to be executed. And that is a mindset 00:17:05.039 --> 00:17:07.680 shift that goes far beyond mathematics. How so? 00:17:08.079 --> 00:17:10.140 Well, I would encourage you listening to this 00:17:10.140 --> 00:17:13.180 to consider your own workflows. How many systems 00:17:13.180 --> 00:17:15.839 in your daily life are currently bogged down 00:17:15.839 --> 00:17:18.980 by metaphorical parentheses? What standard conventions 00:17:18.980 --> 00:17:21.420 are you clinging to just because it is how you 00:17:21.420 --> 00:17:23.740 were initially taught? You might find that some 00:17:23.740 --> 00:17:26.200 areas of your work or thinking could become infinitely 00:17:26.200 --> 00:17:29.099 faster if you just stripped away those conventional 00:17:29.099 --> 00:17:31.700 brackets, embraced a sleeper learning curve, 00:17:31.779 --> 00:17:34.019 and learned to approach the problem in reverse. 00:17:34.440 --> 00:17:36.930 That is a brilliant thought to end on. Thank 00:17:36.930 --> 00:17:38.630 you so much for joining us on this custom deep 00:17:38.630 --> 00:17:41.130 dive into reverse Polish notation. We hope you 00:17:41.130 --> 00:17:43.269 walk away with a little more appreciation for 00:17:43.269 --> 00:17:45.369 that trusty calculator and perhaps a totally 00:17:45.369 --> 00:17:47.589 new perspective on what efficiency really looks 00:17:47.589 --> 00:17:50.490 like. Until next time, keep questioning the obvious.