Empire of the Sum

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Keith Houston: You trace it all the way back, and it’s like, “Oh, the entire recorded history of humanity is kind of driven by the fact that we have to count things.”

Roman Mars: This is author Keith Houston. He writes all about the evolution of the calculator in his new book. 

Keith Houston: My name is Keith Houston, and I am the author of Empire of the Sum: The Rise and Reign of the Pocket Calculator. 

Roman Mars: Well, let’s talk about this need for calculation and for accounting. It seems like we, you know, as organisms seem to recognize that we always need to count more than we have the tools to count. Let’s talk about, like, you know, the historical origin of counting and that drive. 

Keith Houston: I think the funny thing is, in a sense, there’s not a historical origin of it. There’s actually a biological origin of it. It turns out that lots of animals count. There are a series of experiments, most prominently with a parrot in, I think, the 20th century, who was taught to count up to six. Ravens or crows apparently had previously been found to be able to count up to seven. So, the parrot wasn’t that impressive. But the parrot also had a concept of zero, which is incredible. The parrot understood that there was a thing which was there is nothing here to be counted. And so, you know, animals can count. Insects can count. Spiders are not very good. I think some spiders can manage two, and they’re surprised if they see more than two things. And humans can count. Even human babies have some innate ability to count. I think there’s a sort of canonical example, which is if you show a baby some number of objects and then you hide those objects and you take one away and you add one or you add one and then you reveal it again, they are surprised–they display surprise–because the number of things that they’re looking at has changed. So, humans can count even before we’re old enough to be able to articulate what that means. 

Roman Mars: Yeah. Yeah. And then so, you know, in an effort to count–I don’t know how the parrot does it–but we tend to use our fingers and toes and, you know, different parts of our bodies. Could you talk about that and then the process of, you know, weaning ourselves off of that limitation?

Keith Houston: There’s been a bunch of different ethnographic research that shows that we almost certainly learned to count using our fingers. A lot of different groups of humans at different times and in different places have had number systems kind of with linguistic bases of five or ten because, of course, we have five digits on each hand–or maybe 20 because you maybe think of your fingers and your toes as being a kind of a complete set. So, we’ve always had this ability to count with our bodies. We got really, really good at finger counting. There are a bunch of clues in Sumerian writing. The Sumerians were the people who lived in Mesopotamia–the land between the Tigris and Euphrates River–in the ancient Near East. And then what seemed to happen was the Egyptians got in on this finger counting lark as well. And there are some paintings that show Egyptian merchants making interesting shapes with their hands. No one was really sure what this was. And then the same thing recurs in ancient Rome. There’s a statue somewhere in Rome of the god Janus. And he was said to be making signs with his hands that represented the number of days in the year. And, of course, this is even more than ten. It’s more than 60. Someone is counting to more than 300 using their fingers. But again, no one quite knew how. So, we went a really long way with our hands. But, of course, at the same time, we realized that this is not very practical. Your hands are good for recording numbers. They’re not necessarily good for manipulating them–for actually doing maths with them. And that’s where we start to think about calculating devices. 

Roman Mars: The first such calculation device to enter the picture was the abacus. You probably have seen some version of an abacus before–you know, wooden frame with rows of wires cutting through it. 

Keith Houston: Those wires have beads strung onto them–typically ten beads per wire. And you can think of it as, “Okay, this bead or this wire represents the units. This one represents the tens and hundreds and the thousands and so on.”

Roman Mars: It’s unclear from where exactly the abacus originated. But there are versions of this device in ancient civilizations all around the world as early as 300 B.C. 

Keith Houston: There’s a really elliptical reference to what could be an abacus in a book written in China. And Rome and China were talking; merchants were moving back and forth and communicating between these two sorts of superpowers. So, it’s entirely possible that the idea for the abacus went in one direction or the other. I don’t think anyone really knows. But certainly, by this point, you have the concept of the abacus. You have the word “abacus” as well, in fact, in Latin. China and Japan and Korea seem to really love the concept of the abacus almost down to the present day, whereas it seems to kind of go away in the West. The tool that really, I think, succeeded the abacus for us was writing. We got used to what we call Hindu Arabic numerals because they came out of a tradition in India and in the Arab countries to use decimal numbers and a place value notation. So, if I write down the number nine, it means something different. If I just write one nine and if I put another nine beside it, that suddenly means 99. That’s the place value part of it. One of those nines means 90. One of them means nine. And it turns out this is a really flexible way to write numbers. It’s really good for maths. It’s certainly far better than an abacus. So that’s where pen and paper is better. So, people who used pen and paper were called “Algorists.” And the people who use abacuses were called “Abacists.” And there was a bit of a sort of a rivalry between the two of them for quite a long time. And eventually, of course, in the West, the Algorists came out on top. If we’re doing maths by hand, we’re not using an abacus. We’re doing it with a, you know, pen or a pencil on a piece of paper. 

Roman Mars: It sounds like one of the key advantages of being an Algorists–using a pen and paper and a place value system–is that you could keep track of your calculations outside of your own head. 

Keith Houston: Yes. Definitely. You can show your working. 

Roman Mars: You mentioned, you know, the abacus has a long and storied evolution. But when it comes to these counting devices and calculators that you talk about in your book, there’s also this kind of complete obliteration of form sometimes to get to the new one, in a way that’s kind of unlike a lot of other sort of physical object evolution. 

Keith Houston: Yes. There’s definitely a real step change between each sort of class of calculating devices. And I think that is probably the reason why they’re so different to one another. You start off with counting boards and abacus, and in the West, we move towards pen and paper. And then really the next big innovation is a thing called the “slide rule.” 

Roman Mars: The slide rule was a major innovation that came along in the 1600s. It looks a bit like how it sounds. It’s like your average ruler–often no longer than 12 inches–marked with lots of numbers and equipped with a sliding mechanism. The slide rule was created because a new discovery had come along–something called the “logarithm.” Logarithms are basically this fancy metric that makes multiplying big numbers together a lot easier, but not so much easier that you can do it in your head. So, prior to the slide rule, we had to calculate logs using these long charts known as “log tables.”

Keith Houston: So, the basis behind the slide rule were these very, very long books of incredibly accurate logarithmic tables. And you’d look one number up, look another one up, add the two numbers together, look up the third one, and you’ve multiplied them. And the slide rule was just a kind of physical incarnation of that. So that’s why it had a different physical form. 

Roman Mars: The slide rule made calculations a lot faster and less error-prone than using the log charts and pen and paper. 

Keith Houston: It feels like magic and is this incredible thing because multiplication can be such a pain in the neck with pen and paper. 

Roman Mars: I have a fondness for the slide rule as an object. My father graduated with a degree in mathematics, and I remember seeing slide rules around his house. And this very cool looking but tiny and humble tool was the basis of mid-century engineering. I mean, it was used to get the Apollo 11 to the moon. It was used to design airplanes. It was used to build rockets. And I have to admit, it does look a little complicated and daunting if you don’t know how to use it. 

Keith Houston: So, I’ll have a crack at describing how to use a slider. It’s not a tool for radio. So, because it’s like a ruler and because it has these two movable sections or these two sections that move relative to one another, you have to align them. You have to look at a couple of numbers–make sure they’re aligned as precisely as you can. And then you need to look up a result. And so, imagine peering at a normal 12-inch or 30-centimeter ruler as closely as you can to figure out exactly where how long something is and eventually get to the point where the thing that you’re measuring lies between two lines. And so, you just have to guess, “Okay, is it 12.252cm, or is it 12.253cm?” Or whatever number it is. You have to start estimating it. They’re not super accurate!

Roman Mars: And this is what fascinates and confounds me. It’s that when you use the slide rule, at a certain point, you’re essentially needing to estimate your result. It’s this tool that we’ve used to help shape so much of our built environment, and yet it’s inherently kind of imprecise by design. Like, you make a measurement, and you just kind of have to eyeball it at a certain point. And I’m curious how that might have shaped our built environment. 

Keith Houston: Fundamentally, if you’re going to be doing a lot of calculations with a slide rule, everything has to be linear, by which I mean most equations need to just be multiplications or divisions or just adding some constant number. And so, this meant there was a real drive towards simplifying a lot of the equations that governed how, for example, buildings were built, or planes were designed. I seem to remember at university, where I studied physics–wasn’t a very good physicist unfortunately–one of my teachers was an aerodynamicist. That was his thing. And I remember being absolutely flummoxed because, you know, dynamics was so hard. You know, there are lots of cubes and square roots and much more complicated stuff–higher order equations. And this means that if all you have is a slide rule, you have to simplify it. You have to come up with some approximation to the much more complicated thing you’re doing such that you have the ability to do enough calculations with it for it to matter. And so, we ended up with a kind of world where bridges were stronger than they had to be, buildings were, you know, squatter and stronger than they had to be, cars were less efficient, planes were less efficient–all because the slide rule just simplified and reduced the set of complexity we could address. It forced us to look at problems in a simpler way because that was the only practical way to do huge amounts of calculation. 

Roman Mars: And when you know that you’re not as precise as you should be, you err on the side of making planes heavier, making walls wider–that sort of thing. 

Keith Houston: Exactly. Yes.

Roman Mars: That’s amazing to me. And then there’s a certain point–as a society–our math was getting more and more complicated. We also had this desire to be more efficient and calculate faster. So, what changes start to take shape here? 

Keith Houston: So, the calculator–the thing that we might recognize as a calculator–kind of has to have a different form because the slide rule’s form isn’t cutting it. Pen and paper isn’t cutting it. What are you doing? You’re manipulating the raw numbers, you’re entering some numbers, you’re carrying out some operation, and then you are entering some more numbers and carrying out another operation and so on after that. So, I think the form of the calculator kind of had to change to accommodate that. And of course, this is where mechanical calculators come along, and you start to see things that… They don’t look like modern calculators, but they do in some way function like them. 

Roman Mars: Those early mechanical calculators were large and clunky. Some of them sounded a lot like a typewriter. This is the sound of an Olivetti Simplicissima MC3, made in 1941. Its name is a bit of a mouthful, and its size is a bit of a handful–many large handfuls, in fact. One of the earliest and maybe wackiest mechanical calculators developed along the way was called the Curta. It was designed in 1945 by a guy named Curt Herzstark, and it was the shape and size of a pepper grinder. 

Keith Houston: The Curta–William Gibson called it a “math grenade” in one of his novels. It’s a plot device. It’s a McGuffin. And it looks like a Coke can with a bunch of sliders on the side. 

Roman Mars: The Curta was the first digital pocket calculator. It could fit in the palm of your hand, and it was known for its unusual cylindrical shape. 

Keith Houston: And it was the shape because it was driven by a very particular mechanical construct called a “step drum.” And it’s an incredibly clever piece of packaging. And it meant that it was possible to have a genuinely pocket-sized calculator that could add and subtract really reliably. I mean, the story of how it came to be, I think, is as interesting as anything else. It was developed by an Austrian called Curt Herzstark, who ended up being interned in Buchenwald in this horrific concentration camp in the Second World War. And he was offered a chance by his captors if he designed– They somehow knew that he had been a calculator designer or maker before he’d been arrested. And they said, “If you can design this and you can make this, we will give this to the Führer and perhaps he will see fit to pardon you or to grant you freedom.” So, it has this horrible backstory to it that makes the fact that it exists and is such a gem of mechanical design… It’s really weird. I find it quite hard to hold those two ideas in my head at the same time. 

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Keith Houston: This is an incredible event. The U.S. Army newspaper, which is called Stars and Stripes, set up this contest in Japan–postwar Japan–between a private in the U.S. Army, I think it was, and an employee of the Japanese post office, effectively. His name was, if I remember rightly, Tsuyoshi “The Hands” Matsuzaki. I imagine his nickname was part of the reason he was in the contest. 

Roman Mars: The contest was between the Japanese abacus and a newly developed state of the art mechanical calculator from the U.S. to basically see which one was better. Both competitors were considered masters of their respective tools. Matsuzaki used his abacus every day in his job at the Postal Service. And Tom Wood worked in the finance department of the U.S. Army. 

Keith Houston: They had to do a set of additions, a set of multiplications, a set of divisions, and a set of subtractions. And the contest was whoever could finish them most quickly. 

Roman Mars: Tom Wood’s calculator was a luxury item. It was large and was powered by motors turning internal gears. It probably rivaled the price of a car. And the technology behind Matsuzaki’s handheld abacus was about 2000 years old. 

Archival: Old versus the new. The ancient abacus doing battle with a modern calculator. That’s what they come to see. And who’d have thought that the bead and frame–still in common use in the Far East–could stand a chance against a tool of modern times? 

Keith Houston: Matsuzaki won three out of four. I think the one that he didn’t win was the multiplication. And the reason that he won was because he kind of internalized all of these shortcuts that you could do with the abacus. It was, you know, a special skill. And so, there was great, great excitement at this contest. 

Roman Mars: After the competition, newspapers reacted with melodramatic statements, like, “The machine age took a step backward,” and, “Civilization has tottered as the 2000-year-old abacus beat the electric calculating machine.” But the competition also served as inspiration for new calculator manufacturers to push forward the evolution of what would eventually become the pocket calculator. 

Keith Houston: And in fact, one of the knock-on effects was that Casio, the Japanese calculator manufacturer, got started off the back of this. Casio was started by a group of brothers, one of them who’s called Toshiro Cashio. Toshio had read about this particular contest. And rather than being a patriotic Japanese person and sort of cheering Matsuzaki for winning, he was more interested in this mechanical or this electrical electromechanical calculator which had lost the contest. And he thought, “I want to make these.” And the funny thing was at the time, the Casio company–the biggest selling product was a finger ring with a cigarette holder on it so that you could smoke a cigarette at work or, you know, in the bath. And he thought, “Okay, we’re going to build a calculator.” But Japan didn’t have the industrial base to make these electromechanical calculators. They didn’t have enough machinery to build them with sufficient precision. 

Roman Mars: That limitation gave way to a new technological development in calculators. The Casio brothers decided to build their Casio calculators off a device called a “solenoid.”

Keith Houston: So, a solenoid is basically a metal sort of plunger inside an electromagnet, so just a coil of wire that runs round it. And if you energize that coil of wire, the plunger shoots along inside it. And so, you can use them to lock doors. And I think car starter motors have got solenoids in them and so on. And he built a calculator out of solenoids, and they acted as switches. So, every time you typed in a digit, some solenoid would move, that caused another switch to close, and there would be a cascade throughout the calculator to set the number. And this all relates back to early computing. And this is where I find it starts to get really interesting because what calculators are doing is what computers are doing on a small scale–on a scale where the average person would have the chance to buy a digital binary computing device in the sense that we understand it for the first time in human history. Everything up to that point had been decimal, had been gears, had been rotating gears and cams, and so on. And the very first Casio calculator–the 14A–was about the size of a desk. And it chattered away as you typed in numbers and for it to compute the result. But this was the first kind of attainable digital calculating device that the world had ever seen. That’s when the modern calculator comes into existence, I think. 

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Roman Mars: And so how do you take this electromechanical calculator that’s desk sized and make it smaller? What happens when you do that? 

Keith Houston: It turns out that Thomas Edison had actually discovered the thing that would make this possible at a much larger scale. You could build larger, or you could build faster, smaller computers. He had discovered this thing called the Edison Effect, where electrons would cross the empty space inside a bulb with no air inside it. And he kind of discovered this effect, and he didn’t really do anything with it. But others who came after him figured out how they could turn these bulbs into amplifiers. “So, I’ve got one strong current, and I’ve got a weaker current that’s changing. And I can modulate the strong currents so that it matches the weaker current, which is just an amplifier.” So, I can amplify an audio signal, for example. Or I can amplify a telephone call. 

Roman Mars: People built on this development and discovered that you could use vacuum tubes as the basis for building computers and, of course, calculators. These tiny little tubes meant that calculators could be built smaller than ever before. 

Keith Houston: We set out to build an electronic calculator–one that’d be much faster and more flexible than these mechanical ones we’ve been making previously. And so, they hired a guy who’d worked on some of Britain’s earliest computing efforts, and he said, “We are going to use vacuum tubes inside our calculator.” It was called the “Anita.” It was about the size of a cash register. And inside, it had hundreds of these little tubes. There’s a fantastic video somewhere on YouTube of an Anita with the case taken off. And as someone types the numbers, you see these little vacuum tubes light up and flicker. It’s like little fireflies darting around on the inside of the machine. The Anita was just a huge set of electrical switches wired together. And this is what drives the evolution of the calculator. The next thing to come along is the transistor. So, in Bell Labs in the States, they developed basically a tiny amplifier that could be made out of a single speck of silicon or germanium. So, you can make these things very small. And people start making calculators out of transistors because they’re just more switches. Vacuum tubes are switches. Transistors are switches. And so now they make these completely solid-state calculators, which are just festooned with wires. It’s just circuit boards after circuit boards on the inside–all of these components manually wired up. And the next step is the integrated circuit. Someone at Texas Instruments, a guy called Jack Kilby, figured out, “Why are we making all of these transistors on separate bits of silicon or germanium, where we could just make them all in a single bit and then wire them up on this tiny little bit of silicon?” And so that was where arguably the first ever honest to God pocket calculator came from. 

Roman Mars: By 1972, there were hundreds of calculator companies developing thousands of different models of pocket calculators, all vying for that top spot in the market. 5 million calculators sold that year, averaging about $300 a pop. One of the most successful companies that came out of this period was Texas Instruments. TI and their line of calculators had a massive reign, even though they weren’t the first or the cheapest or the smallest or the most efficient. And the rise of the TI calculator is an interesting sort of deviation from the previous evolutionary steps of the calculator. Whereas most of these developments were driven by a company’s need to develop their own system to count their proceeds or a mathematical progression that necessitated a new tool–a more powerful tool–in this case, TI had invented the microchip. And they came up with the idea to make and sell calculators really just as a way to sell their microchips. 

Keith Houston: Absolutely. They came up with a solution, and they were looking for a problem to solve with it. So, Texas Instruments had made a lot of money by selling microchips to the U.S. military and in particular to the nuclear missile program. So, all of those silos dotted across the Midwest with the missiles in them–they would have lots of TI chips sitting inside them in order to run the show. But once you build your fleet of doomsday missiles, you don’t need any more microchips, or at least you don’t need as many of them. And TI found that it just wasn’t getting as many contracts from the military, so they wanted to branch out. They had a problem of “We have the ability to make microchips, but we need a market for it.” And so, Haggerty, the president, and Jack Kilby, the guy who invented the microchip in the first place, were on a plane. And by the time they’d landed, they decided that “we are going to build a pocket calculator, and that is how we’re going to sell more microchips.” Any American school child will know that TI calculators are just everywhere in the classroom. But the funny thing was they didn’t want to make the calculators at first, so they designed the chips for them. They figured out that it’s going to have a printer rather than a display because, at that point, LED displays were too power hungry. They drained the batteries too quickly. So, it had a tiny little solid-state printer–quite a clever piece of kit. And they said to Canon, “We’ve designed what is effectively a pocket calculator.” It wasn’t really–I think it was a couple of pounds in weight–maybe a pocket on a heavy overcoat or something. And they gave Canon the design. Canon designed a production version of it. TI couldn’t actually produce the chips fast enough. They still weren’t quite there with their production techniques. And by the time the Canon Pocketronic, as it was called, came out, other very small calculators are already caught up. In fact, another Japanese company called “Busicom” had released a calculator which was basically the size of a packet of cigarettes, which was the absolute first pocket calculator incontrovertibly. 

Roman Mars: Of course, Texas Instruments eventually developed the TI-83 graphing calculator, which is still in classrooms everywhere. How did that happen? How did they go from a place where they’re just trying to come up with a new way to sell their microchips to a couple of decades later where having a TI calculator is often a requirement, where your teacher tells you that you have to buy one? 

Keith Houston: Yeah. As I understand it, TI started to make more and more components of calculators. And they become quite good at it. They also seem to be quite good at lobbying. So, TI had a relatively large lobbying budget. And they like to make sure that their calculators were required. Partly they would lobby actual lawmakers. There was an attempt to have it written into law in Texas that all students had to take one particular advanced math course–the kind of advanced math course that you might need a TI graphing calculator to complete. They didn’t manage to get that passed, but they did partner with textbook manufacturers so that when you got your math textbook, there’d be a picture of a TI calculator in it. And the steps of the solution to the problem would be using a TI calculator. They also started teaching teachers, which is a very, very clever thing to do if you want to get pupils doing something. So, a couple of teachers at Ohio State University had been quite early to realize that calculators could help students who otherwise find maths quite hard. If you put a calculator in front of a kid who’s been discouraged for so long, then it takes away some of the pressure, it becomes almost something to focus on, and it makes it easier for them. You don’t need to worry so much about addition and subtraction or multiplication and division; they can focus on more complex concepts. And so T.I. eventually started employing these two guys to run a teacher training program that of course used Texas Instruments products to say, “This is how you teach this particular course. That’s how you teach that particular course.” And so, you had this perfect storm where textbooks showed you TI calculators and your teacher had been taught by TI how to teach the course. And I think this is why TI ended up with such a dominant position–in the States, to be fair. In the rest of the world, I think it’s different. In the UK, for example, it was pretty much Casio calculators. It’s all Casio calculators. But my wife, who’s American, very clearly remembers the TI-83 that she had to use in high school. 

Roman Mars: Yeah. And so, during this time, I mean, was there any kind of pushback or resistance to the infiltration of electronic calculators in the classroom? 

Keith Houston: Yes. There was this panic–in the same way that the Egyptians had panicked that they were going to forget about things when they were given writing, you know, 5,000 years ago. There was a whole swathe of people in the U.S. in particular who were worried that kids were not going to learn the right sort of maths because all of their parents had learned laboriously how to add and subtract and multiply and divide. I think they thought their kids had to learn the same things, even if that meant holding them back from more abstract or interesting concepts. 

Roman Mars: It seems like there’s always this sentiment–the “kids today” kind of sentiment. “They should learn how to do things the way we did things.” They did this about new math when my kids were little, and I felt that my kids had a better innate sense of how numbers worked than I did in the way that I rote memorized how to manipulate numbers. But could you talk about the sunset of the pocket calculator–where it’s persisting and, you know, stubbornly hanging on, but also what it means as a symbol today? 

Keith Houston: I think in some ways TI’s hold on calculators in the States, or at least the classroom market, is almost a last gasp. It’s a bit of an outlier because calculators almost everywhere else have disappeared. My opinion is that when the home computer came along and when VisiCalc–which is the very first computerized spreadsheet–came along, it suddenly became possible not just to do simple calculations on your computer, which was something that had been possible since the very earliest computers. But it was possible to do really complicated calculations over and over again and to play around with, “Well, what if we take this mortgage and go for this interest rate? What does that cost us? What if we charge this amount for this particular product and we sell this much?” It became possible to answer all of these what if questions that previously had been just a pain in the neck. And so, the spreadsheet, I think, becomes the tool of choice for people who are really serious about these large, complex, ongoing calculations. And so, the calculator gets pushed out that way. And then it just kind of goes from everywhere else. I mean, if your cash register adds up the total, do you need a calculator there? If your phone has got a calculator on it, do you need a calculator? Well, no, you don’t. But I think our phones and these apps that still persist on desktop computers–they are the afterlife of the calculator. They are the calculator ascended to electronic heaven. They no longer exist in physical form. It’s just their software. Their spirit lives on, but the actual body of the calculator has died off. 

Roman Mars: Well, the calculator as it existed may be obsolete, but I’m glad that the image that I am familiar with still lives on on my phone and my laptop. So, thank you, Keith, so much. This was marvelous. It was so much fun to look back at this sort of nerdy history. Thanks. 

Keith Houston: Thank you again for having me!

Roman Mars: 99% Invisible was produced this week by Lasha Madan. Mix and tech production by Martín Gonzalez. Original music by our Director of Sound Swan Real. Kathy Tu is our executive producer. Kurt Kohlstedt is the digital director. The rest of the team includes Delaney Hall, Chris Berube, Jayson De Leon, Emmett FitzGerald, Christopher Johnson, Vivian Le, Jeyca Maldonado-Medina, Kelly Prime, Joe Rosenberg, Gabriella Gladney, Sarah Baik, and me, Roman Mars. The 99% Invisible logo was created by Stefan Lawrence. Special thanks to Keith Houston. Go read his book Empire of the Sum: The Rise and Reign of the Pocket Calculator. Also, while you’re at it, go read his other books, too–Shady Characters and The Book. They’re all so good. Any 99PI fans will love them. We are part of the Stitcher and SiriusXM podcast family, now headquartered six blocks north in the Pandora Building… in beautiful… uptown… Oakland, California–home of the Oakland Roots Soccer Club, of which I am a proud community owner. As other professional teams leave, the Oakland Roots are Oakland first–always. You can find the show on all the usual social media outlets. You know where they are. You can find links to other Stitcher shows I love as well as every past episode of 99PI at 99pi.org.

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