Advent of Computing - Episode 187 - What's Better Than Binary?

Episode Date: August 17, 2026

Binary is synonymous with digital computing. But is it the only way to crunch numbers? The short answer is no. The long answer, well, that's today's topic. Today we are talking about ternary, aka base 3. From it's early uses in the 19th century, to actual computers, and even theoretical designs; ternary proves to be a difficult topic to track down... and a very unique one. Selected sources: https://www.mortati.com/glusker/fowler/fowlerbio.htm - Information and a reconstruction of Fowler's contraption https://dl.acm.org/doi/epdf/10.1145/776378.776392 - Part I of the TERNAC papers, rationale!   Like Advent of Computing? Then check out the after show! Adjunct of Computing is now LIVE: YouTube Spotify Apple Podcasts  

Can I tell you a dumb small town story? I have this friend who's relatively new to town. He's a transplant from a little bit inland from here. By relatively new, I mean he's lived here about two years. That's not nearly enough time to be a true blue local. As evidence, I present Exhibit 1. He had never been to any of my favorite bars in town. In an attempt to correct that, I planned a night out for us.

We'd hit all my favorite old haunts. Of course, I used to do this particular circuit while I was in college, and while I was much more, let's say, vigorous, it was to be a grand, if slightly scaled back evening. The appointed evening came, and we were off. This buddy of mine is part of my backpacking crew, so as we were ambling through town, we were mainly talking about trails.

We're planning our next big, outing. And if you've never been backpacking, then let me tell you, it takes a lot of planning and a lot of debating. We have a short list of mountains that we want to hit this year, but approaches and timing always turn into a contentious topic. We had just saddled up to one of the bars on our list for the evening when another patron turned to us. If I remember right, he said something along the lines of, dude, were you just talking about backpacking? I love the trails up here. Have you ever been to Red Cap Lake? End quote.

Now, this caught my attention. Not the dude part. This was a man very qualified to start a sentence with dude. It was the location. Red Cap Lake is in the absolute middle of nowhere. It takes about three hours to drive to the trailhead from town, and about a whole day to hike to it. That and the trail's kind of a mess.

It's been trashed by recent. forest fires and landslides. It's not exactly accessible or well known. And as it turns out, I knew about this trail because I had camped there the week before. In fact, I had went out to that lake in part to scope out the trail for a larger trip. There's some mountain passes and some further out lakes near Red Cap that I wanted to go to, but I needed to know the water conditions and how the trail was doing. As it turns out, the springs are all dried up out there right now, so my buddy and I had just decided that we'd delay that trip until a little later in the year. This dude was asking because he'd never been to Red Cap Lake, but he wanted to plan a trip

for himself. We just happened to be in the same bar at the same time. Later that night, my transplant friend and I were laughing about what a small town moment that was. I love these kinds of encounters for a slightly different reason, though. I like it when I get to share secrets, especially if I have to put it in work to discover those secrets. Over a drink that evening, I got to show this dude photos of the trail and the lake and give him a full rundown on trail and water conditions. I knew all the secrets about the hike, because I had just done it. I had driven those three hours and hiked for a day to get those secrets. Today, we're going to be talking about a topic that I've seen described as a secret, a hidden alternate path for computing. It's a technology

that some have said was suppressed. It's an idea that could have radically altered the course of computer history. At least, you'll see some folk claim that on the internet. I've spent some time going out and trying to find those secrets for myself to figure out just how real these claims are. So sit back and I'll let you in on a bit of a secret. Welcome back to advent of computing. I'm your host, Sean Hass, and this is episode 187. What's better than binary? Or, alternatively, you could call this, if base two is so good, why hasn't anyone invented base three? But first, it's time for the plug and announcement corner. I have the usual one here. Adron of Computing has an official after show. It's called Adjunct of Computing, and it's available anywhere you listen to podcasts. If you like this show but you want a more casual discussion of the topics I cover, then you'd really enjoy adjunct of computing. Part two here is a big announcement. I'm going on a vacation. Kind of. There's a bit of a long story here. The short version is I'm going to England for an archival trip.

I've been saving up a lot of Patreon money over the years for this. There's some information in a few archives in England that I need to get my hands on, and the easiest way to do that is to go sort through a bunch of file boxes myself. And I will admit, the idea of a nice vacation to an archive, it's very attractive to me. Sean's big, exciting archival vacation is happening in early September. My tentative plan right now is to take my mobile recording setup with me, and I'm going to be doing something like a live journal on Patreon.

Basically, what I want to do is document and discuss partly the trip, but mainly how archival access works and give live updates to my fans about what I'm finding out. So if that sounds interesting to you, then you should go subscribe to my Patreon. If you go to advent ofcomputing.com, there's a support the show link that will send you over there. For $1 a month, you'll get access to a couple of my old bonus episodes, plus the upcoming Sean on an archival vacation series. All right. Now, let's get into the show proper. Today, we're actually talking about why someone did invent base 3.

Well, it's a very loose way to put it. This is the official ternary episode. We're going to be looking at what ternary logic is, why it was created, and how it's been used. But first, I should explain why this is such an important topic. I recognize that going straight into a comparison of numbering systems could perhaps sound a little dry. So as always, let me add some context. I swear, this is a really interesting topic.

The first breadth of the digital age is in the 1930s. In that decade, a handful of researchers independently decided that binary was the way to go, that vacuum tubes or relays could be used to create binary logic circuits, and that those circuits could operate on binary numbers, add a few more steps and you get electronic digital computers. Crucially, this wasn't some one-off discovery. A pile of folk landed on the same design all at once in total isolation.

George Stibbitts, Conrad Zeus, John At Massoff, and a few others all worked out that binary number systems were the key to a new kind of calculating device. Their logic was all basically the same. You can make circuits that operate on binary numbers. Binary does away with a whole host of issues that analog systems suffer from, and binary allows you to tap into existing mathematical theory. These stories are well-worn, in part because binary does end up becoming the cornerstone of computing. It's one of those fundamental choices that has made computing possible.

To question the power of Bynarer, The signity of this art is to question the power of a tornado. It's irrefutable. Who are you to stand in the way of a force of nature, right? Well, as with all things, there are competing systems. Some early digital computers use base 10. That includes ENIAC and a number of early IBM machines. I think it's pretty clear to see why folk would want decibel machines.

Traditional math is done in base 10. We have 10 fingers. Simple as that. But ternary, or base 3, seems a little more left field. I can say with some confidence, I've never really considered using base 3 for anything. So what's the point? What are the arguments in favor of ternary over binary? Today we'll be tracking down those arguments.

We all know the story of binary, so let's learn the story of its three-sided cousin. Is Ternary actually better than binary? More importantly, what does adoption of Ternary do to a computer? Does it lead to a totally new, totally different type of machine? Or is the difference more subtle? Binary is ancient. At least, humans have had the concept of yes, no, or true, false since way back. The modern system that we're used to, with ones and zeros and easy conversion to and from decimal,

was pioneered by Leibniz back in 1670. We can quibble over how binary develops from there, or about if others invented binary before him. In fact, the scholars in ancient China were using something that looked very close to binary, but I digress. The point is binary is old, and it's easy to see how many people, arrived at systems like binary. True and false or simple concepts. There's not really a lot of subtlety there. Then when does Ternary enter into the picture? From what I found, there's just much less scholarship on Ternary, especially early on. Part of this undoubtedly comes down to the rarity of Ternary. It's a classic case of history being written by Victors. Binary is very important.

It's commonplace today, so there's been a lot of work to reconstruct its history. Ternary doesn't see as much use, so it's been left to the wayside. At least, that's how the sourcing appears to me. Donald Canuth does some untangling of Ternary in the Art of Computer Programming Volume 2. What he presents rhymes with the history of binary. There may have been some use of things like Ternary in the distant past. It was then, in Knuth's words, quote, rediscovered a number of times in the 18th and 19th century.

Early works on ternary and binary, for that matter, are a bit of a slog to decode. For instance, in 1821 John Leslie published The Philosophy of Arithmetic. It's, well, it's new enough that it doesn't use a long S, and let's just leave it at that. It is in English. Leslie doesn't use the word bass. Now, to be fair, there are a number of words that you can use to speak about numbering systems.

Radix is, I believe, the most technical term, as in, ternary is technically called radix three. Leslie uses the term scale, as in binary scale, octary scale, and ternary scale. The philosophy of arithmetic has a large section all about ways to decompose decimal numbers into other scales and implications thereof. But it's done in odd-looking ways. Leslie kind of uses an abacus written on paper. When he displays these decomposed numbers, he uses vertical lines with dots.

So binary uses a line for a zero and a line with a circle on it for one. Interestingly enough, Leslie actually cites the I Ching, which is often seen as one of the earliest forms of binary. But Leslie does this in a weird way. Quote, some feeble traces of the binary notation are found in the early monuments of China. Fu He, the first emperor and founder of that vast monarchy, is venerated in the east as a promoter of geometry and the inventor of a science of which the knowledge has been since lost. The emblem of this occult science appears to consist of eight separate clusters of three

parallel lines or trigrams, drawn one above another after the Chinese manner of writing, and represented entirely or broken in the middle. End quote. Behold, scholarship in the 18th. 20s. But that's a lot about binary. What about Ternary? Leslie has a section for a number of different scales, each with a description of the scales provenance and usefulness. Ternary has a very short section. He basically just says, yeah, base three exists. It uses 0, 1, and 2. Here's how you draw it. But that's it. He doesn't really add anything about its history

or any particularly handy applications of ternary. What Leslie presents here is more accurately termed unbalanced turnary. And I don't mean that Leslie's scale was tilted. Unbalanced means that it uses 0, 1, and 2 to represent values. It's unbalanced in the sense that it's not centered around 0. This is something we don't really think about with decimal or binary. And I think it's fascinating to consider, right? With an odd base, you have the option of choosing a center for your system.

So you can actually have different options for how you represent a number in that base. For ternary, you can use unbalanced or you can use balanced. In balanced turnary, your numbers would be minus one, zero, and one. Now, there are some alternative ways to render that. Some balanced ternary implementations will use false, unknown, and true. Some ternary systems use their own new symbols, but minus one, zero, and one are the most common numbers to use. Why use balance versus unbalanced?

Well, to explain that, let us move to the futuristic year of 1840. I know I often talk about the 1940s is the wild west of computing. West of computing. Anything previous to that period is even more so. Folk have been trying to make calculating machines since, well, since it was realized just how difficult mathematics could get. There's a whole heritage of dudes thinking they can make calculating or numeric recording devices. Charles Babbage is just the one that really got glommed onto in the 20th century. Allow me to introduce one Thomas Fowler, inventor, accountant, and creator of a very early calculating machine. Fowler's device is interesting in its own right, and luckily, it came with a book.

Well, it kind of came with a book. Fowler worked as the treasurer for a poor law union. This was an organization that provided services for impoverished citizens of the UK. As treasurer, Fowler had to do a lot of math, specifically repetitive math. He had to do apportionment calculations for each parish within the region he worked, which ended up just being running the same equations over and over and over again. So he worked up some shortcuts. He figured that a lot of these calculations were difficult to run in decimal,

but easier to run in base 2 or base 3. How this ends up working is a little obtuse. Fowler published a book on his handy math methods in 1840, titled Tables for Facilitating Arithmetical Calculations. But why does math end up being easier when you use lower bases? There are a few contributing factors here. One is complexity. This comes in two forms with numbers, width and breadth.

We all are probably used to talking about binary numbers in terms of width, as in how many digits are used to represent a number. That idea can be applied to any base. Consider a number like 9,999. In decimal, that takes four digits to represent. It's four digits wide, and binary you need 14 digits. So, binaries worse, right? Well, not so fast. That's only one part of the equation.

To encode a number between zero and 9999 in decimal, you have to have 10 unique symbols. You have to have zero all the way through 9. In binary, you only need two. Some math nerds have figured out a number of ways to rate these radix systems for specific numbers. One of the easiest conceptually is to just multiply the width by breadth. That is, digits needed,

multiplied by unique symbols needed. If we do that, then the math for 9999 and decimal scores 40. Binary scores 28. What about ternary? Well, to encode our number in ternary, you'd need just nine digits. That gives us a number.

us a score of 27. You see, Ternary is technically less complex than binary. If you run this calculation for all possible numbers, Ternary ends up scoring just a little better than binary every time. There are more sophisticated measurements that show the same thing. Ternary is less complex than binary, but just by a little bit. In theory, this means calculations in Binary. binary or turnary are less complicated to carry out than in decimal. The trade-off really comes down to repetition. If you're doing binary math on large numbers, you end up repeating very simple operations many times.

That ends up being easier than doing the same operations in decimal because each operation is almost trivial. Multiplying two binary numbers is very, very simple. This is the root of the whole ternary argument, that it has some marginal benefits over binary in terms of efficiency. And that's been known since at least 1840, maybe earlier. We get a few more benefits whom we use balanced ternary specifically. Fowler's system is balanced around zero. He uses minus 1, 0, and 1.

And just as an aside, Fowler also uses weird notation. which, well, I don't know why these nerds keep doing this. Leibniz is using modern binary notation in the 1700s. These guys are just off doing their own thing. Fowler would write a number like the binary 1001 as 3 comma 0. You know, as in you have a value at positions 3 and 0. The ternary notation he uses is even more odd. The book is full of conversion tables.

For ternary tables, he has a positive and negative column. Each column lists which positions hold values. I guess there are a few points here. One is that things are very primitive. Another is that these nerds aren't really in dialogue with prior arts, or rather, they're in a bit of a clumsy dialogue. But anyway, Fowler publishes this book full of tables and math methods for binary and ternary. He also develops what I would call a true contraption.

This is also where I get to add a funny swerve to the story. Fowler was paranoid about someone stealing the idea for his contraption. so he'd build it in secret himself. No records of the design exist. We get just a single account from an observer, and that account is written in 1840s prose, so it's not exactly the clearest thing to read. Fowler's contraption was made out of wood in his own workshop,

and it supposedly was made at a pretty large scale. Now, I don't mean it was powerful, I don't mean it could do large numbers. I mean it was physically big. Not huge, but not clockwork either. It's about three feet long. What did this machine do? Why?

It multiplied and divided in balanced ternary. The details aren't all that important here. It worked with teeth and gears and linkages and little marker ticks. What's important is that ternary is simple enough that a single dude was able to make a ternary multiplying machine from sheets of wood in his old-timey garage. That speaks to a level of simplicity or maybe elegance. A part of that elegance is how balanced ternary handles negative numbers. That is to say, it does.

One of the issues that you'll see come up time and time again in binary computers is the concept of negative numbers. Machines have to use some kind of special encoding to mark that a number is negative. That could be just choosing some bit on the number to represent sign or using something like two's complement, but those are conventions outside of binary itself. Balance ternary just straight up supports negative numbers. Turnary digits can be negative or positive. If you have an odd number of negative digits, your number is negative. If you have an even number of negatives or not at all, the number is positive. This also makes negation simple.

To make a positive ternary number negative, you just flip all the signs. There are a couple other tricks that make balanced ternary really cool, but this should give you a taste. It has some actual benefits, but making use of those benefits is a little more different. difficult than you may imagine. Fowler's contraption never caught on. Turnary doesn't really enter the conversation again until, well, until the advent of computing. It took decades for computers to actually take their modern form. The process started in the 1930s and would continue well into the 1950s. Computers in this early period were very varied. One of the only common denominators was binary. Decimal machines really are the exceptions that prove this rule.

The IBM 650, for instance, is often called a decimal computer, but it used binary inside its own circuits. It only presented as decimal. Now, you know me. I love counterpoints. I love arguments. And I've been looking very hard, but I can find almost no period evidence that binary was ever really questioned. This should be clear from the simple fact that binary computation was independently invented multiple times. If Zeus can come up with the idea of binary using linear clutches trapped inside Nazi Germany and Stivitz can come to the same conclusion using tin cans on his kitchen table. Well, there might be something fundamental going on here. That said, Ternary did enter into some discussions. One of those happened during Project Whirlwind,

and it involves IBM. Well, it tangentially involves IBM. Herb Groch was one of the many engineers involved with Whirlwind. Prior to joining MIT, he had worked for the aforementioned three-letter company. While there, he taught a few courses on mathematics. In one of those, he would use ternary. Specifically, he would teach signed ternary, a.k.a. balanced ternary, because he thought it was neat and had some benefits over binary. In 1951, when he joined Project Whirlwind, he decided to toss around some of his, quote-unquote, kooky ideas. That is his quote not mine. This didn't go very far, but he did write a memo on the matter. In it, he makes a pretty radical argument that ternary is a more natural system to use them binary.

To quote, is it really true that the outside world is best represented by dichotomies? computing machines are basically logical, the argument runs, and the logic of the real universe is too valued. My idea, on the contrary, is that computing machines operate on the basis of logic connected, not with the real world, but rather with a special representation of the world by rational real numbers, end quote. As he goes on, the kernel of the idea starts to take form.

He's basically saying that the deep internals of a computer don't have to be connected to anything. What matters is that a computer can do math. How it does math is irrelevant as long as it can do it reliably. So why bother with binary? Ternary offers distinct advantages. He lays out the same RADDIC's economy argument

that I described earlier, that ternary is technically more simple and more efficient than binary, and that signed ternary allows for some neat savings with signed mathematics. Also, as another side note, Herb introduces his own notation for ternary. At this point, you kind of have to, right? That seems like the tradition. He proposed to represent minus 1, 0, and 1 as capital lambda, 0, and capital V. He calls them, respectively, Lom, O, and V.

Grosch goes on to use that notation and the rest of the memo. It's one of those things that's kind of something to behold. Here's my radical idea about computing. Here's my new notation. Now you have to decode my mathematics if you want to know what I'm talking about. I at one point was told if you're trying to get someone to help you, you need to make yourself easy to help. This appears to be the opposite of that theory. The final leg of Grosha's argument comes down to practicality. This is the real heart of the matter.

If you try to implement a ternary circuit using vacuum tubes, you're going to have a bad time. Tubes are closer to binary divinely. You end up needing to use extra tubes to represent the full LOMOV spectrum. If a binary system needs two tubes per bit, then Ternary ends up needing three or four. That seems to throw some cold water on the whole idea, right? If balanced Ternary is good because it's more efficient than binary, but it actually takes more hardware to implement, then the theory just doesn't really work.

work. It's a neat thought experiment, but not practical. Grosch, though, he's no fool. He wouldn't propose Ternary if there weren't a solution to this problem. That solution is the ferrite core. At least it's a possible solution. Allow me to explain. The benefits of Ternary hinge on having some tri-stable device. You have to have some basic logic element. They can represent three states. Binary strikes of big, in part, because we have many bistable devices, from relays to vacuum tubes to transistors to strips of tin cans on a kitchen table. There are a lot of ways to make a device that can represent true or false. The jump to true, false, and unknown is tricky, but MIT was the right place to make

that leap. One of Whirlwind's big advancements was the development of magnetic core memory. This is a device that uses tiny rings of ferrite to store data magnetically. The actual information is stored by magnetizing the rings called cores to have either a positive or negative polarity. In magnetic core memory, those cores are treated as bi-stable devices. They can be positive or negative, they can have either a 1 or a 0. Grosch believed that cores could also be used as a tri-stable device. But he's muddy on the details. To quote, there is a good possibility that these can be jockeyed into more than two states.

That's the end of the quote. So not exactly brimming with confidence there. Again, this is the crux of the practicality of Ternary. For Ternary to be unequivocally more efficient than binary, to basically put the argument to rest, you have to have some tri-stable device. You need to have the turnary equivalent of a vacuum tube. I've always been honest with you. You can trust good old Sean when he says he isn't a material sciences guy. I've been trying to figure out if Roche is being realistic here. While I was down at VCF West recently, I was able to confer with a number of

people who know ferrite much better than myself. If I cornered you and started talking really fast about tri-stable devices, then thank you. You did me a great service. From what I've read and from what I've heard, you can't really make a practical tri-stable device using ferrite cores. It would be technically possible to have a core at three possible states. Positive magnetization, negative magnetization or no magnetization. But getting ferrite into that state, and more importantly, sensing that zero state would be either impossible or very impractical, at least if you're using a normal ring-shaped ferrite core. And that's completely the case in this early period. From what I've seen, no one in the 1950s at least was able to get a ferrite core to act as a trinary

device. We may come back to this later in the episode, but as it stands in the 50s and the early 60s, I can find nothing in the literature that actually shows a practical tristable ferrite core either being developed or crucially being used. Gross is one of a handful of researchers that have suggested that a ternary computer would be more efficient than a binary computer. The issue, however, comes down to a functional tri-stable device. What about when the rubber meets the road? I've talked a lot of theory here, but what about practice? Has anyone actually tried to make a ternary computer, efficiencies be darned?

The answer is, yes. Allow me to introduce Seton. Work on Seton started at the Moscow State University in 1956. The origin story of this computer is pretty classic. It all started because one Nikolai Brustenstov, a researcher at MSU, wanted a computer. Due to some university politics, he could not have a computer. Here I'm quoting an interview with Brewstenstov from tryingtass.ru. No, this is translated, so the language might be a little bit off.

Quote, back then, the task was very simple. We had to get the M2 machine, which was made in Brooklyn. Slab from Moscow State University. But there was a hitch. During the academic elections, Sergei Lovnik Sobelev, our supervisor, voted not for Brooke, but for Lebedev. Brooke was offended and didn't give me the machine. I went to Sobolov and asked, what am I going to do now? He replied, let's make our own machine, end quote. How hard could it be? Well, very hard, as it turns out. Zobolev tasked his crew with fanning out and surveying existing computer technology.

The initial outlook was grim. Vacuum tubes were discounted due to reliability. Transistors sounded like the way to go, but they weren't accessible to the MSU team. So they took a more radical approach. Bruce and Stov had seen another machine underconstructed. LEM 1 that used ferrite diode logic. This is a whole topic onto itself that I'll go deeper on some other time, so today you get the short story. Diods are just about the most simple semiconductor device possible.

That made them more accessible than transistors in the early days. It's possible to use diodes to construct any non-inverting logic gate. That is, everything but a not gate. You can make ores and ands from diodes pretty easily. In fact, many early computers use diodes for just that. But diodes have to be supplemented. There are quite a number of early machines that use a combination of diodes and vacuum tubes for their logic. But you don't have to use vacuum tubes.

There are other options. One is to use ferrite cores. You know, the same little donuts of ferrite that are used by magnetic. core memory. This is possible by using specific windings. In magnetic core memory, a ferrite bead has a really specific winding of wires that lets you flip the core's magnetization and read a change in its magnetic field. But you can wind cores all kinds of different ways. You can use relatively simple windings to make a core into an and or an or gate. With a little more work, you can make a not gate. That gives you everything you need to construct digital logic circuits. But those circuits

aren't drop-in replacements for vacuum tubes. These ferrite gates have to be pulsed to work. The magnetization of a core is detected by getting it to change magnetic polarity. Basically, you need to put the core into some state, and then you have to send in a pulse to try to put the core into some other state. Your readout is really just a measure of how the core's magnetization changes. If the core is set to one and you try to set it to zero, it'll send out a readable electric pulse when it flips polarity. That's a lot different than a vacuum tube or even a diode, which gives you a continuous output. As a result, these magnetic logic circuits operate a little differently than other logic circuits. While the actual device may be more simple, it's just

ferrite and wire, all the stuff around it seems a little more complex to me. LEM1 used ferrite diode logic to implement a binary computer. Bruce and Stov decided to adopt that same technology, but with a twist. He chose to use ternary instead of binary. Why? Well, that's hard to say. Bruce Instov was given full control over the project. He's kind of the decision point for things. In his interview and in the period papers I can find, he simply says he decided to use terminary.

It's likely as simple as that. The first paper on the computer, small automatic digital machine Seton, doesn't shed much light on the decision. Was it an experiment? Was Bruce and Sov a big fan of 19th century mathematical treaties? We're just not sure. But the first Seton paper does explain why Ternary is preferable to binary.

We get the usual arguments about sign and efficiency, plus one more that's worth mentioning. Ternary makes rounding operations very simple. And Ternary, a round is just a shift. You just have to drop off the least significant digits. And that's it. That means that ternary computers can have radically simplified floating point circuits. So you can do floating point math with fewer devices, basically. Seton was constructed and operational in 1959.

From the outside, it actually looks pretty normal, and it acts like a relatively normal computer. It used as a load store architecture. It runs normal software. There are even high-level languages available for the machine. Most of the papers discussing Seton after its construction are concerned with software development. In other words, it's just like any other computer.

The main benefit is simplicity. Seton was meant to be a small and simple computer, and the use of ternary logic made that possible. At least, that's the claim. It gets a little complicated when you look at the finer details. It turns out that Seton wasn't purely ternary. Internally, it used something called binary-coded ternary. Remember, there aren't tri-stable devices for the MSU team to reach for.

They're using ferrite and diodes. In binary-coded ternary, more mundane binary devices are used to encode base three values. It's the specifics that cause a problem here. Seton uses two binary bits to encode one turnary trick. In other words, it's using two binary devices to create a single turnary device. Just off those numbers, if you were to make a binary version of Seton, it should require less ferrite. That leaves us in an awkward situation, right? and I think this is emblematic of the whole Ternary thing.

The fundamental efficiency gains you get from Ternary are all based off this supposition that a tristable device exists. Once that's out the window, you're left with something like binary-coded Ternary which eats away at your gains. Seton ends up being very simple and very small and efficient, but it would probably be more so if it was just designed as a binary computer.

What you really are left with are efficiency gains due to how you use Ternary. You get more simple adding circuits, built-in signs, easier floating point math, the list goes on. And that makes Ternary really hard to assess. Theoretically, it's more efficient than binary. But in reality, there are feasibility issues that prevent it from reaching its full efficiency. Those issues, however, can be balanced against some of these other gains. The core complexity here is that ternary has fundamental differences from binary. I don't think it's fully valid to hold a binary and a ternary circuit next to each other and say, which is better.

They give you different options. They work in different ways. But it's still the whole issue of a tri-stable device that kind of rubs me the wrong way. If you have to use a combination of binary devices to make a ternary device, then you're going to have issues with efficiency. You're always going to be kind of in a situation where it would be easier to just go the binary route. But what if a tristable device were possible? What if you could make a ternary computer with no compromises?

Well, that just may be possible. I admit that I'm stealing someone else's framework for this part of the episode. But hey, if I steal it and say where it's from, that's a citation, not theft. In 1972, G. Fryder published Motivation for Ternary Computers. It's a few-page-long rationale for the third base. What I find most interesting is how Reader frames the history of Ternary. allow me to jazz it up a little bit. In the beginning, there was the computer,

or rather, there were very primitive computers. Early machines struggled to come into being at all, so their creators were more focused on just getting things to run. Binary was chosen in this period because there were easily available devices that could encode binary data. By the time we reached the 1960s, the basics of computer designers settled. Binary is enshrined as the obvious choice, as a force of nature.

Researchers move from fundamental questions to questions of larger design, architecture, and use. By the 70s, we're in a new era. Machines are well established. We've even created a new science for describing those machines. So, according to Frider, it's time for a reassessment. Is binary the correct solution? Well, if you look at the numbers, then ternary is actually a better choice. To quote,

We are thus faced today with computers in which the basic concepts were checked out and evaluated by incomplete criteria, i.e. those of hardware implementation. End quote. His core argument is that binary was chosen in haste. that our predecessors were so concerned with implementation that they couldn't really consider better options. Now, I will say that's a cogent argument. I don't agree with that argument, but

it is pretty cogent and it makes some good points. As we've discussed, binary wasn't chosen without reason. Hardware was a contributing factor, but so was the larger body of work on Boolean logic. In fact, the Boolean piece, the actual math side, is just as important as the hardware piece. If you look at all the different folk that arrived at binary logic in the 30s, about half of them also land on how important it is to be able to use Boolean math to describe their new circuits. Even Conrad Zeus, in near total isolation, arrived at that conclusion.

Binary is a package deal, and that package is very attractive. I do, however, like this framing. Earlier folk were just trying to get up and running, and later we're able to build on that foundation. I think it shows good instinct to want to reassess that foundation once you get some space from its development. There were also some developments in the middle of the 60s that made that reassessment more, well, let's say, appropriate.

Starting around 63 and 64, there is renewed research into tracts. tri-stable devices. Now, I want to be clear. These are all proposed devices. I've been trying to find machines or even demonstration circuits that use these elements. I haven't gotten very far in that search. Let's group these into a few different categories. The least mind-blowing are simply circuits. These are things that did see use. Seton is the example, right? It's using these ferrite circuits to do ternary logic, but there are also a number of new types of circuits that emerge in this period. We get a pile of proposed circuits to handle ternary, but they're all using binary devices. That includes diodes and eventually transistors.

Some of these implement binary-coded ternary, but others are more direct. One device developed at Argonne Lab in 64 use a tiny diode circuit. Specifically, this element used the then-new tunnel diode. This ends up creating what we'd call a threshold device. That is, it can be put into three different voltage states. Then you assign each range of those voltages to a ternary value. You give each value a voltage threshold. There are a number of threshold devices that show up in the literature,

but they all suffer from a core problem. They're actually just circuits. The Argonne device uses a diode capacitor and a coil. The circuit is constructed and then packed into its own little housing, but to actually use this ternary logic, you need supporting hardware. The 64 paper proposes using transistors for that part. So you have this little custom device that can hold three voltage levels, and then you have a few transistors on top of that.

you end up needing good, old, reliable binary devices to get your turnary device to work. Once you hit that point, it seems to make more sense to just use the transistors to build binary circuits. That's the core issue I see with a lot of these circuit-based or threshold devices. Once you reach for some transistors, well, that kind of seems to defeat the purpose of the exercise, at least when it comes to using these devices for computation. The more compelling devices are all magnetic. One really interesting example comes from the Universidad National del Sour in Argentina. Developed in 64, this device uses tubes.

I mean, kind of. They're similar to magnetic cores just a little longer. There's a little Y dimension to this. The paper describes how to construct a ternary memory system. Each element, each trit, is a tiny glass tube. The tubes are coated in a nickel-iron alloy. Specifically, this is a thin film coating. These will have been made using a sputterer, which, I mean, I think they're super neat.

Sputterers are these machines that vaporize metals and then deposit them onto, well, onto anything that you put inside the machine. It's all done under vacuum and at very high voltages. It lets you create very, very thin and very consistent coatings. One of my old friends actually used a sputterer to coat all his keys in like one or two layer thick coating of gold back in college. They're really useful and really interesting machines, and they use very little material when they construct coatings.

Anyway, back to the tubes. The magnetic properties of these coated tubes are, to use a fun word, and isotropic. That just means they act differently in different directions. If you pass a wire through the middle of the tube and apply a current, the tube becomes demagnetized. But if you wrap a wire around the tube and apply a current, the tube will become magnetized. Depending on the direction of that coil current, you can give the tube a touch. different kind of magnetization, a different polarity. I believe that gives us three states. Reading is fairly simple. It involves a destructive process, just like with ferrite. You essentially

try to force the tube to flip its magnetic state and see if it does. Here you actually try to demagnetize the tube. You send a pulse down its middle. Then you can use a sense wire to read any change in the tube's magnetic polarity. The key difference is that you can get either a positive pulse, a negative pulse, or a no pulse. You just have to be able to handle three states on the other side. The paper goes on to describe how this tubular memory can be used with ternary logic circuits. Those circuits, however, use transistor diode logic. Again, we hit the transistor. Here, the gate they use is constructed using a transistor, a diode, and some resistors and capacitors to pull things together. We're back to the root issue.

If you have to use transistors, then why not just make a binary computer? Are the ternary savings really that worthwhile? So that brings us to the crux of the matter. Are there any proposed ternary logic devices? Well, actually, yes. and this is another magnetic one. In 1963, D.J. Anderson, etc., published a magnetic ternary device in I-Triple-E transactions. This is a weird one that I have mixed feelings about.

I'll just say that up front. The titular device is a bead of ferrite with two holes instead of one. It's an oval chunk of ferrite with two holes drilled side by side by. side. The principle of operation here is a little subtle. According to the paper, the double barrel bead can support four different magnetic states. It's a little hard to describe without a diagram in front of you, but it goes something like this. Two of these states have magnetic flux either clockwise or counterclockwise with respect to the whole bead. That is, total negative or total positive polarization. The other two states are in regards to the two holes.

Either the first hole has negative polarization and the other one has positive, or the first hole has positive and the other has negative. Notice that in these second states, the polarities are always opposing each other. Now, I'm not sure how real this is. Since this is one ferrite core, I think this would have one big magnetic field. I don't think the opposing polarities work. But I'm not an expert. It's been a long time since I've taken electronics and magnetism.

Also, my attempts to recreate this paper have been stymied. I may keep pressuring some of my connections to let me into their lab, because I really want to try this out. It seems like it would be very easy to recreate this device and just see if it does what it says. Alas, for now, I'm just going to trust the paper and just trust that it's correct. Anderson goes on to describe how this ternary core can be used for memory. That part is pretty simple.

You wind one wire around the top edge of both holes, and then you wind a secondary wire around the middle of the core, the little spot between the holes. That lets you put the core into three of the four possible states. Then you can do readout in a similar way to how the tube, memory works. The key difference is that Anderson's cores don't have a non-magnetized state. Instead, you're always flipping between three different possible magnetizations. So cool. You have a magnetic core memory that can store ternary. What makes this paper more interesting is that it jumps from

memory to logic. We are in ferrite after all. That means that Anderson is able to implement magnetic logic. We even get this wild table that tells us how to wrap wires around these cores to create different turnary logic functions. This seems like the most compelling option to me. Magnetic logic is a very real thing. It's used in a number of computers, including Seton. Anderson's design also has a type of symmetry to it that I can really dig. It uses the same physical elements for memory and logic, that points to you.

That points to another layer of efficiency, of sophistication. But there's a caveat. Well, there's a few caveats. I still don't know that I fully trust this paper. Like I said, I really want to just try this out. I want to see if I can make a core and see how it acts. If those third and fourth states with the opposing magnetizations work, then I'll accept that this is a good idea, but they kind of skeez me out.

The other caveat is pretty plain to see. Notice how Anderson's cores have four states but only use three. This is still pretty close to a binary-coded ternary circuit, like we saw with Sutton. In fact, you could probably implement all the same logic that Anderson proposes by using two ferrite cores instead of a single ovoid core. I also have some reservations about manufacturing. It's pretty simple to make a bunch of rings, but a two-hold oval, that seems a little more complex. To make practical use of these ovoid cores to actually make good on their proposed efficiencies, you'd need a method to mass-produce them.

I think that would just be more difficult than mass-producing traditional ferrite cores. Again, we come back to efficiency. The point of turnary is efficiency, but there are issues when it comes to implementing it. So, what if we just forget about reality for a minute? That Frieder paper I mentioned earlier is actually just part one of a two-part series. In part two, Frieder at all describe a little bit of research they carried out. They describe an experiment. They wrote an emulator for a turner.

computer and use that emulator to study the efficiency of that theoretical machine. This, however, is where I run directly into a bit of a wall. So the machine is called Ternak. At least that's what I've been told. The two papers I'm working from give very short reasons for the experiment and pretty short explanation. They do not say the word Ternac. Rather, it seems that a third and larger paper gave that name. I can find citations for the paper. I know the journal it was published in. Wikipedia even cites it, but I can find nowhere that has the journal, not even physical print archives that I could request scans from. So I just have to accept that the emulator was called Ternac. I also have to accept that it existed. This is just what happens when you're this far off

the beaten path. As a result, we have incomplete information on Ternac. What we do know is that Ternac used balanced Ternary specifically. The whole point of the experiment was to see just what gains could be realized using Ternary, so balanced is the natural choice here. It's the details of the emulator that strike me as odd. Okay, so I've seen different sources conflict on if Ternac was written in Fortran or microcode. The microcode option to me is the most exciting because that means that this team would have basically turned a binary computer into a ternary one. It's also what's claimed in the actual paper that I have to work off, so I'm fairly certain they were using microcode. One of the citations in the publicly available papers is to a 72 article titled,

An Environment for Research in Microprogramming and Emulation. It's co-authored by Free Now, I'm avoiding the rabbit hole here. In 69, there was a project at the State University of New York at Buffalo to get really, really into microcode. The university worked with a company called Nanodata to get this new machine called a QM1. It was brand new and it was microcoded. The overall project was to write a bunch of different microcode implementations on the QM1, using it as a lab to test out different computer architectures and designs. This may have also led to a Snowball 4 implementation in microcode, but like I said, I'm

avoiding the rabbit hole right now. I can't say with some certainty that the QM1 was used to implement Ternac. That means that we are talking about a binary machine that was converted to Ternary. That on its own is pretty good, right? The Ternac study compared speed and storage requirements for Ternary versus Binary Designs. I'm sure a more astute reader could figure out which binary computer Ternac was based off of. I can't exactly tell. It was a load store architecture, but beyond that, it just kind of sounds like a 70s computer to me.

The result of the experiment is interesting. We get numbers on arithmetic operations on integer and floating point. When it comes to speed, the ternary design is a mixed bag. Adding is much, much faster, but subtraction is a bit of a wash. The report gives a range of speeds for subtraction, and while Ternary can win on faster figures, it has a much slower tail. But storage is the real kicker. Ternak uses the boogeyman we've come to know and love, binary, coded, ternary.

so it ends up being wasteful. It just takes a lot more bits to store trips. The conclusion of the paper is that Ternac, as an idea, shows promise. That said, I've not been able to find any information on Ternak showing up again. If it did show promise, it appears that it didn't exactly go anywhere. All right. I think I've gotten reading math papers out of my system for a while. I want to take a slightly different tact at the end here.

I think we've answered all our initial questions. Why turnary? Efficiency. What does it change about a computer? Efficiency. A ternary computer doesn't actually look that different from a binary computer when it comes to programming. So really, ternary becomes a matter of efficiency gains. There is one huge part of the conversation that I skipped.

That's something called post-algebra. That's post as in some dude's name, not post as in something beyond algebra, although I do like the idea that there is life after algebra. Postalgebra is a generalization of Boolean algebra. It discusses functions in different possible bases. In other words, you can use post-algebra like Boolean algebra, but for any base. Many of these older ternary papers use post-algebra. However, there are a number of systems that serve the same purpose. Post-algebra isn't the only option.

I think that speaks to something fundamental here. Ternary is not settled, not nearly. It never was. There are a lot of different ideas on how to implement ternary computers. There are a lot of different proposals for ternary circuits, even for tri-stable devices. And there are competing mathematical systems for representing Ternary.

That's why. Binary, on the other hand, has a lot of development to it. We have very well-established options, methods, and mathematics. This is a phenomenon that we run into a lot on the show. It's all a matter of adoption. Binary is used more, so more effort is put into understanding and refining it,

which makes it nicer to use, so it gets used still more. Give that a century and we end up with a very well-codified system. Ternary's never reached enough critical mass to benefit from that kind of cycle. And I don't think that's for lack of trying. As we've seen, there has been a certain amount of work put into making Ternary computers a reality. It just seems that reality has some issues. But who knows? Maybe one day we'll find a very simple tri-stable device,

something easier to manufacture than a transistor. If that ever happens, then these old ternary papers will become deeply prescient. Only time will tell. Until we're living in a ternary future, thanks so much for listening to advent of computing. I'll be back in two weeks with another episode. If you like the podcast, you can support me on Patreon.

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