Unfortunately, during the pandemic, most of us are unable to enjoy the beaches. It’s a shame we can’t see the beautiful waves, feel the refreshing wind on our faces, and move pebbles between lines in the sand to painstakingly and meticulously count our cattle and goods. What? You don’t do that? Oh, of course, of course, neither do I! Haha…

To clarify, today we’re talking about the rich history of the abacus (and not my endeavors with sand on beaches, though there seems to be some strange overlap)!

I think the beginning purpose of the abacus is beautifully summarized by Bruno Mars in his song “Count on Me,” where he sings: “You can count on me like one, two, three, I’ll be there!” Who knew he lived a secret double life as a wooden frame?

But in all seriousness, I’m especially excited about this article because it’s about something very close to my heart. Since I was six years old, I’ve been learning how to use the abacus. Though I had originally joined abacus class because I was jealous that my sister got to play with beads on frame while I didn’t, I remember how my pudgy little fingers grabbed and fumbled around with the beads on my first soroban, i.e. the Japanese abacus (typically a ¼ abacus, which you will understand later!), with my eyes filled with wonder, and how I gradually came to understand numbers and calculations in ways I could’ve never imagined. Though most mathematics isn’t concerned with the details of gritty calculation (despite the unfortunate popular notion that that’s all it is), there is still beauty to be found within these computations, and evidently, the history of how we came to think and process with beads on a rod. It’s hard to express how exactly and extensively learning the abacus has changed my life, but I can give you some examples. It’s somewhat of a magical thing to be able look at a number (that is sufficiently small) and see all these wonderful properties about it in just a few seconds, just because you’ve spent so much time with them.

As painfully nerdy and cliché as it sounds, they feel a bit like old friends (especially when I see some familiar, “nice” numbers pop up in various places)! And practically, it does make life a lot easier! But I swear I’ll throw sand at anyone who asks me to calculate their tip again…just kidding (or not, try it!). There are also some technical neurological benefits to learning the abacus, which is a nice bonus. Regardless, enough of my life story, let’s get to it!

How did it all start?

Imagine you’re trying to count your sheep to fall asleep…except you have no numbers. Excuse me? Okay, it’s fine, you still have your fingers and toes. That’s probably enough…oh no, the sheep are increasing at an exponential rate! Let me gather all my pebbles, sea shells, and twigs, oh god there’s too many of them, what do we do?!

Enter: the abacus. Or rather, the early version, which was a counting board. We have to make a distinction between this and the modern abacus, also called the bead-frame abacus. Early abaci, or counting boards, were pieces of solid material, usually wood, stone or metal, that had grooves carved in or painted lines where small objects, like beads, pebbles, or metal discs, were moved between. The modern abacus is a computational device, typically made of plastic or wood nowadays, that has a frame consisting of several rods with sliding beads on them.

The counting board was born out of necessity. We can’t be exactly sure what the first one was, because they were made out of perishable materials like wood, but we can make educated guesses about their construction and history. One way is by looking at the etymology of the word “abacus.” The Latin word has ancient Greek origins, specifically the word “ἄβαξ” (abax), informally meaning a rectangular board (though it actually means something without a base). This word is conjectured to have originated from the Semitic word “abq,” meaning “dust” or “sand.” This is indicative of the theory that beginning versions of the abacus were simply drawing lines in sand and placing pebbles between them as place holders representing numbers. For example, three pebbles in the 100s column, one in the 10s column, and two in the units, or ones, column represents the number 302.

The reason it was born out of necessity is because people like merchants needed an efficient, easy way to keep track of their goods in trade (or at least this is thought to be the origin, it’s not exactly well-known given its perishability). (Of course it wasn’t the only calculating tool, but it was significant!) But, the big problem with our sand counting board/abacus: they aren’t portable! But travelling merchants needed them to be. Thus, grooves were carved into wooden boards and little wooden discs were the place holders. As the abacus developed, the wooden boards evolved into metal and marble boards with metal markers. Ta-da!

In our efforts to unearth the abacus’s history, it is natural to try and look towards literature and/or art for clues, since the actual abaci couldn’t be preserved. However, this tool was primarily used by “lower” class people, like merchants, so they can’t commonly be found in these mediums. This is a likely reason for why we don’t hear much about the Greek and Roman history of the early abacus in contrast to its deep history in Asia. However, there is an ancient Greek artifact dating back to around 300 BCE, the Darius Vase, that seems to have something that resembles an abacus, or abax. (We’ll get more into the Greek history of the abacus soon!)

Additionally, the Etruscan cameo gives us an image of the Roman counting board, also called the Roman hand-abacus.

Disclaimer: I’m unsure of the accuracy of this image, but I still thought it was an interesting artifact!

Now, we know the motivation for the creation of the abacus! The actual timeline of its evolution is fascinating, but quite extensive. However, we’re going to attempt to create a rough timeline for it because I apparently have no life. Get ready, I’m counting on you to stick with me!

Where did it all start?

We believe one of the earliest instances of the abacus (the counting board version) was in Mesopotamia in 2700–2300 BCE. As we talked about before, the abacus was born out of necessity! Farmers needed a way to keep track of the growing trade and economy, leading to the early abacus. However, as expected, it doesn’t work similarly to the ones today! It followed their base 60 number system (which is responsible for the many measures of sixties in our everyday lives–seconds in minutes, minutes in hours, and so on). Furthermore, physically, they used simple flat surfaces, like stone tablets, as the base and placed stones in the five columns numbered 1, 10, 60, 600, 3600 to count. We think that they eventually used the abacus for basic operations like addition and subtraction, but not for more complex operations like multiplication.

Greek Abacus

While we can conjecture about the earliest abacus, the oldest surviving counting board is the Salamis tablet, discovered in 1846 on the Greek island of Salamis (now kept in the Epigraphical Museum of Athens). Originally, researchers thought it was some sort of game board! It dates back to around 300 BCE.

As you can see, it has five engraved parallel lines at the top and 11 at the bottom, which are bisected by a perpendicular line. You can also see the crack in the middle, as it is now broken in half. Its dimensions are 149cm x 75cm, so it’s quite big! Much bigger than the modern abacus. I’m not going to get into the details of how it was used (as this article is already rather long), but you’re welcome to search it up!

On the other hand, the oldest surviving written information about the abacus is also from the Greeks! In particular, it was mentioned by Greek historian Herodotus, who is indeed a Hero to Us (see what I did there?) as he mentioned that the ancient Egyptians used the abacus as well. Thank you Herodotus for the info! Herodotus also said that the Egyptians manipulated pebbles from right to left, in contrast to the Greek’s method.

Roman Abacus

In ancient Rome, they used a similar computation method to the Greeks: moving counters on a smooth surface. In terms of portability, there is evidence of hand abaci from this time period. They’re exactly what they sound like! They are small enough to fit in the palm of your hand, and have grooves/slots with beads that can slide around as needed. They are similar to the modern abacus in their design, which is to say, they are similar to the soroban (Japanese abacus)and suanpan (Chinese abacus). This similarity may suggest that the abacus spread from Greece and Rome to the east to China, then further along to Japan and Russia.

However, during the Dark Ages in western Europe, the use of abacus kind of died out. But fear not, the Pope is here to give us hope! In particular, Pope Sylvester II, also known as Gerbert d’Aurillac, is credited with reintroducing the abacus to Europe. In fact, he popularized the Hindu-Arabic number system and applied this to the abacus. He had spent some time in Spain, and got this idea from the Spanish Arabs. This allowed him to compute quickly in comparison to others at the time (as they could only use Roman numerals), and this led to the popularity of the abacus (once again) in 11th century Western Europe.

This rebirth of the abacus led to the earliest known printed book on arithmetic on: the Arte dell’Abbaco, an anonymous Italian textbook from the 15th century. During the Renaissance in Europe, the most common abacus used was called a reckoning table, a table with lines that marked off different decimal orders. Instead of pebbles, people used more sophisticated counters–some of which were customized with marks–made of metal, gold, or silver depending on their social position. Following the Arte dell’Abbaco, operations on the reckoning table, or abacus, were discussed and taught in many European arithmetic books up till the 18th century. It made addition and subtraction trivial, but it was more advanced for complex operations and thus harder to learn. This trouble incited some conflict between the abacists, who refused to let go of their traditional reckoning table, and the algorists, who supported the faster form of written computation. Mathematicians and scientists were part of the latter group and adopted it in their works, but the reckoning table continued to be used in business and finance.

This divide is wonderfully illustrated in the following art piece, Typus Arithmeticae, which depicts Dame Arithmetic (the figure in the middle) watching a competition between philosophers Pythagoras (yes, from the Pythagorean Theorem), who is using a counting board, and Boethius, who is performing written computation with Hindu-Arabic numerals. Dame Arithmetic is show to look towards Boethius, indicating her preference. (Hm, I wonder what the artist preferred…)

Now, let’s start our discussion of the modern abacus!

Suanpan (Chinese Abacus)

The Chinese abacus is known as the suanpan, which means calculating tray, and dates back to 1200 CE. It is a ⅖ abacus, i.e. it has two beads on the upper deck and 5 beads on the lower deck.

We believe that the Chinese used the earliest version of the abacus, the counting board, as early as 4th century BCE. It was a wooden surface/plate that was divided into columns with bamboo or ivory sticks, and used the base 10 system (our current number system). Some researchers believe that this was the first use of the decimal system!

The evolution of this abacus led to our modern abacus, the bead-frame abacus, which is more convenient and simpler to use. The first description of such an abacus was in the text Supplementary Notes on the Art of Figures by Chinese mathematician Xu Yue, which dates back to 190 CE. You might notice that the suanpan has two beads in the upper deck in contrast to the single bead in the more common, modern soroban. Though it is a bit redundant, this extra bead helps indicate numbers greater than 9 on a single rod which aids in faster division, but not particularly for other operations.

Soroban (Japanese Abacus)

Now, onto the abacus I use (along with a lot of people nowadays)! The Japanese abacus, or the soroban, dates back to 1600 CE. Initially, the suanpan evolved into a ⅕ abacus in the 14th century, before being adapting into the ¼ design of the soroban (meaning one bead in the upper deck, four in the lower deck), first appearing in 1930. Nowadays, ⅕ abaci are rather rare and ⅖ abaci are scarce outside of China/Chinese communities, but ¼ abaci are predominantly used today due to their efficiency in computation. There are even modern day competitions between abacists and calculators, and often abacists win!

Schoty or счеты (Russian Abacus)

The final major abacus milestone is the Russian abacus, known as the schoty. Though not a lot is known about how it came to be, It was first mentioned in the 17th century in an inventory book! Its design is very different from what we’ve seen so far (though it is thought to be based on the suanpan) as it is based on our two hands: each row has 10 beads, one for each finger. Furthermore, you use it by sliding the beads from left to right on horizontal wires, rather than up and down. It’s actually still used today, especially in Russian shops and markets!

Yupana (Inca Abacus)

The yupana is an abacus dating back to the time of the Incas that was used to carry out operations. It was a grid-based system of trays of various sizes that were carved on the top surface of rectangular boxes. To perform said operations, you would place things like seeds or pebbles into these trays. The existence of a precolonial yupana dating back to 6000 CE demonstrates that the indigenous people that made up the Inca empire in around 1400 CE were mathematically inclined prior to the 1532 Spanish arrival. The Spanish capitalized on the Inca’s advanced mathematical capabilities through such devices to advance their own economy and growth in the 17th century.

Another such device is a quipus, which are colorful, knotted threads or strings that record concepts and numbers. Just like the yupana, they made quick computations possible and effortless for native workers. The following drawing was found in Quechua nobleman Felipe Guaman Poma de Ayala’s letter to the King of Spain. If you look closely, you can also see the yupana in the corner!

Mazepa’s Abacus

Mazepa’s abacus is an abacus that was taken from political figure Ivan Mazepa’s (1639–1709) tent after the 1709 Battle of Poltava. As seen in the picture, it was a wooden box with a framed mirror and an abacus with beads made of red and white bones.

Cranmer Abacus

The Cranmer abacus, named after its inventor Tim Cranmer, is commonly used and taught in many schools for the blind, usually taught in early grades. It gives visually impaired students a tool that is essentially equivalent to written computation in both speed and skill required, and is adapted as necessary to ensure efficiency.

There are many other variations and designs of the abacus, but this article is already very long, so we’ll draw the line for our timeline here!

To end this, we can ask the question: why is the abacus so ever-lasting and effective? First off, it simplified calculation to a visual concept that is fairly simple to learn and teach. We now know that it was also created to be portable, and that’s another big plus!

But in modern times, in my opinion, the reason it is so effective is because it combines different senses and types of learning into one method! You have a visual aid, the abacus, you need to physically interact with it to perform calculations, i.e. touch, and you can even hear the beads click! Furthermore, you have to be present and active in the calculations, as you are providing the directions to the abacus, which means you need to engage with what you’re doing–hence, it vastly improves focus and computation ability. Thus, people who do abacus-based mental calculation are likely to have better numerical memory capacity and good recall to calculate. Especially when the abacus is taught from a young age, it becomes natural to visualize and manipulate the beads mentally (versus the traditional memorization tactic).

Though the abacus sometimes seems like an ancient device that is just a cool thing to play with in a museum, its influence can be seen almost everywhere we look — from computation machines to programs to pop culture! You may not have noticed, but there was an abacus-looking device in the new Pixar film, Soul, that was used by Terry to count the souls!

“The count’s off!” — Terry, the accountant who’s always counting

What’s the difference between Terry and an abacus? You can count on an abacus to not lose the count! (He really took the whole movie to track down one dude causing havoc, and who was even keeping track while he was gone?!) But on the bright side, if you ever find yourself in the Great Beyond, you can now probably steal his job!

Anyways, calc you later! If you found this interesting, make sure to check out the next column! If you have any questions or comments, please email me at apoorvapwrites@gmail.com.

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