The Abacus: The World's First Computing System

by Jesse Dilson, Angelia Pozzi (Illustrator)

The abacus is as useful and effecient a machine today as it was when it was first created centures ago. Whether you're an expert in the latest computer technology or you're mastering arithmetic and word problems for the first time, it won't take long to learn the basics (and even the not-so-basics) of adding, subtracting, multiplying, and dividing on this ingenious and fun-to-use mathematical tool.

Genres: Mathematics, Nonfiction, History, Science

143 pages, Paperback

First published March 15, 1995

Reviews

[Kyle · Rating 4 out of 5]

This is a nice introductory text for using a suanpan (or soroban) abacus, but clearly aimed for the very beginning. The history given is good enough, and the presentation is done well (the picture will be very helpful to first-users). It teaches addition, subtraction, multiplication, and division and gives instructions on how to build an abacus.

I wouldn't recommend the book if you already know the basics of an abacus, but if you are just starting out this is a good reference.

[Hồ Vinh · Rating 5 out of 5]

Numbers have existed for thousands of years. Any true civilization evidently needs to have such a numbering system in place to facilitate the task of counting: first, to serve personal purposes; second, for trading activities; and third, for academic works. Take, for example, a primitive human who needs a means to keep track of his cattle, perhaps putting a pebble into a bowl for every cow he possesses. At one point, it becomes taxing to have that many pebbles in the pocket, so the Babylonians and Egyptians introduced symbols for units and wrote them on papyrus scrolls. They were careless about the symbols' order, so a number could be expressed in various ways, as long as the symbols' presence tallied up to the intended value. The Romans confusingly demanded that alphabets take on the roles of number symbols, but they contributed the key idea that position matters (a smaller-valued symbol standing before or after implies subtraction or addition), hence introducing uniqueness in representing numbers. The Arabic system, in its modern form, wrapped up the latest evolution with a 10-symbol system that can express any imaginable large number and is easy to recognize at an instant.

Now, arithmetic calculations (addition, subtraction, multiplication, division) are the direct usage of the numbering system. The modern approach, excluding a digital calculator, is pen and paper. Before that, Oriental countries, through Eastern merchants, invented the handy abacus, which is the main subject of this book.

An abacus is a wooden frame with 9 columns and beads. Columns, from right to left, indicate units in order of ten: rightmost for units, the next higher for tens, the third for hundreds, etc. A crossbar divides the frame into two halves: heaven, whose beads are worth 5 units each, and earth, 1 unit each. When computing, you only need to lift two fingers: forefinger for the heaven beads and thumb for the earth beads.

Steps to perform calculations are straightforward:

Clear the abacus: all earth beads are down at the bottom, and heaven beads are up at the top.
Set up the first number on the frame. If the value is higher than 4, say, 8, then make use of the heaven bead, say, 1 heaven and 3 earth beads.
Calculate the second number, from right to left, so that if you sum with a value higher than 9, increase 1 earth bead in the higher column, or if you negate with a higher value, decrease 1 earth bead in the higher column to have 10 additional units at the current column.
Upkeep the board so that at any time, at most 1 heaven bead is used in any column.
With the said mechanism, you can take the game up a notch with challenges such as summing 4 numbers or multiplying two-digit numbers. The flow is similar, and you may notice the same mental calculation is just like pen and paper, with the sole difference being no paper wasted. You can also use only heaven beads to do computation for binary numbers.

All in all, pen and paper, I think, are still far superior. You can easily trace back your misstep when doing a long calculation, while the abacus only "stores" the latest state of the computation. That being said, I think the abacus is fun to play with, especially since the mechanical sense easily attracts curious minds that are new to math. The book is well written and approachable for people of all ages.

[Anna · Rating 3 out of 5]

As a self defined mathematics nerd, when I saw this book on a shelf in a local charity shop, I just had to get this book. It promised to be an interesting book which would, at least for me, be a light read and would cover not only basic, but more advanced abacus use. Perhaps naively, I thought this might involve some complicated operations which had a clever solution on the abacus.

As I started the book, I appreciated the light humour as it explored the origin of number systems and calculations. I did enjoy looking at calculations using pebbles and dirt lines which intuitively led to the abacus. I think I would have appreciated a further look into other number systems, but I suppose that's not really the focus of the book.

From this point forward the book flew by, not necessarily because it was written so well, but because most pages had one or two drawings of an abacus on them. Something which is important to develop understanding, but meant that the diminishing number of pages remaining felt like they wouldn't be able to cover harder material that I wanted to read.

I will say that, although it was written slightly strangely (and definitely using language of it's time), the chapter talking about wide use of the abacus in China and Japan was quite interesting, not least because it argued that abaci rivalled the speed of a computer (including setting the dials and switches of course!). I found this snapshot of the time an interesting one and one I did enjoy reading. The age of the book was also quite pertinent in the section about making your own abacus, at one point saying that a cigar box should be cheap and easy to find!

The last section was a little disappointing - I was promised hard calculations and unfortunately just got long division. The methods definitely made sense, but they just never felt very exciting. All in all I think I got my £1.50 out of it, but I was very sad about my not included free abacus (in hindsight how would that even fit in the book).

[Kian.ting · Rating 5 out of 5]

Nice introduction to the Chinese abacus. Learned a lot from it now just need to teach it to my children.

[Brett · Rating 3 out of 5]

Brief, fun book about the history of number theory and human ingenuity.

[Joshua · Rating 4 out of 5]

A fascinating explanation of how to use an abacus and it's history. Everyone in the modern world should read this. It will give you an appreciation of a lot our technology that we take for granted. It will also instill in you the fact that we are not "smarter" than our predecessors. We are standing on the shoulders of their inventions and technology.

[Lev Reyzin · Rating 2 out of 5]

Teaches some history numbers and of the abacus and some basic abacus use, but could have gone into lot more depth on all those counts. Also the book’s discussion of computers is outdated l, and in any case, left a lot to be desired.

[Robert · Rating 3 out of 5]

I picked up an abacus at Borders, I think. The abacus came with this book. It's an interesting read for those of us who did not know how to use one. A decent introductory book.

[Nate Grips · Rating 2 out of 5]

Kinda basic, cute find though