You might have heard stories of how rapid and accurate calculations with an abacus can be, but did you know that the abacus might have been based on an ancient technique using only the human hand, which survives today as the Korean art of Chisenbop?
Chisenbop is an ancient Korean technique for calculations with the human hand. The classic text on Chisenbop in English is The Complete Book of Fingermath.1 Unfortunately, it is expensive, aimed toward children, and takes hundreds of pages to explain principles that an educated adult can learn in a few minutes. One important thing that the book can offer you, however, is page after page of drills. Chisenbop should become a motor skill, not something you have to think about.
Fingermath also uses many full, detailed drawings of hands in action, which is another reason the book is so long. Fortunately, the Wikipedia presents a notation that can radically compress Chisenbop diagrams on the page, as shown in Table 4-2.2
Tip
I added a couple of symbols to the notation myself for this book
(^ and v, which are described in Table 4-2).
You can combine the finger notation across two hands, as shown in the examples in Table 4-3.
This remainder of this hack describes the basic operations of Chisenbop.
Here is how to count to 100 or more on your fingers. Keeping all your other fingers off the table, you press your right index finger to the table. This represents the number 1:
Keeping your right index finger on the table, you press your right middle finger on the table. This represents the number 2:
The next two fingers down represent 3 and 4, respectively:
To represent 5, clear your other four fingers on your right hand (lift them off the table) and simultaneously press your right thumb to the table. Your thumb represents 5:
For 6, keeping your right thumb on the table, press your right index finger down on the table (5 + 1 = 6):
You can get as high as 9 on your right hand by pressing the next three fingers on your right hand in succession so that all the fingers are pressed:
To count from 10 up through 99, you will need to start using your left hand as well.
Clear all the fingers on your right hand and simultaneously press the index finger of your left hand. This is 10. It's analogous to how you count 1 on your right hand by pressing your right index finger.
By adding the fingers of your right hand from 1 through 9, you can get as high as 19:
| Notation | Meaning |
|---|---|
...o- -o... | 11 |
...o- -oo.. | 12 |
...o- -ooo. | 13 |
...o- -oooo | 14 |
...o- @.... | 15 |
...o- @o... | 16 |
...o- @oo.. | 17 |
...o- @ooo. | 18 |
...o- @oooo | 19 |
Of course, to count to 20, you make another exchange. Clear your right hand and press the middle finger of your left hand:
This is analogous to how you count 2 on your right hand because 20 = 2 Ã 10.
Counting by tens, the other numbers up through 90 follow logically:
| Notation | Meaning |
|---|---|
.ooo- -.... | 30 |
oooo- -.... | 40 |
....@ -.... | 50 |
...o@ -.... | 60 |
..oo@ -.... | 70 |
.ooo@ -.... | 80 |
oooo@ -.... | 90 |
And here's a full Chisenbop 99:
If you want to count past 99, you need to remember a number in your head. That number is how many hundreds you need to add to your hand abacus at the end of your calculation. Fortunately, all that involves is tacking the hundreds number onto the front of the number shown by your hands. So, if your hands show this:
and your hundreds number is 3, the number you have counted to is 352, which you can show like this:
Therefore, to break past 99, clear your hands and say to yourself "one hundred." Both hands will now show zero, to which you will add the hundred in your head by prepending one, and the Hubble horizon is the limit!
Addition is simply counting by larger chunks than 1. For example, to add 15 + 23, place your hands in the 15 position:
Now, press two more fingers representing 10 each on the left hand. This means you're adding 20:
Almost there. Now, press three more fingers on your right hand for the 3 in 23:
So, 15 + 23 = 38. It might have been easier to do it this way:
Simply put, if addition is counting forward by chunks, subtraction is counting backward by chunks. Instead of pressing your inner fingers down and moving out, you are lifting your outer fingers and moving in. It's quite simple; it just takes practice.
Here's how to figure 38 â 23 = 15:
Multiplication is just repeated addition. For example, 3 Ã 15 = 45 means 15 + 15 + 15 = 45:
It's useful to drill in adding by arbitrary chunks, starting with counting by twos, moving up as high as counting by nines, and then moving into counting by double digits. You want your Chisenbop to become an unconscious motor skill; otherwise, you might need to keep intermediate results in your head. For example, when multiplying by 15, you might need to repeatedly add 10 and then remember to add 5. Not only is this not the Way of Chisenbop, but it is also error-prone.
Note that when you multiply, you always need to remember a second number in your head, in addition to the hundredsâthat is, how many times you've added the number by which you're multiplying. (Don't read the result off your fingers until you're done.) So, in the previous example, when you first place your fingers on the table in the 15 position, you say, "One!" When you add a second 15, you say, "Two!" And when you add the final 15, you say, "Three!" Now read the result off your fingers: presto, 45!
If multiplication is repeated addition, division is repeated subtraction. You can divide by repeatedly subtracting the divisor until you can't subtract it anymore. The number of times you could subtract the divisor is the result, and the number left over on your fingers is the remainder. Thus, 15 can be subtracted from 45 three times, leaving all fingers clear (a remainder of zero), showing that 45 / 15 = 3, remainder 0. Likewise, 15 can be subtracted from 46 three times, leaving your index finger pressed, showing that 45 / 15 = 3, remainder 1.
In practice, it's probably easier to work in the opposite direction. For example, you can divide a number by 7 by counting sevens until you exceed the number you are dividing. The number of sevens in the number you are dividing is one less than the number at which you finished. For example, to divide 81 by 7, count 7 (1), 14 (2), 21 (3), 28 (4), 35 (5), 42 (6), 49 (7), 56 (8), 63 (9), 70 (10), 77 (11), 84 (12)âoops! That's 12 sevens, which is too many, so there are 11 sevens in 81, with a remainder of 4.
Lieberthal, Edwin M. 1982. The Complete Book of Fingermath. A & W Visual Library.
Wikipedia. 2005. "Chisenbop." http://en.wikipedia.org/wiki/Chisenbop.
Harris, Andy. "Chisenbop Tutorial." http://www.cs.iupui.edu/~aharris/chis/chis.html (this page from Purdue University contains an interactive, animated Chisenbop tutorial and several lessons presented via streaming media).
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