Dactylonomy: “the use of one’s fingers to express numbers.” (Wiktionary). We have all encountered finger-counting at some point; most of us have even been able to count to 10 since we were very young. Counting to 10 on one’s fingers is likely even the origin of the base 10 system. However, only being able to count to 10 is not very useful when you want to express numbers greater than 10, of which there are infinitely many. Has it ever occurred to you that you’re not limited to counting to 10?
Your first thought may be to flash each individual digit in a number. For example, to show the number 42, you’d first show the number 4, then show the number 2, shaking your hand slightly between digits. While this method is generally understood, it is not a static method as you still cannot express numbers greater than 10 in one gesture.
Assigning numbers to arbitrary gestures
You can also assign arbitrary gestures to represent various numbers. This method can work, but this is not necessarily systematic and you will necessarily have many gestures and will have to memorize all of them (not unlike Hanzi). Additionally, the gestures may not be static and would have the same issues as flashing. As such, this method can be difficult to learn, but can nonetheless be convenient and has the potential to allow numbers up to 9999 or more. Examples of implementations of this method are numbers in various sign languages.
This is basically counting on your fingers as you would on a soroban (Japanese abacus).
On each rod on a soroban, there are four beads on the bottom that represent 1 (the “Earth beads”) and a bead on top that represents 5 (the “Heaven beads”). The beads express their value if they are pushed towards the bar. For example, to represent the number 8, the Heaven bead and three Earth beads are pushed to the bar:
Chisanbop, a Korean finger-counting method, uses the same idea. Think of your hands as two rods. Your thumbs are the Heaven beads and your fingers are the Earth beads. Using this method, you can comfortably count up to 9 on one hand and up to 99 on two.
Using your thumb as a pointer, you can divide your fingers into partitions and assign values to those partitions. For example, you can partition each finger into three partitions, each partition corresponding to a bone, and count starting from the outermost bone of the little finger, allowing you to count up to 12 on one hand (168 on two). Alternatively, you can use the joints (including the fingertips) and count up to 16 on one hand (288 on two; alternatively, it can be used to count in hexadecimal). Further partitioning can lead to counting up to 7224 or more on two hands.
Binary is a number system used by computers that expresses all numbers using only two symbols, 0 and 1 (compare the decimal system, which represents all numbers using 10 symbols, 0-9). Each digit in a binary number is called a “bit“, and as you move further to the left of a number, the value of a digit increases by a factor of 2. For example, the binary number 11001 is the decimal number 25. The digits from left to right represent the values 16, 8, 4, 2, and 1; 16+8+1=25.
If you want to learn to decode binary numbers quickly, you should learn finger binary to practice. A finger essentially has two states: lowered and raised; these states can be mapped to 0 and 1 respectively. Treat each finger as a bit and you can count up to 1023 on your fingers. Just be careful when expressing the number 132 or you may get yourself into trouble.
If you’re really advanced, you can even express negative numbers using a sign bit, but I’ll leave that for you to research yourself.
Furthermore, you can use finger ternary (base 3) to count up to 59048; your three finger states are lowered (0), curled (1) and raised (2). However, this requires dexterity and may be difficult to perform.
What do I use? I may occasionally use finger binary or hexadecimal partitioning, but I’m not proficient enough to use either efficiently. I usually just use Chisanbop because it’s easy and I generally don’t need to keep track of more than 100 items at once. I’ve gotten so used to using Chisanbop that it feels weird now counting to 10 using the traditional way.
Do you know of any other counting techniques? Share them below!
- Finger-counting [Wikipedia]
- American Sign Language (ASL) Numbers Discussion [ASL University]
- Soroban [Wikipedia]
- Abacus Tutorial [Abacus: Mystery of the Bead]
- Chisanbop [Wikipedia]
- Your Body is an Abacaus [Instructables]
- Chisenbop tutorial [Andy Harris, Indiana University / Purdue University]
- Binary number [Wikipedia]
- Finger binary [Wikipedia]
- Count Like a Computer [Howtoons]