This is a fascinating chapter in the history of mathematics. Before the widespread adoption of Arabic numerals and paper algorithms in Europe, people performed incredibly complex arithmetic using only their hands. This system, often attributed to the 8th-century monk Bede the Venerable, was a universal language of commerce, theology, and diplomacy across the Roman Empire and medieval Europe.
Below is a detailed explanation of this forgotten "digital" technology.
1. The Historical Context: De Temporum Ratione
While finger-counting dates back to antiquity (Egyptians, Greeks, and Romans all used variations), the definitive manual for the medieval European system comes from Saint Bede, an English Benedictine monk.
In 725 AD, Bede wrote De Temporum Ratione (On the Reckoning of Time). The first chapter, De Computo vel Loquela Digitorum ("On Computing and Speaking with Fingers"), codified a system that allowed users to represent numbers from 1 to 1,000,000 using specific flexions of the fingers and positions of the hands relative to the body.
2. The Mechanics of the System
The system is bifurcated: the left hand handles units and tens (smaller numbers), while the right hand handles hundreds and thousands (larger numbers).
The Left Hand: Units and Tens (1–99)
The left hand is the "working hand" for daily transactions.
The Units (1–9): These are formed by bending the three smallest fingers (pinky, ring, middle) into the palm.
- 1: Bend the pinky finger into the middle of the palm.
- 2: Bend the pinky and ring fingers.
- 3: Bend the pinky, ring, and middle fingers.
- 4: Raise the pinky; keep ring and middle bent.
- 5: Raise pinky and ring; keep middle bent.
- 6: Bend the ring finger only (this is the only distinct departure from the pattern).
- Note: From 7 to 9, the thumb and index finger are used.
- 7: Place the tip of the index finger on the first joint of the thumb.
- 8: Place the tip of the index finger on the second joint of the thumb.
- 9: Place the tip of the index finger on the base of the thumb.
The Tens (10–90): These are formed using the thumb and index finger of the left hand.
- 10: The nail of the index finger is pressed into the middle joint of the thumb.
- 20: The tip of the thumb is placed between the index and middle fingers.
- 30: The thumb and index finger form a circle (a gentle pinch).
- 40: The thumb is placed on top of the index finger (the reverse of 10).
- 50: The thumb is bent toward the palm like a Greek Gamma (Γ).
- 60: The index finger wraps over the bent thumb.
- ...and so on up to 90.
The Right Hand: Hundreds and Thousands (100–9,000)
The right hand "mirrors" the left hand but elevates the value.
- The Hundreds (100–900): You perform the exact gestures used for the Tens on the left hand, but you do them with the Right Hand.
- Example: If making a circle with the left thumb/index is 30, making that same circle with the right thumb/index is 300.
- The Thousands (1,000–9,000): You perform the exact gestures used for the Units on the left hand, but you do them with the Right Hand.
- Example: If bending the pinky on the left hand is 1, bending the pinky on the right hand is 1,000.
Body Posture: The Higher Thousands (10,000–1,000,000)
To count beyond 9,999, the system moves away from just finger joints and incorporates the position of the hand relative to the chest, hips, and shoulders.
- 10,000: Place the left hand flat against the middle of the chest, fingers pointing up.
- 20,000: Place the left hand flat against the chest, but spread the fingers wide.
- 50,000: Place the left thumb against the navel, pointing the hand downward.
- 100,000: Repeat the gesture for 10,000, but use the Right Hand.
- 1,000,000: Clasps both hands together, intertwining fingers (a gesture of completion or infinity).
3. How Calculations Were Performed
This was not just for static display; it was a dynamic calculator. This system allowed for "holding" numbers in memory while performing mental arithmetic.
Example: Addition (25 + 17) 1. Hold 25: On your left hand, form "20" with your thumb/index and "5" with your middle finger. 2. Add 10 (from the 17): Change the "20" gesture to a "30" gesture (circle). You are now holding 35. 3. Add 7: You need to add 7 to the "5" you are holding. Mental math tells you this is 12. 4. Carry the 10: Update your thumb/index from "30" to "40." 5. Register the 2: Change your middle finger "5" to a pinky/ring finger "2." 6. Result: Your hand now displays "42."
This "holding" function was vital before paper was cheap. A merchant could negotiate a price verbally while physically "locking" the sub-total on his hands to ensure he wasn't cheated.
4. Beyond Math: A Silent Language
Bede noted that this system functioned as a silent lingua franca. Because the gestures were standardized across Europe, a monk from Italy could communicate numbers (and by extension, dates, prices, or biblical verses) to a merchant from Germany without speaking the same verbal language.
Furthermore, Bede described how it could be used for cryptography. By substituting numbers for letters (1=A, 2=B, etc.), individuals could silently spell out messages across a room using finger positions—a medieval sign language for spies and scholars.
5. Why Was It Forgotten?
The decline of this system was caused by the introduction of two technologies: 1. Hindu-Arabic Numerals: The shift from Roman numerals (I, V, X) to Arabic numerals (1, 2, 3) made written calculation significantly faster and easier. 2. The Abacus and Writing Surfaces: As paper became cheaper and the abacus more common, the need to hold intermediate sums on one's fingers diminished.
By the Renaissance, the system was viewed as a rustic relic. However, traces of it remain in our language today. The word "digit" comes from the Latin digitus (finger), a direct homage to the time when our fingers were our primary computers.