Counting Like an Egyptian (or Babylonian): Why Our Number System Isn’t the Only Way

When you write down a number today – say, 153 – it feels natural. You use the digits 1, 5, and 3. You instantly know it means one hundred, plus five tens, plus three ones. Our system, using the digits 0 through 9 and the idea of place value (where a digit’s position tells you its value), seems like the obvious way to handle numbers.

But was it always like this? Absolutely not! For thousands of years, brilliant civilizations used entirely different number systems to write down quantities. Some used pictures, some used letters, some used strange wedge shapes pressed into clay. Their systems worked for them, helping them build empires, track trade, and understand the heavens.

Exploring these ancient ways of writing numbers isn’t just a history lesson. It reveals that our current system is just one solution among many. It highlights different ways of thinking about quantity and calculation. And it makes us appreciate the cleverness behind the system we now take for granted. Let’s journey back and see how people counted in Egypt, Babylon, and Rome, and consider why our modern system eventually became dominant – or did it?

Tally Marks: The Oldest Number System

Before any fancy symbols, there was the simplest method: tallying. For every sheep, make a mark. For every day passed, carve a notch. One thing, one mark. We still use this for keeping score in simple games or taking quick counts, often grouping marks by fives (IIII).

The strength of tallying is its simplicity. Its weakness? Big numbers become incredibly long and hard to read. Imagine writing “one thousand” with tally marks! Clearly, growing civilizations needed something better.

Egyptian Pictures: Hieroglyphs for Hundreds

Ancient Egypt, flourishing from before 3000 B.C., developed one of the earliest upgrades. They invented distinct symbols, little pictures called hieroglyphs, for different powers of ten.

• A single stroke ( | ) meant 1.
• A heel bone symbol ( ∩ ) meant 10.
• A coiled rope ( ໑ ) meant 100.
• A lotus flower ( ? ) meant 1,000.
• A pointed finger ( ? ) meant 10,000.
• A tadpole or frog ( ? ) meant 100,000.
• An astonished man ( ? ) meant 1,000,000!

To write a number, they simply drew as many of each symbol as needed, adding up their values. For example, the number 1,213,546 would be written with one astonished man, two tadpoles, one pointed finger, three lotus flowers, five coiled ropes, four heel bones, and six strokes.

Advantages: It’s quite visual and doesn’t rely on place value. You could write the symbols in almost any order (though they usually put larger values first) and still get the same total. An astonished man symbol always meant one million, no matter where it appeared.

Disadvantages: Writing large numbers still required drawing many symbols. Imagine writing 999! And calculations using these symbols were likely cumbersome.

Later, for writing on papyrus (an early form of paper), Egyptians developed more efficient systems with unique symbols for 1-9, 10-90, 100-900, etc., reducing the number of symbols needed but requiring more memorization.

Babylonian Wedges: Clever Place Value (with a Catch)

Meanwhile, in Mesopotamia (modern Iraq), around 2000 B.C., the Babylonians developed a very different and, in some ways, more advanced number system. They wrote by pressing wedge-shaped styluses into soft clay tablets.

They used only two main symbols:

• A vertical wedge (▼) for 1.
• A sideways wedge (◄) for 10.

They combined these to write numbers from 1 to 59. For example, 23 was ◄◄▼▼▼.

Here’s the brilliant part: for numbers 60 and above, they used place value, much like we do. But instead of base ten, they used base sixty (sexagesimal).

• The symbols in the rightmost position represented units (1-59).
• The symbols in the next position to the left represented multiples of 60.
• The symbols in the position further left represented multiples of 60×60 (3600), and so on.

For example, the number 75 (which is 1 x 60 + 15) would be written as:

▼ (space) ◄▼▼▼▼

The ▼ on the left means ‘one sixty’, and the group on the right means ‘fifteen ones’.

Advantages: This place-value system was incredibly powerful and efficient for writing large numbers. It was particularly good for fractions (using places to the right, representing 1/60ths, 1/3600ths, etc.), which made Babylonian astronomy very advanced. We inherit their base sixty system in our minutes and seconds.

Disadvantages: Their big problem, for a long time, was the lack of a zero. How did they show an empty place? Initially, they just left a gap, which could be ambiguous (as discussed in our story about zero). Later, they introduced a placeholder symbol (••), but it wasn’t used consistently like our zero.

Roman Letters: Adding and Subtracting

The Roman system, familiar to us from clocks, buildings, and Super Bowl numbers, dominated Europe for centuries. It’s an additive system, like the early Egyptian one, but uses letters as symbols:

• I = 1
• V = 5
• X = 10
• L = 50
• C = 100
• D = 500
• M = 1000

You generally write the symbols from largest value to smallest, adding them up. For example, CLXXII = 100 + 50 + 10 + 10 + 1 + 1 = 172.

A peculiar feature, added later for efficiency, is the subtractive principle. If a smaller value symbol comes just before a larger one, you subtract it.

• IV = 5 – 1 = 4
• IX = 10 – 1 = 9
• XL = 50 – 10 = 40
• XC = 100 – 10 = 90
• CD = 500 – 100 = 400
• CM = 1000 – 100 = 900

This avoids writing more than three identical symbols in a row (so IIII is avoided by using IV).

Advantages: It doesn’t rely on place value, so the order (mostly) doesn’t matter, reducing certain kinds of errors. It looks quite stately on monuments!

Disadvantages: Writing large numbers can still require many symbols. More significantly, performing calculations like multiplication or division directly with Roman numerals is extremely difficult. People using this system typically relied on calculation tools like the abacus (a frame with beads) or a counting board.

Our System: Hindu-Arabic Numerals Take Over

The system we use today originated in India sometime before 600 A.D. and was spread westward by Arab scholars (hence the name Hindu-Arabic). Its key features are:

1. Base Ten: Uses powers of ten.
2. Place Value: The position of a digit determines its value.
3. Unique Symbols: Has distinct symbols for digits 0 through 9.

Why did this system eventually replace the others in most of the world?

• Efficiency: It’s incredibly compact for writing large numbers compared to additive systems like Egyptian or Roman.
• Calculation: Its structure allows for relatively easy calculation algorithms (the methods we learn for addition, subtraction, multiplication, division) to be performed directly on paper, without needing an abacus.
• Zero Power: The consistent use of zero as both a placeholder and a number was revolutionary, making the place value unambiguous and enabling more advanced mathematics.

It took time, though! Roman numerals persisted in Europe for centuries, even alongside the new system, partly due to tradition and partly due to worries about fraud (it’s easier to change a ‘2’ to a ’20’ than it is to change ‘II’ to ‘XX’). But the sheer computational power and efficiency of the Hindu-Arabic system eventually won out for most mathematical and commercial purposes.

Has Our Number System Really Won? The Computer Age Twist

While the Hindu-Arabic system dominates our handwriting, bookkeeping, and textbooks, the computer revolution added a fascinating twist.

Computers don’t “think” in base ten. At their core, they operate using binary code – base two. Everything is represented by strings of just two digits: 0 and 1, corresponding to electrical switches being off or on.

So, in a way, we now rely heavily on two main number systems:

1. Base Ten (Hindu-Arabic): For human communication and everyday use.
2. Base Two (Binary): For the internal workings of the machines that run our modern world.

Programmers often use intermediate systems like base sixteen (hexadecimal) as a more compact way to represent long binary strings, using digits 0-9 and letters A-F.

This shows that even today, the “best” number system depends on the context and the task at hand. The journey of number systems isn’t necessarily over.

What Numbers Tell Us: A Numerological Viewpoint

Exploring different number systems can also spark reflections from a numerological perspective.

The Power of Ten: Our dominant system is base ten, often linked to our ten fingers (the word digit comes from the Latin for finger). This grounds our primary number system in the human body, the physical form. Does this base choice influence how we perceive the world through numbers? Systems like Babylonian base sixty (linked perhaps to early astronomy and time cycles) or Mayan base twenty might reflect different cultural focuses or ways of relating quantity to the cosmos or the human form (fingers and toes).

Symbolism of the Shapes: Ancient symbols weren’t arbitrary. Egyptian hieroglyphs were pictures of real things (heel, rope, flower, finger, tadpole, man). Could these symbols have carried deeper meanings beyond just their numerical value? Did using a lotus flower for 1,000 imbue that number with a sense of beauty or growth? Did the astonished man for 1,000,000 convey the awe of such a large quantity? Roman numerals used letters – did the values assigned (I=1, V=5, X=10, L=50, C=100, D=500, M=1000) carry any subtle influence from the letters’ other associations or sounds? Numerology often finds meaning in the shapes and sounds of letters and symbols.

Place Value and Potential: Place value systems, like the Babylonian and Hindu-Arabic, rely on the position of a symbol. This introduces an abstract layer – the same symbol can mean different things depending on where it is. This relates to the idea of potential. A ‘1’ isn’t just one; it holds the potential to be ten, a hundred, sixty, or thirty-six hundred, depending on its place. Zero, as the placeholder, becomes the key to unlocking this positional potential. Numerologically, zero represents pure potential, and place value systems visually demonstrate how context (position) actualizes potential into specific values.

Calculation and Flow: Additive systems like the Roman seem static; you just add up fixed values. Place value systems enable dynamic calculation methods (carrying, borrowing). Does the system used influence the feeling of working with numbers? Is one more grounded (additive) while the other feels more like managing flow and potential (place value)?

More Than One Way to Count

The way we write numbers seems so natural, so obvious. But history reveals a rich variety of systems invented by ingenious minds across different cultures. Exploring Egyptian hieroglyphs, Babylonian wedges, and Roman letters reminds us that our Hindu-Arabic system, powerful as it is, is just one way to capture the concept of quantity.

Each ancient number system had its strengths and weaknesses, shaped by the materials available (clay vs. papyrus), the primary uses (building vs. astronomy vs. trade), and perhaps even the underlying philosophy of the culture. Our modern world, reliant on both human-readable base ten and computer-friendly base two, shows that the evolution of number systems continues, always adapting to our needs and technologies. Understanding this history broadens our appreciation for the simple digits 0 through 9 and the long journey they took to become the universal language of quantity we use today.