When there were no digits?

We are so used to letters and numbers that we cannot imagine how people counted without digits. But how did people count in the good old days when digits did not yet exist? Yes, there was such a time, before the invention of digits.

How could that be, digits were not invented yet, but people already knew how to count? How can this even be imagined? It’s quite simple, just look at your fingers — the tool for counting is already there, it’s just that the tool for writing numbers hasn’t been invented yet.

It’s important not to confuse digits and numbers. Digits are symbols used to represent numbers. We currently have 10 digits, but there are many more numbers. 9 is a digit and a number, while 99 is a number written with two digits.

The Greek Numbering System

In Ancient Greece, there were no digits, but there was already an alphabet. The Greeks used letters to write numbers. And they did so in different ways at different times.

In the old Attic numbering system (which was popular until the 3rd century BC), instead of digits, they used the first letters of words from which the name of the number started. For example:

One — “ios”, written ἰος, the first letter is I Five — “pente”, written πέντε, the first letter is Π Ten — “deka”, δέκα, the first letter is Δ One hundred — “hekaton”, ἑκατόν, the first letter is H …

Why start with five? Where are 2, 3, and 4? Well, “two” is two units, written as II. To write 7, they wrote: ΠII, and to write 27, they wrote ΔΔΠII, which means “two tens, one five, and two ones”. If they needed to write 105, they skipped the “zero”, writing just HΠ.

In the new Ionic system, it was different. They used letters in alphabetical order. One was “alpha”, two was “beta”, and so on up to nine. For the numbers 10, 20, 30… 90, they used the next 9 letters of the alphabet. For hundreds, they took nine more. At that time, the Greek alphabet had 27 letters.

Roman Numerals

Everyone knows what Roman numerals look like. But in reality, these are letters, at least some of them are definitely letters.

One hundred — centum was represented by C, and one thousand — mille was M.

But I, V, X — these are either letters from the Etruscan alphabet or special symbols that look very much like letters. The likelihood that the ancestors of the Romans invented special symbols to represent numbers is very low. Especially since the Greeks, their neighbors, used existing letters.

• I — the letter i, possibly similar to the Greek “one”, or maybe just a “stick for counting”
• V — the letter, or maybe a simplified depiction of an outstretched hand with five fingers, simply because it was too lazy to draw all the fingers
• X — the letter, or maybe crossed arms, on which, as we know, there are already ten fingers

Naturally, the number notation system was similar to the Greek one, there was no need to invent separate symbols for two and three when you could simply write II and III.
But the Romans had a positional system. To write “four”, they placed the one before the five, IV, and for “six”, the stick was placed after, VI. Very logical and convenient. Until, of course, you need to count large numbers.

Arabic Alphabetic System

Strangely enough, the Arabs did not use digits. The symbols we consider Arabic numerals are actually Indian digits. Arab mathematicians used the alphabet, just like the Greeks, and this was called “abjadia”, which translates to “alphabet”.

Just as the word “alphabet” came from the first two letters, “alpha” and “beta”, and in Russian “azbuka” comes from “az + buku”, in Arabic, the first four letters “Alif, Ba, Jim, Dal” turned into “a-b-j-a-d-ia”.

From one to nine, they used certain letters, then a series of tens, also ending with the value of 90, and for hundreds, they used the letter ﻍ “ghein” for one thousand.

The Indians themselves in ancient times also used an alphabetic notation for numbers. However, they wrote them from right to left.

Interestingly (though not surprisingly, since the peoples are related), the ancient Jews also used a similar system, with one exception. The numbers 15 and 16 violated the logic and were written as 10+5 and 10+6, or 9+6 and 9+7. This was done to avoid writing the name of God.

Kievan Rus

In Rus’, for writing numbers, they used Glagolitic and later Cyrillic. Just like the Greeks and Arabs, from 1 to 9, from 10 to 90, and so on. The ancient Slavs, to distinguish numbers from letters, placed a special sign called “titlo” above them.

China

In Ancient China, they naturally used characters.

Even today, there exists both a “universal” and a traditionally Chinese form of writing numbers. Moreover, the Chinese form is divided into “everyday” and “formal”, which is stricter. The formal one is used in serious financial documents to protect against forgery.

For example, the number 30 can be written as 三十, or more elegantly as 叁拾.
We do the same when we write numbers in words.

Japan and Korea borrowed the Chinese system for writing numbers with some minor modifications.

In ancient Armenia, as in Georgia, they used alphabetic notation, but they used uppercase letters.

Origin of Digits

What about other ancient peoples? The Babylonians and Egyptians used special signs to denote digits, but they did not use letters. As history has shown, having separate signs for writing numbers turned out to be more convenient.

The first digits appeared in the 7th century AD in India. These were special symbols for writing numbers.
While in Babylon only two types of wedges were used, one for writing ones and the other for writing tens (a binary system before Christ), in India, they invented digits for writing ten numbers. That is, it was the familiar decimal system, plus ten separate symbols for each digit. This was a huge step forward in the development of mathematics.

It’s possible that the ancient Indians borrowed the decimal system from China, but that’s just a theory.

Of all the ancient numeral systems, we still regularly use the Indo-Arabic system.
Indian digits first reached the Arabs, as all trade between India and Europe went through Arab merchants, and soon the digits made their way to the European continent and became known as “Arabic”.

They are written a little differently, simply because Europeans write from left to right. It’s believed that the digits reached Europe through dice, although this is unproven, but it’s an interesting thought.

Look at how the real Arabic digits “two” and “three” are written, rotate them 90 degrees counterclockwise, and you’ll get the familiar “European” shapes. However, Indian analogs do not need to be rotated. This is evidence that the first Arabic digits that reached Europe were depicted on dice for playing games.

But most likely, the digits moved from scholar to scholar. The period between the 8th and 9th centuries AD is called the “Golden Age of Islam” or “Muslim Renaissance”. The Arabs had conquered all they could conquer, had gained access to and studied the works of ancient Greek and Roman mathematicians, and besides, they made their own great contribution to the science of mathematics.
It’s not surprising that Arabic mathematics, and science in general, were more advanced than in medieval Europe. And, naturally, Europeans learned from Arab mathematicians, not the other way around.

What was innovative and useful about Arabic digits:

1. A positional numeral system. The position of a digit indicates whether it is related to ones, tens, hundreds, etc. To write 168, you need 3 symbols, for 3897 — 4. Compare this with the cumbersome Roman system, where the same numbers would be written as CLXVIII and MMMDCCCXCVII.
2. In the Arabic system, there is zero. You can write 201, which means “two hundreds and one”, and the zero shows that there are no tens in this number, just hundreds and ones.

Just two innovations, but so convenient that we still use the Indian system today.