Tally marks

Tally marks, sometimes called hash marks, are a fundamental way to represent numbers. They serve as a basic numeral system used for counting objects or events. This method is categorized as a unary numeral system. In a unary system, you use the same single symbol repeatedly to show a quantity.

This makes tallies perfect for recording ongoing results. For example, you can use them to track the score in a sports game. You do not need to erase or discard old results to add new ones. However, tallies are not ideal for static text. Large numbers would become too long and difficult to read on a page.

To make tallies easy to read, people typically cluster them into groups of five. This grouping provides two major advantages for the user. First, it allows for easy conversion into decimal numbers for higher arithmetic operations. Second, it helps prevent human error. It is much easier for a person to identify a cluster of five than a cluster of ten.

There are several ways to visually distinguish the fifth mark in a group. Some people draw the fifth stroke at an angle to the others. This creates a style known as a "herringbone." Another common method is to draw the fifth mark as a diagonal line. This style is often called a "five-barred gate."

History shows that humans have used counting aids for tens of thousands of years. The earliest examples are not marks on paper, but notched sticks or bones. These artifacts date back to the Upper Paleolithic period. Some of the oldest notched bones were found in Africa during the Late Stone Age. Others were found in Europe during the Aurignacian and Gravettian periods. These tools represent some of the earliest evidence of mathematical thinking in human history.

A significant discovery was made in 1937 in Czechoslovakia. An archaeologist named Karl Absolon led excavations at Dolní Věstonice in Moravia. During this work, he found a prehistoric artifact known as the Wolf bone. This bone dates to the Aurignacian period, approximately 30,000 years ago. It contains 55 marks that may be tally marks. Interestingly, the head of an ivory Venus figurine was found near this bone.

Another important artifact is the Ishango bone. This object was found in the Ishango region of the present-day Democratic Republic of Congo. It is estimated to be over 20,000 years old. Researchers have debated what the marks on this bone actually represent. Some scholars originally believed the marks portrayed a series of prime numbers. However, Peter Rudman argues that the concept of prime numbers likely did not exist then. He suggests that division was developed after 10,000 BC, and prime numbers might not have been understood until about 500 BC. Rudman notes that the marks on the bone do not clearly show multiples of ten or specific prime number patterns. Instead, Alexander Marshack used microscopic examination to suggest the bone might represent a six-month lunar calendar.

Many complex writing systems have roots in these early tally marks. Roman numerals are one example of a system derived from this method. The Brahmi and Chinese numerals for the numbers one, two, and three also share this origin. Even the ogham script may have been derived from tallying.

These systems show how simple counting marks can evolve into sophisticated ways of recording information.

In modern computing, tally marks are represented in the Unicode Standard. In 2015, Ken Lunde and Daisuke Miura proposed encoding various tally systems. While some styles like the box tally were not accepted, the Unicode Standard did include some marks. In June 2018, version 11.0 added the five ideographic tally marks, known as the 正 scheme. It also added two Western tally digits. Currently, only the marks for the numbers 1 and 5 are encoded. The marks for 2, 3, and 4 are intended to be created by combining the mark for 1. This shows how even ancient counting methods find a place in our digital world.