The Ishango Bone: Unraveling the Earliest Evidence of Mathematics in Human History

Introduction

Fifty years ago, Professor J. de Heinzelin discovered the Ishango bone, a 10-cm curved bone found among harpoon heads in the Ishango fishermen village area on the Semliki river shores, near the border between Congo and Uganda. The bone features a fragment of quartz in its narrower top extremity, believed to have been used for tattooing or engraving. The bone’s dating is uncertain but likely around 20,000 years old. This bone is considered to be the first mathematical tool ever used by humans.

Historical Context

The history of the Ishango Bone is crucial to understanding its significance as one of the earliest examples of mathematical thinking in human history. The bone was discovered in the Ishango region, situated in what is now the Democratic Republic of the Congo. This region, during the time of the Ishango Bone’s creation, was part of a vast, fertile area known as the Semliki River Valley. The artefact’s discovery occurred in 1960 during an archaeological excavation led by Belgian geologist Jean de Heinzelin.

Upper Paleolithic Period

The Ishango Bone dates back approximately 20,000 years, placing it in the Upper Paleolithic period, which spans from about 40,000 to 10,000 years ago. This era marked a significant period of human development, characterised by the use of advanced stone tools, cultural diversification, and the emergence of early forms of art, religious beliefs, and societal structures.

Prehistoric Human Habitation

The Semliki River Valley provided a favourable environment for prehistoric human habitation. It was rich in natural resources, such as fish, game, edible plants, and freshwater, making it an attractive location for early human groups to settle and thrive.

Cultural Diversity

The Upper Paleolithic period saw the coexistence of various cultures and groups with distinct linguistic and artistic expressions. Although specific details about the societies inhabiting the region during this time are limited due to the lack of written records, archaeologists have found evidence of social structures, trade networks, and belief systems that shaped the daily lives of these early human communities.

Origin and Purpose of the Ishango Bone

The exact origin and purpose of the Ishango Bone remain speculative, as no direct evidence can definitively reveal its creator’s intentions. However, its discovery amidst other artefacts and remains suggests that it held some cultural or practical significance for its makers. Some theories propose that it might have been a counting tool, a lunar calendar, or even an ancient gaming device.

Contemplation of the Natural World

The Ishango Bone’s intricate tally marks and symbols indicate a degree of abstract thinking and contemplation of the natural world by its creators. The bone’s engravings might have served as a form of communication or record-keeping, aiding in understanding time, seasons, and celestial events.

Cultural Exchange and Trade

The discovery of the Ishango Bone in the Semliki River Valley attests to the presence of cultural exchange and trade between various ancient communities during the Upper Paleolithic period. The bone’s craftsmanship and mathematical notations suggest that knowledge and ideas were shared and transmitted across different groups.

Importance of the Discovery

The Ishango Bone’s significance lies not only in its age but also in what it reveals about the intellectual capacity of our early ancestors. It challenges traditional views of prehistoric societies as solely concerned with survival and basic needs, providing evidence of their ability to engage in complex mathematical thinking and potentially advanced cultural practices.

Physical Characteristics

The physical characteristics of the Ishango Bone provide essential clues about its origin, the materials used, and the methods employed in its creation. These details contribute to understanding the artefact’s historical context and significance in studying early human civilisation.

Material and Preservation

The Ishango Bone is an ancient artefact made from the fibrous bone of an animal, most likely the leg bone of a large mammal such as a baboon or a bovid. The bone’s organic nature makes it susceptible to decay over time, but its preservation was aided by the specific environmental conditions in which it was buried. Being buried in a saturated or oxygen-deprived environment can slow down the decomposition process, and this was likely the case with the Ishango Bone, as it was discovered in the Semliki River Valley.

Size and Shape

The Ishango Bone measures approximately 10 centimetres (about 4 inches) in length. It is relatively small and can be comfortably held in one hand. The bone is slim and elongated, featuring a cylindrical shape with smooth, slightly curved edges. Its size and shape suggest that it was portable and easy to carry around, serving as a personal tool or an object of value to its owner.

Surface Engravings

The most distinctive aspect of the Ishango Bone is the presence of engravings on its surface. These engravings are not haphazard but seem to have been deliberately incised with sharp tools. The engravings consist of a series of vertical columns, and within each column are groupings of notches, marks, and symbols.

Number of Columns

The bone’s surface contains multiple columns of engravings. The exact number of columns varies between different sources, but there are generally three to four primary columns that have been identified. Each column contains different sets of notches and symbols, arranged in distinct patterns.

Aesthetics and Craftsmanship

The engravings on the Ishango Bone display a level of precision and deliberate craftsmanship. The lines are straight and neatly etched into the bone’s surface, suggesting a skilled hand and a purposeful creation process. The bone’s aesthetics may indicate that it was not merely a utilitarian object but one that held cultural or symbolic value.

Mathematical Notations

The bone contains 167 or 168 notches that are arranged in three columns along its length. The column located at the centre of the bone’s most curved side is the most common. These columns are commonly referred to as M, G, and D, which stands for Middle (Milieu), Left (Gauche), and Right (Droite) respectively in French. The M column is composed of eight groups of notches that run from top to bottom, with each group containing 3, 6, 4, 8, 9 or 10, 5, 5, and 7 notches respectively. On the other hand, the G and D columns each have four groups, consisting of 11, 13, 17, 19, and 11, 21, 19, 9 notches respectively. Although they can differ in length and orientation, the notches are mostly parallel within each group.

Marks on the first column:

Marks on the second column:

Marks on the third column:

Tally Marks and Symbols

The engravings on the Ishango Bone fall into three main categories: simple tally marks, complex tally marks, and non-tally marks.

• Simple Tally Marks: The first group consists of basic tally marks, typically arranged in sets of single, double, and triple notches. These tally marks are arranged in a clear and systematic manner, indicating a counting system.
• Complex Tally Marks: The second group includes more intricate arrangements of tally marks, with some columns showing prime numbers, such as 11, 13, 17, and 19. These prime numbers are significant as they are indivisible except by themselves and one, indicating a level of mathematical sophistication in the engravings.
• Non-Tally Marks: The final group comprises engravings that do not fit the typical tally mark patterns. These non-tally marks take the form of crisscross patterns and are subject to varying interpretations. Their purpose and meaning remain uncertain and have been a subject of speculation among researchers.

Simple Tallies

The simple tally marks found on the Ishango Bone are the most straightforward and easily recognisable form of notation. These tally marks consist of straight, vertical lines, and are grouped into sets of one, two, or three marks. The simplicity of these notations suggests their primary purpose as a counting system.

One prevailing theory is that the simple tally marks were used for practical purposes such as recording the number of animals hunted, the quantity of food gathered, or the inventory of goods traded. These marks could have served as memory aids or as a means of keeping track of important information for the group’s survival and economic activities.

The use of tally marks for counting is not unique to the Ishango Bone or the Semliki River Valley. Tally systems have been employed by diverse cultures across time and geographical locations, attesting to their effectiveness as an early form of record-keeping and arithmetic. The presence of these simple tally marks on the Ishango Bone reflects the importance of counting and basic numerical understanding in the daily lives of early human communities.

Complex Tallies

The complex tally marks found on the Ishango Bone represent a significant advancement in mathematical notation. Unlike the simple tally marks, these complex marks involve more intricate arrangements and display patterns related to prime numbers.

For example, one of the columns contains 11 notches, another has 13, and a third features 17 notches. These numbers are prime numbers, meaning they are only divisible by 1 and themselves, with no other whole number divisors. The inclusion of prime numbers on the Ishango Bone is remarkable because prime numbers hold unique mathematical properties and have intrigued mathematicians for centuries.

The presence of prime numbers suggests that the ancient inhabitants of the Semliki River Valley possessed a deeper understanding of number theory and recognized the significance of these special numbers. This level of mathematical sophistication implies that the mathematical knowledge of these early humans went beyond simple counting and had potential applications in various aspects of their lives.

Non-Tally Marks

The non-tally marks on the Ishango Bone are the most enigmatic and subject to diverse interpretations. These markings deviate from the regular tally mark patterns and consist of crisscrossing lines and groups of diagonal marks. The irregular nature of these notations has led researchers to explore various possibilities for their purpose and meaning.

One hypothesis is that the non-tally marks may have been used for more abstract or symbolic purposes. They could have represented astronomical events, lunar phases, or even religious or ritualistic symbols. Some researchers propose that the bone might have functioned as a lunar calendar, tracking the moon’s cycles and helping early humans mark significant events or plan activities related to celestial observations.

However, due to the absence of contextual information and written records from the time of the Ishango Bone’s creation, the true purpose of these non-tally marks remains speculative. The complex and diverse nature of the markings adds to the mystery and allure of this ancient artefact, leaving room for ongoing research and investigation into its significance.

Mathematical Implications

Mathematical notations on the Ishango Bone suggest that early human societies had a form of mathematical communication and cultural exchange. The bone may have been a tool for teaching or passing down mathematical knowledge and practices from one generation to the next. It also implies that there was a shared understanding of numerical concepts within the community, which would have facilitated trade, cooperation, and communication between different groups.

The Ishango Bone’s mathematical notations offer insights into early humans’ cognitive development and intellectual abilities. The ability to engage in abstract mathematical thinking, such as recognising prime numbers, indicates a level of cognitive complexity that goes beyond basic survival instincts. This challenges the traditional view of early humans as purely pragmatic beings and suggests that they had the cognitive capacity for more sophisticated thought processes.

The Ishango Bone is a pivotal archaeological find in the study of the origins of mathematics. It pushes back the timeline of human engagement with mathematical concepts and indicates that mathematical thinking has deep roots in human history. By shedding light on the mathematical capabilities of ancient civilisations, the Ishango Bone helps researchers understand the evolutionary trajectory of mathematical thought and the cultural contexts in which it developed.

The bone’s mathematical notations may have held cultural and symbolic significance for the communities that created it. It could have been used in religious or ritualistic practices, as a calendar for tracking important celestial events, or as a symbol of knowledge and power within the community. The bone’s craftsmanship and mathematical inscriptions could have imbued it with a special status, making it a cherished and revered object within its cultural context.

In conclusion, the mathematical implications of the Ishango Bone extend far beyond mere notations on an ancient artefact. They offer profound insights into early human societies’ mathematical abilities, cognitive development, and cultural practices. The bone’s mathematical notations challenge conventional assumptions about prehistoric civilisations’ intellectual capacities and underscore mathematics’s universality and significance in shaping human history. As an invaluable archaeological discovery, the Ishango Bone remains a focal point of study, enriching our understanding of the origins and evolution of mathematics in human civilisation.