# How Humans Learned to Keep Count

March 24, 2021

“A n

umber is the ruler of forms and ideas… and the cause of gods and daemons.”– Pythagoras

It is an accepted belief that early humans kept count by inscribing tally marks on the walls of their cave or into pieces of wood, bone, or stone. In fact, bones dating as far back as the Stone Ages have been observed to have sequence lines scratched on them indicating someone was keeping a tally of something. Although a crude vertical line might have been the earliest symbol to represent the number one, this system didn’t really work for ciphering larger numbers. Historically, all early number systems had one challenging thing in common. As the count grew, it required creating a new symbol to represent the next value. So, every new symbol immediately needed to be replaced with one that represented an even larger number. Nonetheless, as early civilizations developed in the Mediterranean area, Egyptian, Hebrew, and Greek numerals were extensions of the tally marks used by early humans. The Egyptian system even used the hieroglyph for an open mouth (an elongated oval) with straight lines underneath to represent fractions of a whole. So, the five lines scratched below an oval would indicate that each measure was one fifth.

**Positional Notation Number Systems**

With large populations living far apart, it is rather amazing that the Babylonians, Aztecs, and Chinese civilizations independently developed positional notation number systems at about the same time. By adopting a positional system, those responsible for keeping count could reuse the same symbols by assigning the symbols different values based on their position in a sequence (e.g. – as a single digit the symbol one was equal to one; but used in front of another number, it had a two-digit value of ten). Since the earliest notation likely began with human finger sequencing, it is logical that many numeral systems around the globe are based on ten. However, the ancients were all missing one thing – the zero. The first record of a zero appeared in Mesopotamia around the third century B.C. Prior to that time, numbering systems for other cultures simply left that digit blank. For example, the symbolic positional notation for the number one-hundred eleven would be “1 1” not 101.

**How Ten Fingers Became Twelve Digits**

It would be the advanced civilizations of the Mayans that created a base-20 (vigesimal not decimal) number system even prior to the having a fully developed Mayan language. It is assumed that the Mayan people noticed their toes (possibly due to living in a warmer climate), which immediately doubled the number of available symbols. The Mayan civilization devoted extensive amounts of time in observing and denoting planetary positions using the base-20 system of notation. So, where did twelve months a year or twelve hours in the day come from? That would be from the Babylonian cuneiform method of recording quantities, which is one of the oldest numeral systems dating back 5000 years. The Babylonians had creatively added to the 10-digit system of finger counting by seeing the hand as having four fingers and a thumb. By raising or lowering their thumbs when sequencing numbers, their personal hand-held calculator was a base-12 machine that led to a base-60 system, which is why an hour is sixty minutes and there are 60 seconds in each minute as well as 12 hours in each day and 12 months in each year.

**The Role of Mathematics versus Numerology**

For thousands of years, humans have continued to have a love-hate relationship with numbers. Where mathematics paved the way in explaining many of the complexities of the universe, mathematicians have done little to explain human psychology. However, not everyone was motivated or disciplined enough to apply mathematics to understanding the world where they lived, loved, and died. Thus, numerology evolved as an alternative method of shedding light on the innermost workings of the human mind in lieu of quantitative physics. Nonetheless, some people began to associate recurring numbers (synchronicity) with explaining the coincidences of two or more events where something other than the probability of chance could be involved. For example, the number seven is considered to be magical with seven chakras, seven colors in a rainbow, and seven days in a week. Moreover, the number has religious connections to a much deeper understanding of the meaning of life.

**Advanced Technology of Numeral Systems**

Scientists have assumed that throughout human history we’ve been able to develop more advanced numerical capabilities as new areas of the human brain evolved to meet the challenges of each progressively more complex number system. After all, we do know that during the human development of new calculation skills using additional areas of the brain evolved based on the mathematical challenge at hand. Although it can be conjectured that numerical abilities will continue to advance as numeral systems are combined with the latest technologies, students will no longer have to worry about the best way to record numbers. Instead, they must develop the skills to check the reasonableness of answers and must have a broader range of mathematical knowledge to determine correctness. If the universe can withstand another million years of humankind, it will be intriguing to see where the simple act of counting our fingers and toes ends up taking us.

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