Writing is certainly one of the greatest tools humans have ever invented. Prior to the invention of writing, knowledge could only be passed from one generation to the next via word of mouth. Once writing became a part of everyday life, knowledge could be preserved across time.

There is an ongoing debate between the Egyptologists and the scholars of ancient Mesopotamia as to where and when the first writing system was devised. But the evidence shows that by no later than 2600 BCE the Sumerian writing system was capable of expressing the full range of the Sumerian language, including such nuances as meter and alliteration.

The Sumerians made writing a foundational part of their culture. Transactions such as the purchase of real estate, marriage, and divorce were recorded on cuneiform tablets. These tablets could actually be used by citizens in the Sumerian equivalent of a court of law. One tablet of a type known as a “ditilla” from ancient Sumer records a trial involving a woman whose uncle assumed ownership of her house and kicked her out. She took her case to a local magistrate, and a scribe recorded the proceedings. The woman and her uncle both appeared before the magistrate. Both were required to swear before a statue of the village god that they would tell the truth. Then both sides were allowed to present their cases. The woman presented a cuneiform tablet that recorded her purchase of the house, and it also recorded that the transaction was witnessed by two of her friends. The two friends accompanied her and testified that indeed they witnessed the sale. If the uncle had a defense, it isn’t recorded on the ditilla. So the magistrate awarded the house to the woman, and the uncle was forced to move out. This vignette played out hundreds of years before Hammurabi built the first Babylonian empire in the 18th century BCE.

None of that would have been possible without a writing system. The simple act of recording a real estate transaction– one that we now take for granted every day– transformed society by making it possible for ordinary people to seek and obtain a form of justice in a society that didn’t have lawyers, or laws, or a police force.

Writing enabled people of the ancient world to record their thoughts, their beliefs, and their achievements. The world of ancient Egypt would look far more mysterious to us if we didn’t have the pyramid texts and the coffin texts to tell us what the ancient Egyptians believed about life after death.

Today we have the marvelous treasures of ancient writings to help us understand how ancient people lived and thought. A man named Sin-leqi-unninni wrote an epic poem known as the Epic of Gilgamesh in Akkadian, in roughly 1200 BCE while he lived in Babylon. That epic includes a story of a great flood that would have wiped out all life on Earth had it not been for the defiance of a god, Ea, who warned a man named Ut-napishtim and advised him to build a boat. But long before the time of Sin-leqi-unninni, the story of the Flood was told in at least two previous versions, in Sumerian. This history shows that the story of the Flood in the Bible has antecedents in Mesopotamia that go back to a time probably 2000 years prior to that of the very earliest writings of the Bible.

Mathematics has also proven to be a powerful tool. We can frame the laws of physics as mathematical equations and then use those equations to deduce properties and behaviors of the world around us. For example, Newton’s Universal Law of Gravitation was used to deduce the location of the planet Neptune from an observed wobble in the orbit of the planet Uranus.

I would argue that mathematics is a type of language. It has a grammar and a syntax. An equation such as the following is one that follows the rules of the language of mathematics:

5X + Y = 0

whereas the following equation makes no sense:

= 5X / 2 – $

Mathematical equations can all be translated into natural language. The following equation:

5X + Y = 0

can be expressed in natural language as follows:

five times (the value of the variable X) plus (the value of the variable Y) equals zero

So is mathematics a language? Well, it clearly has linguistic elements. As I said above, it has both grammar and syntax. But though its symbols may bear a superficial resemblance to the letters of an alphabet, they don’t combine the way that letters combine into words. The rules for the use of mathematical symbols are much more strict than for the use of the letters of an alphabet, or for the words of a sentence.

And furthermore an equation can be transformed by the rules of mathematics to arrive at deductions. Here’s an example:

5X + 7 = 0

5X = -7

X = -(7/5)

The method for arriving at the above result can be described in natural language, as can be the underlying assumptions of the types of mathematical objects employed (i.e. the elements of a mathematical field). But the natural language formulation of such equations obscures the solution, whereas the mathematical form makes it easier to follow.

Yes, mathematics is a type of language– but it’s one with rules that are far more structured and strict than those of any natural language. So for that reason I think it’s best to think of mathematics as a symbolic system based purely on logic in which every component has a valid natural language transliteration.

Is language the greatest innovation in history? I don’t think that’s a question that requires an answer. The innovations of using fire for light, for defense against predators, and for cooking were certainly immensely transformational. As discussed above, mathematics has been immensely transformational. I don’t think it’s an exaggeration to say that the space program would not have been possible without the innovation of mathematics.

But regardless of whether it’s the greatest innovation ever, writing is without question indispensable to modern society. Without writing we would have little insight into the past, and the task of passing on what we have learned to future generations would be vastly more difficult.

Copyright (c) David S. Moore, 2022

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