By Ben Tolkin
Great question, but it will need quite a long answer! You're asking about two of the most fundamental of human activities: mathematics and language. I'll start with letters.
Who invented letters?For the most part, letters weren't just “invented” by a single person one day (though there are a couple of interesting exceptions I'll talk about at the end!) The letters we use for writing English (and the letters used by most European languages) are slightly modified versions of the letters used by the Romans for writing Latin, which were based on Greek letters, which in turn came from even earlier ones... Almost every writing system currently used is descended from just a handful of very early writing systems.
Writing was invented independently in at least two places: the Fertile Crescent (modern-day Iraq) in 3000 BCE, and ancient Mesoamerica (Central America and Mexico) around 600 BCE. The development of writing in China in 1200 BCE was also probably independent, and its development in ancient India and Egypt may have been as well. Other than that, all parts of the world seem to have only gotten writing by borrowing it from their neighbors; Europe, Central Asia, and Africa had writing brought to them by cultural exchange, migration, or conquest.
The most basic system of recording information is pictographic: you represent an object by simply drawing a picture of it. What makes a system of recording information writing as opposed to just drawing pictures is the ability to record abstract ideas and concepts through non-representational symbols. The earliest writing symbols used a mixture of pictures and symbols representing ideas: if you wanted to record that you'd sold a bull to someone for two chickens, you'd just draw a picture of a bull, two pictures of chickens, and some symbol representing a “trade”. As time passed, these pictures became more and more stylized, looking less and less like real objects. These scripts are known as logographic or ideographic writing systems; each symbol represents a word or idea.
This saves time (it's easier to draw a symbol everyone knows stands for “bull” than draw an accurate picture of a bull, every time) but it made the pictures hard to understand unless you'd been taught their meanings. If you look at very old artifacts, you can make out some of the pictures and what they mean, but later systems like cuneiform in the Middle East, hieroglyphics in Egypt, and bone script in China don't really look like pictures at all.
|Cursive Egyptian hieroglyphs|
|Chinese bone script|
It's important to remember that for most of history, very, very few people could read or write. The thousands of complicated symbols in these writing systems were hard to learn, but the only people who learned them were professional scribes; being able to read and write used to be a full-time job!
Most writing systems today are not logographic (some Chinese characters can be considered logographic, but the writing system as a whole is more complicated.) Almost every language instead uses a phonographic writing system, like an alphabet: each letter represents a sound. (Other such systems are syllabaries, where each letter represents a syllable, and abjad, where each letter represents a consonant.) Languages have tens of thousands of words, but only a handful of sounds, so alphabets are much easier to learn than logographic writing systems. So who invented phonographic writing?
Like many important inventions, it seems to have developed from multicultural interaction. Ancient Egypt was a crossroads for many cultures speaking many different languages, and Egyptian scribes needed a way to record them. The Canaanites were a Middle-Eastern group that spoke a language in the Semitic family, that would eventually become the ancestor of modern Hebrew and Arabic. Egyptians scribes used a combination of pictographic, logographic, and phonographic writing called hieroglyphics to write their own language, but when recording the Canaanite language, used hieroglyphics to simply represent sounds: each consonant sound was represented by the hieroglyphic of a word that began with that sound in the Semitic language. For example, “house” was pronounced bayt in early Semtic languages (and still is in Hebrew today!), so the hieroglyphic for “house,” a rectangle, would be used wherever there was a “B” sound. The first letter of this alphabet was 'alp, a picture of a bull's head.
Believe it or not, those Egyptian hieroglyphics are the ancestors of the letters you're reading right now! 'Alp and bayt eventually turned into the Alphabet, and if you know what to look for, you can see traces of the original hierogylphics in letters today (Don't think the letter “A” looks much like a bull's head? Turn it upside down!) The Canaanite writing system was the basis for Phoenician, a language spoken by great sailors and explorers of the Mediterranean, who spread it to Greece; Greek writing inspired numerous systems on the Italian peninsula, that would eventually give rise to Latin, and the Roman Empire's conquests throughout Europe made it the dominant writing system on the continent. In the east, Phoenician was also an ancestor of Aramaic, which was the basis of Arabic; Arabic in turn became the basis for Persian and Urdu scripts used in Iran and Pakistan. Some suspect that Phoenician is also the basis of writing in India. Since Indian writing systems are used from Central to Southeast Asia, if this is true, it means almost everyone on Earth writes in a script descended from Phoenician.
|This diagram shows how some major alphabets descended from Phoenician. The column in the middle is the Phoenician alphabet. To its left, you can see the letters of the Greek alphabet, and how they were based on Phoenician writing, and to the left of that, the Roman alphabet, based on Greek. On the right, you can see first the Hebrew alphabet, then Arabic.|
That is a very brief history of how letters came to be. I haven't even talked about lowercase letters, invented in the Middle Ages to be easier to write with a pen, rather than inscribed in stone! I encourage you to do more research on this fascinating topic, but do want to quickly discuss what I mentioned in the beginning: there are some cases where a single person did just "invent" letters.
Most of the time, these are still heavily based on earlier writing systems: Cyrillic, the alphabet used in Russia and much of Eastern Europe, was created a by a team of scholars, and based mainly on Greek. The Armenian alphabet was developed by a single linguist around 400 AD, and seems to be based on Greek and Persian alphabet. In 1821, a Cherokee linguist named Sequoyah developed the first writing system for Cherokee, based on Latin letter forms.
Alphabets that are purely invented without previous reference are called constructed alphabets, and are usually made just for fun, or as a work of art: J. R. R. Tolkien made alphabets for his fictional Elvish languages, for example. Sometimes, people construct alphabets because they feel the current one doesn't work: the playwright George Bernard Shaw promoted the Shavian alphabet to be an alternative to the Latin one. There is only one example of a constructed alphabet actually being widely used, and that's Hangeul, the writing system for Korean!
|This is a page from an early guide on how to read Hangeul. The simple, geometric shapes are the Hangeul letters, and the Chinese characters explain how to use them.|
Korean used to be written using Chinese characters. Many languages in East Asia were written using Chinese, in much the same way that hieroglyphics were used for writing Semitic languages; characters were used to represent sounds without much regard for meaning. Languages like Japanese adapted and modified Chinese characters to fit their language, but a Korean king named Sejong the Great decided that to promote literacy in his realm, he needed a perfectly logical alphabet completely suited to the Korean language. In 1443, a team of scholars assembled by Sejong completed Hangeul, a writing system that has been recognized the world over for its clarity and logic; each consonant represents the shape of the tongue in the mouth, while each vowel reflects the philosophical ideals of the kingdom. This makes Korean the only language with an alphabet completely unrelated to any other!
For more information on alphabets, you can check out Omniglot, an online encyclopedia of languages and writing systems. And to learn more about Egyptian hieroglyphics, look at this post on the Cambridge Science Festival blog!
But what about numbers? We're not finished yet!The simplest way of recording numbers is a unary system, in which each mark (a numeral)represents an object being counted. The number two? Two marks. The numbers seven? Seven marks. This system is easy to learn and understand, and very sufficient for writing small numbers. The trouble comes when you want to record a number higher than what the human mind can easily comprehend. Writing down two hundred marks isn't just tiring, it takes just as long to read as to write; you can't tell at a glance the difference between two hundred and two hundred and ten markings.
Still, this system is still widely used for counting small numbers; different kinds of tally marks are used around the world to keep score in games. And believe it or not, unary numbers were the basis of the most popular number systems in the West for over a thousand years: Roman numerals. Though there are a couple of fancy rules involved in Roman numerals to make them shorter to write down, the principle is the same as any unary system: read the number by adding up the numerals. X is ten, V is five, and I is one: XXVI is ten + ten + five + one = twenty-six.
Learning to read Roman numerals can be fun if you want to quickly translate inscriptions on old buildings, but it's not very useful in the modern world. Like all counting systems based on a unary model, it's hard to use above a certain value; the highest symbol in Roman numerals is M, for a thousand, so any number of multiple thousands will take a long time to write. Addition and subtraction are pretty easy, but multiplication is a chore, and division is... well, I'll include a link explaining division at the end, but let's just say it's no fun. These days, we use a positional number system instead.
In a positional system, you don't just add up each numeral; the position of a numeral affects its value. We write twenty-six as 26, the numeral 2 followed by the numeral 6. But because of the 2's position, we know it doesn't really mean "two," it means "twenty": two times ten. Who invented this system?
Like writing, positional numbers were likely invented in two separate locations: both ancient Chinese and Indian civilizations used similar positional number systems. However, the Indian system was more comprehensive: the Indian mathematician Brahmagupta was the first to treat the numeral zero as a number like all the rest, and it is this system that forms the basis of our modern writing system. Ancient Indian mathematicians had a tremendously outsize impact on math: algebra, trigonometry, and negative numbers were all perfected during the Golden Age of Indian mathematics, from roughly 400 to 1600 CE.
|Numeral systems from around the world, all based on the original Indian numbers|
But while Indian cultures used a positional number since at least 700 CE, it wouldn't spread to Europe until the Middle Ages. The person most associated with Indian numerals in the West is mathematician Leonardo Bonacci, or Fibonacci, who introduced the new system of writing numbers to Europe in 2012. He had learned the numerals from travelling about the Mediterranean and meeting Arabic traders, who had learned it from the studies of Persian mathematical genius al-Khwarizmi. For this reason, the numbers used in the West are sometimes called "Arabic numbers," even though Arabic-speaking countries call their numbers "Hindi numbers."
This is, again, an extremely brief summary! I didn't even mention some of the most interesting writing systems in history, the Babylonian and Mayan systems! You may not have thought that such a simple question would take so long to answer, but that's the strange thing about the history of science: sometimes the most simple ideas take the longest time to establish. The alphabet and numerals we use today seem perfectly natural to us, but they were created by complicated and messy cultural changes. It's one of the reasons history is so interesting: you get to see the weirdness hiding behind everything we see as ordinary.
For more information on numbers, there's no better resource than Isaac Asimov's Asimov on Numbers (ISBN: 067149404X). To learn how to divide using Roman numerals, start with mathematician Lawrence Turner's page here.
Ben Tolkin once spent a summer teaching himself Elvish. His recommended strategy for learning important things is to ask the questions so obvious no one can think of an answer to them.