By Ben Tolkin
Great
question, but it will need quite a long answer! You're asking about
two of the most fundamentally
human activities: language
and
mathematics.
I'll start with letters.
Who invented letters?
For
most languages, there wasn't just one person who “created”
letters. (Though there are a couple of interesting exceptions I'll
talk about at the end!) The letters we use for writing English and
most European languages are slightly modified versions of the letters
used by the Romans for writing Latin. Those were based on earlier
Greek letters, which in turn came from even earlier ones... Almost
every modern writing system is descended from just a handful of very
early sets of letters.
Writing
was developed 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 only started 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 method of writing things down is pictographic: to
write about something, you just draw a picture of it. What makes it
writing, as opposed to just making art, is when you start
drawing not just objects, but abstract concepts represented by
symbols. The earliest writing symbols used a mixture of pictures and
symbols representing ideas. Let's say if you wanted to record that
you'd traded 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, very old artifacts, you might
be able to make out some of the pictures,
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 |
It's
important to remember that for most of history, very, very few people
could read or write. These writing systems had
thousands
of complicated symbols, but the only people who had
to learn
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
are still pictures of the thing they represent, but most are not.)
Almost every language instead uses a phonographic writing
system, like an alphabet: each symbol represents a sound. (Other
phonographic systems include syllabaries, where each letter
represents a syllable, and abjad, where each letter represents a
consonant.) While a language might have tens of thousands of words,
they only have a few 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 interactions between different cultures. Ancient Egypt
was a crossroads for many cultures speaking many languages, and
Egyptian scribes needed a way to record all of them. One of these
cultures was the Canaanites, a Middle Eastern group that spoke a
language in the Semitic family (an ancestor of modern Hebrew and
Arabic.) Egyptian scribes used a pictographic and logographic writing
system called hieroglyphics to write their own language, but when
recording the Canaanite language, they just used hieroglyphs to
represent sounds: each consonant sound was represented by the
hieroglyph of a word that began with that sound. For example, “house”
was pronounced bayt in early Semtic languages (it still is in
Hebrew today!), so whenever there was a "B" sound, scribes
would just write the hieroglyph for “house,” a rectangle. 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 hierogylphs 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 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. 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 "invent" letters.
Many
of these were still based on previous 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 for fun, or as a work of art, like J. R. R.
Tolkien's alphabets
for his fictional Elvish languages. Sometimes, people construct
alphabets because they think the current one is too confusing: the
playwright George Bernard Shaw wanted
people to use his
Shavian
alphabet, which
he thought made more sense than the Latin one.
There is only one example of a constructed alphabet being
widely used for a real language,
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. |
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 humans can easily count. 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 markings and two
hundred and ten.
Still,
this system is still widely used for counting small numbers; around
the world, people use different
kinds of tally
marks 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: to read the number, add 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
cool if you want to 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 with high numbers; 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 tremendous 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 traveling 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."
Again,
this is
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.
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