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E - 105 : Arabic Numerals and the Antikythera Mechanism

Updated: Apr 16, 2021


Found in 1902 near Antikythera, the Mechanism built in the first century BC is now on display in the National Archeological Museum in Athens


When crossing to Corfu from Puglia this summer, there will be one thing that is not going to change: the numerals. Not that the numbers in the Greek and the Roman alphabet were the same. They differed as the letters did. The numerals we use today however are borrowed from the Hindu-Arabic culture. Thus we can read numerical information on Greek road signs.

Greek Road Sign - the Date is understandable without any knowledge of the Greek Alphabet


As with many things, I discovered the history of numbers by chance. When working in retail banking in Zurich in 1985, I once walked through the medieval town centre looking for a restaurant. On St Peter’s Place, once the site of a Roman temple, was a bookstore which always had interesting exhibits in the windows. A book titled “The History of Numbers” caught my attention. I still remember its light blue color. I skipped my lunch and used the money to buy the book. Written in 1983, it tells how numbers were invented by Sumer and in the Hindus valley, where they were used for accounting and astronomy. They then made their way to Egypt, Phoenicia and eventually to Greece. Numbers were expressed by Alphabetic symbols or letters. To express big numbers, many symbols were needed. But in antiquity, calculations that required more than 4 digits were rare. For people’s everyday life, the system was simple and adequate.


Since we are all familiar with Roman numbers, I am using them to illustrate the inbuilt troubles with this system. To write a seven digit number like 2’458’977, one needs 17 symbols in Latin (the Greek number system comprised eve 27 symbols). Using that many symbols makes larger mathematical operations difficult to execute but most of all time consuming.


Question to you: can you easily add the Roman numerals?

__________

MMCDLVMMMCMLXXVII + 2’458’977+

________

MCXXVMCXVII = 1’126’117=

______________

MMMDLXXXVCLIV 3’585’154


It is easy on the right hand side but for the left you probably needed a note pad as I did. From this simple example above it is quite obvious why the Arab decimal system replaced the Roman numbers so quickly in the early middle ages.


I thus assumed that complicated math was not possible until our culture had Arab numbers and used the decimal system. But important questions remain. How does my assumption square with the fact that the Greeks were able to calculate the circumference of our globe or the distance to the moon or create an analogue computer like the Antikythera Mechanism whose 50 precise gears could calculate the positions and the movements of the sun, the moon and the planets 250 years ahead including solar and lunar eclipses? I must have been missing something.



Thanks to St. Andrews McTutor, which talks about the history of math, I found the answer. Have a look yourself on the site below:


https://mathshistory.st-andrews.ac.uk/HistTopics/Greek_numbers/


For bigger numbers, Greek scientists did not use their cumbersome numeral system. Already Archimedes used exponentials to express big numbers. So rather than looking for a way to write the number of 10’000’000 with many symbols, he simply used 10 to the power of 8. Wow! Could not believe when I read this. Archimedes just leapfrogged the decimal system to express his numbers with exponentials. No wonder the Greek mathematicians and scientists could do such complex work! They did not need the decimal system from India!

Working Replica of the Antikythera Mechanism - it took decades to figure out how it worked


For us ordinary citizens though, the Arabic-Hindu decimal numbers are perfectly adequate. We can calculate almost anything we want. The Arabic numerals are so convenient, they did not only replace the Greek and the Roman numbers. They replaced all other number system in the world. Thus mathematics has become a universal language that everybody can understands.


We thus won't need a lexicon after arriving in Corfu. We can read the numerals used in Greece as they are.









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