On November 13, long distance runners from all over the world converged on Athens for the 29th Athens Classic Marathon. This old arithmetically-challenged emperor assumed that it was organized to celebrate the 2,500th anniversary (25th centenary) of the Battle of Marathon, fought in 490 BC. However, the official logo of the Association of International Marathons and Distance Races (pictured here) makes it clear that they considered 2010 to be the centenary. So who's correct?

**An Ancient Event**

It used to be thought that the Battle of Marathon was fought in 491 BC. That date can be found in the *Cambridge Ancient History* (original edition) volume 4 (1926) by J.A.R. Munro, although others had long championed 490 BC.

It was well known that ten years had separated the two Persian invasions of Greece. The Greek victory over Xerxes at Salamis, ending the second Persian attempt, occurred in 480 BC, but some scholars clung to the view that, because Xerxes had actually set out from Susa in 481 BC, counting back 10 years gave 491 BC for Marathon.

(Thucydides may have contributed to the confusion when he wrote that the Battle of Marathon occurred ten years after the expulsion of the tyrant Hippias from Athens, which had occurred in 511/0 BC. Confusingly, the Attic calendar ran from summer to summer, so that, technically speaking, the tenth anniversary of the expulsion of Hippias spanned 491 and 490 BC. However, it is known that Phainippos, the Athenian archon for 490/89 BC, was in office at the time of the Battle of Marathon, which virtually guarantees that it fell in 490 BC.)

**Dating Problem**

However, the AIMDR (and they're not the only ones) have fallen foul of a different problem; a problem that continues to bedevil chronological calculations involving BC and AD dates. (See previous post for BC and AD dates.) This problem is caused by the absence of Year Zero.

Arithmetic calculations involving negative numbers (like BC dates) and positive numbers (like AD dates) assume that zero is the pivot, the fixed point between the two types of numbers. Subtract minus-10 from 10 and the result is 20.

Unfortunately, historical chronology doesn't work the same way. AD 10 is only 19 years after 10 BC, not the 20 years that we might naturally assume. (Think about it: 9 BC is one year later, 8 BC is two years later, ..., 1 BC is nine years later, AD 1 is ten years later, AD 2 is eleven years later, ..., AD 10 is nineteen years later.) Similarly, AD 2010 (the anniversary celebrated by AIMDR on their logo) is only 2,499 years after 490 BC. (Let's ignore the fact that they've gone for "2010 AD" instead of AD 2010.)

Only J.A.R. Munro and his fellow supporters of a battle in 491 BC could justifiably have celebrated last year! However, *this year*, all those keen runners who braved the unseasonal chill of Athens last week to run in the 29th Athens Classic Marathon were, perhaps unknowingly, celebrating the *real* anniversary, the 25th centenary of the greatest battle in ancient Greek history. Congratulations to all of them!