For example, there are 365.2422 days within a year. If we counted only 365 days within a single year,we would soon find that the seasons were occurring at the wrong time of the year.
The problem of commensurability was recognized in antiquity. The Julian calendar, named for Julius Caesar, was established in the year 46 B.C., and was used subsequently throughout Europe. This calendar corrected the errors that had accumulated, used 365 days per year, and added one extra day every four years (the leap year). Under this scheme, the year was assumed to have 365.25 days. Although this is very close to the true number of 365.2422, even this small difference would amount to an appreciable error over a few centuries.
This error was eventually recognized during the Middle Ages. The most recognizable problem with the calendar was that the vernal (spring) equinox, a phenomenon that could be observed by a trained astronomer, was falling a few days before the traditional date of March 21. This might have been a trivial problem had the peoples of Europe not been Christian.
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