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In the face of this complexity, early societies sought understandable answers. These societies were not mathematically sophisticated and often lacked even the concept of fraction. Lacking a theoretical understanding of astrophysics, and hampered by relatively poor mathematics, most early societies tended to adopt certain predictable responses. |
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Pesky and troublesome fractions were simply ignored. The year length simply might be rounded off to 365 days, for example. |
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Values were often selected by criteria in which mathematics and observation only played a part. Religious considerations were also important, so values that seemed "right" could be selected. Simple is often "right," so the year might be 360 days, which is simply 12 months of 30 days. |
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Values were assumed to be constant. Once a value was discovered by dint of laborious observation, it was assumed to be perpetually true. This attitude persisted well into the Age of Enlightenment in Europe. |
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Where accuracy was required for some reason, records were kept. Calculations were made using what modern readers would regard as an arithmetic of finite differences. By using tables and recorded data, early observers were able to predict the motions of the Moon and some planets with a good degree of accuracy for short periods. |
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The novice may be horrified to learn that there are several different ways to define the basic units of day, month, and year. I will dispose of these matters fairly quickly, using only the relevant definitions in later work, and introducing the others only as discussion requires. |
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Three definitions of day are relevant: |
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Sidereal The interval between two successive transits of a fixed star across the observer's meridian. |
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Solar The interval between two successive transits of the Sun across the observer's meridian. |
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Mean solar The interval between two successive transits of a fictitious body across the observer's meridian the "mean Sun," which moves at a uniform rate along the equator. |
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