Black Genesis: The Prehistoric Origins of Ancient Egypt
Black Genesis: The Prehistoric Origins of Ancient Egypt
Black Genesis: The Prehistoric Origins of Ancient Egypt
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APPENDIX 2<br />
SOTHIC CYCLES AND IMHOTEP’S CALENDAR WALL<br />
<strong>The</strong> Sothic cycle is the duration <strong>of</strong> synchrony between a 365-day <strong>Egypt</strong>ian civil calendar and the heliacal rising <strong>of</strong> Sirius.<br />
A difficulty with calculating this cycle lies in defining heliacal rising. <strong>The</strong> basic concept <strong>of</strong> heliacal rising is the day <strong>of</strong><br />
the year on which Sirius first seems to reappear on the eastern horizon just before the sun rises. Obviously, it would be<br />
problematic if we were to apply this purely visual definition. If the weather happened to be cloudy or the sky was filled<br />
with dust, an otherwise viewable reappearance would be missed, perhaps for many days. A more sensible definition could<br />
be the day on which Sirius would be visible, if the viewing conditions were optimal, and optimal is defined as a specific<br />
angular relationship <strong>of</strong> sun, Sirius, and horizon.<br />
In order to understand the Sothic cycle, we must first look at two related cycles. Today the length <strong>of</strong> the tropical year<br />
is 365.2422 days, so that a 365-day civil calendar would return the day <strong>of</strong> summer solstice to the same calendar date<br />
every 1,507.1 years. (We can call this the solstice-to-civil cycle.) Today the length <strong>of</strong> the sidereal year (with respect to the<br />
distant stars) is 365.2564 days, so that a 365-day calendar would return a star sign or zodiac constellation date to the<br />
same calendar date every 1,423.8 years. (We can call this the sidereal-to-civil cycle.) This difference between the siderealto-civil<br />
cycle <strong>of</strong> 1,423.8 years and the solstice-to-civil cycle <strong>of</strong> 1,507.1 years is due to the precession <strong>of</strong> Earth’s pole, the<br />
precession <strong>of</strong> the equinox. If Earth did not precess, then the sidereal-to-civil cycle would be the same as the solstice-tocivil<br />
cycle. Further, those sidereal and solstice rates are as measured today, while the actual precession rate varies slightly<br />
over time, which means these cycle durations also vary. Because the heliacal rising is a combination <strong>of</strong> sidereal and solar<br />
measurements—essentially, a complex addition <strong>of</strong> the two—we would expect the Sothic cycle, to first approximation, to<br />
be the average <strong>of</strong> the sidereal and solstice cycles, which, given today’s rates, would be 1,465.4 years. This is remarkably<br />
close to the purely calendar-based cycle <strong>of</strong> 1,460 years—the cycle between two types <strong>of</strong> civil calendar systems (one that<br />
adds a day every four years, like our leap year, and a fixed, 365-day calendar such as the <strong>Egypt</strong>ian civil calendar).<br />
Yet we would expect an actual Sothic cycle to vary from our rough estimate, due to several factors. First, the<br />
precession rate varies with time; the rate has been steadily increasing since roughly 8000 BCE. Today, the precession rate<br />
is about 50.29 arc seconds per year, while around 4000 BCE the rate was roughly 1 arc second per year slower. Due to<br />
this effect alone, almost half <strong>of</strong> one year would be added to the Sothic cycle over the span <strong>of</strong> about two Sothic cycles. A<br />
second factor is that the tropical year itself also changes over time—but this effect is orders <strong>of</strong> magnitude smaller. A<br />
third factor, more difficult to estimate but which has a greater effect, is due to the change in declination <strong>of</strong> the star and its<br />
drift in right ascension relative to the vernal point—the day relative to solstice moves steadily through the year so that the<br />
angular relationship <strong>of</strong> star to sun to horizon is altered.<br />
Still, we can fairly easily use SkyMapPro to measure the Sothic cycles. First, we set the latitude to that <strong>of</strong> Djoser’s<br />
step pyramid (29.871 degrees north) and we set the year to 2781 BCE and we set the day to summer solstice. <strong>The</strong> result<br />
is that on that day, when Sirius is at altitude 1 degree, the sun is at altitude -8.96 degrees 45 minutes before the center <strong>of</strong><br />
the sun disk passes the horizon. This is clearly a good reference for heliacal rising, because Sirius is certainly bright<br />
enough to be seen briefly under such conditions. We call this summer solstice day, the first day <strong>of</strong> Thoth (1 Thoth) on the<br />
<strong>Egypt</strong>ian civil calendar, and we note that SkyMapPro calls this day July 16, 2781 BCE. We make this the definition <strong>of</strong><br />
Sirius heliacal rising—the day <strong>of</strong> the year when Sirius is at altitude 1 degree and the sun is simultaneously at altitude -<br />
8.96 degrees or lower. Next, we search for the previous year when Sirius rose heliacally on a first day <strong>of</strong> Thoth (1 Thoth)<br />
according to the <strong>Egypt</strong>ian civil calendar. We know that SkyMapPro uses Julian years (365.25 days per year), so we note<br />
that what SkyMapPro calls July 16, 4241 BCE, is a first day <strong>of</strong> Thoth on the <strong>Egypt</strong>ian civil calendar. When we look at<br />
that date, we see that when Sirius was at 1 degree altitude, the sun was at -9.41 degrees altitude just below the horizon,<br />
and the day before 1 Thoth, the sun was only -8.70 degrees below the horizon—less than our criterion <strong>of</strong> 8.96 degrees—<br />
so in that year the first day <strong>of</strong> Thoth was indeed the day <strong>of</strong> reappearance <strong>of</strong> Sirius.<br />
We must remember, however, that a given date for heliacal rising <strong>of</strong> Sirius should persist for about four years in a<br />
row on the <strong>Egypt</strong>ian civil calendar, so in order to nail down the exact Sothic cycle, we must check the following years.<br />
We see, then, that two years later, 4239 BCE, on the first day <strong>of</strong> Thoth with Sirius at altitude 1 degree, the sun was -9.05<br />
degrees altitude, which still satisfies heliacal rising (and this time, eleven days before summer solstice). In later years, all<br />
the way up until 2781 BCE, the first day <strong>of</strong> Thoth was not the heliacal rising date. So this Sothic cycle extended from<br />
4239 BCE to 2781 BCE (in Julian years), which is 1,459 <strong>Egypt</strong>ian civil calendar years.<br />
By a similar method, we find that the next first day <strong>of</strong> Thoth-Sirius heliacal rising was 1325 BCE (twelve days after