Was Ptolemy’s “5-degree rule” simply a Fudge Factor?

The dictionary defines “fudge factor” as “a number included in a calculation to account for error or unanticipated circumstances or to ensure a desired result.”

Image from https://wockenfusscandies.com/blog/brief-history-fudge-enjoy-taste-homemade-fudge-facts-flavors/

In Tetrabiblos III:10, Ptolemy discusses the 12 Places (topoi) of Hellenistic astrology with reference to determinng the length of life, but he puts an interesting twist on his definition of the Places. Instead of using Whole Signs as Places, which was a common practice among astrologers of the time, he used an Equal House System (allegedly from an early Hellenistic text by Asclepius) and further modified this ancient system by stating that the equal 30-degree houses should be counted from 5 degrees above the horoskopos (ascendant degree) instead of from the ascendant degree itself. Unfortunately, Ptolemy does not explain his rationale for counting houses from 5 degrees above the ascendant.

Many later astrologers, like William Lilly in England, accepting Ptolemy’s words on authority rather than reason, came to regard Ptolemy’s 5-degree rule as sacrosanct and found various ways to justify it, despite the logical contraditions that it generates. Morinus in France, for example, argued that the influence of the house was weakest toward the end of the house and planets late in a house were conjunct the next cusp, so the planetary influence would be felt more in the next house than in the house the planet acutally occupied.

Ptolemy, however, was using a variation of Whole Signs as 30-degree Houses, and signs have quite distinct boundaries. One would not say the a planet within 5 degree of the end of Aries is, for all intents and purposes, really in Taurus. Since the houses are analogous to the signs, how can one justify saying that a planet toward the end of a house should, for all intents and purposes, be in the next house.

If we view Ptolemy’s 5-degree rule in the context of the entire Tetrabiblos, we may gain a broader perspective. Ptolemy was a natural scientist and not a practicing astrologer. As a scientist, one of his aims was to advocate the adoption of the tropical zodiac rather than the fixed sidereal zodiac positions in use by his contemporaries. In addition, such tables were often off by a couple of degrees. Ptolemy, impressed by the work of Hipparchus who discovered the precession of the equinoxes some three centuries earlier, argued that the cardinal signs should begin at the equinoxes and solstices of the Sun. Logically, then, Ptolemy would have considered the tables in use by astrologers of his period to be in need of a correction factor of roughly 5 degrees to convert the values from sidereal to tropical because of precession.

Let’s consider a chart from Ptolemy’s period. Vettius Valens apparently used his own birth chart as an example in his Anthologies. The chart in question is that of a man born on Februar 8, 120 CE at about 6:49 PM LMT in Antakya, Turkey. Valens tells us it has an Ascendant of 8 Virgo, Moon at 7 Scorpio, Sun at 22 Aquarius, Mercury also in Aquarius, and Saturn in Cancer. Valens was apparently using the version of the sidereal zodiac available in the tables of his period. Here is a modern approximation of Valens’ birth chart, using the Raman ayanamsa and Equal Houses from the sidereal Ascendant.

Valens Natal Chart, Raman sidereal ayanamsa, Equal Houses from Ascendant

In analyzing this chart, Ptolemy would still use Equal Houses from the Ascendant, but he would apply his fudge factor of 5 degrees to begin counting the Equal Houses from 3 Virgo 10′ rather than 8 Virgo 10′. In other words, his fudge factor would give a rough tropical ascendant of 3 Virgo 10′. Let’s calculate the actual tropical value using Solar Fire software.

Valens’ tropical birth chart. Asc is now 4 Virgo 25. Mercury lies in Capricorn tropically but in Aquarius sidereallly. Saturn lies in Gemini tropically but in Cancer sidereally. Clearly, Valens used the sidereal zodiac in his calculations. Most likely the positions in the tables he used were off by a degree or two. Ptolemy’s 5-degree fudge factor gives an Ascendant of 3 Virgo 05′ which is close to the precisely calculated value of 4 Virgo 25′

If my analysis of Ptolemy’s intent is correct, then the “5-degree above rule” has no value for astrologers who use the tropical zodiac. For sidereal astrologers, the original “5-degree rule” would now be something like a “24-degree below rule” to take the current ayanamsa into account.