93. The Numan Cycle
- M Campbell
- Jul 30
- 41 min read
Updated: Sep 4
An analysis of the changes made to the calendar by the Roman king Numa Pompilius (traditionally 715–673 BC), by Leonardo Magini, offers an intriguing window into how the solar and lunar years were made to work together. The cycle underpinning the reforms made by Numa was in fact highly sophisticated, and would have functioned not only as a way of reconciling the solar and lunar years, but may also have included the movements of the planets. However, the great contrast between the clumsy attempts at reform in Numa's day and the sophistication of this system, which was far older, gives pause for reflection. Where did it come from, and how accurate was it?
Numa's Reforms and the Enigma of the Ancient Calendar
In the traditional Roman account, Numa Pompilius, the second king of Rome (c. 715–673 BC), succeeded the warrior Romulus and turned his focus to religion, ritual, and timekeeping. His reforms to the Roman calendar are recorded in various sources, most notably in Macrobius’ Saturnalia, which gives a detailed, though at times confused, overview of how the Roman year evolved. Before Numa, the Roman calendar, as instituted by Romulus, consisted of only ten months, beginning in March, and spanning 304 days. This scheme, according to Macrobius, included four months of 31 days and six of 30, with no formal mechanism to reconcile the calendar with either the lunar or solar year.
"Rome too had its own year, arranged—on the authority of Romulus—in a series of ten months. The year used to begin in March and to consist of three hundred and four days..."(Macrobius, Saturnalia 1.12.3) (1)
Numa expanded the calendar to twelve months and restructured the year to bring it in line with lunar cycles. He added fifty days to the old 304-day year, and then subtracted one day from each of the six 30-day months, yielding fifty-six days. These he used to create two new months: January, dedicated to Janus, the god of beginnings and transitions, and February, sacred to Februus, associated with purification and the rites of the dead. This brought the total length of the calendar to 354 days, roughly the number of days in twelve synodic lunar months (354.36708 days).
"Numa added fifty days to the year, to enlarge it to three hundred and fifty-four days, the period which he believed to correspond with the completion of twelve circuits of the moon." (Macrobius 1.13.1) (2)
Later, Numa added an additional day, raising the total to 355, in homage to the principle of odd numbers, which were held to be auspicious.
"In honor of the odd number (a mystery which nature had brought to light even before the time of Pythagoras), Numa added a day to the year..."(Macrobius 1.13.5) (3)
As Macrobius notes, this move ensured that most months had an odd number of days, preserving a numerological harmony, with only February left as an even-numbered month, symbolically appropriate given its funereal associations. Numa also aligned Roman timekeeping with Greek practice by introducing a system of intercalation to correct for the drift between lunar months and the solar year. Since 12 lunar months fall about 11¼ days short of a full solar year, intercalary days had to be added regularly. Following the Greek model, the Romans adopted an 8-year cycle (octaeteris), inserting 90 extra days over this span. But unlike the Greeks, they introduced an additional day for numerological reasons, which gradually threw the calendar out of step with the seasons.
"Six months having thirty days each... and four comprising thirty-one days each..."(Macrobius 1.12.3) (4)
This intercalation was implemented not at the end of the year, but after the Terminalia festival on February 23rd, reflecting both ritual priorities and the desire to keep March as the year's symbolic beginning. Yet the process proved unwieldy and error-prone. Priests were in charge of the intercalations, and as Saturnalia later explains, they sometimes abused or neglected the practice, manipulating the year for political or fiscal ends. Eventually, the confusion was so great that Julius Caesar, with the help of the Egyptian astronomer Sosigenes, instituted the Julian reform in 46 BC.
The Romans resolved to follow this system too, but they were not successful, since they overlooked the fact that, as I have already reminded you, they had added one day to the Greek reckoning out of respect for the odd number, with the result that over the period of eight years there could be no conformity with the true position either in the number of the intercalated days or in their place in the calendar. [12] However, before the mistake was discovered, they calculated that in each period of eight years ninety days were to be reckoned as supernumerary, in accordance with the example of the Greeks, and they distributed these intercalary days by means of four intercalations, of twenty-two and twentythree days alternately, every two years. But after every eighth year there was a surplus of eight intercalary days, the product of the single days by which, as we have said, the Roman reckoning of the length of their common year exceeded that of the Greeks. [13] When this error, too, was recognized, it was corrected as follows: in every third period of eight years sixty-six intercalary days were inserted, instead of ninety, to make up for the twenty-four days by which the Roman reckoning had exceeded the Greek in that number of years.(Macrobius 1.13.12) (5)
One passage from Plutarch reveals the rationale behind Numa's intercalation scheme:
“Numa recognized that the discrepancy between the sun and the moon was eleven days; the revolutions of the moon were completed in 354 days, and those of the sun in 365. He doubled those eleven days, and made a month of 22 days, which he intercalated every two years after February. This intercalary month is called by the Romans 'Mercedonius.'” (6)
Livy confirms that Numa’s system was lunar in origin, but adjusted carefully to keep pace with the solar year:
“He divided the year according to the course of the moon into twelve months; but because each lunar revolution is not exactly thirty days, and the solar year would thus be incomplete, he corrected the deficiency by the insertion of intercalary months, arranging them in such a way that, every twenty-four years, the sun returned to the same position it had started from, and every annual discrepancy was corrected.” (7)
The evidence suggests that Numa's reforms, though modest and partially inconsistent, were founded on principles far more complex than he or his contemporaries could have fully understood. As the French 18th century historian of astronomy Jean-Sylvain Bailly remarked, Numa lived in a time and place without sophisticated astronomy, that was still fairly uncivilised. He is philosophical about Numa's insistence on using an odd number, to the detriment of the precision of his reforms:
Thus this philosopher-king, who gave wise laws, this man who perhaps assigned to the sun its true place—who at the very least understood the movements of that star and those of the moon with reasonable accuracy—made the revolutions of the sun and the moon, as well as the order of civil life, conform to his reverence for the odd number.
This inconsistency, however, is not surprising when we consider that even the most enlightened nations have shown similar examples. Day drives away the darkness of night, but the shadows remain. As long as there are bodies, there will be shadows beside the light; as long as there are men, error will remain close to sublime knowledge. (8)
Yet the system Numa instituted seems to reflect knowledge of precise astronomical cycles, not only concerning the sun and moon but, as Leonardo Magini has argued, possibly including the planets as well. Indeed, the so-called Numan cycle described by Magini implies a highly structured calendrical framework capable of reconciling the solar year (365.242199 days), the synodic lunar month (29.53059 days), and the sidereal lunar month (27.32166 days). It even anticipates long-term adjustments to maintain alignment across celestial rhythms, resembling systems found in Babylonian, Indian, and Egyptian traditions. Bailly, ever alert to the echoes of ancient science hidden in myth and legend, speculated that the earliest peoples measured time using a variety of intervals, some of which were based on lunar phases, others on stellar risings, and still others on fractional or symbolic segments of the day and night. He cited examples of cultures with one-month, two-month, or even six-month “years,” and of myths that embed astronomical knowledge in the guise of poetic enigmas, such as the riddle of Cleobulus: “He has twelve children, each bearing thirty or thirty-one sons, half bright, half dark...”
In this light, Numa appears less as an innovator and more as a conduit, a figure through whom fragments of a much older and more refined astronomical tradition were preserved, albeit imperfectly. The question, as Bailly himself asked, remains: Where did he get this knowledge from? It is tempting to view Numa’s calendar not as a Roman invention, but as a relic of a lost science, preserved through ritual and custom long after its underlying principles were forgotten.
There is an interesting inconsistency about the history of the 8 year system. Ancient sources give conflicting indications about whether Numa Pompilius understood or deliberately implemented an intercalation cycle based on the 8-year octaeteris, a lunar-solar reconciliation method known to later Greek astronomers. Macrobius (Saturnalia, 1.13.9–13) describes how the Romans, following the Greek example, adopted a system of inserting 90 days over an 8-year cycle through alternating intercalations of 22 and 23 days every two years. However, he notes that the Roman version included an additional day per year for reverence to the odd number, causing their calendar to fall out of step over time:
"After every eighth year there was a surplus of eight intercalary days, the product of the single days by which [...] the Roman reckoning of the length of their common year exceeded that of the Greeks" (Saturnalia 1.13.12).(9)
Macrobius even claims that this error was eventually corrected by reducing the intercalation to 66 days every third octennial period. However, this assumes a level of calendrical and astronomical understanding that seems at odds with the state of science in Numa's day (traditionally 715–673 BC), not just in Rome but even in Greece! As Bailly observed in his Histoire de l'astronomie ancienne, this 8-year cycle wasn't formalised in Greece until two centuries later, noting that in Numa's time:
"Greece was not so advanced. It had this eight-year period two centuries later" (p. 195).(10)
And yet, as Bailly also remarks with puzzlement, Numa appears to have followed such a scheme in some form:
"He divided it into four months [...] of which he inserted one every two years". (11)
This has led some modern analysts like Leonardo Magini to suggest that the system behind Numa's reforms reflects not simply an 8-year cycle, but a more complex 24-year cycle, though it does not reconcile the lunar and solar years any more precisely. This is not inconsistent with the idea that an 8-year cycle was a visible subunit within a longer and more esoteric system. After all, 24 is simply 8 × 3. The ancient technique of using multiple octaeterides (e.g., three 8-year cycles) was known in Mesopotamian and temple astronomy, even if not codified in urban civic calendars. Thus, what Macrobius seems to report may be a partial or misunderstood version of a deeper and older system, misapplied or remembered imperfectly in Roman civic use. The Roman reverence for odd numbers (as Macrobius says) may have further skewed this borrowing, introducing errors into what may originally have been a mathematically sound design.
This discrepancy between the apparent simplicity of Numa's reforms and the complexity of the underlying astronomical logic invites an important question: was Numa working from a misunderstood fragment of a much older, more advanced tradition? If so, this would lend weight to the idea of a lost technical knowledge preserved in priestly schools, sanctuaries, or oral traditions rather than through public institutions.
What follows is an exploration of that system, looking at its structure, its logic, and its likely origins. By looking at the cycle Magini has identified and analysed, and comparing it with other ancient cosmologies, we may glimpse the sophistication behind Numa’s seemingly clumsy reforms, and understand why this calendar, though flawed in execution, was rooted in something far more enduring than the reign of a Roman king.
Numerical Analysis of the Numan Calendar System in Ancient Sources
What exactly do the ancient sources tell us about the structure of the Numan calendar? The system appears to have been based on a lunar framework with intercalations designed to harmonise solar and lunar motion, and possibly to track planetary motion as well. Macrobius (Saturnalia, 1.13.13) and other classical authors describe the calendar as consisting of 8-year lunar sub-cycles intercalated to align with the solar year. Specifically:
Each lunar year = 355 days
Intercalary days = total of 246 over 24 years
Total duration of the Numan Cycle = 24 years
Total days = (24 × 355) + 246 = 8 766 days
This yields an average solar year of 365.25 days. This is slightly above the more accurate value of 365.242199, and could imply the existence already in place of a four or eight year cycle which would resolve the 0.25 into an integer number of days, allowing a leap day every four years. This matches the Julian approximation of the solar year.
There are three cycles of lunar years, the first is 8 lunar years, so 355 x 8 + 90 days. The second is 8 lunar years , and 90 days also, so 2930 days. The third is 8 lunar years but as 355 x 8 + 66 = 2906 days. Total of 8766 days, which can be repeated 25 times to match the 600 Chaldean period then. 600 x 365.25 is also 8766 x 25 days.
It is surprising that this 24 year cycle, so finely calibrated to lunar, solar, and planetary rhythms, is not more widely recognised in the historiography of ancient timekeeping. Yet perhaps a vestige of this cycle survives in a domain we take entirely for granted: the division of the day into 24 hours. It is well known that ancient astronomers often used large cycles of years as frameworks from which smaller subdivisions of time could be derived. In the Hebrew calendar an hour is divided into 1 080 parts and a day into 25 920 parts, reflecting the traditional value assigned to the precessional cycle, and a harmonic number. A 24 year cycle that successfully harmonised diverse celestial motions may have recommended itself, not only for calendrical purposes, but as a cosmological model whose symmetry could be mirrored at other scales. The segmentation of the day into 24 equal parts may reflect the enduring legacy of such a cycle, as an artefact of an astronomical worldview that saw harmony in number, proportion, and periodic return.
A period of 8766 days relates to these lunar cycles as follows:
296.8 synodic months of 29.5306 days
320.844 sidereal months of 27.3216 days
322.135 draconitic months of 27.2122 days
318.132 anomalistic months of 27.5546 days
With carefully placed intercalary days, this system aligns with several key astronomical cycles:
Celestial Body | Number of Cycles | Period (Days) | Error |
Sun (tropical year) | 24 × 365.2422 | 8,765.81 | +0.19 days |
Moon (synodic month) | 297 × 29.5306 | 8,770.59 | -4.59 days |
Venus (synodic) | 15 × 583.92 | 8,758.8 | +7.2 days |
The calendar’s feast days correspond to the completion of major cycles like the Saros (eclipses), lunar nodes, apsides, and planetary conjunctions, forming a symbolic map of the sky embedded in myth and ritual.
Magini identifies four key alignments:
March 15, Year 19: End of the Saros cycle – Feast of Anna Perenna (eclipse allegory)
October 14–15, Year 19: Completion of the line of lunar nodes – October Equus (ritual of sacrifice and celestial transition)
June 20, Year 10: Node passes First Point of Aries – Feast of Summanus (symbolic lunar fall)
January 5, Year 9: Apsidal line revolution – Compitalia, dedicated to Hecate Trivia, goddess of crossroads
Each of these events corresponds to actual astronomical cycles.
Why would a period of 24 years work well as the foundation of a time-keeping system?
A 24 year cycle offers a compelling and versatile basis for timekeeping, particularly in ancient calendrical systems that aimed to reconcile the movements of the sun, moon, and planets. Unlike shorter cycles such as the Metonic 19-year cycle or longer and more cumbersome ones like the Chaldean 600-year period, the 24-year cycle strikes a balance between precision, manageability, and symbolic resonance. It serves as a numerically rich and astronomically effective framework. To begin with, the solar year, specifically, the tropical year, is approximately 365.242199 days. The Julian calendar simplifies this as 365.25 days, inserting a leap day every four years to account for the fractional day. Over a 4-year period:
4 Julian years = 4 × 365.25 = 1461 days
4 Tropical years = 4 × 365.242199 = 1460.968796 days
Difference over 4 years = 1461 - 1460.968796 ≈ 0.031204 days
Thus, every 100 Julian years, the error accumulates to about 0.031204 × 25 = 0.78 days. This is one reason why the Gregorian calendar introduced a correction every century (by skipping leap years in most century years). Now, extending to 24 years:
24 Julian years = 24 × 365.25 = 8766 days
24 Tropical years = 24 × 365.242199 = 8765.812776 days
Difference = 8766 - 8765.812776 = 0.187224 days
This yields an error of less than 5 hours over 24 years, showing the practical accuracy of a 24-year framework. The lunar month, or synodic month, is approximately 29.53059 days. Over 99 lunations:
99 × 29.53059 = 2923.52841 days
8 Tropical years = 8 × 365.242199 = 2921.937592 days
Difference = 2923.52841 - 2921.937592 = 1.590818 days
So, 99 lunar months slightly exceed 8 solar years by about 1.6 days, which is a remarkably close alignment and made 8-year cycles an appealing choice for early lunar-solar synchronisations. Ancient civilisations, including those who developed the early Easter computus, like Hippolytus of Rome in 222 CE, capitalised on this relationship.
The significance of 8 is even deeper when seen in relation to the planet Venus. Venus completes 5 synodic cycles in approximately 8 Earth years:
5 × 583.92 = 2919.6 days
8 Tropical years = 2921.937592 days
Difference = 2921.937592 - 2919.6 = 2.337592 days
Thus, Venus returns to nearly the same position in the sky every 8 years relative to Earth and the sun. This cycle was symbolically important to many ancient cultures, from the Sumerians to the Maya. If we combine the 8-year lunar/solar cycles into a larger system, three such cycles equal 24 years:
3 × 2923.52841 = 8770.58523 days (lunar)
24 Tropical years = 8765.812776 days (solar)
Difference = 8770.58523 - 8765.812776 = 4.772454 days
The slight discrepancy (under 5 days) over 24 years could be managed by intercalations. Macrobius mentions that religious scruples sometimes caused the omission of intercalary periods, suggesting that the system was flexible, though guided by astronomical principles.
Ancient Mesopotamian systems used even longer cycles. The Chaldeans employed a brilliant 600-year cycle to reconcile solar and lunar time:
600 × 365.242199 = 219145.3194 days
7421 lunar months = 7421 × 29.53059 = 219144.92639 days
Difference = 0.39301 days over 600 years
Accuracy ratio = 219144.92639 / 219145.3194 = 0.9999982
This is an extremely accurate reconciliation, but its length made it impractical for routine civil use. However, its logic may have inspired shorter sub-cycles like 60 years (1/10 of 600), which also performs well:
60 × 365.242199 = 21914.53194 days
742.096 lunar months ≈ 21914.53194 / 29.53059 = 742.096
The 19-year Metonic cycle, which aligns 235 lunar months with 19 solar years:
19 × 365.242199 = 6939.60178 days
235 × 29.53059 = 6939.68865 days
Difference = -0.08687 days
Accuracy ratio = 6939.60178 / 6939.68865 = 0.9999875
While this cycle accumulates nearly a day of error every 220 years, leading to visible drift over long periods, it is nevertheless extremely impressive as a way of reconciling the solar and lunar years. The Hebrew calendar compensates by assigning 7 leap years in each 19-year cycle using a simple modulo rule:
Leap Year if: (7 × Hebrew Year + 1) mod 19 < 7
This yields 235 months over 19 years: 228 regular + 7 leap months
Being only 19 years long, the Metonic cycle has the advantage of being manageable within human lifetimes. There are other options also, to reconcile the solar and lunar years, such as 353 years, 1803 years, 76 years, 84 years or 8 years. In fact, the accuracy in reconciling the solar and lunar years is matched equally by the 8 year and 24 year cycles, and these are both less accurate than six other possible cycles that could have been used (see the list below). Why discard these, in favour of a 24 year cycle? Could it be that a 24 year long cycle also accommodates other cycles? Below is a brief recap of some of these cycles in order of precision for the lunar and solar cycles matching up, starting with the most precise.
353 years or 4366 lunar months
353 x 365.242199 / 29.53059 = 4365.9979786
4365.9979786 / 4366 = 0.999999537
1803 years or 22300 lunar months
1803 x 365.242199 / 29.53059 = 22299.98401
22299.98401 / 22300 = 0.9999992829
600 years or 7421 lunar months
600 x 365.242199 / 29.53059 = 7420.959737
7420.959737 / 7421 = 0.99999457
19 years or 235 lunar months
19 x 365.242199 / 29.53059 = 234.99705834
234.99705834/235 = 0.99998748
76 years or 940 lunar months
76 x 365.242199 / 29.53059 = 939.988233
939.988233 / 940 = 0.99998748
84 years or 1039 lunar months
84 x 365.242199 / 29.53059 = 1038.93436
1038.93436/1039 = 0.99993683
8 years or 99 lunar months
(sometimes 100 lunations are known as a 'Great Year', 8 solar years and a month)
8 x 365.242199 / 29.53059 = 98.9461298
98.9461298 / 99 = 0.999455857
24 years or 297 lunar months
24 x 365.242199 / 29.53059 = 296.8383895
296.8383895 / 297 = 0.999455857
To understand the deeper astronomical logic behind the 24-year cycle, we could first consider a striking feature: its relationship to Venus. The number 8, a divisor of 24, plays a key role. Venus has a synodic period of approximately 583.92 days, meaning it returns to roughly the same point in the sky (as seen from Earth) every 584 days. Five such synodic periods total 2,919.6 days, which is extremely close to 8 solar years (8 × 365.2422 = 2,921.94 days). This makes Venus one of the cleanest planetary fits within an 8-year framework. Since 8 divides evenly into 24, Venus neatly integrates into the 24-year system. But what of the other planets? Their cycles do not seem to fit neatly within a 24 year period.
Below is a table showing the values for the cycles of the five classical planets. The sidereal period of a planet is the time it takes to complete one full orbit around the Sun relative to the fixed stars. This is the planet's true orbital period and is crucial for understanding the planet's place in the cosmic structure. However, from the standpoint of Earth-based observation, the synodic period is perhaps more relevant. The synodic period measures how often a planet returns to the same position in the sky relative to the Sun as seen from Earth. Since calendars are rooted in solar years and our position on Earth, it is the synodic cycle that governs how planetary phenomena reoccur in visible patterns.
Planet | Sidereal Period (days) | Synodic Period (days) |
Mercury | 87.9691 | 115.88 |
Venus | 224.701 | 583.92 |
Mars | 686.98 | 779.94 |
Jupiter | 4332.59 | 398.88 |
Saturn | 10759.22 | 378.09 |
Starting with Saturn, how do these cycles fit in with a 24 year, or 8766 day cycle? The following is based on Leonardo Magini's research (12):
Saturn
For Saturn, the sidereal period is about 29.457 years, but its synodic period is approximately 378.09 days. Over 57 synodic periods, Saturn completes very nearly 59 solar years (57 × 378.09 = 21,561.13 days; 59 × 365.2422 = 21,544.29 days), an error of only about 16.84 days. If we look at 59 years as 2 full 24-year cycles plus 11 years (2 × 24 + 11 = 59), Saturn's position resets almost exactly. That is, Saturn reappears in nearly the same position in the sky at the same time of year. This is a very nice coincidence, but then it gets better. If we look to see how many times the sidereal period fits within 59 years, the result is twice.
59 x 365.242199 / 10 759.22 = 2.002867.
So the numbers for Saturn become: 59 solar years, 57 synodics, 2 sidereals, and the great advantage of these numbers is that they are integer numbers of solar years.
How, then does the 24 year cycle fit with this? This 59-year Saturn cycle can be represented as 2 Numan cycles (48 years) plus 11 years, hence the note: "2 cycles + 11 years."
We could visualise this relationship with three concentric circles, or three lines on a timeline, showing the solar years, from 1 to 59, then 2 full sidereal revolutions every 29.4571 years, and then the 57 synodic cycles every every 378.091 days. This triplet (2, 57, 59) exemplifies how the 24 year cycle could have been used as a foundational block from which larger harmonies, like Saturn's cycle, can be composed through multiplication and addition.
Saturn 2, 57, 59
Jupiter
Jupiter has a synodic period of about 398.88 days. After 76 synodic revolutions, Jupiter returns to nearly the same solar position in 83 years (76 × 398.88 = 30,715.0 days; 83 × 365.2422 = 30,314.1 days), a close alignment. These 83 years are expressible as 3 full 24-year cycles (72 years) plus 11 years, mirroring the Saturn format. When we divide 76 periods of 398.88 days by the number of days in a sidereal period, the result is very close to 7. (398.88 x 76 / 4 332.59 = 6.99694)
So the triplet associated with Jupiter becomes: 83 solar years, 76 synodics, 7 sidereals.
Jupiter 83, 76, 7
Mars
Mars has a synodic period of approximately 779.94 days. Over 37 synodic periods (37 × 779.94 = 28 857.78 days), Mars returns to nearly the same position after about 79 solar years (79 × 365.2422 = 28 853.13 days), an alignment accurate to within 4.65 days. 79 = 3 × 24 + 7 years. How many sidereal periods fit within this period of 79 years? 79 x 365.242199 / 686.98 = 42.0014. Incredibly, the result is 42, almost exactly. The triplet associated with Mars is therefore: 79 years, 37 synodics, 42sidereals.
Mars 79, 37, 42
Venus
Venus, as previously discussed, has a synodic cycle that fits almost perfectly into 8 years (5 synodic periods), which means that within a single 24-year cycle (3 × 8), the Venus cycle resets exactly three times, reinforcing its centrality. If we divide these 8 years by the sidereal cycle for Venus, the result is 13. 8 x 365.242199 / 224.701 = 13.00367. The triplet associated with Venus is therefore: 8 years, 5 synodics, 13 sidereals. Incredibly, though this is well known, 5, 8 and 13 are all Fibonacci numbers.
Venus 8, 5, 13
Mercury
Mercury's synodic period is approximately 115.88 days. Over 145 synodic periods, Mercury returns after 16,802.6 days, equivalent to about 46 years (46 × 365.2422 = 16,799.5 days), a remarkably tight match. These 46 years divided by the sidereal period give 190.989, very close to 191. (46 x 365.242199 / 87.9691 = 190.98912)
The triplet associated with Mercury is therefore: 46 years, 145 synodics, 191 sidereals. Another intriguing aspect of the 24 year cycle is that these 8766 days are almost exactly 100 sidereal Mercury orbits of 87.969 days. This 24-year cycle is surely as much about lunar-solar reconciliation as it is about synchronising the inner planets, especially Mercury, whose speed and recurrence structure the whole pattern. Is this why Mercury is considered the messenger?
Mercury 46, 145, 191
Overall, the planets are organised within this system in terms of cycles of years which are integer numbers, as follows:
Planet Approx. Cycle (Solar Years)
Venus 8
Mercury 46
Mars 79
Jupiter 83
Saturn 59
The Numan cycle is 24 years long, so exactly 3 cycles of Venus of 8 years, which happen to match almost perfectly 99 lunations of 29.53059 days. In this way, Venus, the sun and the moon can be monitored as one sun-system.
These values represent close approximations where the planet returns to nearly the same position relative to Earth, the Sun, and (often) the fixed stars. The calendar isn't as much about daily accuracy as it is about long-term coherence. In this system, time is structured not as isolated orbits but as interwoven returns. These solar-year-based returns allowed ancient astronomers to build multi-decade frameworks for celestial timing, such as the 24-year Numan cycle.
The genius of the 24-year cycle is not that it perfectly contains each planet's cycle, but that it serves as a flexible base unit. Through clever additive combinations (e.g., 2×24 + 11), multiple planetary cycles can be synchronised. This modular structure allows for compound alignments that can be repeated and forecasted with considerable accuracy. It's a framework for astronomical synthesis, where celestial, calendrical, and ritual time all meet.
The table below shows how these cycles connect:
Planet | Sidereal Rev. | Synodic Rev. | Solar Years | Position Reset | Numan Cycle Format |
Saturn | 2 | 57 | 59 | 28 Feb, 11/III | 2 cycles + 11 yrs |
Jupiter | 7 | 76 | 83 | 28 Feb, 11/IV | 3 cycles + 11 yrs |
Mars | 5 | 37 | 79 | 4 Mar, 8/IV | 3 cycles + 7 yrs |
Venus | 3 | 5 | 8 | 28 Feb, 24/I | within 1 cycle |
Mercury | 46 | 145 | 46 | 1 Mar, 23/II | 1 + 22 years |
These values suggest that the planetary cycles can be expressed quite accurately in terms of the cycle of 24 years.
A little speculation
A striking feature of the planetary timing system tied to the 24-year cycle is the recurrence of the numbers 11, 22, and 7. The number 22 divided by 7 is a well-known ancient approximation of π, the fundamental ratio for any circle. The number 7 reflects the totality of the classical planets, including the Sun and Moon, which were the basis of ancient astronomy and astrology, and which gives us the number of days in a week today. The number 22 is symbolic across multiple traditions. In the Hebrew alphabet, there are 22 letters, and this number is often seen as the building blocks of creation itself. In the Tarot, there are 22 Major Arcana cards, representing the archetypal journey of spiritual and psychological development. In Kabbalistic and Hermetic thought, the 22 paths connect the 10 sefirot on the Tree of Life, representing the dynamic structure of divine emanation and human ascent. In numerology, 22 is considered a "Master Number", the "Master Builder". Remarkably, there are also 22 intercalary days in Numa’s calendar. These resonances suggest that the calendrical system, whether by direct design or serendipity encoded layers of symbolic and astronomical meaning into its structure.
In the pattern of the planetary alignments with the 24-year cycle, this symbolism appears numerically: 1 cycle + 22 years (Mercury), 2 cycles + 11 years (Saturn), 3 cycles + 11 years (Jupiter), and 3 cycles + 7 years (Mars). These suggest a modular structure.
If we set aside Venus, which fits precisely within a single 24-year cycle, and whose 8 year cycle can be accomodated to resolving the discrepancy between the solar and lunar year to a fairly high degree of accuracy, the remaining four planets could all be tracked with a circular device divided into 22 points (for Mercury, Saturn and Jupiter) and the diameter divided into 7 points (Mars). This would be particularly interesting from a metrological point of view because each section of he circumference would be equal to the sections on the diameter, providing pi was understood to be 22/7. Furthermore, if the diameter of the circle tracking the moon, earth's solar year and Venus were 80 cm long, the circumference would be 99 inches long, with a 39.375 inch per metre ratio. Each planet would also need a separate small circle for tracking the number of revolutions made within the 24 year period (earth, moon, Venus), or the number of 24 year periods completed, before counting the final 11, 22, or 7.
Each planetary cycle would simply require a marker to rotate through these divisions (7, 22, 8 and 99) at the appropriate pace. After completion of one full 24 year cycle, Mercury's tracker would move to the circle with 22 divisions on the circumference, and move one division per year, to complete the full cycle of 46 years. After completion of two full 24 year cycles, Saturn's tracker would move to the circle with 22 divisions and move 2 spaces each year, to complete the full 59 year cycle. Jupiter would do the same but after three full 24 cycles completed. Mars would need to complete three full cycles of 24 years, before moving to the circle, but to the diameter not the circumference, and moving one division at a time per year. Venus would move up and down along the diameter of another circle with a diameter of 8 divisions, and after three such cycles of 8 years were completed, a full Numan cycle of 24 years would have elapsed, which could then be marked on to the counters for the other planets. This eight year cycle would also correspond to 99 lunations, which could be tracked on the circumference. The diagram below attempts to illustrate how this would work. There isn't technically a need to have two circles, especially since the 99 lunations are also a multiple of 11, but it's easier to visualise this way. Also this system is only necessary if particular units of measure are required to track the passage of one year and one lunation. But since 29.53059 cm on a diameter give 365.24836 inches on a circumference, with calculator pi and the modern value for the metre and inch ratio, 39.3700787402 inches per metre, it's interesting to think in these terms. Also curious is the fact that 7 x 29.53059 inches on the diameter of a circle would create 20 megalithic yards, of 32.484 inches, on the circumference.
Could there once have been a similar geometric model to track the relative motions of the planets in this way? Who knows. Such a system would in any case be quite useful, and resonate with ancient mathematical mysticism.
It seems this 24-year cycle offered a highly structured yet flexible foundation, deeply rooted in the interplay of celestial motions. It was not simply a civil invention, but a harmonised cosmological model integrating numerical symbolism, astronomical observation, and ritual order. While ancient sources like Plutarch and Livy attribute these reforms to Numa's desire to reconcile lunar and solar years, the actual framework seems to be derived from an integrated planetary model. This coherence supports Bailly's observation that Numa's calendar demonstrates a level of astronomical precision ahead of contemporary Greek knowledge, raising the intriguing question of where he might have acquired such sophisticated insights.
The graphs above offer a visual representation of the key planetary synodic return cycles within the Numan framework over just over 100 years:
Venus returns every 8 years, creating a regular rhythm.
Mercury, Saturn, Mars, and Jupiter each complete a near-alignment with the Earth-Sun system after their respective years.
These longer cycles are shown as single occurrences within the 105-year period.
A Hidden Harmony? The Role of the Number 24
The number 24 is an interesting one to have for a cycle. It is both 3 x 8, 8 being a Venus cycle, and 6 x 4, with 6 connecting to the Chaldean cycle of 60, or 600 years, and 4, the Sothic or Olympic cycle, to harmonise the quarter day present in a 365 day year after 4 years. A fundamental principle in ancient timekeeping, which that Bailly articulates clearly, is that time was not universally measured according to a fixed, linear standard like the solar year, but instead through diverse cycles and intervals, each of which might be called an “année” (year). Ancient civilisations employed a wide array of temporal units: lunar months, stellar months, synodic periods, seasonal markers, and even fractions of days, depending on context and purpose. Bailly notes, for instance, that among the Egyptians there were “years” of one, two, three, or six months, and that some peoples, lacking a fixed solar year, defined a year simply as “the space of one day” (Bailly, Histoire de l’astronomie ancienne, p. 207). This flexible system of temporal reckoning, often linked to astronomical cycles, was not only practical but also symbolic. Some traditions counted a single day as two revolutions, some subdivided a day into as many as eight “revolutions,” reflecting divisions aligned with planetary hours or ritual frameworks.
Earth and Venus
Earth's sidereal year is 365.256 days. Venus's sidereal period is 224.701 days. How can these two periods be reconciled? Eight earth years are 2 922 days, and in that period, there is an almost exact match to the Venus cycle. As Earth completes 8 orbits, in relation to the background of the stars, Venus completes about 13 orbits. (224.701 x 13 = 2921.113)
This period is also approximately equal to 5 synodic cycles of Venus occur (5 × 584 ≈ 2920 days)
This is known as the 8:13 Earth-Venus resonance. It means that every 8 years, Venus appears in almost the same place in the sky, relative to both Earth and the Sun. The result is the beautiful 5-petalled pattern Venus traces in the sky over this period of time, which was well known in ancient times. It's worth noting that the numbers 5, 8 and 13 are Fibonacci numbers, and are linked to the way flowers and plants grow, among other things.
Jupiter-Saturn Cycle (Great Conjunctions)
Jupiter and Saturn are the two slowest visible planets. Jupiter’s sidereal period is 11.862 years and Saturn’s sidereal period is 29.457 years. Their synodic cycle (time between conjunctions as seen from Earth) is 19.859 years, which means that roughly every 20 years, Jupiter and Saturn appear together in the sky in what's called a Great Conjunction.
What’s more, every three Great Conjunctions (which is then roughly 60 years), they return to nearly the same part of the zodiac. This is a key time in ancient calendar systems, and perhaps the basis of the sexagesimal counting system used by the Babylonians, who were excellent astronomers.
The thing that sets the Numan system apart, however, is that it doesn’t rely directly on synodic or sidereal periods as we define them today. Instead, it tracks how many solar years it takes for a planet to return to approximately the same position in the sky, relative to the Earth, the Sun, and sometimes the fixed stars. These are whole-number year cycles, forming a kind of schematic harmony, rather than pinpoint astronomical events. The concern is not with daily precision, but with long-term coherence, creating a system in which planetary rhythms can be coordinated and remembered over decades.
Though rooted in Roman tradition, the Numan system may have far older origins, and likely had a wider geographical footprint. Intriguingly, a related 24 000 year cycle appears in Indian sources, possibly as part of the Yuga doctrine. The French astronomer Le Gentil, in his Voyages dans les Mers de l’Inde, and then, based on his reading of Le Gentil, Jean-Sylvain Bailly, in his Histoire de l’Astronomie Ancienne, noted a mysterious 24 000 year cycle in Indian cosmology. The purpose of this cycle was unknown, and as both Le Gentil and Bailly realised, the Brahmins who told Le Gentil about it didn't in fact understand it themselves. Rather, they had inherited it from some long forgotten time, as part of a system of which only a few debris had survived. Bailly and Le Gentil assumed the 24 000 year period was a slightly miscalculated value for the cycle of precession, not so far off from the more accurate 25 920 or 26 000 years. Could it have been the ancestor of the Numan calendar? Was the Numan system the Roman echo of a lost astronomy of planetary harmonics preserved in myth and reform?
The Indian 24 000 Cycle
In his travels across India in the 18th century, French astronomer Le Gentil documented an astronomical tradition among Indian astronomers involving a 24 000-year cycle.
The Brahmins are not very versed in this science & they had not made some very interesting discoveries. We see nothing in antiquity to prove to us that the Egyptians ever knew the precession of the Equinoxes; but we find it known among the Brahmins. They suppose that the Stars advance annually by 54 seconds from West to East; that's it, not only the base or the foundation of their astronomical calculations, but also of their belief during the time of creation. By means of this movement of 54 seconds, they formed periods of several million years; they introduced them into their religion, as indicating the age of the world, what it must still last;- The Brahmins take great pains to teach these daydreams to children in schools. It does not seem easy to me to know from where the Brahmins have drawn this precession from the Equinoxes of 54 seconds per year, all the more so because they do not know practical Astronomy. If they observe the eclipses of the Sun and the Moon, it is solely for a reason of religion; but if we suppose that this precession of the Equinoxes of 54 seconds their comes from the Brahmins, and that these recognized this movement by a long flight of observations, the annual movement of the Stars would be slower today than it would not have been then, since it is only found 50 seconds; but we can't guess anything on a subject as obscure as that one seems to me to be. Here however some thoughts that have come to me since I wrote this, and which I submit to the judgement of my readers. The principal periods which the Brahmins use, & from which their other periods seemed to me to derive, make ten years of three thousand fixed hundred years; but I find in Berose, a Chaldean author, two similar periods; the neros of fifty years, & the saros of three thousand six hundred. But both periods of sixty & of three thousand six hundred years, are exactly contained in that of twenty-four thousand years, coming from the annual movement of the Stars of 54 seconds. I conjecture that the neros & the saros of Bérose have the same movement in principle, and that the ancient Chaldeans knew the precession of the Equinoxes! I will detail this idea in my Astronomy of the Brahmins. With these acquaintances worthy of our attention, remarkable for their antiquity, the Brahmins do nothing. touching the Comets: the Indians believe that these make kinds of vines of the wrath of Heaven. They were amazed to see me spend part of the nights to observe the comet which appeared in 1769; they asked me many questions about the cause of this phenomenon. What finished astonishing them was to see this Comet again at the end of the month of October in the first days of November, in accordance with what I had predicted to them, as well as to all of Pondicherry.
Having read Le Gentil's memoires, the astronomer Jean-Sylvain Bailly observed:
The entire revolution [of the fixed stars] is 24 000 years... This number exactly divides the number of years in each of the four Indian ages.(11)
The recognition of this distinction implies an awareness of the precession of the equinoxes, the slow drift of the stellar background due to Earth's axial wobble. Bailly suggests that this was rediscovered by Hipparchus, but may have been known earlier in Asia, noting:
Their zodiac has two different divisions... They have two zodiacs, one fixed and the other mobile, which shows that they did not first know the movement of the fixed ones. (14)
Among the many enigmas embedded in ancient timekeeping systems, the mysterious 24 000-year cycle observed by Le Gentil in India and discussed at length by Jean-Sylvain Bailly stands out. Its recurrence across disparate cultures and cosmologies suggests something more than coincidence. Far from being a crude approximation of axial precession, the 24 000-year cycle may in fact be linked to the Numan cycle of 24 years. The number 24 recurs with unusual regularity in ancient systems. It is divisible by both 3 and 4, invoking triangular and square symmetries. It is 6 × 4, echoing the Chaldean sexagesimal framework and the 4-year Olympic and Sothic cycles that harmonise the quarter-day discrepancy in the solar year. It is also 3 × 8, with 8 marking the resonant Earth-Venus cycle, the 8-year period in which Earth orbits the Sun 8 times while Venus completes nearly 13 revolutions, forming a 5-petaled pattern in the sky. As these numbers, 5, 8, 13, are Fibonacci numbers, linked to natural growth patterns and sacred geometry, the 24-year module may have had both astronomical and symbolic justifications. The Numan cycle was about whole-number harmonies, over fairly long periods of time.
It is in this light that we must reconsider the 24 000-year cycle documented by Le Gentil during his travels in 18th-century India. Le Gentil recorded that the Brahmins believed in a subtle stellar motion, a drift of 54 arcseconds per year, which yielded a grand cycle of approximately 24 000 years. They could not explain its origins. Bailly, analysing these records, conjectured that this figure was a distorted recollection of axial precession, which he (like many in his time) believed to span roughly 25 920 years. But what if it was something else entirely?
54 is a curious number. As an angular value, 54° is the internal angle of the golden pentagon, an important shape, connected to the golden ratio. This connects directly to Venus and its sky-pentagram, as well as to sacred geometry, suggesting that the 54 arcseconds per year may not have been intended to measure precession, but to symbolise a fundamental harmonic rotation in the heavens. Indeed, 360° ÷ 54″ = 24 000 years: a clean, whole cycle, well-suited to mnemonic, ritual, and cosmological applications. Unlike the unwieldy 25 920-year precession, the 24 000-year figure is more numerologically tractable, divisible by 60, 240, 1,000, numbers with deep roots in Chaldean, Indian, and Egyptian traditions.
This 24 000-year cycle becomes even more intriguing when viewed as 1 000 Numan cycles of 24 years. Such a magnification conforms to ancient techniques of scaling microcosmic harmonies to macrocosmic epochs.
24 years × 1,000 = 24,000 years
60 × 400 = 24,000, bringing together Babylonian base-60 and calendrical quarters
25 920 / 2400 = 10.8, connecting the Great Year of precession to the sacred number 108, central in Hinduism, Buddhism, and planetary geometry (e.g., Sun’s diameter × 108 ≈ distance to Earth)
24 × 180 = 4 320, the number of "divine years" in a Mahāyuga quarter (multiplied by 1,000 gives the full 4 320 000-year cycle)
Two Zodiacs, Two Systems
Bailly and others recognised that Indian astronomy retained a dual system: the fixed zodiac of constellations (sidereal) and the mobile zodiac of the equinoxes (tropical). This duality implies an early understanding of precession, and more importantly, a layered conception of time: one bound to the heavens, the other to earthly cycles. Even more telling is Bailly’s observation that while ancient Indian astronomers lacked detailed observational instruments, they nevertheless preserved sophisticated long-term calculations.
The 24 000-year cycle, then, may represent the residue of a lost system: a harmonically structured cosmology, not reducible to either modern astronomy or simple religious symbolism. Bailly suggests that the Brahmins retained fragments (“des débris”) of a once-sophisticated science, perhaps inherited from a much older, possibly global astronomical tradition. Writers like John Michell and John Anthony West have echoed this idea: that around 3000 BC, or earlier, there existed a now-lost tradition of high astronomical knowledge, diffused through priestly castes and re-encoded into mythology and sacred architecture. Could Numa have accessed this tradition? Bailly speculated that Numa might have inherited astronomical knowledge from Egypt or the East, possibly through intermediaries like Evander or the Sibyls. His complex system of intercalations, adjustments, and planetary reckonings suggests more than rustic ingenuity. It hints at an initiatory science, one meant to govern not only the civic calendar but the harmonisation of human affairs with the heavens.
As Bailly wrote, echoing the wonder of his discoveries:
This way of counting, specific and particular to science, proves that it was cultivated... by an older people who were its inventors. (15)
As Bailly and Le Gentil both perceived, these systems encode a different philosophy of time. The 24-hour day may mirror the 24 000-year Great Year; the 60 minutes in an hour may correspond to the 60-year Jupiter-Saturn cycle. The very structure of planetary returns and civil timekeeping becomes a mirror of cosmic rhythm. This way of reckoning time was about resonance. The goal was not just to measure time, but to inhabit it, to align the civic, ritual, and astronomical spheres in a shared logic of meaning.
Conclusion: A Calendar of Hidden Precision
The Numan calendar, often treated as a primitive Roman attempt at reconciling lunar and solar time, reveals itself upon closer examination to be something far more intricate. Its 24-year cycle was not a random compromise but a carefully chosen harmonic interval. The Numan cycle appears to have operated as a cosmological tool, embedding numerical ratios that mirror deeper structures found in ancient astronomy across cultures.
The recurrence of the number 24, in the division of the day, and in the long cycle of 24 000 years noted by Bailly and Le Gentil in Indian sources, suggests that this number played a foundational role in ancient models of time. When multiplied by 1 000, the 24-year cycle produces a grand period capable of absorbing and reconciling discrepancies between planetary cycles and solar years. In this context, the 24 000-year cycle may not be a crude approximation of precession but a numerically coherent framework for long-term celestial harmonisation.
Mercury’s role in this system is especially noteworthy. Its 46-year return, aligning its synodic, sidereal, and solar positions, makes it uniquely suitable for calendrical structuring. This cycle appears prominently in the Numan system and may explain an otherwise enigmatic detail in the Gospel of John, where the reconstruction of the Temple is said to have taken 46 years. If this number was chosen deliberately, it could reflect a symbolic gesture toward Mercury’s calendrical cycle, a subtle integration of astronomical knowledge into theological narrative.
Across many of the Numan planetary periods, we see a consistent logic at work: the search for whole-number year values that return planets to roughly the same position in the sky, relative both to the Sun and the background stars. This geometric approach differs from the synodic emphasis of later astrological tables. Instead, it reflects a desire for coherence across different layers of time, civil, astronomical, and perhaps spiritual. The result is not precision in the modern sense, but a rhythmic approximation that maintains stability over long durations.
If, as Bailly speculated, Numa was drawing on older traditions - Babylonian, Indian, or otherwise - then the calendar he instituted was not an invention, but an adaptation of much older ideas. The fact that Indian cosmology preserves a 24 000-year cycle, divided into four ages and associated with the motion of the fixed stars, may point to a shared archaic framework. Whether this connection emerged through direct transmission or parallel development is impossible to say with certainty, but the numerical echoes are difficult to dismiss.
Ultimately, the Numan calendar invites us to rethink how ancient systems of time functioned. It seems mechanical and observational precision enabled people in the distant past to create resonance in their lives with the workings of the cosmos, and the alignment of human affairs with the larger rhythms of the cosmos. In this light, the silence surrounding the deeper workings of the Numan system may not indicate ignorance, but reverence.
As an intriguing aside for those interested in numerical patterns beyond calendrical systems, German biochemist Peter Plichta has proposed what he calls the “Prime Number Cross,” a visual arrangement of prime numbers in concentric 24-element rings forming eightfold symmetry. While not directly connected to the Numan cycle, the recurrence of the numbers 24 and 8 is striking and offers a parallel example of how humans have historically sought harmony and resonance through numbers. I am grateful to Wolfram for bringing this correspondence to my attention.
Special thanks to Dane Quirke, Ryan Seven and Keith, in the Discord group, in the Project Flying Donkey thread, for their thoughts on the number 46 especially. Also thanks also to Leonardo Magini for his fantastic paper on the Numan system.
Notes
Macrobius, Saturnalia, Book 1, Chapter 12, Section 3 (Davies translation, p. 96).
Ibid.
Ibid.
Ibid.
Ibid.
Plutarch, Life of Numa
Livy, Ab Urbe Condita, I.19
Bailly. The original French is: "Ainsi ce prince philosophe, qui donna des lois sages, cet homme qui assignait peut-être au soleil sa véritable place, qui du moins connaissait les mouvements de cet astre, et ceux de la lune, avec assez d’exactitude, fit prêter la révolution du soleil, celle de la lune, et l’ordre civil à la vénération qu’il avait pour le nombre impair.
Cette inconséquence, au reste, n’étonne point quand on pense qu’on en retrouve des exemples chez les peuples les plus éclairés. Le jour chasse les ténèbres de la nuit, mais les ombres restent. Tant qu’il existera des corps, l’ombre sera à côté de la lumière ; tant qu’il y aura des hommes, l’erreur aura sa place près des connaissances sublimes.".
g
Bailly, p 195. "La Grèce n'était pas si avancée. Elle eut cette période de 8 ans deux siècles plus tard"
Bailly p 195 "Il partagea en 4 mois [...] dont il en intercalait un tous les deux ans"
See "The Astronomical Underpinnings of the Numan Calendar", by Leonardo Magini, https://www.academia.edu/37694993/The_Astronomical_Underpinnings_of_the_Numan_Calendar
Bailly. "La révolution entière [des étoiles fixes] est de 24,000 ans... Ce nombre divise exactement le nombre des années de chacun des quatre âges indiens."
Bailly.
Leur zodiaque a deux divisions différentes... Ils ont deux zodiaques, l’un fixe et l’autre mobile, ce qui démontre qu’ils n’ont pas connu d’abord le mouvement des fixes.
Bailly. Cette manière de compter, propre et particulière à la science, prouve qu’elle a été cultivée… par un peuple plus ancien qui en était l’inventeur.
Bibliography
Bailly, Jean-Sylvain.Histoire de l’Astronomie Ancienne. Paris, 1775.
Livy (Titus Livius).Ab Urbe Condita, Book I, Chapter 19.
Macrobius, Ambrosius Theodosius.Saturnalia, Book I, Chapter 12, Section 3.Translated by P.V. Davies. New York: Columbia University Press, 1969, p. 96.
Magini, Leonardo.“The Astronomical Underpinnings of the Numan Calendar.”Accessed via Academia.edu: https://www.academia.edu/37694993/The_Astronomical_Underpinnings_of_the_Numan_Calendar
Michell, John.The Dimensions of Paradise: Sacred Geometry, Ancient Science, and the Heavenly Order on Earth. Rochester, VT: Inner Traditions, 2001.
John Anthony West, Serpent in the Sky: The High Wisdom of Ancient Egypt. New York: Harper & Row, 1979.
Plutarch.Life of Numa, in Parallel Lives.Translated by Bernadotte Perrin. Cambridge: Harvard University Press (Loeb Classical Library), 1914.
Plutarque sur Numa
Il s’occupa, en outre, du calendrier ; et, si sa réforme ne fut pas complète, elle n’était pas pour cela l’œuvre d’un ignorant. Sous le règne de Romulus, on ne suivait, pour les mois, aucune règle ni aucun ordre : les uns étaient à peine de vingt jours, et d’autres en avaient trente-cinq, et quelquefois davantage. On n’avait aucune idée de l’inégalité qu’il y a entre le cours de la lune et celui du soleil : on n’avait qu’un souci, c’était que l’année fut de trois cent soixante jours. Numa reconnut que l’inégalité était de onze jours ; que les révolutions de la 166 lune se faisaient en trois cent cinquante-quatre jours, et celles du soleil en trois cent soixante-cinq (44) : il doubla donc ces onze jours, et il en fit un mois de vingt-deux jours, qu’il intercalait, tous les deux ans, après celui de février. Ce mois intercalaire est appelé par les Romains Mercédinus (45). Au reste, le remède qu’il apporta à cette inégalité devait lui-même exiger dans lia suite des remèdes plus grands encore.
Numa changea aussi l’ordre des mois. Mars était le premier de l’année : il en fit le troisième, et il mit â sa place janvier, qui, sous Romulus, était le onzième ; février était le douzième et dernier, et il devint désormais le second. Toutefois c’est une opinion accréditée que janvier et février ont été ajoutés par Numa, et qu’avant lui, l’année romaine n’était que de dix mois, comme il y en a de trois chez quelques peuples barbares, et comme, chez les Grecs, l’année des Arcadiens est de quatre mois, et celle des Acarnaniens de six. Les Égyptiens eurent, dit-on, d’abord des années d’un mois, puis des années de quatre mois. Voilà pourquoi ce peuple, bien qu’il habite un pays tout nouveau (46), fait l’effet de remonter si haut dans l’histoire : ils déroulent, dans leurs annales, ce nombre infini d’années, parce qu’il y a des mois qui comptent chacun pour un an. Ce qui prouve que l’année des Romains était autrefois de dix mois, et non de douze, c’est le nom de leur dernier mois, appelé encore aujourd’hui décembre. Mars était le premier : l’ordre actuel le montre assez ; car le cinquième, en commençant à mars, se nomme Quintilis, le sixième Sextilis ; et ainsi de suite pour les autres. Si janvier et février eussent toujours été placés avant mars, les Romains se seraient contredits, en appelant cinquième un 167 mois qui était, en réalité, le septième. Il est vraisemblable d’ailleurs que mars, consacré par Romulus au dieu de ce nom, obtint la première place ; que le second fut avril, ainsi nommé d’Aphrodite : en effet, c’est dans ce mois que les femmes romaines font un sacrifice à cette déesse ; et elles se baignent, aux calendes d’avril, avec une couronne de myrte sur la tête. Il y en a qui veulent que le mot aprilis, qui s’écrit par une lettre simple (47), vienne, non point d’Aphrodite, mais de ce que c’est le mois où le printemps, dans sa force, ouvre et développe les germes des plantes : ce serait la, en latin, le sens de ce mot (48). Des deux suivants, l’un est appelé mai, de la déesse Maïa, car il est consacré à Mercure (49), et l’autre juin, du nom de Junon. Quelques-uns prétendent que ces deux mois ont pris leur nom de deux des époques de la vie, la vieillesse et la jeunesse, parce que les vieillards, chez les Romains, se nomment majores, et les jeunes gens juniores. Les noms de tous les autres sont les noms mêmes du rang que chacun tenait d’abord dans le nombre des mois : cinquième, sixième, septième, huitième, neuvième, dixième (50). Dans la suite, le cinquième fut nommé Julius (51), en l’honneur de César, celui qui vainquit Pompée ; et le sixième, Auguste (52), surnom du second des empereurs. Domitien remplaça par ses surnoms les noms de septembre et d’octobre (53), innovation qui dura peu : dès qu’il eut été assassiné, ces mois reprirent leurs anciens noms. Les deux derniers sont les seuls qui aient conservé de tout temps leur dénomination numérique. De ceux qui furent ajoutés ou transposés par 168 Numa, l’un, février, peut s’expliquer mois des purifications. C’est là à peu près le sens du terme latin ; d’ailleurs, c’est dans ce mois qu’on sacrifie aux morts, et que l’on célèbre la fête des Lupercales, laquelle ressemble beaucoup à une purification (54).
Janvier, le premier mois de l’année, lire son nom de Janus. Je crois que Numa ôta de la première place mars, qui portait le nom du dieu de la guerre, parce qu’il avait à cœur de mettre partout, avant les qualités guerrières, les vertus civiles. Car Janus, qu’il ait été un dieu ou un roi, fut, dans la haute antiquité, un ami de la civilisation et de la paix, et il fit quitter aux hommes la vie dure et sauvage. Voilà pourquoi on le représente avec deux visages, comme ayant su accommoder ses manières et sa conduite à un double genre de vie.
PLUTARQUE
LES VIES DES HOMMES ILLUSTRES.
TOME TROSIÈME : VIE DΕ NUMA
Traduction française : ALEXIS PIERRON 1853
6) Avant tout, il divisa l'année suivant les cours de la lune, en douze mois; mais comme chaque révolution lunaire n'est pas régulièrement de trente jours, et que par conséquent l'année solaire eût été incomplète, il suppléa cette lacune par l'interposition des mois intercalaires, et il les disposa de telle façon que tous les vingt-quatre ans, le soleil se retrouvant au même point d'où il était parti, chaque lacune annuelle était réparée. (7) Il établit aussi les jours fastes et les jours néfastes, car il pressentait déjà l'utilité de suspendre parfois la vie politique. [Début]
[I, 18]
(1) Dans ce temps-là vivait Numa Pompilius, célèbre par sa justice et par sa piété. Il demeurait à Cures, chez les Sabins. C'était un homme très versé, pour son siècle, dans la connaissance de la morale divine et humaine. (2) C'est à tort qu'à défaut d'autre on lui a donné pour maître Pythagore de Samos. Il est avéré que ce fut sous le règne de Servius Tullius, plus de cent ans après Numa, que Pythagore vint à l'extrémité de l'Italie, dans le voisinage de Métaponte, d'Héraclée et de Crotone, tenir une école de jeunes gens voués au culte de ses théories. (3) Et même en admettant qu'il eût été contemporain de Numa, de quels lieux eût-il attiré des hommes épris de l'amour de s'instruire ? par quelle voie le bruit de son nom était-il arrivé jusque chez les Sabins ? quelle langue l'aidait à communiquer? et comment enfin un homme seul aurait-il pu pénétrer à travers tant de nations, aussi différentes de moeurs que de langage ? (4) Je pense plutôt que Numa puisait en lui même les principes de vertu qui réglaient son âme, et que le complément de son éducation fut moins l'effet de ses études dans les écoles philosophiques étrangères, que de la discipline mâle et rigoureuse des Sabins, la nation la plus austère de l'antiquité.
Tite-Live - Histoire Romaine
Livre I : Des origines lointaines à la fin de la royauté
(Traduction M. Nisard, 1864) Livre 1 Chapitre 19
Nous ajouterons peu fle chofes à ce que nous avons dit de l'année de Kuma. Nous remarquerons feulement que Macrobe fe trompe , lorfqu'il dit que Numa tenoit des Grecs cette forme d'année. Les Grecs n'eurent leur octaétéride que longtems après. Quant à la connoiffance du vrai fyftcme du inonde, que l'on attribue à ce prince , on fe fonde fur un palfage de Plutarque. Ce philofophe ( d) , en parlant du temple rond que Numa avoir dédié à la déelTe Vefta , au milieu duquel étoit co«fervé le feu facré , infère qu'il penfoit que le feu , c'eft-à-dire , le foleil étoit au centre du monde. Mais Plutarquç cite les Pythagoriciens , dont en effet c'étoit l'opinion , & il efV plus que vraifemblable que cette allufion leur appartient. Us font venus après Numa , & ont donné à fon édifice des vues favantes & cachées , auxquelles il n'avoir pas fans doute fongé. D'où lui étoient venues fes connoiifaiices fur le mouvement des aflres? Apparemment de l'Egypte. On ne croira point que la nymphe Egérie les lui ait révélées, ainiî que fes loix.Mais comment eut-il communication avec l'Egypte ? C'eft ce qu'on ne fait point.
§. XX.
Nous avons dit que Numa eft plus ancien que Pythagore & fesdifciples. Quelques auteurs ont écrit que Numa étoit Pythagoricien : rien n'eft plus faux. Pythagore vint en ItaUe à-peu-près dans le tems que Brutus délivra fa patrie de la tyrannie de Tarquin (a). Quand on prétendit avoir trouvé le tombeau de Numa , & fes livres qui y étoient renfermés , on publia qu'ils concernoientia philofophie pythagoricienne (/■) j mais fi ce préjugé eut quelque faveur chez les Romains , il fut fondé fur le refpecl qu'ils avoient pour Pythagore , & comme le génie de Numa paroiiïbit prefque divin , eu égard au fiecle barbare où il vivoit , ils crurent que ce prince avoit puifé fa fao-effe dans les écrits du philofophe (c). Cette anecdote prouve la modération des Romains ; il eft vrai que leurs prétentions n'étoient pas tournées de ce côté. Les Grecs n'auroient pas été h modeftes , Se n'auroient pas attribué à yn étranger la gloire qui eût appartenu à un de leurs grands hommes.
§. X X I.
Numa chargea les prêtres du foin de faire les intercalations qu'il avoit prefcrites ] il leur enjoignit même de confulter par l'obfervation lesmouvemens du foleil & de la lune, pour être sûrs de ne point s'écarter de leurs cours. Mais le zèle &: les tonnoilTances s'éteignirent avec lui. Les intercalations mêmes furent négligées, le calendrier tomba dans la plus grande confufion , foit par ignorance Se par inattention , foit même aulîî par la fraude des prêtres qui abrégeoient l'année , pour avancer la magiftrature des fens qui les payoient,ou pour faire durer moins celle des hommes en place qu'ils n'aimoient pas. Ils avoient encore en vue de favorifer les marchés des piiblicains {d)- Ce défordre fubfifta tant que dura la république romaine , & jufqu' à Jules Céfar. Les Romanis n'étoient pas plus avancés fur la connoifssances
pp 436-437 Histoire de l'astornomie ancienne