Exhibit E: The 8-year Calendar in Tuc d'Audoubert
Fig. 11. Tuc d’Audoubert. Engraved signs in a small rotunda and on the walls and ceiling
of the adjoining, barrel-vaulted corridor (view from below). Ca. 15,000 BP.
of the adjoining, barrel-vaulted corridor (view from below). Ca. 15,000 BP.
Fig. 12. Diagram of the essential 8-year calendar.
Discussion: A small recess in Tuc d’Audoubert features a remarkably uniform decoration: long files of identical signs, each consisting of a vertical line with an attached buckle. They look like quarter-moons on sticks, and in fact, they make sense when read as a means of counting months. There is, a total of 99 such “month” signs in the recess, a number that may reflect the 99 months of an eight-year calendar (the Octaëteris), which is known from historical sources, and which endeavors to synchronize the cycles of the moon and the sun. More telling than the total number of signs, however, the three files of “month” signs (Fig. 11, A, B, C) count 31 signs each (the end of the series in the rotunda is worn but still countable), and the 31 is a highly significant number, because it captures the basic principle of the 8-year calendar, namely, the insertion of an extra (intercalary) month after every 30 regular months. This principle is easily explained, as follows.
The discrepancy between 12 months and a solar year is 11 days. After two years this increases to 22 days, which is less than a full month (29/30 days), but after three years it becomes 33 days, which is more than a month. So, the 8-year calendar resolves the problem by intercalating a month every two-and-a-half years (that is, every 30 months). After 8 years--and three cycles of 31 months--the correlation of lunar months and solar years is, empirically, very close to the starting-point. This scenario is precisely illustrated in Tuc’s three files of 31 “months” (Fig. 11 A, B, C)—that is, 7 ½ years—plus the six signs in adjacent niches (D and E) that may account for the remaining half-year (cf. Fig. 12). The 99 “month” signs in the Tuc recess and, in particular, the three signature files of 31 signs prove the artists’ understanding of the inner workings of the 8-year calendar.
Implicit in this scheme is a practice of observing the phases of the moon with special attention to half-year intervals—no doubt, at the winter- and summer-solstices. This practice was, however, second nature for the Ice Age peoples, who understood the solar year as a waxing half (from mid-winter to mid-summer) and a waning half (mid-summer to mid-winter), analogous to their perception of the month as a waxing and a waning half (as demonstrated by Alexander Marshack’s analyses of lunar calendars)--hence their attention to the 2 ½-year intervals as well as to the completed 8th year.
Thousands of years later, Neolithic cultures discovered that the same basic pattern of leap-months generated an even more precise luni/solar calendar if pursued for 19 years. For its time, however, the 8-year calendar was a significant intellectual achievement.
The discrepancy between 12 months and a solar year is 11 days. After two years this increases to 22 days, which is less than a full month (29/30 days), but after three years it becomes 33 days, which is more than a month. So, the 8-year calendar resolves the problem by intercalating a month every two-and-a-half years (that is, every 30 months). After 8 years--and three cycles of 31 months--the correlation of lunar months and solar years is, empirically, very close to the starting-point. This scenario is precisely illustrated in Tuc’s three files of 31 “months” (Fig. 11 A, B, C)—that is, 7 ½ years—plus the six signs in adjacent niches (D and E) that may account for the remaining half-year (cf. Fig. 12). The 99 “month” signs in the Tuc recess and, in particular, the three signature files of 31 signs prove the artists’ understanding of the inner workings of the 8-year calendar.
Implicit in this scheme is a practice of observing the phases of the moon with special attention to half-year intervals—no doubt, at the winter- and summer-solstices. This practice was, however, second nature for the Ice Age peoples, who understood the solar year as a waxing half (from mid-winter to mid-summer) and a waning half (mid-summer to mid-winter), analogous to their perception of the month as a waxing and a waning half (as demonstrated by Alexander Marshack’s analyses of lunar calendars)--hence their attention to the 2 ½-year intervals as well as to the completed 8th year.
Thousands of years later, Neolithic cultures discovered that the same basic pattern of leap-months generated an even more precise luni/solar calendar if pursued for 19 years. For its time, however, the 8-year calendar was a significant intellectual achievement.
Exhibit F: The 8-year Calendar in the Castillo Cave.
Fig. 13. Sign composed of red dots in the Castillo Cave. Ca. 15,000 BP.
Fig. 14. Schematic rendition of the Castillo sign, showing the number of dots in each segment.
Discussion: This complex sign (Fig. 13) may not be immediately recognizable as calendrical, but the three long, parallel lines--the left wing of the sign (e, f, g)—each counts 31 signs, thus revealing the presence of the 8-year calendar. An affiliated, short line of six dots (h) completes the number of months (99) for fully eight years.
The central and right-hand part of the design (a – d, Fig. 13) was apparently painted before the left wing and is not directly part of the 8-year calendar; it does, however, record bits of knowledge that were basic to the formation and application of this calendar, and which calendar-makers needed to memorize. Thus the first element of the design, the vertical line of 16 dots, combines with the attached parallels of 12, 13, and 14 (see the diagram, Fig. 14) to provide the sums of 28, 29, and 30—of which the first is the number of days recaptured with a leap-month after 2 ½ years, while the other two are the alternating numbers of days in a regular month. The final elements (i, j and k, Fig. 13), number respectively 8, 17, and 12 dots, of which the first represents the years of the calendar and the last one the months of an ideal year, while the long, middle one combined with the line of 16 might represent the 33 days that the moon would gain after three years--should the practitioner miss the intercalation at a 2 ½ year mark.
These additions to the 8-year calendar proper may be seen as mnemonic devices, a collection of numbers that were prerequisite elements of a calendar-maker’s craft. We must not forget that in the pre-literate culture of the artists, all knowledge was quickly and irretrievably lost if not endlessly reiterated, to the effect that a schematic illustration of the calendar could support the ever-elusive oral communication of detailed knowledge; though less effective than written records, visual representations were likely indispensable resources.
Significantly, the Castillo calendar is painted in the same, alcove-like corner of the cave as the above-discussed map of Cantabria, a coincidence that surely reflects the artists’ pride in the state of their intellectual culture. We may fairly see their achievement in handling space and time as an advance toward a proto-scientific mind-set.
The central and right-hand part of the design (a – d, Fig. 13) was apparently painted before the left wing and is not directly part of the 8-year calendar; it does, however, record bits of knowledge that were basic to the formation and application of this calendar, and which calendar-makers needed to memorize. Thus the first element of the design, the vertical line of 16 dots, combines with the attached parallels of 12, 13, and 14 (see the diagram, Fig. 14) to provide the sums of 28, 29, and 30—of which the first is the number of days recaptured with a leap-month after 2 ½ years, while the other two are the alternating numbers of days in a regular month. The final elements (i, j and k, Fig. 13), number respectively 8, 17, and 12 dots, of which the first represents the years of the calendar and the last one the months of an ideal year, while the long, middle one combined with the line of 16 might represent the 33 days that the moon would gain after three years--should the practitioner miss the intercalation at a 2 ½ year mark.
These additions to the 8-year calendar proper may be seen as mnemonic devices, a collection of numbers that were prerequisite elements of a calendar-maker’s craft. We must not forget that in the pre-literate culture of the artists, all knowledge was quickly and irretrievably lost if not endlessly reiterated, to the effect that a schematic illustration of the calendar could support the ever-elusive oral communication of detailed knowledge; though less effective than written records, visual representations were likely indispensable resources.
Significantly, the Castillo calendar is painted in the same, alcove-like corner of the cave as the above-discussed map of Cantabria, a coincidence that surely reflects the artists’ pride in the state of their intellectual culture. We may fairly see their achievement in handling space and time as an advance toward a proto-scientific mind-set.
Selections from iceageiconology.net, Chapter XI, Addendum.
© 2023 by Jesper Christensen, Art Historian, Ph.D.
E-mail: jespersc@hotmail.com.
© 2023 by Jesper Christensen, Art Historian, Ph.D.
E-mail: jespersc@hotmail.com.