Golden Hat - Calendars

Calendars

The gold cones are covered in bands of ornaments along their whole length and extent. The ornaments - mostly disks and concentric circles, sometimes wheels - were punched using stamps, rolls or combs. The older examples (Avanton, Schifferstadt) show a more restricted range of ornaments than the later ones.

It appears to be the case that the ornaments on all known Golden Hats represent systematic sequences in terms of number and types of ornaments per band.

A detailed study of the Berlin example, which is fully preserved, revealed that the symbols probably represent a lunisolar calendar. The object would have permitted the determination of dates or periods in both lunar and solar calendars.

Since an exact knowledge of the solar year was of special interest for the determination of religiously important events such as the summer and winter solstices, the astronomical knowledge depicted on the Golden Hats was of high value to Bronze Age society. Whether the hats themselves were indeed used for determining such dates, or whether they simply represented such knowledge, remains unknown.

The functions discovered so far would permit the counting of temporal units of up to 57 months. A simple multiplication of such values would also permit the calculation of longer periods, e.g. metonic cycles.

Each symbol, or each ring of a symbol, represents a single day. Apart from ornament bands incorporating differing numbers of rings there are special symbols and zones in intercalary areas, which would have had to be added to or subtracted from the periods in question.

The system of this mathematical function incorporated into the artistic ornamentation has not been fully deciphered so far, but a schematic understanding of the Berlin Golden Hat and the periods it delimits has been achieved.

In principle, starting with zone Z_i, a sum is achieved by adding a relevant contiguous number of neighbouring sections: Z_i .. Z_i+n. To reach the equivalent lunar or solar value, from this initial sum must be subtracted the sum of symbols from the intercalary zone(s) within the area counted.

The illustration depicts the solar representation on the left and the lunar one on the right. The red or blue fields in zones 5, 7, 16 and 17 are intercalary zones.

The values in the individual fields are reached by multiplying the number of symbols per zone with the number of rings or circles incorporated in each predominant symbol. The special symbols in zone 5 are assigned the value of "38", as indicated by their number.

Example

Zone 12 is dominated by 20 repetitions of punched symbol No. 14, a circular disc symbol surrounded by 5 concentric circles.

Thus, the symbol has the value of 20 x 5 = 100.

The smaller ring symbols placed between the larger repetitions of No. 14 are considered as mere ornaments and thus not counted.

Through this system, the Hats can be used to calculate a lunisolar calendrical system, i.e. a direct reading in either lunar or solar dates, as well as the conversion between them.

The table can be used in the same way as the original Golden Hats. To determine the number of days in a specific time period (yellow fields), the values of the coloured fields above are added, reaching an intermediate sum. If any of the red intercalary zones are included, their sum has to be subtracted. This allows the calculation of 12, 24, 36, 48, 54 and 57 synodic months in the lunar system and of 12, 18, 24, 36, 48, 54 and 57 sun months (i.e. twelfths of a tropical year).

Example

To determine a 54 month cycle in the lunar system, the numerical values of the green or blue zones 3 to 21 are added, reaching a sum of 1,739 days. From this, the values of the red intercalary fields 5, 16 and 17 are subtracted, The result is 1739-142=1597 days, or 54 synodic months of 29.5305 days each.

The overall discrepancy of 2 days to the astronomically accurate value is probably the result of a slight imprecision in the Bronze Age observation of synodic and solar month.