Re: what is etymology? (linguistics and biology)

While preparing a glossary of the new Magdalenian words,
part 18, Meeting the Minotaur in the labyrinth of Minos --
a triumph of early mathematical astronomy, told about in
the form of a legend

Minos was the mythical king of Knossos. He got his laws
from Zeus. This happened every nine years. Daidalos built
a palace for Minos, and a labyrinth for the Minotaur. This
creature, half bull half man, asked for human flesh, and
was given seven young women and seven young men
from Megara every year, or every nine years. Daidalos
informed Ariadne about the labyrinth. Ariadne got a long
thread, fixed one end outside the labyrinth, and gave the
other end to Theseus. Holding his end of Ariadne's thread,
Theseus entered the labyrinth, met the Minotaur, killed him,
and saved the fourteen young women and men. Following
the thread, they found their way out of the labyrinth and
sailed home to Megara.

This legend may convey information on a long-time calendar,
complementary to the one of Mallia (explained in the previous
message). Theseus and the young women and men from
Megara represent the number 19; the young men and women
19 days each, Theseus 19 years. Minotaur symbolizes a short
cycle of 9 lunar years, and a long cycle of 235 lunations. Minos
symbolizes a medium cycle of 9 solar years. The labyrinth
of the Minotaur and palace of Minos symbolize the challenge
of a calendaric calculation. And Ariadne's thread symbolizes
the mathematical intuition and skills leading through such a
task.

9 lunar years or lunations, calculated by means of the very
ancient algorithm 30 29 30 29 30 29 30 29 30 ... days, yield
266 days. 266 days are 7 plus 7 times 19 days.

*** 9 lunar years correspond to 7 plus 7 periods of 14 days

19 periods of 19 days yield 361 days. Add 4 and occasionally
5 days for a year of 365 and sometimes 366 days. 9 years
are 9 x 19 or 171 regular periods of 19 days, and require two
more periods of 19 days (additional days summed up over
nine years). All in all we get 173 periods of 19 days for 9 years.
A very good value, less than five hours short of the actual
duration of nine years.

*** 9 solar years correspond to 173 periods of 19 days

Now let us have a look at the relation of solar and lunar years,
or simply years and lunations:

3 years are roughly 37 lunations

8 years are about 99 lunations

3 plus 8 years are about 37 plus 99 lunations

11 years are about 136 lunations

8 plus 11 years are practically 99 plus 136 lunations

19 years are practically 235 lunations

11 plus 19 years are practically 136 plus 235 lunations

30 years are practically 371 lunations

The last equation is the one from Mallia (see the previous
message). The equation before is excellent, well-known
to eperts on archaeo-astronomy:

*** 19 solar years correspond to 235 lunar years

All three results together:

9 lunar years absorb 7 plus 7 periods of 19 days

9 solar years absorb 173 periods of 19 days

19 solar years absorb 235 lunations

The smaller numbers absorb the larger ones. First,
the number 19 loses - young men and women lost
in the labyrinth of the Minotaur and palace of Minos.
Then it wins - Theseus overcoming the Minotaur.

If my interpretation holds, the legend of Minotaur was a
fable around a triumph of early mathematical astronomy.
Ariadne and Theseus may even commemorate a historical
pair of mathematicians from Knossos and Megara.

Regards Franz Gnaedinger www.seshat.ch




While preparing a glossary of the new Magdalenian words,
part 17, a lunisolar calendar of 30 years at Mallia in Crete

Here again the basic Azilian lunisolar calendar from Goebekli
Tepe, 11 600 - 9 500 BP. A year had 12 months of 30 days
each, plus 5 and occasionally 6 days, while 63 continuous
periods of 30 days yield 1,890 days and equal 64 lunations.

The numbers of this calendar are made up of small factors,
which is the reason why the calendar can be modified in so
many ways. An unsolved problem, however, is the relation
of year and lunation.

This problem may have been solved by an astronomer of
Mallia, east of Knossos, on the northern shore of Crete.

In a corner of the central western court of the palace of Mallia
lies a "kernos," a large round stone resembling a mill stone.
Into the center of the surface had been carved a pair of wide
concentric bowls, while 33 small bowls and one big bowl
adorn the margin. Consider a bowl as a week of 11 days,
three bowls as a month of 33 days, and use the big bowl on
the margin for marking leap days (you may place colored
stones into the bowls). Now you may count years as follows:

year 1 11 months or 33 weeks plus 2 days
year 2 11 months or 33 weeks plus 2 days
year 3 11 months or 33 weeks plus 2 days
year 4 11 months or 33 weeks plus 2 days
year 5 11 months or 33 weeks plus 3 days

5 years are 55 m or 165 w plus 11 d or 1 w

5 years are 166 weeks or 1,826 days

30 years are 10,956 d or 996 w or 332 m

30 years last 10,956 days or 996 continuous weeks or
332 continuous months - 30 years have 330 regular months
plus 66 additional days that are the equivalent of 2 months.

Now let us calculate the number of lunations occurring in
this long period of time. From the Goebekli Tepe calendar
we know that 1,890 days equal 64 lunations. 945 days equal
32 lunations. Multiply these numbers by a factor of 11 and
you obtain

10,395 days for 352 lunations

The oldest algorithm for counting calculations goes like
this: O o O o O ... 30 29 30 29 30 ... days for 1 2 3 4 5 ...
lunations. Calculate 19 lunations this way and you obtain
561 days. So we have

561 days for 19 lunations

Add these numbers to the previous ones, and you obtain

10,956 days for 371 lunations

10,956 days are 30 years in the calendar of Mallia !

We got a very fine practical equation: 30 years are 332
continuous months of thirty-three days or 996 continuous
weeks of eleven days or 10,956 days or 371 lunations.

You can run the lunisolar calendar of Mallia for 30 years.
30 actual years are only 1.266 days longer, while a lunation
obtained via the above equation (10,956 d / 371 l) is even
better than the one provided by the Goebekli Tepe calendar
(1,890 d / 64 l, or 945 d / 32 l), only about 38 seconds per
lunation. And you can handle this long-time calendar with
whole numbers, no need for fractions and other complicated
mathematical tools.




While preparing a glossary of the new Magdalenian words,
part 16, calculating lunations for sixty years

The earliest lunisolar calendars I reconstructed so far - from
the Lebombo bone in Central Equatorial Africa, 35 000 BP,
and from the Lascaux cave, 17 000 BP - use the same
algorithm for calculating lunations: O o O o O ... 30 29 30 29
30 ... days for 1 2 3 4 5 ... lunations (O representing 30 days,
o representing 29 days).

The Azilian lunisolar calendar from Goebekli Tepe, 11 600
- 9 500 BP, used other numbers. A year had 12 months of
30 days each, plus 5 and occasionally 6 days, while 63
continuous periods of 30 days yield 1,890 days and equal
64 lunations.

"Beer-sheba" means The well of the divine Seven (Cyrus
H. Gordon, in one of the four volumes of Eblaitica, 1987,
1990, 1992, 2002). The week of seven days, as we are
still using it, may have been introduced by the people of
Beersheba, perhaps already by the mysterious people
of Anatolian origin who settled in Safadi 5 500 years ago.
A week of seven days, enumerated in the way we do,
not caring about months and years, allows this version
of the basic calendar. A year has 12 months of 30 days
each, plus 5 and occasionally 6 days, while 135 weeks
of seven days yield 945 days and equal 32 lunations.

For southern Crete in the Middle Minoan and the Argolis
in the Middle Helladic period of time I found another version
of the same calendar, using a week of nine days. A year has
12 periods of 45 days each, plus 5 and occasionally 6 days,
while 21 continuous periods of 45 days, or 105 weeks of
9 days, yield 945 days and equal 32 lunations.

Now let us have a look at these calculations in the light of
the above algorithm O o O o O ... 30 29 30 29 30 ... 30 59
89 118 148 177 207 236 266 295 325 354 384 413 443
472 502 531 561 590 620 649 679 708 738 ... days.
.
The numbers 266, 413, 679 are divisible by 7, while 679
plus 266 equals 945. Of interest for the calendar of Safadi
/ Beersheba: 23 plus 9 lunations are 97 plus 38 weeks of
seven days or 679 plus 266 days, all in all 945 days or
32 lunations, to be counted as follows:

OoOoOoOoOoOoOoOoOoOoOoO OoOoOoOoO

The numbers 207, 531, 738 are divisible by 9, while 738
plus 207 equals 945. Of interest for the calendar of southern
Crete and the Argolis: 25 plus 7 lunations are 82 plus 32
weeks of nine days or 738 plus 207 days, all in all 945 days
or 32 lunations, to be counted as follows:

OoOoOoOoOoOoOoOoOoOoOoOoO OoOoOoO

Using the above algorithm you can easily count lunations
for long periods of time, the mistke will be less than half
a day in sixty years.


.

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