Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Ariadne's thread
Replies: 86   Last Post: Jan 28, 2013 5:19 AM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Franz Gnaedinger Posts: 330 Registered: 4/30/07
Re: Ariadne's thread
Posted: May 7, 2012 8:52 AM
 Plain Text Reply

River Map Ho-T'u and Magic Square Lo-Shu
of Early China (revised and illustrated version)

2) Mapping the River of Time ? a lunisolar calendar
encoded in the Yellow River Map of ancient China
that inspired the I Ching or Book of Changes

The Stone Age way of counting lunations was to
lay out pebbles, 30 29 30 29 30 29 30 ? pebbles
for 1 2 3 4 5 6 7 ? lunations or synodic months.

15 and 17 lunations counted that way yield 443
and 502 days respectively, together 945 days for
32 lunations, doubled 1890 days for 64 lunations.

The Göbekli Tepe lunisolar calendar had a month
of 30 days and a basic year of 12 months or 360
days. Add 3 days of midsummer and 2 days of
midwinter and you get a regular year of 365 days.
Add 3 midwinter days instead and you get an
occasional leap year of 366 days.

63 periods of 30 days are 1890 days and correspond
to 64 lunations, as found above. One lunation,
calculated that way, lasts 29 days 12 hours 45 minutes,
exact value 29 d 12 h 44 m 2.9 s (average from 1989 AD),
mistake less than one minute per lunation, or half a day
in a lifetime.

Now for the River Map Ho-T?u. A dragon-horse emerged
from the Yellow River Ho, bearing a map on its back,
the Yang numbers 1 3 5 7 9 given in light circles and
the Yin numbers 2 4 6 8 10 given in dark circles arranged
in a square, inner square 1 3 2 4 sum 10, outer square
6 8 7 9 sum 30, individual numbers given as lines of light
or dark circles, beginning with 1 at the bottom of the inner
square, in clockwise direction. The center is held by a
domino five in light circles, below and above a line of five
dark circles each, together the Yin number 10.
http://www.seshat.ch/home/china01.GIF

The number 10 represents a basic year of ten periods
of 36 days, in all 360 days. Add the vertical line of the
domino five for 3 midsummer days and the remaining
circles for 2 midwinter days and you get a regular year
of 365 days. If you add instead the horizontal line of
the domino five for 3 midwinter days you obtain an
occasional leap year of 366 days.

25 years require 6 leap years (in all 9131 days).
The number 6 is given as sum of the vertical line
and horizontal line of the domino five (central circle
counted twice). The number 25 is the sum of the
Yang numbers 1 3 5 7 9.

The number 36 of the calendar period is the sum of
the numbers 1 2 3 4 5 6 7 8. The square of 8 equals
64. Outer square of the River Map 6 8 7 9 sum 30.
The product of the Yang numbers 7 and 9 equals 63,
times 30 days 1890 days or 64 lunations or 2 by 2
by 2 by 2 by 2 by 2 lunations, mirrored in the cycle
of 64 binary hexagrams in the I Ching.

64 lunations correspond to 63 periods of 30 days,
128 lunations to 126 periods of 30 days or 105 periods
of 36 days, yielding the l/p ratio 126/105. Simpler ratios
are 6/5 or 12/10 and 11/9. Generating additive number
sequences of more l/p ratios:

6/5 (plus 11/9) 17/14 28/23 39/32 50/41 61/50 ?

Best value: 50 periods of 36 days for 61 lunations.

12/10 (plus 11/9) 23/19 ? 78/64 89/73 ?

Best value: 73 periods of 36 days for 89 lunations.

89/73 (plus 128/105) 217/178 345/283 473/388 ?

Best value: 388 periods of 36 days for 473 lunations,
mistake not even six seconds per lunation, a good
hour in a lifetime.

The period of 36 days offers many practical, good,
very good and excellent values for counting lunations
over long periods of time ? mapping the river of time,
as it were.

(The River Map is a reconstruction. I?d like to make
a suggestion: instead of halving the Yin number 10
one might arrange it as a circle around the domino
five. Outer square 20 by 20, inner square 16 by 16,
diameter of a small circle 1, distance between the
centers of two small circles on a straight line 2,
radius of the circle of the basic year 4, diameter 8,
outer diameter 9, inner diameter 7
http://www.seshat.ch/home/china03.GIF
http://www.seshat.ch/home/china02.GIF
http://www.seshat.ch/home/china02a.GIF )

The River Map Ho-T?u was complemented by the
Magic Square Lo-Shu on the back of a tortoise that
also emerged from the Yellow River Ho (David Eugene
Smith)

4 9 2
3 5 7
8 1 6

5 heaven (domino five)

1 north and winter and water
3 east and spring and wood
9 south and summer and fire
7 west and autumn and metal

2 earth
4 wood
6 metal
8 earth

The Magic Square may be seen as a world map.
Time is present insofar as the cardinal directions
go along with the seasons of the year.

(to be continued)

Date Subject Author
11/17/11 Franz Gnaedinger
11/17/11 Milo Gardner
11/18/11 Franz Gnaedinger
11/18/11 Milo Gardner
11/19/11 Franz Gnaedinger
11/19/11 Milo Gardner
11/20/11 Franz Gnaedinger
11/20/11 Milo Gardner
11/20/11 Milo Gardner
11/21/11 Franz Gnaedinger
11/22/11 Franz Gnaedinger
11/22/11 Milo Gardner
11/23/11 Franz Gnaedinger
11/24/11 Franz Gnaedinger
11/24/11 Franz Gnaedinger
11/24/11 Franz Gnaedinger
11/24/11 Milo Gardner
11/25/11 Franz Gnaedinger
11/26/11 Franz Gnaedinger
12/2/11 Franz Gnaedinger
12/2/11 Milo Gardner
12/3/11 Franz Gnaedinger
12/4/11 Franz Gnaedinger
12/4/11 Milo Gardner
12/5/11 Franz Gnaedinger
12/5/11 Milo Gardner
12/7/11 Franz Gnaedinger
12/8/11 Milo Gardner
12/10/11 Franz Gnaedinger
12/12/11 Franz Gnaedinger
12/12/11 Milo Gardner
12/13/11 Franz Gnaedinger
12/13/11 Milo Gardner
12/15/11 Franz Gnaedinger
12/15/11 Milo Gardner
12/15/11 Milo Gardner
12/16/11 Franz Gnaedinger
12/16/11 Milo Gardner
12/18/11 Franz Gnaedinger
12/18/11 Milo Gardner
12/19/11 Franz Gnaedinger
12/20/11 Franz Gnaedinger
12/20/11 Milo Gardner
12/21/11 Franz Gnaedinger
12/22/11 Franz Gnaedinger
12/23/11 Franz Gnaedinger
12/24/11 Franz Gnaedinger
12/29/11 Franz Gnaedinger
1/2/12 Franz Gnaedinger
1/3/12 Milo Gardner
1/4/12 Franz Gnaedinger
11/28/11 Velev, Petyr
1/6/12 Franz Gnaedinger
1/6/12 Milo Gardner
1/9/12 Franz Gnaedinger
1/17/12 Franz Gnaedinger
1/19/12 Franz Gnaedinger
1/19/12 Milo Gardner
1/27/12 Franz Gnaedinger
2/10/12 Franz Gnaedinger
2/28/12 Franz Gnaedinger
3/2/12 Franz Gnaedinger
3/23/12 Franz Gnaedinger
3/24/12 Milo Gardner
4/9/12 Franz Gnaedinger
4/10/12 Franz Gnaedinger
4/13/12 Franz Gnaedinger
4/17/12 Franz Gnaedinger
4/18/12 Franz Gnaedinger
4/18/12 Franz Gnaedinger
5/5/12 Franz Gnaedinger
5/7/12 Franz Gnaedinger
5/7/12 Milo Gardner
5/8/12 Franz Gnaedinger
5/8/12 Milo Gardner
5/8/12 Franz Gnaedinger
5/8/12 Franz Gnaedinger
5/9/12 Franz Gnaedinger
5/10/12 Franz Gnaedinger
8/14/12 Franz Gnaedinger
1/13/13 Franz Gnaedinger
1/19/13 Franz Gnaedinger
1/23/13 Franz Gnaedinger
1/23/13 Franz Gnaedinger
1/24/13 Franz Gnaedinger
1/26/13 Franz Gnaedinger
1/28/13 Franz Gnaedinger

© The Math Forum at NCTM 1994-2018. All Rights Reserved.