next message in archive
next message in thread
previous message in archive
previous message in thread
Index of Subjects
Index of Subjects
Hi Jane: That could work crudely, then bisecting the resulting segments (easy with a 2-peg rope compass) nicely gets you to the suggested 12 segments. Having constructed the circle with their rawhide or rope compass, the builders presumably would start at one point on the perimeter and measure off 5 equal length radius units in succession, easy. The problem is that this leaves the 6th segment too long (6*r/2*Pi*r = 3/Pi = only 0.955, not 1.0 -- the last segment would be ~4.7% too long, or 4.7 feet for a 100 foot radius circle). Human vision for comparing line lengths is good to about 1% (meaning that differences less than 1% can't be detected reliably, but those greater than 1% can be), so it would be immediately apparent to the builders that they had screwed up. It depends upon the accuracy required: Thom apparently claimed a variance of fractions of a millimeter in establishing his megalithic yard of 2.72 feet, so a 4.7% error would not work at all for him -- but this claimed precision seems wildly improbable, and has been widely disputed.
My guess is that if you had 2 pegs placed at two right angle points on the constructed circle, easily done, you could guess fairly accurately where to put two more pegs on the perimeter to trisect that quadrant. Using a ruler (maybe a knotted rope), you could adjust the position of the last two pegs a bit to give equal lengths to any required degree of accuracy, perhaps satisfactorily by eye within 3-4 successive approximations. The problem seems to be that I thought that this was supposed to be done by pure geometry and measurement based on a megalithic yard, not by trial and error. I'm not sure if there is any evidence that neolithic cultures used knotted ropes for measurement either, though others elsewhere apparently did.
The supposed connection between the megalithic yard and astronomical measurements suggested to have been used to derive it is treated at some length in Wikipedia under 'Pseudoscientific metrology'. A nice read if you like fantasy.
Steve
________________________________________
From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on behalf of Dave&Jane Schlosberg [dschlosb-g@ns.sympatico.ca]
Sent: Monday, August 18, 2014 8:47 AM
To: naturens@chebucto.ns.ca
Subject: Re: [NatureNS] Neolithic stone rings etd.
Since the radius goes almost exactly 6 times around the circumference,
perhaps early builders used that to divide their circles.
-----Original Message-----
From: Stephen Shaw
Sent: Monday, August 18, 2014 2:25 AM
To: naturens@chebucto.ns.ca
Subject: RE: [NatureNS] Neolithic stone rings etd.
Hi Dave: You need an astronomer with an interest in history for this, so
stand by, hopefully, for input.
Meanwhile, this astronomical observatory idea originated I think with
Alexander Thom, based on his idea of a a common unit of length, the
megalithic yard (MY) of 2.72 feet. This unit supposedly had been used with
precision to lay out British and French neolithic stone circles. While this
seems not to have been entirely discredited, later critics doubted that
there was a unit with this precision in universal use, and that distances
could have been measured adequately instead simply by pacing-out, not
necessarily by using a common physical yard-stick. I can't remember the
connection, but the MY supposedly was somehow related to an astronomical
cycle, indicating that you must have had active neolithic astronomers to
make the connection. Perhaps someone else can remember the connection, or
if I've got this wrong.
Not sure about the universal '12' ideas. The main units of time that we and
presumably earlier populations used were based on 3 quite different
astronomical cycles that are unrelated. Days are/were measured based on
Earth's daily rotation on its axis, easily counted though not precisely
constant. Months depended on the Moon's rotation about Earth, easily
observed as recurring phases of the Moon. Years are/were measured in time
units based on the Earth's orbiting around the Sun -- much more difficult to
calibrate accurately, probably accounting for the need to calibrate by
building fancy sunrise-observing structures, accurate to the day at
solstices. Very important for correct crop planting. Unsurprisingly,
neither of the smaller units in use at present divide exactly into the
largest unit, the year, or into each other, hence yearly movement of Easter,
calendar day regression and the need for leap years. Not clear how you
would use a megalith with one annually precise alignment axis to tell the
time (for instance the day, month) at other times of the year.
I've forgotten most Euclid, but how do you subdivide a circle easily ('a
snap') into 12 subunits? I can see how you draw the first line and find its
centre (will become the centre of the circle) with a rawhide
compass-divider, and how you can draw the second diameter at right angles to
this with the same gear, and then complete the circle. You are then left
with a circle with 4 equal quadrants, each of which has to be subdivided
finally into 3 segments to make a total of 12, like the hours on a clock.
Isn't this the difficult problem of trisecting the angle (bisecting is a
snap with a simple compass, but I thought trisection was not)? Please
advise.
Once you've somehow accomplished the trisection of 4 segments into 12
sub-segments with 30° central angles, then 24, 48, 96... segments are easy
(bisection), as you imply. But subunits of 60 segments are not part of this
series, so that remains rawhide-unexplained too.
Steve (Hfx)
________________________________________
From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on
behalf of David & Alison Webster [dwebster@glinx.com]
Sent: Sunday, August 17, 2014 7:34 PM
To: NatureNS@chebucto.ns.ca
Subject: [NatureNS] Neolithic stone rings etd.
Dear All, Aug 17, 2014
The August issue of National Geographic has an article that features the
stone rings and other old (~5000 yrs.) structures of the Orkney Islands.
From this article & Wikipedia; the circular Ring of Brodgar; spaced for 60
stones of which 27 remain and the slightly nearly circular but elliptic (so
they say) ring of the Stones of Stenness; spaced for 12 megaliths with
perhaps 1 or 2 never erected.
Is it now so widely recognized that such structures served as
observatories (an analog calendar and crude sundial) that it is too obvious
to mention ? Alignment to the winter solstice at sunset (which would also
fit the summer solstice at sunrise I think) is mentioned but surely these
could have been used to keep track of time throughout the year.
Even short stones would cast a long shadow at sunrise and sunset and the
changes in direction with time would be consistent from year to year. A
circular structure with 12 stone