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Hi Dave, Eleanor, others,
Interesting, just the ticket -- a link from Dave's first URL got me to
http://www.maeshowe.co.uk
from which if you click -> Neolithic Orkney -> Chambered Cairns, you get a description including neolithic longevity. Quoting in part:
... "Unfortunately most sites were cleared out in the past without the benefit of modern techniques. However several cairns were excavated recently and produced much data. The Maeshowe-type cairns at Quanterness (St Ola) and Howe (Stromness) and the Orkney-Cromarty type cairn at Isbister (South Ronaldsay) yielded large quantities of human and animal bones, artifacts and other material from which much has been deduced about the lives of the people buried there...
"The picture is of a hard life, with few people living longer than 30 years, and most dying before 25. Arthritis was common in adults, while mortality in childhood was high. Usage of the tombs lasted for several centuries, and in the two recent excavations partial remains of large numbers of individuals were buried, with up to 400 at each of Isbister and Quanterness. Some cairns, such as Maeshowe, contained no bones on excavation, whilst other earlier excavations failed to yield the detail of the recent work. The lack of bones and other artefacts in many instances may simply mean that the cairns were cleared out at some unknown time in the past...."
... "That the Neolithic people went to such lengths in housing their dead, in contrast to later times, suggests that ancestors were very important to them. While much has been discovered about the material aspects of these people's life, nothing has been revealed about the rituals and social aspects of their life except that the very large effort implied in the construction of these monuments suggests that the society was well organised and had resources beyond mere subsistence farming".
Life span: Eleanor, the short life span quoted above is what I had remembered, apparently correctly, but incorrectly linked just to the Skara Brae site.
Cairn, tomb or not: Dave, the reason why you ruled out Maeshowe as a tomb or ossuary (among other possible uses, like a winter solstice observatory) was that it contained no bones. But as the text above indicates, it was opened long ago and probably cleared out; other tomb structures were found intact with many human bones.
Art work: The text (dated 2002) indicates that little was known by 2002 about the social aspects of life, but then I ran into a 2014 post about the August 19th end of the 2014 excavation season at the Ness of Brodgar (a half mile from the Ring of Brodgar). This has recently uncovered a small part of a previously unsuspected, astonishingly large neolithic complex of many buildings, interpreted as a temple complex, that must be what Dave referred to briefly in his original post. This links to an August Natl Geographic article, which is probably only partly reproduced at
http://ngm.nationalgeographic.com/2014/08/neolithic-orkney/smith-text
that is, there is text there but only a few pictures. The text says that 650 pieces of neolithic art have been recovered to date, though none were illustrated in what was on view. Perhaps when these are fully described, catalogued and available for viewing, they may give some indication of whether the local people actually ever used artificial aids like straight edges (proto-rulers) and primitive compasses for drawing things. Dave cites some plausible reasons why such evidence often would have disappeared from the historical record, assuming that it once existed, while I'd prefer to see some evidence, however slender, for its existence first, before believing in the technical savvy of these rude mechanicals.
Astronomical observations: the main entrance passage at Maeshowe is apparently lined up accurately to observe the winter solstice, when the setting sun's rays (if not obscured by cloud) directly illuminated the lower back wall of the main chamber. Videos linked to the URL above from photographer Charles Tait and inspired by the same Victor Reijs (Dave's 2nd URL) indicate, however, that illumination of the back wall can be observed over 22/23 days before and after the solstice, which would coincide in length with two of Thom's megalithic months, MM (1MM = 1/16 of a year). This appears to confound the exact determination of the solstice, but from Reijs' illumination-duration graph, that can be got from observing the day on which the illumination of the back wall is briefest. Reijs suggests that the Maeshowe structure in association with a nearby mountain may have been designed to observe the two proximate MMs, not just the actual solstice day. Perhaps they observed a prolonged 46 day winter festival? (a parallel with the current N. American practice of advertizing Christmas starting around October, perhaps?)
According to Reijs's plan of Maeshowe, each of the three side chambers is blind-ending, unlike the main passageway, so can't be used for observing anything extra, stone mirrors or not. Perhaps they put oil lamps in there for dim background illumination while observing in the main chamber? Bronze mirrors are known from later, but I've never heard of stone mirrors and am not sure how you could make one smooth or uniform enough to act as a useful specular reflector. Obsidian (volcanic glass) is black (poor reflector even if you have jeweller's rouge to polish it with) doesn't come flat and would probably not have been available in the Orkneys. Adding neolithic white paint (galena?) -- or modern paint -- would act only to produce an excellent light diffuser like the bathroom wall next to your shaving mirror, not a speculum.
Steve
________________________________________
From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on behalf of David & Alison Webster [dwebster@glinx.com]
Sent: Sunday, August 31, 2014 9:25 PM
To: naturens@chebucto.ns.ca
Subject: Re: [NatureNS] Neolithic stone rings - encore.
Hi Steve & All, Aug 31, 2014
Looking at cave art first, cave surfaces tend to be anything but plane
so would be unsuited for the kind of decoration that eventually ended up in
plane geometry. But carve art, exquisitely carved spear throwers etc. going
back 50,000 (?) yrs. demonstrate the innate urge to decorate. And of course
shortly after pottery appeared so did decoration of pottery but the surfaces
of unfired pottery, easily marked by accident and usually not plane, don't
fit the demands of plane geometry decorations.
So called primitive people had to cope with the limitations of materials
and means that were available to them. Their culture was primitive but they
had to be resourcefull, inventive and physically fit. Civilization is great
but it probably enables the survival of the least fit. Until very recently
(~mid-1800s) practical knowledge came well before theoretical explanation; a
whatever works approach.
As I indicated previously I think, these early exploratory sketches
would frequently be lost. In the Neolithic and earlier the selection of
potential plane surfaces would be limited to stone or hides (smoke tanned
leather or rawhide) stretched on a frame. One can draw fine lines on a slate
with a fragment of slate (Believe it or not we used slates for the first
several weeks in primary school !). But if you wipe a slate with anything
remotely moist then any marks present are lost forever.
Ornamentation of leather packs logically would have started early in
hunter-gatherer times shortly after humans started clustering as extended
family or tribe groups. When you break camp at dawn some mechanism is needed
to quickly recognize your bag or there will be fights every morning.
I happen to have on hand a sample of weaving art that is stunning; the
Attikamek Snowshoe. Will post an image on Flickr eventually & mention it. I
bought the book about 1994 because I had heard about the practical rawhide
harness described there.
Getting back to the Orkneys; did they have a straightedge ? The walls
and most of the corbeled roof of Maeshowe, about 4700 years old are still
intact thanks to very precise dressing and perfect fit of the sometimes
large sandstone components. So they had good quality straight edges and
much more.
In some sensational accounts Maeshowe is called a tomb. But somewhere on
the internet I read recently that it contained one human skull and a horse
skeleton; some tomb ! It was without doubt a very well designed and built
solar observatory. But the measurements taken and tests conducted (that I
have run into) barely scrach the surface.
A view from above is given on page 2 of--
http://www.orkneyjar.com/history/maeshowe/solstice.htm
Note that the North, South and East chambers each have a fairly narrow
passage leading to a much wider chamber; are these chambers high enough for
a child to sit in ?. Reijs (next URL) pays no attention to these and
considers only light cast anywhere on the back wall. Logically these
chambers are observation rooms where the observer can sit in complete
darkness so as to more readily see where light passing directly through the
East passage hits the chamber wall or reflected from a polished stone mirror
painted white (they did have white paint) held at 45o entered the North or
South chamber. As a guess these three chambers were designed to observe the
Winter Solstice (North), 22 days before and after (East Chamber) and >>22
days before and after (South Chamber).
The above URL has a large number of secondary links.
Additional detail in--
http://www.iol.ie/~geniet/maeshowe/eng/3rdstone.htm
Yt, Dave Webster
----- Original Message -----
From: "Stephen Shaw" <srshaw@Dal.Ca>
To: <naturens@chebucto.ns.ca>
Sent: Friday, August 29, 2014 3:15 PM
Subject: RE: [NatureNS] Neolithic stone rings - encore.
> Hi George, Dave, others:
> I haven't seen the National Geographic article Dave cited: did they use a
> straightedge to incise the lines? The idea raised by both of you is that
> interesting and even useful constructions could have been discovered
> accidentally, operationally by 'pre-geometrical' people 'doodling'
> casually with implements like primitive rulers and compasses. Obviously
> this is impossible to deny directly, so the follow-up question is whether
> there is any evidence that any early 'pre-geometrical' cultures actually
> might have done this, and whether any such discoveries were passed on, to
> become part of the local culture. I don't remember ever seeing evidence
> of this and couldn't find any in a cursory search.
>
> All the remarkable, artistic palaeolithic inscriptions on cave walls seem
> to have been inscribed freehand, and this seems true also in the later
> spiral megalithic incisions on rocks. In Lascaux type caves, you don't
> find straight-ish lines like spears drawn with a straightedge and roundish
> images constructed in a way that suggests a compass was used. By
> contrast, in some later Egyptian inscriptions (Book of the Dead, papyrus
> versions starting 1550 BC) it is difficult to see how vertical lines
> separating hieroglyphs that straight could have been drawn without a
> straightedge for guidance, but that seems to be about the first indication
> of this. Round things like images of the sun still didn't seem to be
> drawn with a compass in a few images that I looked at, but perhaps someone
> has better information. It would be surprising if Egyptian temple
> architects didn't have compasses as well as rulers.
>
> George, if you don't already know it, I came across
> 'Compass-and-straightedge_construction' on-line, which gives a repeating
> animation of constructing a hexagon inside a circle that might supplement
> your students' efforts. It also discusses/solves the classical problems
> of trisecting a line segment and trisecting an angle. The related link to
> the 'Neusis construction' used widely by the Greeks, is interesting but
> rather opaque as to particular usage.
> Steve
> ________________________________________
> From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on
> behalf of George E. Forsyth [g4syth@nspes.ca]
> Sent: Friday, August 29, 2014 12:49 AM
> To: naturens@chebucto.ns.ca
> Subject: Re: [NatureNS] Neolithic stone rings - encore.
>
> Hi,
>
> I teach this same process in grade seven math! We use a primitive
> compass, a paper clip and two pencils. We also look at the use of this
> symbol in historic terms, a hex. The students all associate "hex" with
> a bad spell used by a witch or sorcerer, but soon find that it was
> used in northern European history as sign or symbol of good luck and
> fortune. The Pennsylvania "Dutch" use it as a protection on their
> barns, as a bearer of protection.
>
> Interesting wondering how so many discoveries could have been made by
> "primitive" people without the computers and communication of our world.
>
> Cheers, George Forsyth
>
>
>
> Quoting David & Alison Webster <dwebster@glinx.com>:
>
>> Hi Steve & All,
>> We appear to be in essential agreement on this. Practical
>> geometric insights would likely all have come by accident in the
>> course of small scale and perhaps perishable decorative art
>> exercises; and once recognized and learned perhaps incorporated as a
>> part of practical culture long before any attempt theoretical
>> analysis. The latter requires leisure.
>>
>> That same article provides a good example of this process on page
>> 33. where parallel evenly spaced straight lines engraved in stone
>> cross a sequence of other straight lines to produce a double row of,
>> what we would call isosceles triangles. And then secondary patterns
>> are inscribed within these triangles; some messy and some
>> attractive. The two long sides of one of these original triangles is
>> neatly bisected and the points joined to form a triangle of
>> identical shape but half as high. Then the base of the original
>> triangle is bisected and the points joined to form a total of four
>> identical triangles all within the original triangle that was twice
>> as high.
>> If that rather attractive pattern were to become widely used
>> then someone would eventually notice that when the height of a
>> figure like this is doubled the area will be four times as great.
>> And if this became understood then someone might notice that the
>> same applies to squares and rectangles. And those experienced in
>> dividing fields for various purposes would say "Well duh".
>> Decorative arts would also likely have revealed the circle
>> hexagon connection. If drawing careful circles using a forked stick
>> with one side sharpened and the other charred
>> had come into common usage at some point then someone would
>> eventually have noticed that by placing the pointed arm anywhere on
>> a circle the charred end would pass through the center. And someone
>> would have noticed that this can be repeated 5 more times to yield
>> an attractive flower-like pattern with six-fold symmetry. Drop the
>> arcs that extend beyond the original circle, join the adjacent
>> points of the 6 petals and you have a hexagon just fitting a circle.
>> Perhaps more than one person on naturens will recall attempting
>> to draw this figure exactly, using an even more primitive compass,
>> as a pre-school rainy-day amusement.
>>
>> Yours truly, Dave Webster, Kentville
>>
>>
>> ----- Original Message ----- From: "Stephen Shaw" <srshaw@Dal.Ca>
>> To: <naturens@chebucto.ns.ca>
>> Sent: Friday, August 22, 2014 3:48 PM
>> Subject: RE: [NatureNS] Neolithic stone rings - encore.
>>
>>
>>> Hi Eleanor,
>>> Many years ago I recall reading that the neolithic denizens of
>>> Skara Brae used to cache the bones of their forebears in an
>>> ossuary, on stone ledges somewhere in their dwellings. One of the
>>> memorable findings was that experts analyzed these bones as to time
>>> of death, revealing that practically nobody at Skara Brae had lived
>>> beyond the age of 30, apparently testifying to the hard life there.
>>> I couldn't find any mention of this latterly, searching a couple
>>> of recent sources e.g. Wikipedia. Did you come across any such
>>> information when you were there: is it still believed that they had
>>> nearly all died by an age that we would consider a very young? I'm
>>> not sure that this is reflected in other early societies -- not the
>>> contemporary Egyptians, I think, who however were presumably much
>>> better fed.
>>>
>>> Hi Dave: Maybe this flogging a dead horse, but I think you have it
>>> backwards. In fact I suggested that the neolithic farmers could
>>> well have 'solved' what would later be called the "inscribed
>>> regular hexagon conjecture" by a simple practical-knowledge
>>> construction procedure of the sort that you advocate, without any
>>> foundation in theoretical geometry that would not arrive until much
>>> later, usually associated with the Greeks. At the same time, it's
>>> not clear why stone circle-makers would have been sequentially
>>> pegging out the boundary of a large circle by trial and error to
>>> make any such discovery (if that's how they did it), if they didn't
>>> have some informal geometrical insight in the first place. But I
>>> doubt that they could get that simply from looking at snowflakes,
>>> without a magnifying glass and ruler, though we did see plenty of
>>> snowflakes when we lived in Scotland.
>>> Steve
>>> ________________________________________
>>> From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca]
>>> on behalf of Eleanor Lindsay [kelindsay135@gmail.com]
>>> Sent: Tuesday, August 19, 2014 11:45 AM
>>> To: naturens@chebucto.ns.ca
>>> Subject: Re: [NatureNS] Neolithic stone rings etd.
>>>
>>> On a completely different aspect of this topic, I spent time in Orkney
>>> in the '70s during the early displays of the first discovery of ancient
>>> dwellings which became exposed at Skara Brae after a major storm tore
>>> masses of turf off the nearby shoreline, uncovering an entire
>>> prehistoric village of stone houses with connected walkways. It was not
>>> hard to understand why this site had been chosen as the nearby cliffs
>>> around the bay consisted of a type of rock that, to this day still
>>> appears to shelve off in long slim slabs; these slabs were evident in
>>> every house and what, for me, remains so memorable was their use for
>>> everyday needs which were identical to ours today - small horizontal
>>> slabs inserted at various levels in the walls to provide shelves and,
>>> most striking of all, rectangular bed frames on the ground consisting of
>>> narrow strips of the stone slabs for the sides, tall upright slabs for
>>> the head and slightly smaller ones for the foot of the bed - exactly how
>>> we still do it today!! And what I saw at that time is only a mere
>>> fraction of what has been discovered since then...
>>> The other site there that made a deep impression was the standing stones
>>> circle at the Moor of Brodgar; seeing it there in its (at least at that
>>> time) splendidly isolated setting looking no different than the day it
>>> was completed made a very powerful impression that left poor beleaguered
>>> Stonehenge, with all the traffic whizzing by, way behind.
>>>
>>> Orkney is a totally fascinating place to visit, not so much for its
>>> scenery, but for its spectacularly rich endowment of an amazing variety
>>> of prehistoric to second world war history.
>>>
>>> Eleanor Lindsay
>>>
>>>
>>>
>>> On 18/08/2014 9:07 PM, David & Alison Webster wrote:
>>>> Hi Steve & All,
>>>> I think you are confusing theoretical logic with practical know how
>>>> and these northern folk had an impressive amount of know how.
>>>>
>>>> For example, the walls of the Knop of Howar (occupied 3700
>>>> BC-1800 BC) are still standing. How many of our structures will still
>>>> be around 4000 years from now ? They lived on islands so likely knew
>>>> how to build boats that could actually be steered ( able to go out,
>>>> turn around and come back) and which cost less than a king's ransom.
>>>>
>>>> You don't need to be a Greek Philosopher to notice that the 6
>>>> points of an undamaged snowflake are of equal length, and would
>>>> therefore fit a circle of diameter equal to the distance between
>>>> opposite points. And you need only look at some of those prehistoric
>>>> cave paintings or ornamented spear throwers to realize how visually
>>>> gifted some of these early people were.
>>>>
>>>> Ivory and bone needles, some so thin that horsehair was the
>>>> probable thread, date from 15,000 BP. It takes skill and a steady hand
>>>> to craft the necessary stone gravers and then carve and polish even a
>>>> relatively crude needle.
>>>>
>>>> Over much of the last 10,000 years fires were made using a fire
>>>> drill or a fire plow. Try this some fine afternoon, as a test of
>>>> eye-hand coordination and physical stamina.
>>>>
>>>> Based on current conditions around the world and examples from
>>>> recorded history and prehistory that I have noticed, I suspect that,
>>>> at least over the last 30,000 years, there has never been a shortage
>>>> of creative and inventive people, only a shortage of conditions in
>>>> which these qualities could be exercised without penalty.
>>>>
>>>> Yt, Dave Webster, Kentville
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> ----- Original Message ----- From: "Stephen Shaw" <srshaw@Dal.Ca>
>>>> To: <naturens@chebucto.ns.ca>
>>>> Sent: Monday, August 18, 2014 3:30 PM
>>>> Subject: RE: [NatureNS] Neolithic stone rings etd.
>>>>
>>>>
>>>>> Eureka, Dave, you have it, the hexagon inscribed within a circle! I
>>>>> even used this for something a while ago, so can't see why I missed
>>>>> it here.
>>>>>
>>>>> However, this came from the Greeks ~2000+ years ago, not Neolithic
>>>>> folk (NF) 5-6000 years ago, so it amounts to proposing that the NFs
>>>>> must have discovered the inscribed hexagon arrangement independently
>>>>> themselves. I don't think that even earnest contemplation of a
>>>>> regular hexagon like a bee's wax cell would suggest immediately to
>>>>> the observer that for a regular hexagon, radius R exactly equals side
>>>>> length L as a neat rule. On the other hand, if some enterprising NFs
>>>>> had a radius rope and two pins like you suggested and stepped around
>>>>> the perimeter of their initial circle accurately, at the 6th step
>>>>> they would have found themselves exactly back at the origin, so could
>>>>> plausibly have discovered the R=L rule that way and then passed it
>>>>> around by word of mouth to others. Could this even have filtered
>>>>> down to the Greeks?
>>>>> Steve
>>>>> ________________________________________
>>>>> From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca]
>>>>> on behalf of David & Alison Webster [dwebster@glinx.com]
>>>>> Sent: Monday, August 18, 2014 2:03 PM
>>>>> To: naturens@chebucto.ns.ca
>>>>> Subject: Re: [NatureNS] Neolithic stone rings etd.
>>>>>
>>>>> Hi Steve, Jane & All,
>>>>> The logical way to lay out a 12 post observatory is as follows.
>>>>> 1) Find a relatively level area of open land with unobstructed
>>>>> horizons from ~NE through S to ~NW.
>>>>> 2) Prepare 7 relativey slim and untapered, smooth rossed posts; say
>>>>> 2" in diameter
>>>>> 3) Select the center point and mark it with one of these posts.
>>>>> 4) Select a radius for the circle, braid a loop in one end of the
>>>>> rawhide length that is large enough to just slip down over the posts
>>>>> as this will be used numerous times. A wooden yoke at the other end
>>>>> would increase precision.
>>>>> 5) Sight from the center post to the Pole Star and mark the position
>>>>> of the North and then the South posts using the radius strand. These
>>>>> act as a baseline and enable checking the length of the rawhide
>>>>> radius strand which if not well oiled and protected can shrink or
>>>>> stretch.
>>>>> DIGRESSION:
>>>>> The hexagon must have been noticed even before the first crude
>>>>> tools were made; Bee & wasp hives/nests, snowflakes, drying silty mud
>>>>> deposits, Thallose Liverworts, some large celled Mosses... And if the
>>>>> 6 points of a hexagon are joined by drawing lines between opposite
>>>>> points you have a cluster of six equilateral triangles. Therefore the
>>>>> radius of a circle is exactly equal to the distance between the six
>>>>> points of a hexagon that fall on that circle.
>>>>> END OF DIGRESSION
>>>>> 6) Using the above one can proceed to fix the location of the
>>>>> remaining 4 points of the hexagon. If the ground is readily marked
>>>>> (weak sod or cultivated) one could simply inscribe an arc from the
>>>>> center post at the approximate location of the next post and then
>>>>> measure this exactly by moving the radius strand to the previously
>>>>> fixed post (initially the North or South post). If the ground is not
>>>>> readily marked then use of two strands of equal length would be
>>>>> indicated.
>>>>> 7) If one proceeded to locate post positions, starting at the North
>>>>> post, then the distance from the 4th post should be one radius strand
>>>>> from the South post provided no errors have been made.
>>>>> 8) Having installed the 6 posts of a hexagon one need only bisect the
>>>>> arc between adjacent posts (as before, most readily done if the soil
>>>>> is easily inscribed); bisect the line between posts, mark with
>>>>> temporary post flush with ground then swing the radius strand around
>>>>> the center post until it lies over the flush post. Repeat five more
>>>>> times and you have 12 posts equally spaced around a circle.
>>>>>
>>>>> After this has been digested I will describe how to mark a 60 post
>>>>> circle. Some decades ago, for amusement, I went back in time mentally
>>>>> and worked out a way to divide a disk edge into 360 equal parts using
>>>>> stone-age hardware and the 60 post layout would use the same
>>>>> stone-age "math".
>>>>>
>>>>> Yt, Dave Webster, Kentville
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> ----- Original Message -----
>>>>> From: "Stephen Shaw" <srshaw@Dal.Ca<mailto:srshaw@Dal.Ca>>
>>>>> To: <naturens@chebucto.ns.ca<mailto:naturens@chebucto.ns.ca>>
>>>>> Sent: Monday, August 18, 2014 2:25 AM
>>>>> 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<mailto: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<mailto: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 stones is a snap to lay out if you have
>>>>>> enough
>>>>>> rawhide and this natural and practicable number likely accounts for
>>>>>> our 12
>>>>>> signs of the zodiac, 12 months of the year and 24 hours in the day.
>>>>>> But a
>>>>>> ring with 60 markers is slightly more tricky to lay out, using
>>>>>> Neolithic
>>>>>> hardware, then say a ring of 48 or 96. The number 60 has the
>>>>>> advantage of
>>>>>> being divisible by 2,3,4,5&6 so the designer of this ring was just a
>>>>>> step
>>>>>> away from a 360o circle; dividing a circle into 60 or 360 parts is
>>>>>> essentially the same problem and both have similar advantages if
>>>>>> fractions
>>>>>> are difficult to deal with.
>>>>>>
>>>>>> Yt, Dave Wwbster, Kentville
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> -----
>>>>>> No virus found in this message.
>>>>>> Checked by AVG - www.avg.com<http://www.avg.com>
>>>>>> Version: 2014.0.4745 / Virus Database: 4007/8051 - Release Date:
>>>>>> 08/17/14
>>>>>>
>>>>>
>>>>>
>>>>> -----
>>>>> No virus found in this message.
>>>>> Checked by AVG - www.avg.com
>>>>> Version: 2014.0.4745 / Virus Database: 4007/8051 - Release Date:
>>>>> 08/17/14
>>>>>
>>>>
>>>
>>>
>>> -----
>>> No virus found in this message.
>>> Checked by AVG - www.avg.com
>>> Version: 2014.0.4745 / Virus Database: 4007/8064 - Release Date:
>>> 08/19/14
>>>
>
>
>
>
> -----
> No virus found in this message.
> Checked by AVG - www.avg.com
> Version: 2014.0.4745 / Virus Database: 4007/8110 - Release Date: 08/27/14
>
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