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Snowshoe image is now at
https://www.flickr.com/photos/91817127@N08/15105080315/
DW
----- Original Message -----
From: "David & Alison Webster" <dwebster@glinx.com>
To: <naturens@chebucto.ns.ca>
Sent: Sunday, August 31, 2014 9:25 PM
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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