next message in archive
no next message in thread
previous message in archive
previous message in thread
Index of Subjects
>> The hexagon must have been noticed even befor
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
>>
>
next message in archive
no next message in thread
previous message in archive
previous message in thread
Index of Subjects