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>> to draw this figure exactly, using an even more pr
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.
>
>