vase:




There are a few things that occurred to me, inspiring a few ideas to explore and
either confirm or refute their merit.

1. Given that there is all of this "sacred geometry" stuff that people go on
about, what is it's origin and why?

I think that we are taking a look at objects and structures that are designed
using a method much like we use CAD, however I think we can agree that the
ancients didn't have computers as we know them, and they probably used an
absolute measurement system different than our own.
But what makes absolute units irrelevant, and simultaneously preserves the
constants that we see?
Relative measurements.  In geometry class, everything is laid out with a compass
and straightedge, and nothing is measured in "units".  But everything is
measured in relation to line segment lengths, radii, etc.
The Greeks apparently got a lot of their knowledge from the Egyptians, and so
this comports with what we (think we) know about history.

2. If the designers used a well-developed system to lay out the design
parameters of objects and structures, and it was a relative system, then it
seems likely that they made use of all of the methods used in standard geometry.
  Things would be laid out using arcs and lines and ratios.  Pi would naturally
show up everywhere because ... circles.

3.  Alex Dunn and Nick Sierra used a sphere in their metrological analysis - not
because they were trying to show that a sphere in any way "matched" the surface
of the vase, but more to show that the distance of the surface to the ideal
sphere was very constant along the vertical axis (among other reasons).
You showed that the overall vase shape deviates from an ellipsoid with your
overlay.

It occurred to me that if I was going to build a machine with a tooling guide
that was inspired by classical geometrical methods, then I'd use a lot of
circular arcs.  Which led me to think that the vase might more strongly resemble
a vesica piscis, or when the circle centers do not lie on the the other circle,
what is called a geometrical lemon.  This is also exactly the inner surface of a
spindle torus.

I've spent a lot of time developing some macros for use in fitting circles and
spheres to measured data sets, and coming up with a way to compare the vase to
the lemon shape.  Fortunately, POV-Ray has some inbuilt functions and primitives
that ultimately make that task a lot simpler, and I was able to devise a 3D
texturing pattern that is essentially an unsigned distance function of the
lemon.  By applying this pattern to the vase mesh, it maps the closeness of fit
of the mesh to the lemon.

The result is obviously sensitive to the radii of the generating torus, as well
as the vertical positioning of the pattern.  I used the data from your recent
Twitter post to estimate the arc of the side of the vase, and using the chord
length and depth of that putative circle segment, calculated the radius of the
required circle.  I used the vertical height of the maximal external radius of
the vase, since that made the most sense, in terms of the machining operation.

(I'm going to try to use the data points from scanning the vase to fit a circle
using the least-squares stuff, and see what happens with that)

****
And here's what's interesting:   The curvature/shape of the vase seems to be
reasonably consistent with that below the handles, and only deviates above that.
 Of course, that's as far as a tool traveling along a fixed arc could make it
before beginning to machine away the torus that would eventually give rise to
the handles.  Also, the only significant deviation from that curvature is right
along the centerline of the two circles.
Owning a lathe myself, this would typically be the area that an operator is most
likely to accidentally come in contact with, either with a tool, the tool
support, or some other fixture or tool being moved in close proximity to the
spinning work.

4.  I think it might be a prudent change of tactics to think about how the vase
would have been machined - the order of operations, and see if that inspires any
new ideas and areas of investigation.

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Attachments:
Download 'vaselemoncomparison.png' (1167 KB)

Preview of image 'vaselemoncomparison.png'

Op 12/03/2023 om 18:46 schreef Bald Eagle:
> I've been going over this a bit with, and following the excellent work of Marián
> Marčiš, and I just sent him this email regarding my most recent work on the
> vase:
> 
That is a *very* good comment Bill. Thanks for sharing.

I don't know if you know the archaeological work at the Apollo Temple in 
Dydima, Turkey. Scratched on the inner walls of the sanctuary are the 
faint outlines of the construction plans made by the architects, and 
they did use geometry pretty close to what you describe. The same for 
the columns (some very subtle design indeed!) etc. No 'magic' was used! 
;-) ...and neither did I when I modelled the temple in Moray, Silo, and 
finally POV.

In other Ancient World sites identical architectural plans have been 
found, e.g. in Rome.

It has been a long while since I read up on this (20+ years) and I don't 
know if I still have documentation about these matters. I shall investigate.

-- 
Thomas

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Thomas de Groot <tho### [at] degrootorg> wrote:

> That is a *very* good comment Bill. Thanks for sharing.

Thanks - it's always hard to know where these things will lead, and hopefully
there are a lot more interesting and educational discoveries to be made.


> I don't know if you know the archaeological work at the Apollo Temple in
> Dydima, Turkey. Scratched on the inner walls of the sanctuary are the
> faint outlines of the construction plans made by the architects, and
> they did use geometry pretty close to what you describe. The same for
> the columns (some very subtle design indeed!) etc.

Looks like the big article I'd like to lay my hands on is

Lothar Haselberger
Scientific American
Vol. 253, No. 6 (December 1985), pp. 126-133 (10 pages)

It's on JSTOR is anyone has access.
https://www.jstor.org/stable/24967878

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Op 13/03/2023 om 20:00 schreef Bald Eagle:
> Thomas de Groot <tho### [at] degrootorg> wrote:
> 
>> That is a *very* good comment Bill. Thanks for sharing.
> 
> Thanks - it's always hard to know where these things will lead, and hopefully
> there are a lot more interesting and educational discoveries to be made.
> 
I am sure there are indeed.

> 
>> I don't know if you know the archaeological work at the Apollo Temple in
>> Dydima, Turkey. Scratched on the inner walls of the sanctuary are the
>> faint outlines of the construction plans made by the architects, and
>> they did use geometry pretty close to what you describe. The same for
>> the columns (some very subtle design indeed!) etc.
> 
> Looks like the big article I'd like to lay my hands on is
> 
> Lothar Haselberger
> Scientific American
> Vol. 253, No. 6 (December 1985), pp. 126-133 (10 pages)
> 
> It's on JSTOR is anyone has access.
> https://www.jstor.org/stable/24967878
> 
>
That's him indeed. Unfortunately, I do not have access. :-(

-- 
Thomas

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This is about the Pantheon in Rome, but it mentions Didyma.

https://journal.eahn.org/article/id/7477/

-- 
Thomas

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You're really not going to believe this:

https://unsigned.io/artefact-analysis/

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Le 2023-03-18 à 13:37, Bald Eagle a écrit :
> 
> You're really not going to believe this:
> 
> https://unsigned.io/artefact-analysis/
> 
Yes, hard to believe how hard some peoples work to impose some arbitrary 
meaning to some objects or proportions.

«Conclusions In Summary

Based on the best understanding we currently have of the object, and on 
the knowledge of normal fundamental limits of physics and laws of 
nature, we have to conclude:

     That this object was fabricated on a highly sophisticated 
subtractive manufacturing system, from a solid piece of granite.
     That the manufacturing system would require, at the very least, 
sophisticated mechanical technology and high-precision components.
     That the manufacturing system would necessarily have been guided by 
an automated control system, which could read the design as input, and 
produce the required motions as output.
     That a turing machine, of considerable sophistication, would most 
likely have been employed to create and operate on the design, and to 
finally transfer it to the manufacturing system.

There is no way, in which we can attribute the production of this 
artefact, to anyone who do not possess, at minimum, the level of 
technological sophistication and capabilities mentioned above. This 
raises some very interesting questions regarding the origin of the 
object, which we hope to be able to explore in future work.»

WHY does the author totally ignore that it could have been made entirely 
by hand WITHOUT any technology more advanced than Bronze age tools and 
lot of available time.
Once roughly carved, the object can get meticulously refined and 
smoothed by hand.

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On 2023-03-18 16:10 (-4), Alain Martel wrote:
> Le 2023-03-18 à 13:37, Bald Eagle a écrit :
>>
>> You're really not going to believe this:
>>
>> https://unsigned.io/artefact-analysis/
>>
> Yes, hard to believe how hard some peoples work to impose some arbitrary
> meaning to some objects or proportions.
> 
> «Conclusions In Summary
> 
> [snip]
> 
> There is no way, in which we can attribute the production of this
> artefact, to anyone who do not possess, at minimum, the level of
> technological sophistication and capabilities mentioned above. This
> raises some very interesting questions regarding the origin of the
> object, which we hope to be able to explore in future work.»

ALIENS!

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Alain Martel <kua### [at] videotronca> wrote:

> WHY does the author totally ignore that it could have been made entirely
> by hand WITHOUT any technology more advanced than Bronze age tools and
> lot of available time.
> Once roughly carved, the object can get meticulously refined and
> smoothed by hand.

Because they never tried. Because they have no clue what can be achieved with
simple hand tools and time. Because they don't think about the amount of time
one had in those days. Time to observe, time to learn a skill, time to produce.

ingo

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Op 19-3-2023 om 08:08 schreef ingo:
> Alain Martel <kua### [at] videotronca> wrote:
> 
>> WHY does the author totally ignore that it could have been made entirely
>> by hand WITHOUT any technology more advanced than Bronze age tools and
>> lot of available time.
>> Once roughly carved, the object can get meticulously refined and
>> smoothed by hand.
> 
> Because they never tried. Because they have no clue what can be achieved with
> simple hand tools and time. Because they don't think about the amount of time
> one had in those days. Time to observe, time to learn a skill, time to produce.
> 
> ingo
> 

Amen.

I was going to answer exactly in this same vein indeed. That whole 
"sophisticated" mathematical description just doesn't prove... anything 
at all about the real technical skill of ancient sculptors.

-- 
Thomas

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