Thanks to Roger for checking my analysis.
He notes that my calculations for the full tower's afternoon-prayer
shadow-line follows the curve generated by Fer de Vries' software. (Fer
verified this for me as well.) Roger's point of difference is what to do
with the memorial's unique two-height Tower of Voices gnomon, with the
deep slot cut down its spine:
Your procedure of changing the gnomon height to force
curvature does tend to keep the line in the trees near
the winter solstice. This seems to be one of several extra
steps in your analysis to force the data to fit the
hypothesis. Such extra explanations would be cut out by
Occam's Razor.
I would just make a couple of points here. First, the two-height gnomon
is a direct result of applying Occam's Razor. The height of the full
height gnomon is determined, not by the upraised crescent tips of of the
gnomon's crescent shaped top, but by the bottom of the crescent at the
top of the tower. Only the bottom of the crescent forms a consistent
gnomon. The upper crescent tips are ten feet apart, defining very
different tower locations, but the bottom of the crescent is a
consistent location. Following this same rule--going to the highest
point of solid shadow--automatically yields the lower tower height later
in the year when sun through the upper slot starts reaching the ground
at Islamic prayer times.
Second, Occam's Razor calls for the simplest explanation of the facts,
but it doesn't call for simplifying the facts. The fact is, if one is to
look at this tower as a gnomon, it is indeed a tricky two height gnomon.
This is the work of the designers, not me, and there is only one way
that I can see to account for it. I think my explanation is actually
quite simple. If this is an Islamic prayer-time sundial then the
designers perpetrated a fraud against the Park Foundation, which is a
federal crime. Anyone contemplating such a crime would want to try to
get away with it, which would require hiding it, hence the tricky
two-height gnomon.
The alternative hypothesis is that the prayer-shadow-line falls
consistently within the first ellipse of trees by coincidence. But then
it would have to also be a coincidence that a line drawn across the tips
of the surrounding crescent of trees points almost precisely towards
Mecca, as does the bisector of the giant red maple crescent down at the
crash site. These coincidences would require a new theory of
probability, which again is inconsistent with Occam's Razor.
There are uncertainties in my analysis, stemming from discrepancies in
the site-plan PDFs. I will see if I can get ahold of a more complete set
of plans, and will put up a link here if I succeed.
Thanks to Roger and Fer and everyone else for your interest. You people
are a wonderful resource and I just want everyone to know how much I
appreciate it.
Sincerely,
Alec Rawls
-----Original Message-----
From: Roger Bailey [mailto:[EMAIL PROTECTED]
Sent: Wednesday, October 12, 2005 1:25 PM
To: Alec Rawls; [email protected]
Subject: [SPAM] RE: Hidden sundial discovery, fixed position hafir with
dual-height gnomon
Hello Alec and all,
On 16 September I noted the "controversy brewing over the proposed
memorial marking where Flight 93 was taken down on 9/11. People are
rightfully outraged that the memorial selected is a red crescent
(crescent of embrace) and its axis is pointed at Mecca. What an
inappropriate if inadvertent symbol. See
http://www.flight93memorialproject.org/crescent_of_embrace.asp
for the official story and
http://forum.chronwatch.com/forum/viewtopic.php?t=20960 for one of many
strong opinions on this subject."
I was surprised when no one commented on this posting. Your message
brought up the topic of the Flight 93 Memorial again, this time with a
direct sundial connection, a hidden "hafir" sundial using the "Tower of
Voices" to show the Moslem afternoon (asr) time of prayer. After reading
your note and linked blog, I wrote to you off list to say I was willing
to check your analysis. Here is a summary of this review based on my
knowledge of sundials
(extensive) and Moslem traditions (limited).
I agree that the concentric oval sections in the shadow of the tower
look somewhat like the hafir sundial figure (F3Hafir 40.gif) from the
article** by de Vries, Mattox and Oglesby. I also agree that your
calculations of the shadow path from the top of the tower for the asr
time of prayer is essentially correct and falls on the broad band of
trees. But in my opinion, this data does not really support your
premise that the "Tower of Voices" is a hafir sundial. Given two equally
predictive theories, I tend to use Occam's Razor* and choose the
simpler.
Moslem pray times are generally astronomically defined. See James
Morrison's sml note "East and West" 17 September and the de Vries
article**. From this article, the figure F3 attached shows the noon and
afternoon prayer time shadow lengths plotted in polar coordinates
through the year. The concentric oval shape that looks like the
concentric arcs of trees at the memorial is due only to the method of
plotting in a circle. As you know, the resulting sundial is not fixed
but must to be turned around the vertical gnomon to orient the sun
shadow to the date to read the prayer time. Many portable altitude dials
like Shepard's Cylinders work in similar ways.
There are many examples of sundials showing Moslem prayer time lines.
Check this example, a drawing by Claude-Henri Eyraud of a very complex
horizontal dial with five gnomons and many lines at Kairouan, Tunisia.
The asr prayer line "Nasr" is cast by the north gnomon.
http://www.ens-lyon.fr/RELIE/Cadrans/Musee/Kairouan/PlanKairouan.pdf
Here is the link to the description in French based on pictures by Rene
Rohr. You can use google languages to translate it from French.
http://www.ens-lyon.fr/RELIE/Cadrans/Musee/Kairouan/Kairouan.htm
I will you send off list more pictures of vertical declining sundials on
mosques in Istanbul with similar prayer lines.
The shadow lines for prayer times on a fixed surface are quite different
from the ovals in F3. In your blog site article, figure 4, they are
the
outer pink lines. Fer de Vries' ZW2000 program *** has the option of
calculating the Moslem prayer lines. The attached figure F2 Prayers.gif
is an example from ZW2000 showing the lines for zuhr, asr-awwal and
asr-tani for the latitude of the memorial site. These lines are not a
close or natural fit to the curved arc of trees at the memorial site.
Between the two solstice declination lines the prayer lines are hour
lines curved near the summer solstice and straightening out towards the
winter solstice. If you had seen these figures first, I doubt that you
would have come to the conclusion that the was a hidden sundial. Your
procedure of changing the gnomon height to force curvature does tend to
keep the line in the trees near the winter solstice. This seems to be
one of several an extra step in your analysis to force the data to fit
the hypothesis. Such extra explanations would be cut out by Occam's
Razor.
Although I don't agree with your hypothesis, I do agree that the
memorial must be changed. There cannot be any possible suggestion that
the memorial appears to be a red crescent oriented to Mecca with a
minaret showing Moslem prayer times. It must be a memorial for the
victims, not the perpetrators. It doesn't matter if the architect is a
trickster, negligent or incompetent, the design is fatally flawed.
Let's Roll!
Roger Bailey
Walking Shadow Designs
N 48.6 W 123.4
* See http://en.wikipedia.org/wiki/Occam's_Razor
** See "Hafir and Halazun" Fer J. de Vries, Mac Oglesby, William S.
Maddux, NASS Compendium 6-2 June 1999 or
http://home.iae.nl/users/ferdv/haf-hal2.htm
and the ZW2000 program at
*** http://www.de-zonnewijzerkring.nl/eng/index-vlakke-zonw.htm
-
