Friday, October 07, 2005
Crescent Tower is Islamic prayer sundial
Is the Tower of Voices from the Crescent of Embrace memorial for Flight 93 an Islamic sundial? Islamic prayer times are determined by shadow positions. Muslims are instructed to commence afternoon prayers (called Asr prayers), when the length of an object’s shadow is the length of its mid-day shadow, plus the object's height. The “Tower Section” detail from the Crescent of Embrace PDF’s gives the tower height as 93 feet. Plugging this height, and the latitude and longitude of the crash site, into J. Giesen’s awesome Sun Shadow Applet, it is easy to calculate for any date the exact direction and length of the Tower’s shadow at the time for Asr prayers. The following graphic plots mid-month Asr-prayer-time shadows on the Tower Plan for June through October.
Figure 1: Asr prayer shadows for June 16th (the shortest day of the year) in red; July 16th, in green; August 16th, in blue; September 16th, in yellow; October 16th, in orange. Scroll down to Part II for calculations.
After October, the tower’s shadow at Asr prayer times takes on a different shape. The tower itself is a long extruded crescent. It is cut at the top on a 45 degree angle with the crescent tips reaching up into the sky away from the sun, enhancing the crescent shape at the end of the tower’s shadow (visible in figure 1). Another feature of the tower is a pair of substantial slots cut vertically into the sun-side of the tower, one at the bottom and one at the top.
Figure 2. Looking up the crescent shaped tower. Notice the substantial slot, cut maybe a quarter of the way down the spine of the tower, starting at the top. A similar slot at the bottom forms a doorway from the sun-side of the tower into its crescent shaped bottom. The upper tip of the bottom slot is visible at bottom of the graphic.
At all of the mid-month Asr prayer times up through October, sunlight comes through this slot at so much of an angle from the side that it gets blocked by the east-side crescent arm. By November, this has changed. Asr prayer times have started coming early enough in the day that at least some of the sunlight coming through the slot at the top of the tower is unblocked by the crescent walls when Asr prayer time is reached.
This transition point is actually depicted in the Tower Plan, excerpted in figure 1 above. Notice that the shadow depicted in the plan has thin strips of sunlight coming through the slots at the top and the bottom of the tower. The tower shadow in this graphic is pointing exactly 45 degrees from north. (Add 180 degrees to get the corresponding azimuth of the sun: 225 degrees from north.) On what date do Asr prayers correspond to an azimuth of 225 degrees? November 1st, according to the Sun Shadow Applet.
How much before November 1st sunlight might make it through the slots at Asr prayer time one cannot tell for certain from the PDF's, but the Tower Plan graphic seems to be depicting a very thin vertical of sunlight getting through the slots at this point, indicating that as the sun continues west, this vertical of sunlight will quickly get closed out. What we can say for certain is that from November 1st on, sunlight passing through the slots will reach the ground at Asr prayer times.
The sunlight coming through the upper slot at Asr prayer times defines a second tower height, corresponding to the bottom of the upper slot. Only below the slot will the tower shadow become solid. (I applied the same rule for determining the upper tower height, measuring to the bottom of the shadow-casting crescent rather than to its upward reaching tips. This is also why I am measuring shadow length starting from the sun-side of the tower. The bottom of the upper crescent, and the bottom of the upper slot, are both features of the sun-side of the tower.)
How much lower is the lower tower height? Just look at the how far down the upper shaft of sunlight comes in the tower shadow from figure 1. These graphics are all CAD generated, and as anyone who has ever used Computer Aided Design programs knows, illumination tools calculate the actual shadows that the defined structures would cast, given a specified light source. Using pixel counts, the tower to the bottom of the upper slot is 82% of the height of the tower to the bottom of the upper crescent. Using this height to determine mid-November and mid-December Asr-shadows yields the following full set of mid-month Asr-prayer shadows:
Figure 3. Same as figure 1, plus Asr-prayer shadows for mid-November (aqua); and mid-December (fuchsia). Again, calculations are detailed in Part II, below. The mid-January Asr-prayer shadow will be the same as for mid-November. Mid-February will be the same as mid-October, etcetera.
Lastly, I added in the implied Asr-prayer-line, using November 1st as the transition date between upper and lower tower heights:
Figure 4. On any day of the year, when the lowest point of the top of the tower's shadow reaches the outer pink line, Asr prayer time has arrived. Notice that the prayer line remains contained within the inner arc of trees.
It sure looks like Murdoch designed the Tower of Voices to be a very clever and reasonably accurate Asr-prayer-sundial. There are some contra-indications however.
First, the Tower Section detail of the PDF’s shows the upper slot to be only 8% of the full tower height, less than 8 feet out of 93, not the 18% rendered in the tower shadow shown in the Tower Plan. So which is the true design? Figure 2, looking up the inside of the tower, also shows the upper slot extending much more than 1/12th of the way down. Is the Tower Section detail a deception, so that if someone tries to calculate shadow positions and compare them with Asr prayer times, they will be thrown off? That would be pretty exotic behavior on the part of the designers, but remember, what is being tested here is the hypothesis that the designers have indeed built hidden Islamic meaning into the Crescent memorial. In other words, the hypothesis is that the designers HAVE engaged in some very exotic behavior. Thus the need to invoke exotic behavior as an explanatory device does not necessarily serve as counter-evidence.
In any case, the Tower Section does not match up with the other two tower graphics. Either it does not depict the actual design or they do not depict the actual design. The fact that the tree line tracks the Asr-prayer line for five months makes me suspect that the correct graphic (the one depicting the actual design) is the one that continues this pattern to the end of the year. The only way to tell for certain is to get hold of Murdoch's computers.
Another discrepancy is how the Tower Section detail shows the tower standing on a mound that rises almost ten feet above the surrounding grade level. Does this mean that the full tower height is actually 103 feet, not 93 feet?
"Tower Section" detail. Shows short vertical slots top and bottom and shows land to east and northeast of Tower to slope away from Tower base.
But here too, the Tower Section is inconsistent with the other drawings. The main Crescent PDF contains a topo map that shows the ground sloping upwards from the tower to the northeast and east (where Asr-prayer shadows land). In the 50 odd meters from the tower to the inner ellipse of trees, the ground could easily come up 10 feet. If it does, then there would still be a rise to the Tower platform from the west (the view depicted in the Tower Section), but the land from there to the trees on the opposite side would be level. If this is not what is happening, if the ellipses of trees actually remain below the tower platform on all sides, then the height of the platform should be added to the height of the tower when calculating the length of Asr-prayer-time shadows. The resulting Asr shadows would still follow the contour of the first and second ellipses of trees, but they would fall approximately between these rows of trees rather than remaining contained within the first ellipse of trees.
INTERJECTION/UPDATE: I found a legible topo map of the Tower site on TerraServer . The grade DOES slop upwards from the tower towards the northeast, at just a little less than 10 feet per 50 meters. Below is the Tower part of the topo from the site-plan PDF, and a snippet of the Terra-server map.
Tower site with Topo lines. Hard to read.
TerraServer topo map of same site. The red cross marks tower site (as best as I can eye-ball it). The blue line angles 27 degrees above east (the middle of the arc swept by Asr-prayer-shadows), and 112 pixels long (100x51). The scale (according to TerraServer) is 2 meters/pixel. Thus the grade rises 40 feet in 224 meters heading in the prayer-shadow direction.
This proves that the Tower Section detail is out of whack. Apparently whoever worked out this little scheme was afraid that the sundialists would nail him! Lot’s of other stuff is hidden in the Crescent memorial, but it has all been there in the plans to find. This is the first thing I have come across where the plans themselves are deceptive.
The upshot for the sundial analysis is that the height of the tower above where its shadows land seems to be the 93 feet indicated on the Tower Section detail. All the platform does is bring the bottom of the tower up to the level of the inner ellipse of trees.
Of course there could be some grading plan that would change this. Again, we would have to get hold of Murdoch’s computers to be sure of the plan. What we can be certain of (END INTERJECTION) is that from June through October, Asr-prayer-time shadows follow the contour of the ellipses of trees pretty much exactly. Also certain is that after October, Asr-prayer-time shadows cast by the crescent at the top of the tower no longer follow the contour of the ellipses of trees, but sunlight passing through the upper slot will during this period reach the ground at Asr prayer time, defining a lower tower height that brings Asr-prayer-time shadows back closer to the contour of the inner ellipse of trees (all the way back to the original contour if the slot is cut as deeply as indicated in the Tower Plan).
That’s pretty damning. I don’t think it would be possible to do that by accident, any more than I think that the other Islamist features I have discovered in the Crescent plan could possibly be by accident. A brief review:
New visitors may not have seen my earlier report, detailing my discovery that the memorial wall, down near the crash site, has a separate upper section, precisely centered on the huge crescent of red maple trees. To see the calculations verifying this precise centering, or the details of anything else I summarize here, visit the earlier post.
So there is a separate section of memorial wall, centered so as to make it integral with the larger crescent structure, while the lower memorial wall, the one with forty translucent blocks inscribed with the names of the forty murdered Americans, sits off to the side. Who could that upper memorial wall be for? Looking closely, it also has translucent blocks. Three of them it turns out. But there were four terrorists. Forty four dead. Forty three translucent blocks? If the upper memorial wall is a memorial to the terrorists (turning the entire structure into a memorial for the terrorists, with Americans on the side) then where is the forty-fourth translucent block?
It turns out that there IS a forty-fourth translucent block, also on the line of the flight path that the two sections of memorial wall lie along. It is the large glass block at the upper crescent tip, the one that dedicates the entire site.
View up the flight path from the crash site. Lower and upper sections of memorial wall on left. Forty-fourth translucent block at Portal above. Artist left out copse to allow clear view of flight path.
This hidden-in-plain-sight forty-fourth translucent block is, like the tricky two-height sundial tower, part of a pattern of seeming contra-indications which, when examined closely, reveal intent. First, there is a copse of trees that sits almost exactly on the center-line of the huge red maple crescent that gives the Crescent of Embrace its name.
Crescent and star.
If the copse sat exactly on the center line of the crescent, it would be positioned exactly as the star on an Islamic flag. Such positioning would be indefensible, but when one looks closely, to see what there is about the upper third of the copse that might explain why the crescent if centered on this part of the copse, one finds the upper section of memorial wall.
Then there is the second mystery. If this wall is a memorial to the terrorists why does it only contain three translucent blocks? This leads to the discovery of the forty-fourth translucent block, which in turn resolves the most important contra-indication of all. When the tips of the red maple crescent are defined by the furthest extents of the red maple trees, the orientation of the crescent is 1.7 degrees off Mecca. Is the pattern of precision behind seeming imprecision repeated here as well?
Just draw a precise Mecca line through the center of the circle that the red crescent partly inscribes and see what crescent tips it defines. The bottom crescent tip is unambiguous. There is a last red maple sitting directly on the circle of the crescent. It is at the top where a spray of features makes alternative crescent tips possible. Drawing a perpendicular to the true Mecca line inwards along the Mecca line until it hits the unambiguous bottom crescent tip, what crescent tip is defined on top? The large glass block dedicating the entire site. The forty-fourth translucent block on the flight path to death.
Could this be come kind of coincidence to the 100th power? A coin flip coming up heads a hundred times in a row? No. Because if you go back up to the Tower of voices, you find exactly the same two orientations planted in the array of crescent shaped lines of trees surrounding the Tower. This was the subject of my first report on the Tower of Voices (subsequent to my report on the upper terrorist-memorial wall). The two most protruding crescent tips point the same 1.7 degrees off Mecca that the red maple crescent does. There is then a second available choice for the lower crescent tip, slightly less obvious, but the obvious second choice, that creates a second orientation, this time precisely on Mecca (as precisely as the pixel resolution of the graphics can determine).
Graphic from my first Tower of Voices post. Red line, crossing two outer most crescent tips, is 1.7 degrees off Mecca. Aqua line, crossing four other crescent tips, and the next crescent tip in at the bottom, orients precisely on Mecca.
Can it be a coincidence that the two orientations of the main crescent, one 1.7 degrees off Mecca, one precisely on Mecca, are duplicated in the Tower array? What are we up to now, five hundred heads in a row? Is the object here to NOT believe the evidence, no matter how many times over it constitutes proof? Not for me it isn’t. But if anyone is unpersuaded, here are a hundred more heads in a row:
In addition to constituting an Islamic prayer-time sundial, the Tower of Voices has a couple of other notable features. There are dozens of ways to draw lines out from the tower to the many different features of the array of trees around the Tower. There are only three ways, however, to draw lines outward from the tower that cross the ends of two or more rows of trees. All three are significant.
INTERJECTION/UPDATE/POSSIBLE-NONSENSE-ALERT: Looking more closely, I found 3 or 4 more rays from the tower that touch multiple tips of rows of trees, none of which, at first glance, have any obvious significance, so the seeming significance of the first three may be…just a random run of unlucky coin tosses. The first three, as originally described:
Line 1: exactly fifteen degrees counterclockwise from north, three rows of trees end along the same ray out from the tower. [(x, y pixels) at 300% zoom = (-62, 231).] Fifteen degrees west of north is the precise angle of the flight path into the crash site.
Three lines from the tower touch the ends of more than one row of trees: 1) flight path (orange); 2) line to center of giant crescent (blue); 3) line to upper tip of giant crescent (red).
Line 2: moving around to thirty degrees clockwise from north, a line coming in from the northeast to the tower is touched on its upside by the end of an outer crescent of trees and on its lower side by the end of an inner crescent of trees. If this line is extended to the southeast, it touches the end of another crescent of trees. Extended down towards the crash site, this line goes through the exact center-point of the red maple crescent. [ (x, y pixels) = (178, 310).]
Both of these features are innocuous. They simply tie the site together and do not in themselves convey any Islamic or Jihadist meaning. They do however, make clear that the designer has intentionally used lines through the tower that cross the tips of multiple rows of trees to indicate meaningful directions. This suggests that the exact Mecca line, crossing four crescent tips, is indeed intended. It also makes the third direction out from the tower that crosses multiple crescent tips not too much of a surprise.
Line 3: come up 8 degrees clockwise from the line between the Tower and the center of the crescent. At that angle (38 degrees from north) a ray out from the tower crosses two of the lower crescent tips. [(x, y pixels) = (164, 210).] Extend this line down towards the large red crescent, and it points directly at the upper red crescent tip, the location of the large glass block that dedicates the entire site and defines the precise Mecca orientation of the large crescent.
To the casual observer, this third direction from the Tower would also seem innocuous. It points to the place where the flight path enters the memorial, the place where the site is dedicated. What is wrong with that? Nothing, unless you know that the glass block dedicating the site defines a second orientation of the red crescent, pointing exactly to Mecca, and that it is the forty fourth translucent block on the flight path, implicating the fourth terrorist (and hence the other three). Very clever. The stinker who designed this loves to hide in plain sight.
END POSSIBLE-NONSENSE ALERT
That the crescents of trees point by themselves directly towards Mecca (instead of just implicating the red crescent, and its orientation towards Mecca) is necessary to complete the Islamist design. If the tower indicates Muslim prayer times, as it does, the faithful are going to need to know which way to face. Just go stand on a straight line between the most protruding crescent tips, face the northeast tip, and you are facing 1.7 degrees from Mecca. Good enough. Move in a few feet to the left and look down the line that connects three crescent tips and you are facing Mecca exactly. Can’t miss.
Two features of the tower itself are also significant. Notice that on the Tower Plan, the elliptical platform on which the tower is built, is depicted with a dark outline extending around a symmetrical portion of its northeast tip. (The Tower Section detail reveals this line to be a short solid wall that serves as a bench.) A line due north from the edge of the tower hits right at the end of this stone or concrete bench.
Black arc ends directly north of trailing shadow edge of tower (red vertical).
Thus the end of the arc shaped bench provides a reasonably accurate marker for the time of shortest shadow, which is one of the five times each day that Muslims are called upon by their religion to pray. Due north is not a precise indicator of shortest shadow, because the Earth wobbles in its orbit. To provide a precise indicator of mid-day prayers, the end of the bench would have to be stepped, with each step representing a pair of months, or signs of the zodiac, telling an observer just where the shadow line should fall to indicate mid-day at a given time of year. Some such feature may have been planned. The Crescent of Embrace PDF’s that are available from the Park Foundation do not contain that level of detail.
Finally, there is the crescent shape of the tower, the crescent shape of the tip of the shadow that it casts, and its name, the Tower of Voices. I was prompted to look into the tower portion of the memorial by commentators who noted that the tower not only looks like a stylized minaret, but that a minaret is a literal “tower of voices,” from which religious functionaries cry out the daily calls to prayer in Islamic locales. Turns out these commentators were right in their suspicions. The Tower tells the time for Islamic prayers. It’s a gigantic minaret/Islamic-sundial, “visible from the highway,” as the site plans brag.
None of us would be too surprised to discover that a “liberal” multi-culturalist architect thought it would be a nice idea to include Islam in the memorial to Flight 93. After all, this unfortunate misunderstanding we are involved in with the Islamo-fascists has two sides, right? Isn’t our goal is to appreciate each other? And we all know that violence is never the answer, blah, blah, blah. Of course the heroes of Flight 93 proved the opposite, but this memorial is much more than multi-culturalism run amok. This is a thorough-going memorial to the terrorists. Every main feature of the entire structure is either determined by, or multiply tied in with, the upper section of memorial wall (the terrorist memorial wall) and the forty-fourth translucent block on the flight path (the fourth terrorist memorial block).
It is hard to imagine that Murdoch was not at least a full co-conspirator in this evil. If it was just the red crescent and the placement of the upper memorial wall, and the orientation on Mecca, the landscape architect might conceivably have snuck in those parts of the terrorist memorial on his own, but the Tower of Voices is multiply tied in as well. The only plausible explanation is that Murdoch tried to defraud the federal government on behalf of the terrorists. That is a federal crime. He and his associates need to be hauled before Congress for questioning and likely prosecution.
One of the revelations for me in pursuing this investigation is the astounding range of powerful analytical tools that are available to anyone over the internet. When I wanted to check whether the Crescent of Embrace site plan is oriented towards true north, I was able to compare features on the site plan to features visible on Google Earth and verify that north on the site plan is a smidgen off of true north. (I suppose it could also be Google that is a smidgen off of true north, but the two are close enough to determine that the site plan is at least not based on magnetic north, and represents the architects’ understanding of true north.)
When I was wondering whether the culprit could be the landscape architect Nelson Woltz, I came across a crescent shaped amphitheater he installed at Westminister Presbetyrian Church in Charlottesville. I tried to see on Google Earth if the amphitheater is oriented towards Mecca but the photos did not have enough resolution, so I googled “Charlottesville aerial photos,” found a set of high rez photos commissioned by the city, and was able to clear Woltz of suspicion in this earlier case. The internet is stacked!
To analyze the sundial operation of the Tower of Voices, I called upon a host of internet resources I had no idea existed. Qibla.org has a calculator that gives Islamic prayer times for any longitude and latitude. Giesen’s Sun Shadow Applet is a tool developed for sundial enthusiasts that calculates the shadow that any object, vertical or tilted, will cast at any time of day, at any point in the world, and it is child’s play to use.
The Sun Shadow Applet gives results in polar coordinates. When I needed to translate these into Cartesian coordinates, I used the online coordinate translator provided by The Kusashi Group. These resources make it possible for anyone to plot the tower-sundial’s Asr-prayer shadows to the pixel on their computer screen. If anyone wants to verify my calculations, the steps are as follows.
Step 1 is easy. The Tower Section gives the tower height as 93 feet to the bottom of the upper crescent. If you want to add the height of the tower base, just count pixels. Zoom in on the Tower Section in the Tower of Voices PDF, take a screen shot (Alt + Print Screen), paste into Microsoft Paint, and use the line tool to count pixels in the attached scale. Zooming to 200%, I get 24 ft = 115 pixels. (I’m not certain, but I think this should be the same on every viewscreen, regardless of resolution.) The height of the base then measures 46 pixels = 9.6 feet. I leave out the height of the base in my shadow calculations, assuming that the topo map is right and the ground rises between the tower and the trees. Someone else may want to calculate exactly how much further out the Asr-prayer shadow line will fall if I am wrong.
Step 2: For the tower height to the base of the slot, I use 82% of 93 feet, giving me as my two tower heights, 28.35 meters and 23.25 meters. (I convert to meters because the Sun Shadow Applet uses meters. Feet to meter converter available here.)
Step 3 is to pick a date and use the Sun Shadow Applet to find the length of the shortest shadow on that day (the mid-day shadow), and the time of day when the Tower’s shadow is the length of the noon shadow plus the tower height (the time when Asr prayers are supposed to commence). A shortcut is just to look up the Asr prayer time on an Islamic prayer finder. Comparing the two methods verifies that they yield identical results.
For instance, for June 16th (the shortest day of the year), qibla.org says that Asr prayers at the Flight 93 crash site should commence at 4:15 PM. (Set the qibla.org calculator to the coordinates of the crash site: 40.3 N latitude and 78.54 degrees W longitude. Turn off the Daylight Savings Time option, and set the hour to -5 GMT.) That this is the correct Asr-prayer time can be verified using the Sun Shadow Applet. Plug the crash site coordinates into the Applet, turn off its Daylight Savings Time option, set hours to -5 GMT, set the shadow-caster height to 28.35 meters, then poke around for the time of shortest shadow. (Sundialists call a sundial’s shadow-caster a “gnomon.”) On June 16th, the time of shortest shadow turns out to be 12:15 PM, when the Tower of Voices will cast a shadow 8.631 meters long. Thus Muslims should begin afternoon prayers when the Tower shadow is 36.981 meters long (8.631 meters + 28.35 meters).
The Applet gives the shadow length at 4:15 PM (the Asr-prayer time indicated by qibla.org) as 37.231 meters, which is about a foot longer than the exact Asr shadow length. A minute earlier yields a shadow length of 36.975, which is only off by a couple of inches, and is still longer than the exact Asr shadow length (Asr prayers are supposed to commence AFTER the prescribed shadow length has been reached), so maybe qibla.org is off by one minute with its Asr-prayer time, but close enough. They obviously are using the noon shadow + height method and are calculating it pretty accurately. Thus instead of poking around with the Shadow Applet looking for precise Asr prayer times, I just use the qibla.org calculations.
Qibla.org also allows users to calculate Asr prayer times using a second method (“hanafi” rather than “shafii”), where prayer time is defined by a shadow length of noon-shadow plus TWICE the tower’s height. I haven’t worked through that set of calculations yet, but it will be interesting to see where these hanafi shadows land.
Step 4 is to take the polar coordinates of the Asr prayer shadows (degrees and meters) and convert them to Cartesian coordinates (meters and meters), then into pixels. I’ll work through the calculations for June 16th (the shortest day of the year) in detail, then present the remaining the mid-month calculations through December in summary form.
June 16th, 2005
Qibla.org places the Asr prayer time for June 16th at 4:15 PM. For this date and time, the Shadow Applet yields a shadow 37.21 meters long at an azimuth of 270.4 degrees clockwise from north. Looking away from the sun instead of towards the sun, this direction becomes 90.4 degrees clockwise from north (270.4 – 180). Subtract this from 90 and multiply by -1 to get degrees up from east of -.4.
Degrees up from east is the polar orientation assumed by the Kusashi coordinate translator. Put the shadow length in the “modulus” box and the angle in the “argument” box. Leave the optional +/- boxes empty and press “compute.” The resulting “real” component is the Cartesian x and the resulting “imaginary” component is the Cartesian y. Translating to (x,y) coordinates, (37.21 meters, -.4 degrees) becomes (37.21 meters, -.19 meters). This then has to be converted to pixels on the Tower Plan, which uses a different scale than the Tower Section detail. On the Tower Plan (at 1200% zoom), 694 pixels = 480 ft. = 146.304 meters. Thus 1 meter = 4.74 pixels. Translating from meters to pixels yields (x, y) pixel coordinates for the top of end of the tower shadow of (176, -1).
Performing the same calculations for the other mid-month dates yields:
July 16th
Asr = 4:19 PM; (modulus, argument) = (38.54, 2); (x, y) in meters = (38.52, 1.35); (x, y) in pixels = (183, 6), which is virtually on top of the line for June, and just a few pixels longer. The changes become more rapid as the sun gets lower.
August 16th
Asr = 4:09 PM; (mod, arg) = (43.38, 10.9); (x, y meters) = (42.6, 8.2); (x, y pixels) = (202, 39).
September 16th
Asr = 3:41 PM; (mod, arg) = (51.21, 24.1); (x, y meters) = (46.75, 20.91); (x, y pixels) = (222, 99).
October 16th
Asr = 3:06 PM; (mod, arg) = (62.23, 38); (x, y meters) = (49.04, 38.31); (x, y pixels) = (232, 182).
November 16th
For November and December, there are two shadow ends to calculate, one taking the bottom of the top crescent to be the top of the tower and one taking the bottom of the upper slot to be the top of the tower.
Is there a historical precedent for this kind of Islamic-prayer-time sundial? It turns out that Islamic sundials exist, but that they are not designed as fixed emplacements. Rather, they are portable constructs with the months of the year inscribed in a circle around the outside. The user rotates the sundial so that the current time of year is oriented along the shadow line. When the shadow of the sundial’s vertical reaches the prayer-line for that date, it’s time to face Mecca.
On the left: an ancient hâfir, with daylight divided into 12 hours. On the right: a modern hâfir, with day and night divided into 24 equal length hours. Only hour lines are shown. Prayer lines are a bit more circular, since prayer times get earlier as the sun gets lower.
A hâfir's prayer lines. Actual hâfirs contain both hour lines and prayer lines, here separated for clarity. Graphics from the sundial page of de Vries, Oglesby and Maddux.
De Vries, Oglesby and Maddux say they have found no existing examples of historical sundials that would qualify as hâfirs.
[[[CORRECTION. I had originally said that De Vries, Oglesby and Maddux had not found examples of fixed position Islamic Sundials, but such a sundial would by definition NOT be a hâfir, and hence is not what they were referring to. Thanks to Fer de Vries for pointing out my mistake. Notice that with this correction (and my understanding that there is nothing unique about a fixed position Islamic sundial) the following two paragraphs don't make any sense.
NONSENSE ALERT. The Following two PP's left in only people have already commented on them.
No tricky dual-height tower would be needed to make a fixed position Islamic prayer sundial. Just mark a line on the ground that follows the Asr-prayer-time shadows of a single height vertical. This would, however, create a shape that does not LOOK like a traditional hâfir.
Is this why Murdoch went with the tricky dual-height tower? Notice that the traditional hâfir has an ellipsoid shape very similar to the ellipses of trees surrounding the Tower of Voices. The two-height tower allows the Tower of Voices to pay homage to the traditional variable-position hâfir while still giving reasonably accurate Asr-prayer-time readings from a fixed position sundial. It also hides the sundial’s Islamic nature behind a layer of misdirection.
END NONSENSE ALERT. The zig zag asr line is a bit of misdirection, but the sensible explanation for it is so that the tree line will not be immediately recognized by a competent sundialist as a traditional fixed position Islamic sundial. BEGIN WARLIKE THOUGHTS ALERT.]]]
This is the kind of invention that scholarly monks produce, with an unhealthy dose of Islam’s religiously sanctioned deception (“taqiyya”) thrown in for bad measure. It is brilliant, really, if you happen to be a stinking Islamo-fascist moron. Not that I’m against clever Islamic representations in general. Only when they are incorporated in a terrorist memorial.
The implication seems to be that Murdoch is some kind of secretly festering Ayatollah Khomeini. How does that happen? Hard to figure. But there is no denying it. Murdoch, or someone who pulled the wool over his eyes, is an Islamo-fascist. What are we are up to now, a thousand heads in a row? Isn’t that more quarks than exist in the universe? As I argued in my first report, these kinds of constructs can no more be random than a monkey can sit down and type a page of Iago ON THE FIRST TRY. In a thousand eons of random arrangements, a maximally accurate dual-height, Asr sundial, together with a mid-day prayer indicator, set in an array of crescents oriented precisely on Mecca, might pop up by chance, but if an architect sits down and produces it on the first try, it is NOT chance.
Then there is the fact that the Tower’s Islamic coincidences coincide in multiple ways with the Crescent memorial’s other page of Iago: the terrorist memorial wall and crescent, also oriented precisely on Mecca. This is pure evil. This IS Iago, living amongst us. He needs to be uncovered and destroyed, as do all of his Wahabbist, Salafist, Jihadist ilk. Islamo-fascism is conspiracy to commit murder. Every last person who has made an adult choice to follow the Islamo-fascist path needs to be dead. American William Joyce was executed for treason by the British after WWII for his role as the axis radio propagandist Lord Haw Haw. We aren’t hanging traitors these days, but we ought to be.
Figure 1: Asr prayer shadows for June 16th (the shortest day of the year) in red; July 16th, in green; August 16th, in blue; September 16th, in yellow; October 16th, in orange. Scroll down to Part II for calculations.
After October, the tower’s shadow at Asr prayer times takes on a different shape. The tower itself is a long extruded crescent. It is cut at the top on a 45 degree angle with the crescent tips reaching up into the sky away from the sun, enhancing the crescent shape at the end of the tower’s shadow (visible in figure 1). Another feature of the tower is a pair of substantial slots cut vertically into the sun-side of the tower, one at the bottom and one at the top.
Figure 2. Looking up the crescent shaped tower. Notice the substantial slot, cut maybe a quarter of the way down the spine of the tower, starting at the top. A similar slot at the bottom forms a doorway from the sun-side of the tower into its crescent shaped bottom. The upper tip of the bottom slot is visible at bottom of the graphic.
At all of the mid-month Asr prayer times up through October, sunlight comes through this slot at so much of an angle from the side that it gets blocked by the east-side crescent arm. By November, this has changed. Asr prayer times have started coming early enough in the day that at least some of the sunlight coming through the slot at the top of the tower is unblocked by the crescent walls when Asr prayer time is reached.
This transition point is actually depicted in the Tower Plan, excerpted in figure 1 above. Notice that the shadow depicted in the plan has thin strips of sunlight coming through the slots at the top and the bottom of the tower. The tower shadow in this graphic is pointing exactly 45 degrees from north. (Add 180 degrees to get the corresponding azimuth of the sun: 225 degrees from north.) On what date do Asr prayers correspond to an azimuth of 225 degrees? November 1st, according to the Sun Shadow Applet.
How much before November 1st sunlight might make it through the slots at Asr prayer time one cannot tell for certain from the PDF's, but the Tower Plan graphic seems to be depicting a very thin vertical of sunlight getting through the slots at this point, indicating that as the sun continues west, this vertical of sunlight will quickly get closed out. What we can say for certain is that from November 1st on, sunlight passing through the slots will reach the ground at Asr prayer times.
The sunlight coming through the upper slot at Asr prayer times defines a second tower height, corresponding to the bottom of the upper slot. Only below the slot will the tower shadow become solid. (I applied the same rule for determining the upper tower height, measuring to the bottom of the shadow-casting crescent rather than to its upward reaching tips. This is also why I am measuring shadow length starting from the sun-side of the tower. The bottom of the upper crescent, and the bottom of the upper slot, are both features of the sun-side of the tower.)
How much lower is the lower tower height? Just look at the how far down the upper shaft of sunlight comes in the tower shadow from figure 1. These graphics are all CAD generated, and as anyone who has ever used Computer Aided Design programs knows, illumination tools calculate the actual shadows that the defined structures would cast, given a specified light source. Using pixel counts, the tower to the bottom of the upper slot is 82% of the height of the tower to the bottom of the upper crescent. Using this height to determine mid-November and mid-December Asr-shadows yields the following full set of mid-month Asr-prayer shadows:
Figure 3. Same as figure 1, plus Asr-prayer shadows for mid-November (aqua); and mid-December (fuchsia). Again, calculations are detailed in Part II, below. The mid-January Asr-prayer shadow will be the same as for mid-November. Mid-February will be the same as mid-October, etcetera.
Lastly, I added in the implied Asr-prayer-line, using November 1st as the transition date between upper and lower tower heights:
Figure 4. On any day of the year, when the lowest point of the top of the tower's shadow reaches the outer pink line, Asr prayer time has arrived. Notice that the prayer line remains contained within the inner arc of trees.
It sure looks like Murdoch designed the Tower of Voices to be a very clever and reasonably accurate Asr-prayer-sundial. There are some contra-indications however.
First, the Tower Section detail of the PDF’s shows the upper slot to be only 8% of the full tower height, less than 8 feet out of 93, not the 18% rendered in the tower shadow shown in the Tower Plan. So which is the true design? Figure 2, looking up the inside of the tower, also shows the upper slot extending much more than 1/12th of the way down. Is the Tower Section detail a deception, so that if someone tries to calculate shadow positions and compare them with Asr prayer times, they will be thrown off? That would be pretty exotic behavior on the part of the designers, but remember, what is being tested here is the hypothesis that the designers have indeed built hidden Islamic meaning into the Crescent memorial. In other words, the hypothesis is that the designers HAVE engaged in some very exotic behavior. Thus the need to invoke exotic behavior as an explanatory device does not necessarily serve as counter-evidence.
In any case, the Tower Section does not match up with the other two tower graphics. Either it does not depict the actual design or they do not depict the actual design. The fact that the tree line tracks the Asr-prayer line for five months makes me suspect that the correct graphic (the one depicting the actual design) is the one that continues this pattern to the end of the year. The only way to tell for certain is to get hold of Murdoch's computers.
Another discrepancy is how the Tower Section detail shows the tower standing on a mound that rises almost ten feet above the surrounding grade level. Does this mean that the full tower height is actually 103 feet, not 93 feet?
"Tower Section" detail. Shows short vertical slots top and bottom and shows land to east and northeast of Tower to slope away from Tower base.
But here too, the Tower Section is inconsistent with the other drawings. The main Crescent PDF contains a topo map that shows the ground sloping upwards from the tower to the northeast and east (where Asr-prayer shadows land). In the 50 odd meters from the tower to the inner ellipse of trees, the ground could easily come up 10 feet. If it does, then there would still be a rise to the Tower platform from the west (the view depicted in the Tower Section), but the land from there to the trees on the opposite side would be level. If this is not what is happening, if the ellipses of trees actually remain below the tower platform on all sides, then the height of the platform should be added to the height of the tower when calculating the length of Asr-prayer-time shadows. The resulting Asr shadows would still follow the contour of the first and second ellipses of trees, but they would fall approximately between these rows of trees rather than remaining contained within the first ellipse of trees.
INTERJECTION/UPDATE: I found a legible topo map of the Tower site on TerraServer . The grade DOES slop upwards from the tower towards the northeast, at just a little less than 10 feet per 50 meters. Below is the Tower part of the topo from the site-plan PDF, and a snippet of the Terra-server map.
Tower site with Topo lines. Hard to read.
TerraServer topo map of same site. The red cross marks tower site (as best as I can eye-ball it). The blue line angles 27 degrees above east (the middle of the arc swept by Asr-prayer-shadows), and 112 pixels long (100x51). The scale (according to TerraServer) is 2 meters/pixel. Thus the grade rises 40 feet in 224 meters heading in the prayer-shadow direction.
This proves that the Tower Section detail is out of whack. Apparently whoever worked out this little scheme was afraid that the sundialists would nail him! Lot’s of other stuff is hidden in the Crescent memorial, but it has all been there in the plans to find. This is the first thing I have come across where the plans themselves are deceptive.
The upshot for the sundial analysis is that the height of the tower above where its shadows land seems to be the 93 feet indicated on the Tower Section detail. All the platform does is bring the bottom of the tower up to the level of the inner ellipse of trees.
Of course there could be some grading plan that would change this. Again, we would have to get hold of Murdoch’s computers to be sure of the plan. What we can be certain of (END INTERJECTION) is that from June through October, Asr-prayer-time shadows follow the contour of the ellipses of trees pretty much exactly. Also certain is that after October, Asr-prayer-time shadows cast by the crescent at the top of the tower no longer follow the contour of the ellipses of trees, but sunlight passing through the upper slot will during this period reach the ground at Asr prayer time, defining a lower tower height that brings Asr-prayer-time shadows back closer to the contour of the inner ellipse of trees (all the way back to the original contour if the slot is cut as deeply as indicated in the Tower Plan).
That’s pretty damning. I don’t think it would be possible to do that by accident, any more than I think that the other Islamist features I have discovered in the Crescent plan could possibly be by accident. A brief review:
Misdirection and resolution as architectural method
New visitors may not have seen my earlier report, detailing my discovery that the memorial wall, down near the crash site, has a separate upper section, precisely centered on the huge crescent of red maple trees. To see the calculations verifying this precise centering, or the details of anything else I summarize here, visit the earlier post.
So there is a separate section of memorial wall, centered so as to make it integral with the larger crescent structure, while the lower memorial wall, the one with forty translucent blocks inscribed with the names of the forty murdered Americans, sits off to the side. Who could that upper memorial wall be for? Looking closely, it also has translucent blocks. Three of them it turns out. But there were four terrorists. Forty four dead. Forty three translucent blocks? If the upper memorial wall is a memorial to the terrorists (turning the entire structure into a memorial for the terrorists, with Americans on the side) then where is the forty-fourth translucent block?
It turns out that there IS a forty-fourth translucent block, also on the line of the flight path that the two sections of memorial wall lie along. It is the large glass block at the upper crescent tip, the one that dedicates the entire site.
View up the flight path from the crash site. Lower and upper sections of memorial wall on left. Forty-fourth translucent block at Portal above. Artist left out copse to allow clear view of flight path.
This hidden-in-plain-sight forty-fourth translucent block is, like the tricky two-height sundial tower, part of a pattern of seeming contra-indications which, when examined closely, reveal intent. First, there is a copse of trees that sits almost exactly on the center-line of the huge red maple crescent that gives the Crescent of Embrace its name.
Crescent and star.
If the copse sat exactly on the center line of the crescent, it would be positioned exactly as the star on an Islamic flag. Such positioning would be indefensible, but when one looks closely, to see what there is about the upper third of the copse that might explain why the crescent if centered on this part of the copse, one finds the upper section of memorial wall.
Then there is the second mystery. If this wall is a memorial to the terrorists why does it only contain three translucent blocks? This leads to the discovery of the forty-fourth translucent block, which in turn resolves the most important contra-indication of all. When the tips of the red maple crescent are defined by the furthest extents of the red maple trees, the orientation of the crescent is 1.7 degrees off Mecca. Is the pattern of precision behind seeming imprecision repeated here as well?
Just draw a precise Mecca line through the center of the circle that the red crescent partly inscribes and see what crescent tips it defines. The bottom crescent tip is unambiguous. There is a last red maple sitting directly on the circle of the crescent. It is at the top where a spray of features makes alternative crescent tips possible. Drawing a perpendicular to the true Mecca line inwards along the Mecca line until it hits the unambiguous bottom crescent tip, what crescent tip is defined on top? The large glass block dedicating the entire site. The forty-fourth translucent block on the flight path to death.
Could this be come kind of coincidence to the 100th power? A coin flip coming up heads a hundred times in a row? No. Because if you go back up to the Tower of voices, you find exactly the same two orientations planted in the array of crescent shaped lines of trees surrounding the Tower. This was the subject of my first report on the Tower of Voices (subsequent to my report on the upper terrorist-memorial wall). The two most protruding crescent tips point the same 1.7 degrees off Mecca that the red maple crescent does. There is then a second available choice for the lower crescent tip, slightly less obvious, but the obvious second choice, that creates a second orientation, this time precisely on Mecca (as precisely as the pixel resolution of the graphics can determine).
Graphic from my first Tower of Voices post. Red line, crossing two outer most crescent tips, is 1.7 degrees off Mecca. Aqua line, crossing four other crescent tips, and the next crescent tip in at the bottom, orients precisely on Mecca.
Can it be a coincidence that the two orientations of the main crescent, one 1.7 degrees off Mecca, one precisely on Mecca, are duplicated in the Tower array? What are we up to now, five hundred heads in a row? Is the object here to NOT believe the evidence, no matter how many times over it constitutes proof? Not for me it isn’t. But if anyone is unpersuaded, here are a hundred more heads in a row:
Other tower features
In addition to constituting an Islamic prayer-time sundial, the Tower of Voices has a couple of other notable features. There are dozens of ways to draw lines out from the tower to the many different features of the array of trees around the Tower. There are only three ways, however, to draw lines outward from the tower that cross the ends of two or more rows of trees. All three are significant.
INTERJECTION/UPDATE/POSSIBLE-NONSENSE-ALERT: Looking more closely, I found 3 or 4 more rays from the tower that touch multiple tips of rows of trees, none of which, at first glance, have any obvious significance, so the seeming significance of the first three may be…just a random run of unlucky coin tosses. The first three, as originally described:
Line 1: exactly fifteen degrees counterclockwise from north, three rows of trees end along the same ray out from the tower. [(x, y pixels) at 300% zoom = (-62, 231).] Fifteen degrees west of north is the precise angle of the flight path into the crash site.
Three lines from the tower touch the ends of more than one row of trees: 1) flight path (orange); 2) line to center of giant crescent (blue); 3) line to upper tip of giant crescent (red).
Line 2: moving around to thirty degrees clockwise from north, a line coming in from the northeast to the tower is touched on its upside by the end of an outer crescent of trees and on its lower side by the end of an inner crescent of trees. If this line is extended to the southeast, it touches the end of another crescent of trees. Extended down towards the crash site, this line goes through the exact center-point of the red maple crescent. [ (x, y pixels) = (178, 310).]
Both of these features are innocuous. They simply tie the site together and do not in themselves convey any Islamic or Jihadist meaning. They do however, make clear that the designer has intentionally used lines through the tower that cross the tips of multiple rows of trees to indicate meaningful directions. This suggests that the exact Mecca line, crossing four crescent tips, is indeed intended. It also makes the third direction out from the tower that crosses multiple crescent tips not too much of a surprise.
Line 3: come up 8 degrees clockwise from the line between the Tower and the center of the crescent. At that angle (38 degrees from north) a ray out from the tower crosses two of the lower crescent tips. [(x, y pixels) = (164, 210).] Extend this line down towards the large red crescent, and it points directly at the upper red crescent tip, the location of the large glass block that dedicates the entire site and defines the precise Mecca orientation of the large crescent.
To the casual observer, this third direction from the Tower would also seem innocuous. It points to the place where the flight path enters the memorial, the place where the site is dedicated. What is wrong with that? Nothing, unless you know that the glass block dedicating the site defines a second orientation of the red crescent, pointing exactly to Mecca, and that it is the forty fourth translucent block on the flight path, implicating the fourth terrorist (and hence the other three). Very clever. The stinker who designed this loves to hide in plain sight.
END POSSIBLE-NONSENSE ALERT
That the crescents of trees point by themselves directly towards Mecca (instead of just implicating the red crescent, and its orientation towards Mecca) is necessary to complete the Islamist design. If the tower indicates Muslim prayer times, as it does, the faithful are going to need to know which way to face. Just go stand on a straight line between the most protruding crescent tips, face the northeast tip, and you are facing 1.7 degrees from Mecca. Good enough. Move in a few feet to the left and look down the line that connects three crescent tips and you are facing Mecca exactly. Can’t miss.
Two features of the tower itself are also significant. Notice that on the Tower Plan, the elliptical platform on which the tower is built, is depicted with a dark outline extending around a symmetrical portion of its northeast tip. (The Tower Section detail reveals this line to be a short solid wall that serves as a bench.) A line due north from the edge of the tower hits right at the end of this stone or concrete bench.
Black arc ends directly north of trailing shadow edge of tower (red vertical).
Thus the end of the arc shaped bench provides a reasonably accurate marker for the time of shortest shadow, which is one of the five times each day that Muslims are called upon by their religion to pray. Due north is not a precise indicator of shortest shadow, because the Earth wobbles in its orbit. To provide a precise indicator of mid-day prayers, the end of the bench would have to be stepped, with each step representing a pair of months, or signs of the zodiac, telling an observer just where the shadow line should fall to indicate mid-day at a given time of year. Some such feature may have been planned. The Crescent of Embrace PDF’s that are available from the Park Foundation do not contain that level of detail.
Finally, there is the crescent shape of the tower, the crescent shape of the tip of the shadow that it casts, and its name, the Tower of Voices. I was prompted to look into the tower portion of the memorial by commentators who noted that the tower not only looks like a stylized minaret, but that a minaret is a literal “tower of voices,” from which religious functionaries cry out the daily calls to prayer in Islamic locales. Turns out these commentators were right in their suspicions. The Tower tells the time for Islamic prayers. It’s a gigantic minaret/Islamic-sundial, “visible from the highway,” as the site plans brag.
None of us would be too surprised to discover that a “liberal” multi-culturalist architect thought it would be a nice idea to include Islam in the memorial to Flight 93. After all, this unfortunate misunderstanding we are involved in with the Islamo-fascists has two sides, right? Isn’t our goal is to appreciate each other? And we all know that violence is never the answer, blah, blah, blah. Of course the heroes of Flight 93 proved the opposite, but this memorial is much more than multi-culturalism run amok. This is a thorough-going memorial to the terrorists. Every main feature of the entire structure is either determined by, or multiply tied in with, the upper section of memorial wall (the terrorist memorial wall) and the forty-fourth translucent block on the flight path (the fourth terrorist memorial block).
It is hard to imagine that Murdoch was not at least a full co-conspirator in this evil. If it was just the red crescent and the placement of the upper memorial wall, and the orientation on Mecca, the landscape architect might conceivably have snuck in those parts of the terrorist memorial on his own, but the Tower of Voices is multiply tied in as well. The only plausible explanation is that Murdoch tried to defraud the federal government on behalf of the terrorists. That is a federal crime. He and his associates need to be hauled before Congress for questioning and likely prosecution.
Part II: calculations
One of the revelations for me in pursuing this investigation is the astounding range of powerful analytical tools that are available to anyone over the internet. When I wanted to check whether the Crescent of Embrace site plan is oriented towards true north, I was able to compare features on the site plan to features visible on Google Earth and verify that north on the site plan is a smidgen off of true north. (I suppose it could also be Google that is a smidgen off of true north, but the two are close enough to determine that the site plan is at least not based on magnetic north, and represents the architects’ understanding of true north.)
When I was wondering whether the culprit could be the landscape architect Nelson Woltz, I came across a crescent shaped amphitheater he installed at Westminister Presbetyrian Church in Charlottesville. I tried to see on Google Earth if the amphitheater is oriented towards Mecca but the photos did not have enough resolution, so I googled “Charlottesville aerial photos,” found a set of high rez photos commissioned by the city, and was able to clear Woltz of suspicion in this earlier case. The internet is stacked!
To analyze the sundial operation of the Tower of Voices, I called upon a host of internet resources I had no idea existed. Qibla.org has a calculator that gives Islamic prayer times for any longitude and latitude. Giesen’s Sun Shadow Applet is a tool developed for sundial enthusiasts that calculates the shadow that any object, vertical or tilted, will cast at any time of day, at any point in the world, and it is child’s play to use.
The Sun Shadow Applet gives results in polar coordinates. When I needed to translate these into Cartesian coordinates, I used the online coordinate translator provided by The Kusashi Group. These resources make it possible for anyone to plot the tower-sundial’s Asr-prayer shadows to the pixel on their computer screen. If anyone wants to verify my calculations, the steps are as follows.
Step 1 is easy. The Tower Section gives the tower height as 93 feet to the bottom of the upper crescent. If you want to add the height of the tower base, just count pixels. Zoom in on the Tower Section in the Tower of Voices PDF, take a screen shot (Alt + Print Screen), paste into Microsoft Paint, and use the line tool to count pixels in the attached scale. Zooming to 200%, I get 24 ft = 115 pixels. (I’m not certain, but I think this should be the same on every viewscreen, regardless of resolution.) The height of the base then measures 46 pixels = 9.6 feet. I leave out the height of the base in my shadow calculations, assuming that the topo map is right and the ground rises between the tower and the trees. Someone else may want to calculate exactly how much further out the Asr-prayer shadow line will fall if I am wrong.
Step 2: For the tower height to the base of the slot, I use 82% of 93 feet, giving me as my two tower heights, 28.35 meters and 23.25 meters. (I convert to meters because the Sun Shadow Applet uses meters. Feet to meter converter available here.)
Step 3 is to pick a date and use the Sun Shadow Applet to find the length of the shortest shadow on that day (the mid-day shadow), and the time of day when the Tower’s shadow is the length of the noon shadow plus the tower height (the time when Asr prayers are supposed to commence). A shortcut is just to look up the Asr prayer time on an Islamic prayer finder. Comparing the two methods verifies that they yield identical results.
For instance, for June 16th (the shortest day of the year), qibla.org says that Asr prayers at the Flight 93 crash site should commence at 4:15 PM. (Set the qibla.org calculator to the coordinates of the crash site: 40.3 N latitude and 78.54 degrees W longitude. Turn off the Daylight Savings Time option, and set the hour to -5 GMT.) That this is the correct Asr-prayer time can be verified using the Sun Shadow Applet. Plug the crash site coordinates into the Applet, turn off its Daylight Savings Time option, set hours to -5 GMT, set the shadow-caster height to 28.35 meters, then poke around for the time of shortest shadow. (Sundialists call a sundial’s shadow-caster a “gnomon.”) On June 16th, the time of shortest shadow turns out to be 12:15 PM, when the Tower of Voices will cast a shadow 8.631 meters long. Thus Muslims should begin afternoon prayers when the Tower shadow is 36.981 meters long (8.631 meters + 28.35 meters).
The Applet gives the shadow length at 4:15 PM (the Asr-prayer time indicated by qibla.org) as 37.231 meters, which is about a foot longer than the exact Asr shadow length. A minute earlier yields a shadow length of 36.975, which is only off by a couple of inches, and is still longer than the exact Asr shadow length (Asr prayers are supposed to commence AFTER the prescribed shadow length has been reached), so maybe qibla.org is off by one minute with its Asr-prayer time, but close enough. They obviously are using the noon shadow + height method and are calculating it pretty accurately. Thus instead of poking around with the Shadow Applet looking for precise Asr prayer times, I just use the qibla.org calculations.
Qibla.org also allows users to calculate Asr prayer times using a second method (“hanafi” rather than “shafii”), where prayer time is defined by a shadow length of noon-shadow plus TWICE the tower’s height. I haven’t worked through that set of calculations yet, but it will be interesting to see where these hanafi shadows land.
Step 4 is to take the polar coordinates of the Asr prayer shadows (degrees and meters) and convert them to Cartesian coordinates (meters and meters), then into pixels. I’ll work through the calculations for June 16th (the shortest day of the year) in detail, then present the remaining the mid-month calculations through December in summary form.
June 16th, 2005
Qibla.org places the Asr prayer time for June 16th at 4:15 PM. For this date and time, the Shadow Applet yields a shadow 37.21 meters long at an azimuth of 270.4 degrees clockwise from north. Looking away from the sun instead of towards the sun, this direction becomes 90.4 degrees clockwise from north (270.4 – 180). Subtract this from 90 and multiply by -1 to get degrees up from east of -.4.
Degrees up from east is the polar orientation assumed by the Kusashi coordinate translator. Put the shadow length in the “modulus” box and the angle in the “argument” box. Leave the optional +/- boxes empty and press “compute.” The resulting “real” component is the Cartesian x and the resulting “imaginary” component is the Cartesian y. Translating to (x,y) coordinates, (37.21 meters, -.4 degrees) becomes (37.21 meters, -.19 meters). This then has to be converted to pixels on the Tower Plan, which uses a different scale than the Tower Section detail. On the Tower Plan (at 1200% zoom), 694 pixels = 480 ft. = 146.304 meters. Thus 1 meter = 4.74 pixels. Translating from meters to pixels yields (x, y) pixel coordinates for the top of end of the tower shadow of (176, -1).
Performing the same calculations for the other mid-month dates yields:
July 16th
Asr = 4:19 PM; (modulus, argument) = (38.54, 2); (x, y) in meters = (38.52, 1.35); (x, y) in pixels = (183, 6), which is virtually on top of the line for June, and just a few pixels longer. The changes become more rapid as the sun gets lower.
August 16th
Asr = 4:09 PM; (mod, arg) = (43.38, 10.9); (x, y meters) = (42.6, 8.2); (x, y pixels) = (202, 39).
September 16th
Asr = 3:41 PM; (mod, arg) = (51.21, 24.1); (x, y meters) = (46.75, 20.91); (x, y pixels) = (222, 99).
October 16th
Asr = 3:06 PM; (mod, arg) = (62.23, 38); (x, y meters) = (49.04, 38.31); (x, y pixels) = (232, 182).
November 16th
For November and December, there are two shadow ends to calculate, one taking the bottom of the top crescent to be the top of the tower and one taking the bottom of the upper slot to be the top of the tower.
Full tower height:December 16th
Asr = 2:38 PM; (mod, arg) = (77.143, 49.9); (x, y meters) = (49.69, 59.01); (x, y pixels) = (236, 280).
Shadow from bottom of upper slot:
82% of (236, 280) is (194, 230).
Full tower height:These are the shadow lines plotted in my figures 3 and 4 (using the lower tower heights for November and December).
Asr = 2.34 PM; (mod, arg) = (86.92 , 55.4); (x, y meters) = (49.36, 71.55); (x, y pixels) = (234, 339).
Shadow from bottom of upper slot:
82% of (234, 339) is (192, 278).
A new kind of hâfir?
Is there a historical precedent for this kind of Islamic-prayer-time sundial? It turns out that Islamic sundials exist, but that they are not designed as fixed emplacements. Rather, they are portable constructs with the months of the year inscribed in a circle around the outside. The user rotates the sundial so that the current time of year is oriented along the shadow line. When the shadow of the sundial’s vertical reaches the prayer-line for that date, it’s time to face Mecca.
On the left: an ancient hâfir, with daylight divided into 12 hours. On the right: a modern hâfir, with day and night divided into 24 equal length hours. Only hour lines are shown. Prayer lines are a bit more circular, since prayer times get earlier as the sun gets lower.
A hâfir's prayer lines. Actual hâfirs contain both hour lines and prayer lines, here separated for clarity. Graphics from the sundial page of de Vries, Oglesby and Maddux.
De Vries, Oglesby and Maddux say they have found no existing examples of historical sundials that would qualify as hâfirs.
[[[CORRECTION. I had originally said that De Vries, Oglesby and Maddux had not found examples of fixed position Islamic Sundials, but such a sundial would by definition NOT be a hâfir, and hence is not what they were referring to. Thanks to Fer de Vries for pointing out my mistake. Notice that with this correction (and my understanding that there is nothing unique about a fixed position Islamic sundial) the following two paragraphs don't make any sense.
NONSENSE ALERT. The Following two PP's left in only people have already commented on them.
No tricky dual-height tower would be needed to make a fixed position Islamic prayer sundial. Just mark a line on the ground that follows the Asr-prayer-time shadows of a single height vertical. This would, however, create a shape that does not LOOK like a traditional hâfir.
Is this why Murdoch went with the tricky dual-height tower? Notice that the traditional hâfir has an ellipsoid shape very similar to the ellipses of trees surrounding the Tower of Voices. The two-height tower allows the Tower of Voices to pay homage to the traditional variable-position hâfir while still giving reasonably accurate Asr-prayer-time readings from a fixed position sundial. It also hides the sundial’s Islamic nature behind a layer of misdirection.
END NONSENSE ALERT. The zig zag asr line is a bit of misdirection, but the sensible explanation for it is so that the tree line will not be immediately recognized by a competent sundialist as a traditional fixed position Islamic sundial. BEGIN WARLIKE THOUGHTS ALERT.]]]
This is the kind of invention that scholarly monks produce, with an unhealthy dose of Islam’s religiously sanctioned deception (“taqiyya”) thrown in for bad measure. It is brilliant, really, if you happen to be a stinking Islamo-fascist moron. Not that I’m against clever Islamic representations in general. Only when they are incorporated in a terrorist memorial.
The implication seems to be that Murdoch is some kind of secretly festering Ayatollah Khomeini. How does that happen? Hard to figure. But there is no denying it. Murdoch, or someone who pulled the wool over his eyes, is an Islamo-fascist. What are we are up to now, a thousand heads in a row? Isn’t that more quarks than exist in the universe? As I argued in my first report, these kinds of constructs can no more be random than a monkey can sit down and type a page of Iago ON THE FIRST TRY. In a thousand eons of random arrangements, a maximally accurate dual-height, Asr sundial, together with a mid-day prayer indicator, set in an array of crescents oriented precisely on Mecca, might pop up by chance, but if an architect sits down and produces it on the first try, it is NOT chance.
Then there is the fact that the Tower’s Islamic coincidences coincide in multiple ways with the Crescent memorial’s other page of Iago: the terrorist memorial wall and crescent, also oriented precisely on Mecca. This is pure evil. This IS Iago, living amongst us. He needs to be uncovered and destroyed, as do all of his Wahabbist, Salafist, Jihadist ilk. Islamo-fascism is conspiracy to commit murder. Every last person who has made an adult choice to follow the Islamo-fascist path needs to be dead. American William Joyce was executed for treason by the British after WWII for his role as the axis radio propagandist Lord Haw Haw. We aren’t hanging traitors these days, but we ought to be.
