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Tuesday, July 19th 2016

21:14

More on the Golden Taj Mahal

  • STATE OF EXISTENCE: jittery

T­­his entry is a continuation of the previous one, as well as being a part of the lengthy series of phi. I might just mention that, in terms of our physical states, June and I are doing okay. We are still waiting to hear what Dr. B is going to do about some of June’s test results of a couple of weeks ago, and waiting gets old pretty quickly, as we all know.

So, once again I escape into the real world of real numbers, exploring the uses and misuses of phi. I mean, what we used to consider the “real” world has become so surreal at the moment that I can’t bring myself to write on it. Besides, there’s no shortage of commentaries on that realm. So I seek shelter in the part of the world that’s not going to change and its Creator. If you’re tired of reading about phi, or never were interested to begin with, I understand. But please don’t repeat the time-worn myths after passing up this opportunity to reflect on the matter under the gentle guidance of your devoted bloggist.

In the previous entry, I focused on one particular set of pictures supposedly showing how the golden ratio shows up in the entryway to the Taj Mahal, but that this case rests on a glaring mistake, which anyone should have been able to catch apart from knowing any math. Actually, if you examine a larger area than the entry gate, the reason for this strange placement of the golden rectangle entry becomes a little clearer, but no less arbitrary. There seems to be an additional desire for bigger and better golden rectangles, and the inconsistency concerning the entryway not only remains, but is actually expanded by some further dubious interpolations.

I’m going back to the broadly circulated set of pictures that I labeled Pictures 1 and 2 last time. Here is Picture 1 by itself, and, in order to make it easier to talk about what’s happening here, I’ve labeled some important junctures of the lines with letters.

Taj Mahal Lines

Among the various lines, two apparent golden rectangles are created. One can be described by ACFH, and the other one by BDEG.

Taj Mahal Side Rectangles

These two rectangles can only be golden if they overlap. My measurements fall into the levels of tolerance that we cannot help but allow for. Each rectangle starts from the inside of the opposite decorative door frame and goes either left or right to the edge of the building as it is visible in a picture straight onto the front. These extensions are supposed to be squares, and we know that a square added to a golden rectangle creates a new, larger golden rectangle.

Taj Mahal Side Squares

In this illustration, the two squares are ABGH and CDEF—together with rectangle BCFG—are thought to make up two new golden rectangles.  

The idea of two golden rectangles created by overlap is clever, though it would have required a lot of subtlety on the part of the architects of the Taj Mahal. I can’t say how such a construction would fit in with the supposed aesthetic appeal of phi. Is our vision supposed to shift back and forth, first catching this rectangle, then that one? For all that I know, such may be the theory and, given the initial assumptions, it could be true, I suppose. But it’s also a leap, and I'm not convinced of the assumptions. We’ve already found that the golden rectangle, as placed in in the entryway, compromises the light-colored decorative frame as a feature of the building (which is then covered up in the alleged close-up shot that I have called Picture 2 in the previous entry). I don’t know which idea came first, the two larger, overlapping golden rectangles or the imposition of the golden ratio on the entryway. Regardless, in either case, the arbitrary choice with regard to the doorway is still a hindrance.

Moreover, we also need to question the geometrical integrity of the two supposed squares. It should be immediately obvious that points A and D have no architectural anchorage whatsoever. They appear above the balustrade cutting through the small turrets at no particular locations of interest, except that they mark the end of the straight line outward from C to A and from B to D. The internet illustration make it just as clear as my depictions. Here is how it looks on one side:

Taj Mahal No Squares

The fact of the matter is that these squares simply do not exist. The front of the building ends before the square is finished and the wall is bent at an angle to form a new facet of the  chamfered corner. (I just learned the word “chamfer.” It’s a decoration on what would otherwise be the stark edge of a 90° corner.) In the picture below you see how the top line of the supposed square ADFH does not stay on course heading left from B to I, though one can blame the photographic angle for that apparent anomaly. However, the shift at points I and J is integral to the building itself since the building has an edge there and begins a new facet. The decorations of the Taj include some optical illusions, but this is not one of them. There is no square here, but an edge in three-dimensional space, and I don’t think that it would occur to anyone looking at the Taj in real life, rather than as a flat picture, to see a square at these locations. I, for one, didn’t. Consequently, when combined with the contrived rectangle of the entry way, there is still no golden rectangle here. But, as I keep insisting, numbers are beautiful, but beauty does not depend on certain numbers. 

 

 

4 Comment(s).

Posted by Dan from D&O Celtic Jewelry:

I design a lot of jewelry around symbols found in nature. When I wrote this post, I had just designed a pentagram pendant for someone. The #1 question I get asked is what these various symbols mean. After a while it was easier to write them up and direct people to my web site for answers.

I got the information about the Golden Ratio from various web sites and what a friend of mine shared with me. I do not pretend to be an expert. I only used the Fibonacci spiral picture because it had the rectangles showing the Golden Ratio. It is pretty clear to me that the Taj Mahal is a great example of the Golden Ratio in design, so I am not sure what the point was in all of this.

-Dan

This comment has been moderated by the blog owner

Wednesday, August 24th 2016 @ 23:51

Posted by Winfried Corduan:

Dan, I hope you understood that there is no ill will towards you in my discussion. How could there be, since I don't even know you? I made sure to underscore that attitude by providing links to your business. It looks like you produce good stuff, and I really appreciate your seriousness about the symbols you incorporate.
The point of using your picture of the Taj Mahal as an example was simply to illustrate that some well-meaning folks get misled into finding the golden ratio in places where it simply cannot be. More specifically, your golden rectangle starts at the base of the building, but then goes way up into the sky. How can one claim that the Taj Mahal exhibits the golden ratio when the rectangle that is supposed to surround it stretches far above the actual building?
If you would like me to take you and your picture out of my discussion, I'll be glad to do so. From where I sit, I'd much rather you took that misleading picture off your site--in which case I need to drop the reference to your site anyway.
Again, as I said in my entry, I don't want to hurt people, and please forgive me if I did so, despite my best intentions. My concern has been correctness with regard to phi and the golden ratio. Thanks. Win
Thursday, August 25th 2016 @ 17:06

Posted by Dan at D&O Celtic Jewelry:

Winfried,

The passage that seemed to indicate that I was somehow trying to profit by spreading misconcpetions was confusing and it could easily be interpreted the way I did.

If you Google "Taj Mahal Golden Rectangle", my blog shows up on page 4 of the results. So there are many people who are seeing the same thing I am seeing. I updated the image to show what dimensions I feel appear to have a Golden Ratio. No, the entire building does not fit perfectly into a Golden Rectangle. The contention is that the ratio of certain dimensions appear "Golden".

This entire thing could have been avoided if you had simply contacted me before you did this post. I would have made the same corrections that I have made to my post, and I might have still let you discuss this on your own site. I might have also returned the favor and linked to your site as a resource for people to learn more about this subject. I'd still be willing to entertain this idea if you revise or remove this post.

Dan
Thursday, August 25th 2016 @ 18:41

Posted by Winfried Corduan:

Dan, consider it done. Win
Thursday, August 25th 2016 @ 19:05

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