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Sunday, July 17th 2016


The Golden Taj Mahal Revisited


I promised a couple of entries ago that, if I were to run across the misleading information concerning the Taj Mahal and the golden ratio again, I would  point out the website that carried it. As it has turned out, after a little more searching I found that the picture I had in mind is not on just one site, but is being copied from site to site, apparently without anyone looking at it too closely. In fact, it is sometimes paired with a second picture that is clearly inconsistent with the first one. The site I chose to mention comes from "Project Steam,"  and it is written in a gentle and friendly manner. The author provides a catchy response to the idea that, since phi's decimals extend to infinity, it cannot be applied anywhere as a measurement. If I may quote,

Now, I am not a mathematician; I am an artist. So my reaction to this argument is to shrug and say, “Meh, close enough.” If that sort of blasé attitude offends your mathy sensibilities, you should probably stop reading now.

The math fan inside of me is taken aback; my writer's instinct loves the prose. I compromise and say that, if you're writing about a subject, you still should avoid obvious goofs. I don't see any math errors. However my concern should be as clearly visible to the artist as to the recreational math fan, maybe even more so. As you know, I have been measuring the purported golden rectangles as depicted in various images by pixels. It's super-easy to do so with Paintshop Pro, and I assume similar programs, such as Photoshop, are just as good in that respect. However, in this case, measurements are totally unnecessary. You can see the manipulations without knowing any math. I doubt that the author of the post is the creator of these picture, but still, I don't understand how he could post them without noticing the glitch. 

Here are the two pictures in question, already combined into one image on that website so that a discrepancy should be easy to catch. 

project steam taj

Picture 1 (PS)                                                                                     Picture 2 (PS)

taj mahal golden fudgetaj mahal golden fudge

Picture 3 (mine)                                                     Picture 4 (mine)

I had remembered the adjustment correctly when I reported on it. Specifically, I recalled the placement of the golden rectangle at the entrance (Picture 1 and reproduced from memory in Picture 3), which did, indeed, come close enough to the value of phi to satisfy not merely the artist, but the casual math player in me. But then I realized that there was an issue with how the rectangle was arranged, namely with the top being above the light-colored frame, and the sides inside of it, as highlighted with the teal lines in Picture 4.  

And now, if I may, I would like to direct your attention to the close-up as shown in Picture 2 on the top right. In that picture the rectangle encloses the entire outside of that decorative frame. The difference is visually undeniable. My measurements came out to a ratio of 1 : 1.3, not close enough for anyone I would hope. How can one miss the difference in where the lines are drawn? Maybe the artistic author re-posted the pictures as he found them wherever he found them and didn't pay much attention because he didn't think it would make any difference. But it does; phi is all about a number, and a different number can't substitute for phi. I don't intend to drag out a lecture on the virtue of precision in whatever you do. "Good enough" may be--no, it is--good enough at times. However, if you're illustrating the golden ratio, and the illustrations are not illustrating the golden ratio, what good is what you're doing? The choice here seems to be between either an arbitrary golden rectangle that disregards the architecture and decorations or a rectangle that follows the features of the building, but not the golden ratio. 

My point, once again, is simply that golden-ratio-mania is leading people to find phi all over the world, linking the beauty of a building to a specific number, and imposing it on objects where it is neither present nor needed. I'm not opposed to finding the golden ratio where it is, and if it's contributing to the beauty of something, very well. But if we feel as though we need to find phi in some contorted way in every beautiful structure, we are doing ourselves and the object a disfavor because then we are mechanizing our aesthetic sensibility. 

I have had the privilege to visit the Taj Mahal. When you first walk onto the compound you cannot see it because your view is obstructed by a rather high wall, and you're too close to look over it. Then, once you walk through the inner gate, there it is, the Taj Mahal, right in front of you, larger than life--and incredibly beautiful. No reproduction that you've seen before can really do justice to the magnificent structure now in full view. Does it embody the golden ratio? I can't find it. Is it an unbelievably gorgeous sight? Absolutely. Would it be more beautiful if it did manifest the golden ratio? I don't see how it could be. 

Taj Mahal Entry Gate

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