Around 1990, Dr. George Markowsky, professor of computer science at the University of Maine, intended to present a talk about the wonders of the golden ratio to his school's Classics Club. Like any good scientist, he decided to double-check the "facts" before he repeated what he had read so often in textbooks, newspapers, and scholarly papers,¹ but his findings were not at all what he expected. "I collected all of the usual stories about the golden ratio being used to design the Great Pyramid and the Parthenon, as well as about its aesthetic properties and its use by painters," writes Markowsky. "I found the references to be quite vague, and in the process of trying to make my talk more precise, I actually began to look up measurements of buildings. Much to my surprise, the results did not support the claims that were being made about the golden ratio."² Markowsky's research resulted in a paper titled, "Misconceptions about the Golden Ratio," which appeared in the January 1992 edition of The College of Mathematics Journal.
One of the more interesting claims refuted in Markowsky's paper is the idea that the golden rectangle is the most "visually satisfying of all geometric forms."³ Using a diagram consisting of 48 randomly arranged rectangles all having the same height but with widths ranging from 0.4 times the height to 2.5 times the height,⁴ Markowsky informally surveyed attendees to his lectures to find which rectangle they most preferred. His results show the average person cannot pick out the golden rectangles within the diagram (there are two), and that, aesthetically speaking, the most pleasing rectangle has a ratio of 1.83 instead of Φ (the golden ratio).
Below is the diagram from Dr. Markowsky's paper featuring the 48 rectangles he presented to the people in his lectures. Using the format (row, column), which rectangle do you like most?
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¹ Markowsky, George (2005). Book Review: The Golden Ratio. Retrieved June 3, 2010 from {www.ams.org/notices/200503/rev-markowsky.pdf}.
² Idem.
³ Markowsky, George (1992). Misconceptions about the Golden Ratio. Retrieved June 3, 2010 from {www.math.nus.edu.sg/aslaksen/teaching/maa/markowsky.pdf}.
⁴ Idem.
15 comments:
(5,5)
It might be a stupid remark, but is it possible that movie frames ratios, widescreen TVs / computers changed our appreciation of height/length ratio, so that we are now more enclined towards wide rectangle ratios than to the shorter golden one? After all, the world is now invaded by widescreens, and cinemascope has a certain virtue, visually speaking, of making everything look a bit more gorgeous.
But, once again, it might be a naive supposition...
armel: there might be something in your theory. The standard aspect ratio for cinema projection in the USA is 1.85, not a million miles from the 1.83 value reported as optimally visually pleasing in the paper. Coincidence? :-)
I doubt it. The original book is from 1992 (as you can see below the article).
Don't forget that peoples perceptions are influenced by what is around, ie optical illusions. Most people would find it hard to pick which one they like with all the other rectangles around them. Put each rectangle on a single sheet and then get people to pick and you will get a different result.
I think what @CaptainJester is saying is right on. Correct me if I'm wrong but it seems like this Professor is missing the whole point. The point of things like the golden ratio and golden rectangle is that they are about visually pleasing _Relationships_ as they apply to the whole of what someone is looking at.
You can't just put a bunch of boxes on a page and expect to choose the one that conforms to the golden rectangle. I would guess that people's choice would have just as much to do with a boxes position on the page and the elements surrounding it as the ratio of the individual box.
Besides that, just on a anecdotal level, though these ideas don't work in every situation I think any artist will tell you that they are very useful and work most of the time. I know they have worked for me.
anonymous : I didn't think only of the last 10 years. Movies have been a great cultural influence on everyone for the past 60 years. The inventions of cinemascope and 1:1.85 are still prior to the writing of this book, I think, and, when speaking of computer and tv, I just wanted to say that the omnipresence of these ratios is now so that older, less extended rectangles, such as the Academy ratio, don't seem so appealing. In other words, what would have been true in 1992 would be even truer today.
It is interesting to see that Gone with the wind was shot in an academy ratio, but was then re-released in widescreen versions, cropped at the top & bottom, to look more gorgeous and epic. After all, this was far before 1992.
Having studied and used the root in compositions I can only say it works.
The fact that this man has found some discrepancies in here and there does not lessen the usefulness of the Golden Ratio from being a pretty good design template.
@jonathan and @jeff,
It isn't enough to say "I have made compositions, using the Golden Ratio, and they have worked."
You must also have a control group. You must be able to say "I have made similar compositions using similar, but different, ratios, such as 2:1, or 1.6:1, and they have not worked."
You didn't make it clear if that was the case.
Regarding the poll, people often choose what they are familiar with and ignore the rules.
Do you know the place on earth which is compatible to this golden ratio:
http://www.youtube.com/watch?v=xxSECWeVoKc
There's a saying that mathematicians and computer scientists are very smart but they are fools when they step outside their chosen professions.
I read the original paper and I think that the professor is missing the point. For example, in art, what matters is the *impression* the painting gives you. I'm pretty sure that if we were to create visual heat maps (where the eye wanders) of famous paintings, the golden rectangle would come up.
As for his rectangle-picking survey, the average human mind can only process a few items at a time. Give it an enormous haystack and of course it won't pick out the needle.
Why is φ (1.6180339...) an inherently more appealing ratio for a rectangle to have than say... 1.69 or 1.66, or even 1.5, 1.6, or 1.7? It makes little sense (from a visual point of view) to single out this exact ratio over any other, and I can only roll my eyes at those who fetishize and vehemently include it in their compositions. Just another trick used by the novice in an attempt to infuse their own art with flair, and yet another attempted shortcut to excellence in composition.
That is not to say that φ does not exist in nature or that φ was not used deliberately in some ancient artworks, but you will find more myths than truths about φ out there. I myself believed most of the claims about φ until I read Markowsky's article, and Keith Devlin's two articles: Link. Link.
On the topic of the rectangle diagram itself, the survey was an "informal experiment" as Markowsky said, so obviously it should only be taken for what it is; a digression into anecdote. The point he made in the article, however, remains valid.
@Uriel Avalos
There is no reason to suppose that an averaged-out heat map, such as the one you have described, would lead to a golden rectangle (or any recognizable shape for that matter). This is merely wishful thinking on your part.
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