Golden Ratio Enthusiasts: Phi Fantasies

Golden RectangleIntroduction

We crave deep meaning and connection. What is so bad about that? Special vibrant meaning can stir warm feelings and awe in us. Similarly, love gives us a great hormonal pleasure kick, and so we sometimes imagine it where it does not exist.

Our imaginations are wonderful — they allow us to enjoy the fictions of novels and movies. Our imaginations allow us to get bonding-joy over fictitious religious myths and mercenary football teams.

The cravings of our self-deceptive magical minds also display themselves in the drier, cerebral world of physics and mathematics. The “irrational” number φ phi (1.61803…) contains such stories.

Phi, “the golden ratio”, can be found many places in nature. But many math enthusiasts want to see it as a source of beauty and truth, hallucinating it in places it does not exist. The religious and the non-religious alike can over-read the reach of numbers. That over-reading is a habit of our meaning-hungry human minds.

The Parthenon & Phi

parthanonThe Parthenon is a beautiful ancient Greek Athenian temple built and decorated between 447 and 432 BCE. One of the Parthenon’s adornments is the famous statue of Athena done by the great Greek sculpture named Phidias. In fact, Phi (φ) is the first letter in Phidias (Φειδίας).  Thus in 1909 Mathematician Mark Barr used that letter to name the golden ratio in honor of Phidias because of his supposed use of the Golden Ratio all over the Parthenon and thus supposedly giving it a magical beauty. But it seems that this is false and thus Phi is misnamed. Mathematicians actually also sometimes call Phi “Tau” (τ) from the greek word tomi meaning “section” or “cut” — the Golden Section.
[btw, that is the tau in CAT scan: Computer Axial Tomography]

So to see how this myth of PHI in the Parthenon happened, let me quote Mario Livio’s book, “The Golden Ratio” (pgs 73-74):

Most books on the golden Ratio state that the dimensions of the Parthenon, …. fit precisely into a Golden Rectangle. This statement is usually accompanied by a figure similar to that in figure 23. The Golden Ratio is assumed to feature in other dimensions of the Parthenon as well. For example, in one of the most extensive works on the Golden Ratio, Adolph Zeising’s Der Golden Schnitt (The Golden Section; published in 1884), Zeising claims that the height of the facade from the top of its tympanum to the bottom of the pedestal below the columns is also divided in a Golden Ratio by the top of the columns. This statement was repeated in many books, such as Matila Ghyka’s influential Le Nobre d’or (The Golden Number, peared in 1931).

The appearance of the Golden Ratio in the Parthenon was seriously questioned by University of Maine mathematician George Markowsky in his 1992 College Mathematics Journal article “Misconceptions about the Golden Ratio.” Markowsky first points out that invariably, parts of the Parthenon( e.g., the edges of the pedestal; Figure 23) actually fall outside the sketched Golden Rectangle, a fact totally ignored by all the Golden Ratio enthusiasts. More important, the dimensions of the Parthenon vary from source to source, probably because different reference points are used in the measurements. This is another example of number-juggling opportunity afforded by claims based on measured dimensions alone. Using the numbers quoted by Marvin Trachtenberg and Isabelle Hyman in their book Architecture: From Prehistory to Post-Modernism (1985), I am not convinced that the Parthenon has anything to do with the Golden Ratio. These authors give the height of 45 feet 1 inch and the width of 101 feel 3.75 inches. These dimensions give a ratio of width/height of approximately 2.25, far from the Golden ratio of 1.618… Markowsky points out that even if we were to take the height of the apex above the pedestal upon which the series of columns stands ( given as 59 feet by Stuart Rossiter in his 1977 book Greece), we still would obtain a width/height ratio of about 1.72, which is closer to but still significantly different from the value of PHI.


So, it appears that Phi is not part of some intentional magical beauty design of the Parthenon — in fact it is not even there. But authors over the last centuries have passed this mistaken idea, over and over. In fact, the error is in the name of the number itself.

Repeating a fiction long enough, and people will not doubt it. This happens even with our intuitions about Mathematics. Gods or no gods, we love inspiring myths.

Note: This post is part of a Phi series I started years ago — it is fun to write again.


Filed under Philosophy & Religion

5 responses to “Golden Ratio Enthusiasts: Phi Fantasies

  1. Glad you are writing more again!

  2. I’ve never understood Fibonacci fantasies. Yes, approximations appear in nature. But my attitude has always been “Yawn!”.

    And I am a mathematician.

  3. @David: Thank you

    @ Neil: Yes, I agree. But coming from a mathematician, it is much more meaningful.

    FYI to Readers:
    Fibonacci series is : 0,1,1,2,3,5,8,13,21,34,55,89,144
    It is generated by each element being the summation of the two elements before it with the initial setting as 0,1 (or 1,1 — in some models).
    And if you divide any two consecutive digits in the series, the quotient approximates phi closer and closer as the series progresses.

  4. As an older person now with decades of experience in both the “tangible” realities of science and day-to-day life…but always tempered with the heritage I was born into…I find that life’s path is made up of many trails…

    On those trails, we find those that seem to only see “the numbers” and those that can’t look past them…Some create meaning where there is none, while others try to tear meanings apart that others have just because they can’t see a meaning that fits their interpretation of a given narrative…i

    The golden section or angle does exist in nature and the universe at large it seems. Those that look closely and are open see more…those that only can look critically see less…either way it is but an interpolation within a constant in existence as we know and understand it now…

  5. @ Jay: Sorry, I have can not understand your point — even after reading twice. But if I’d have to guess, I’d say you are a “Golden Ratio Fan” who is criticize those that don’t have the amazing open vision you do due to your age, your heritage and inability to be trapped by numbers and analysis.

    Did I get that right?

    “Meaning” is a funny thing: it is subjective, open to manipulation, essential and so much more.

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