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Do Painters Peak at the Golden Mean?

The views expressed are those of the author and are not necessarily those of Scientific American.


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“Beauty is truth, truth beauty,” — that is all
Ye know on earth, and all ye need to know.

– John Keats

The golden mean, or divine proportion, has fascinated philosophers, mathematicians, artists, and scientists for centuries. Represented as a fraction by the decimal .6180 (to four decimal places), ancient Greek philosophers believed that this ratio is truth and beauty. Some even believe it’s a fundamental characteristic of the universe.

Indeed, the Golden Mean does appear in the most astounding places.

From shells:

To hurricanes:

To spiral galaxies:

To rose petals:

To koala bears:

To butterflies:

To the human face:

But does human creativity also conform to the golden mean?

P.H. Franses, professor of applied econometrics in the Netherlands, looked at the peak level of creativity among 189 of the most famous modern art painters who created art between 1800-2004. Creativity researchers tend to look at absolute age of peak creativity, but curiously, no one has looked at relative age (“defined as the age of the top creation divided by the total lifespan”).

On average, each painter was 41.92 years old when he or she created his or her most expensive art.

What fraction of their lives was this, on average? The mean age at which the most expensive work of these artists was created divided by the year of death minus year of birth, was 0.6198:

According to Franses, this is “only 0.0018 away from the divine fraction.”

Make of it what you will. See paper here.

© 2013 Scott Barry Kaufman, All Rights Reserved

images credit: io9; goldennumber.net [nature, art]; knowknowledge.com; phimatrix.com; fabiovisentin.com; huffingtonpost.com; tehcute.com

Scott Barry Kaufman About the Author: Scott Barry Kaufman is Scientific Director of The Imagination Institute and a researcher in the Positive Psychology Center at the University of Pennsylvania, where he investigates the measurement and development of imagination. His latest book is Ungifted: Intelligence Redefined. Follow on Twitter @sbkaufman.

The views expressed are those of the author and are not necessarily those of Scientific American.





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  1. 1. Uncle.Al 4:02 pm 12/15/2013

    http://math.ucr.edu/home/baez/week203.html

    Link to this
  2. 2. Looie 12:54 pm 12/16/2013

    I left a rather sarcastic comment here that apparently was removed, so let me try a more formal comment. If we look at the plot on the bottom of the article, we see a distribution that rises sharply from zero at around x = 0.3 (obviously because artists almost never produce their best work as children), and then shows only minor changes over the rest of the domain. Ignoring statistical variation, there is a very broad peak centered near x = 0.4, and then a very slow decrease all the way up to x = 1.0. A distribution like that naturally yields a mean near 0.6, but the important thing is that there is no excess tendency for individual artists to produce that particular value. This is such a blatant misuse of statistics that I wonder whether it was intended as a test of our ability to recognize bogosity — or perhaps as a covert way to draw attention to a bogus paper.

    Regards, Bill Skaggs

    Link to this
  3. 3. sbkaufman 1:39 pm 12/17/2013

    Dear Bill Skaggs,

    Thanks for your comment, and pointing out some of the statistical limitations of the study.

    The paper I referenced is not a bogus paper. In fact, it was published in one of the most prestigious peer-reviewed journal articles in the field of creativity.

    The author, P.H. Franses, is a trained statistician and econometrician, and is well aware of the statistical information you pointed out. As he told me, “many comments are to be expected, and I am happy with that. I just calculated an average and note it is very close to a familiar number. Calling that ‘misuse’, well, I leave that up to you.”

    The golden ratio connection aside, his technique is innovative in our field. Up to this point, creativity researchers have looked at absolute age of peak creativity, not relative age. Hopefully this intriguing little study will spur more creativity researchers to investigate relative peak creativity across various domains of creativity (e.g., music, science). It would indeed be incredible if numerous domains approached the golden mean, but certainly not expected!

    As a brief backstory, Franses told me he became interested in this research when he noticed that some people get Nobel prizes for things they created much later in life. He then came across a book by Cummings and wondered how it would be for painters. At the same time, he had done some work on business cycles and there he became acquainted with the notion of optimality and its link with fibonacci numbers.

    While the connection may seem a reach, I admire the innovative methodology and creative connection he made, even if it proves to be noise, or random coincidence (which is entirely possible). As a creativity researcher, I encourage new methodologies in the field, and even novel interpretations. Of course, it’s up to science to help us all get a clearer picture on what’s really going on.

    Best,
    Scott

    Link to this
  4. 4. Looie 4:57 pm 12/17/2013

    Thanks for the reply, Scott. I still find it strange that you take this seriously, but the idea of looking at the relative age of peak productivity does seem plausible, given that a substantial fraction of highly creative people have impulse-control problems that tend to shorten their lifespans.

    Regards, Bill Skaggs

    Link to this
  5. 5. SZissou 10:54 am 12/18/2013

    Donald Simanek of Lock Haven University has good page illustrating how the supposed correspondence of the Fibonacci sequence and the Golden Mean to natural objects has been misrepresented.

    http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm

    Spoiler: the shell of the chambered nautilus (top of page) is not a Golden Spiral.

    Link to this
  6. 6. Asynsis 2:01 am 12/19/2013

    Da Vinci’s (other) Code: Golden Ratio in Time reveals how geometry and thermodynamics co-evolve & design 4 Complexity with the Asynsis principle-Constructal law of design in nature & culture.
    http://www.scoop.it/t/asynsis-principle-constructal-law

    Link to this
  7. 7. Asynsis 2:13 am 12/19/2013

    From consciousness to celestial mechanics – it’s innate in nature and it’s ultimately explained by Asynsis principle geometries of Constructal law thermodynamics.
    Giulio Tononi: Integrated Information Theory. http://vimeo.com/53787308 http://en.wikipedia.org/wiki/Integrated_information_theory
    Sphere music: Min work, plus stability, max entropy-export via feedback: @ASYNSIS-@constructal http://tallbloke.wordpress.com/2013/02/20/a-remarkable-discovery-all-solar-system-periods-fit-the-fibonacci-series-and-the-golden-ratio-why-phi/ … pic.twitter.com/FPzMdNjyNR
    http://about.me/asynsis

    Link to this
  8. 8. Zonkorias1 4:22 am 12/21/2013

    What makes you think the expensiveness of a work of art correlates with the level of creativity?

    Link to this

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