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Can Beauty be described in terms of mathematics?

  1. Mar 31, 2013 #1
    This is Dr. Stephen Marquadt.

    http://img404.imageshack.us/img404/1373/stephenmarquardt.jpg [Broken]

    When he was a young child, his mother was horribly disfigured in a car crash. So he eventually took the route of becoming a reconstructive plastic surgeon.
    As a plastic surgeon, he had to work out a method of making his patients beautiful again.

    This led to his claim to fame, the Golden Ratio Mask, as can be seen in my profile. He constructed it based on the Golden Ratio.

    Throughout the ages, the golden ratio has fascinated both the ancient Greeks and Renaissance men. Marquadt said he was inspired by Da Vinci, who spent a great deal of time analyzing the human body and its beauty.

    The golden ratio also appears in golden spirals and in a regular pentagram.

    [PLAIN]http://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Golden_ratio_line.svg/200px-Golden_ratio_line.svg.png[PLAIN]http://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Pentagram-phi.svg/200px-Pentagram-phi.svg.png[PLAIN]http://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Fibonacci_spiral_34.svg/200px-Fibonacci_spiral_34.svg.png [Broken]

    A recurring idea is that beauty can be seen in objects where the golden ratio is expressed. Examples include the Parthenon, sculptures and even seashells. (From Disney's Donald in Mathmagic Land, a pretty cool cartoon)

    http://img843.imageshack.us/img843/513/lolles.png [Broken]

    Based on this idea, the Golden Ratio Mask was constructed. According to Marquadt, any face that fits the mask will be considered beautiful.

    Here's a video of Marquadt on John Cleese's The Human Face. (skip to 2:07)


    continued (ends at 2:32)


    So the basic principle is that all beautiful faces have something in common, following a certain geometrical template. Whereas ugly faces are all distortions of the beautiful template.

    http://imageshack.us/a/img404/9075/grfemmask.gif [Broken]http://imageshack.us/a/img839/8360/masksuperimposed1.jpg [Broken]

    Some claim the mask is best suited for Caucasians. But it still works out quite well.


    Lastly, this Youtuber has done reconstructive Photoshop surgery on some girl's photo. I think the end result speaks for itself.


    So what do you guys think? Can beauty be reduced to a mathematical abstraction and can this be explained? Or does beauty still lie within the purview of our conundrums of philosophy?
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Apr 1, 2013 #2
    or there could be something that allows us to perceive such ratios as beauty
  4. Apr 1, 2013 #3
    I'm working on a hypothesis for a reason for this. Am I allowed to speak? May be some biologists here could correct me.
  5. Apr 2, 2013 #4
    I'm sorry, did I interrupt you?:frown:

    There's nothing I'd love to do more than correct you...but correct what?

    Fantastic! What is it? Or are we gonna have to wait while you're developing it?
  6. Apr 2, 2013 #5
    Am I the only one who doesn't find this to be very beautiful??
    Last edited by a moderator: May 6, 2017
  7. Apr 2, 2013 #6
    There is even a unit for beauty, the milliHelen

  8. Apr 2, 2013 #7


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    Isn't this Destro, from the GI Joe movie? What, you don't find evil guys to be beautiful ?

    Yeah, I have to agree, it's pretty awful looking.

    On the other hand, I find the thought that beauty can be reduced to math to be hilarious so at least this thread is good for a chuckle.
  9. Apr 2, 2013 #8
    Ooh, I have heard this several times before. Someone even said it looked like the CG enemy from The Lawnmower Man.

    But it's not just the mask itself, but a face that adheres to it.

    I was quite impressed by the Photoshop surgery.
    If you've got an ugly friend just send me his photo and I'll turn him into Prince Charming. :tongue:

    You should watch Donald in Mathmagic Land. It's quite a classic.

    I think Marquadt's made some contribution in establishing a standard of beauty.
    He had to, because he's a reconstructive surgeon.
    Last edited: Apr 2, 2013
  10. Apr 2, 2013 #9
    Let's watch this part


    Marquadt explains the difficulties of being a reconstructive surgeon. He talks about a common standard of beauty. So ugly faces are deviations from the "golden" template.

    Here's my bad analogy:
    "Happy families are all alike; every unhappy family is unhappy in its own way" -Tolstoy
  11. Apr 2, 2013 #10
    I see four problems with studying beauty from a scientific perspective:

    1) Beauty isn't constant. Over the course of history, it has been redefined several times.

    2) Beauty depends on culture. Western ideals are different from other cultures.

    3) Even within the same culture and time period, people don't agree on how beautiful some people are. There is no consistent & universal measure of beauty unlike physics, which has an underlying system of principles. I'm sure many people living in the West hate how women are presented.

    4) Ethics. I'm not going to expand on this, but I'm sure some people are against it for ethical reasons.
  12. Apr 2, 2013 #11

    Ok, here is my initial thought.

    The cone and rod cells within our retina is distributed as given in the following website.

    The distribution of the rod/con cells may be having a golden ratio.
    The fovea centralis itself or the cone cell distribution within the fovea centralis may have a golden ratio.

    So human eye gets a well distributed , well focused and well stimulated image which is passed to the brain.

    The cell multiplication is done in Fibonacci series.
    http://milan.milanovic.org/math/english/division/division.html [Broken]
    Last edited by a moderator: May 6, 2017
  13. Apr 2, 2013 #12
    Keep in mind that golden ratio is applicable not just for humans. It is applicable for structures, architectures etc.
  14. Apr 2, 2013 #13
    There is even a golden ratio for sports cars that involves rectangles, but that is another topic.

    As far as beauty the golden ratio has been around a long time.

    Cutting to the chase, no pun intended.

  15. Apr 2, 2013 #14
    Is it alright if I lump the first three points into one problem?

    As a reconstructive surgeon, Marquadt needs to know what most of society considers beautiful.

    In the above video, he talks about the difficulties of being a surgeon and mentions a study on ranking faces and which achieved a near universal result.
    (and thereby made his job easier :smile:) He also mentions the null effect of culture.

    This is quite easy to carry out. Just get a bunch of faces and get your friends to rank them. Rope in your seniors, colleagues, acquaintances etc.

    As for ethics, it isn't a problem with the study itself, but such a study may affect self esteem and lead to deeper societal issues.
  16. Apr 2, 2013 #15

    It'd be cool if it really had a phi distribution.

    Personally I think it's due to the way our brain works. Like biologically in-built. If you watch the first part of the documentary, babies supposedly get repulsed by ugly faces.
    Last edited by a moderator: May 6, 2017
  17. Apr 2, 2013 #16
    Someone should measure the scanning speed. It's interesting that our concepts of beauty may be biological in origin.

    The Rapide S looks good from the side but awful from the front. Which car do you think is the most ...beautiful?

    Here's another fun test. Think of all the handsome, beautiful people you know. Think of all the butt ugly ones too. :tongue:
    They may be nerdy, or Mr. Popular, but just focus on their beauty.

    Then place the mask over their faces. This should verify whether the mask matches your standard of beauty.:cool:
    Last edited: Apr 2, 2013
  18. Apr 2, 2013 #17


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    Last edited: Apr 2, 2013
  19. Apr 2, 2013 #18
    Yeah, it is old! haha. I did mention da Vinci. So a few hundred years old. Stuff like the Vitruvian man.
    The golden ratio mask is relatively new.

    It's more than just symmetry, it's also about proportion.
    Last edited: Apr 2, 2013
  20. Apr 2, 2013 #19


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    Proportion and symmetry go hand in hand. This is not new, it's only new to you.
  21. Apr 2, 2013 #20
    Oh I'm sorry, you didn't mention proportion the first time round.

    Well, I did admit that the idea was old. The mask seems new, though perhaps it's an expansion of da Vinci's Vitruvian man.
    Last edited: Apr 2, 2013
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