Can Beauty be described in terms of mathematics?

[tade]

This is Dr. Stephen Marquadt.

http://img404.imageshack.us/img404/1373/stephenmarquardt.jpg

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





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



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)

https://www.youtube.com/watch?v=E1kqMk3jFD8



continued (ends at 2:32)

https://www.youtube.com/watch?v=5pRJtjlHj_M


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 http://imageshack.us/a/img839/8360/masksuperimposed1.jpg


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.

https://www.youtube.com/watch?v=N4fUjzqCC-8&hl=en-GB


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?

 

[tade]

or there could be something that allows us to perceive such ratios as beauty

 

[jobyts]

or there could be something that allows us to perceive such ratios as beauty

I'm working on a hypothesis for a reason for this. Am I allowed to speak? May be some biologists here could correct me.

 

[DiracPool]

I'm working on a hypothesis for a reason for this. Am I allowed to speak? May be some biologists here could correct me.

Am I allowed to speak?

I'm sorry, did I interrupt you?

May be some biologists here could correct me.

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

I'm working on a hypothesis for a reason for this.

Fantastic! What is it? Or are we going to have to wait while you're developing it?

 

[micromass]

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

Am I the only one who doesn't find this to be very beautiful??

 

[Andre]

There is even a unit for beauty, the milliHelen

1 millihelen is the amount of beauty needed to launch a single ship.

 

[phinds]

Am I the only one who doesn't find this to be very beautiful??

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.

 

[tade]

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.

Am I the only one who doesn't find this to be very beautiful??

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:

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.

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.

 

[tade]

Let's watch this part

https://www.youtube.com/watch?v=JO9tOuSrnrk

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

 

[Turion]

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.

 

[jobyts]

I'm sorry, did I interrupt you?



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



Fantastic! What is it? Or are we going to have to wait while you're developing it?

Ok, here is my initial thought.

The cone and rod cells within our retina is distributed as given in the following website.
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/rodcone.html#c2

The distribution of the rod/con cells may be having a golden ratio.
OR
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

 

[jobyts]

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.

Keep in mind that golden ratio is applicable not just for humans. It is applicable for structures, architectures etc.

 

[edward]

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.

The actual golden ratio, first defined by the Greek mathematician Euclid to have a value of about 1.618, is a myth, Bejan said. To him, the phenomenon of the golden ratio is not its value like pi, which is observable in nature and quantitatively important.“The true phenomenon is that all of us, without talking to each other, tend to be attracted to the ratio like insects to light,” he said.A large part of this attraction may be attributed to the speed at which we can visually process an object, Bejan added. The optimal efficiency occurs when the time taken to scan horizontally equals the time it takes to scan vertically. Since we have two front facing eyes, we naturally scan horizontally at a faster rate than we do vertically, because one eye can take over for the other after a certain point of rotation.

Cutting to the chase, no pun intended.

From an evolutionary perspective, Bejan believes that humans continuously strive for movement, a quality of our species reflected in our appreciation of the golden ratio. Something that can move us quickly increases our accessibility to opportunities.

http://www.dukechronicle.com/articles/2013/02/26/golden-ratio-gives-sports-car-natural-appeal

 

[tade]

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.

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 ) 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.

 

[tade]

Ok, here is my initial thought.

The cone and rod cells within our retina is distributed as given in the following website.
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/rodcone.html#c2

The distribution of the rod/con cells may be having a golden ratio.
OR
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

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.

 

[tade]

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.
http://www.dukechronicle.com/articles/2013/02/26/golden-ratio-gives-sports-car-natural-appeal

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.

 

[Evo]

This is old, old stuff. Facial symmetry has been accepted as a basis of attractiveness for a long time.

Perhaps you should do some reading on the subject.

http://en.wikipedia.org/wiki/Facial_symmetry

 

[tade]

This is old, old stuff. Facial symmetry has been accepted as a basis of attractiveness for a long time.

Perhaps you should do some reading on the subject.

http://en.wikipedia.org/wiki/Facial_symmetry

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.

 

[Evo]

But it's more than just symmetry, it's also proportion.

Proportion and symmetry go hand in hand. This is not new, it's only new to you.

 

[tade]

Proportion and symmetry go hand in hand. This is not new, it's only new to you.

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.

 

[Evo]

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.

I've been allowing this thread so far, but you need to know that the forum rules also apply here in GD. I think this thread is ready to be closed because you failed to research this before posting.

 

[tade]

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.

I tried these tests myself and they seem to confirm what Marquadt said.

 

[Ryan_m_b]

I find all this highly dubious. Beauty is a very controversial and complicated subject and studies on it are very hard to do without cultural bias. I find it hard to believe that a simple and superficially universal explanation can exist.

 

[glueball8]

http://www.damtp.cam.ac.uk/events/strings02/dirac/speach.html

yes, I did read the thread.

 

[tade]

I find all this highly dubious. Beauty is a very controversial and complicated subject and studies on it are very hard to do without cultural bias. I find it hard to believe that a simple and superficially universal explanation can exist.

But perhaps the explanation is really that simple. :)

There are some key ideas, such as all beautiful faces look alike.



Of course, everyone has existing beliefs and natural resistance to new ideas. So why not test it out?

 

[tade]

http://www.damtp.cam.ac.uk/events/strings02/dirac/speach.html

yes, I did read the thread.

sorry, how is that related to the main topic?

 

[Ryan_m_b]

There are some key ideas, such as all beautiful faces look alike.

Please present peer-reviewed studies detailing this so that we can discuss their methodology.

Of course, everyone has existing beliefs and natural resistance to new ideas. So why not test it out?

I'm not resisting this proposal because of some innate desire to resist but that it sounds incomplete and flawed in the manner in which it approaches the topic. If someone were to demonstrate it to a high degree then I would change my mind.

Regarding a specific point of your OP as an example. The photoshop youtube clip shows a young woman who, to my mind, is far more attractive before the photoshopping. She fits more within beauty-magazine version of beauty at the end because she is, amongst other things, thinner faced but don't mistake that for some form of universal beauty. This whole thread smacks to me of retrospective justifications for the beauty myths of society.

 

[tade]

Please present peer-reviewed studies detailing this so that we can discuss their methodology.

I'm not resisting this proposal because of some innate desire to resist but that it sounds incomplete and flawed in the manner in which it approaches the topic. If someone were to demonstrate it to a high degree then I would change my mind.

Regarding a specific point of your OP as an example. The photoshop youtube clip shows a young woman who, to my mind, is far more attractive before the photoshopping. She fits more within beauty-magazine version of beauty at the end because she is, amongst other things, thinner faced but don't mistake that for some form of universal beauty. This whole thread smacks to me of retrospective justifications for the beauty myths of society.

Oops, as you can see, I accidentally pissed off Evo in this thread.

I don't want to repeat this mistake. Sorry Ryan.


This thread is just meant for some casual discussion, I should have included that in the first post (but now I can't edit it ).

 

[Ryan_m_b]

Sorry but you can't really have casual discussion on a factual topic with such important ramifications. One of the first things that sprung to my mind, especially with regards to that photoshop video which you claim "speaks for itself", is how such research poorly done will fuel further problems with body image amongst developing men and women.

This is not an area where a casual back and forth discussion can really be had in a bubble, disconnected from its effects. Especially as many of the claims and points upon reflection contain hideous subtexts. For example; that woman looks better when we apply this (so far unproven) theory of beauty, therefore she is ugly as she is. Or even worse the very basic claim that there is an objective value for beauty and if you don't posses it or don't share the value there is something abnormal about you. This topic is ripe for culturally normative assumptions and as such should be approached as carefully as possible, first exploring possible bias in those assumptions.

 

[tade]

Sorry but you can't really have casual discussion on a factual topic with such important ramifications. One of the first things that sprung to my mind, especially with regards to that photoshop video which you claim "speaks for itself", is how such research poorly done will fuel further problems with body image amongst developing men and women.

This is not an area where a casual back and forth discussion can really be had in a bubble, disconnected from its effects. Especially as many of the claims and points upon reflection contain hideous subtexts. For example; that woman looks better when we apply this (so far unproven) theory of beauty, therefore she is ugly as she is. Or even worse the very basic claim that there is an objective value for beauty and if you don't posses it or don't share the value there is something abnormal about you. This topic is ripe for culturally normative assumptions and as such should be approached as carefully as possible, first exploring possible bias in those assumptions.

Interesting, I've never thought about this in that manner.

I found my old copy of Donald in Mathmagic Land after ten years
Then a few days later I found John Cleese's documentary in a library.

So I decided, perhaps I could have a casual discussion on beauty. The hideous subtexts hadn't crossed my mind before. Apologies.

 

[Ryan_m_b]

Apology accepted. To my mind this is one of those issues that is more in the realm of social sciences than it is biological even, let alone mathematics. It has obvious implications in medical science but beauty as a cultural phenomenon should be treated as such first rather than fallaciously reified.

 

[tade]

This may make me appear callous, but I did not view those subtexts as particularly hideous.

To me, I just accepted this simple fact of life: some people are more beautiful than others.
Most of it is beyond our control.Perhaps you attach greater emotional value to those subtexts.

It is often said that men care more about the looks of their partner compared to women. I think I'm quite impartial, I don't place large significance on beauty.

But everyone has different opinions. To each his own.

 

[tade]

To my mind this is one of those issues that is more in the realm of social sciences than it is biological even, let alone mathematics. It has obvious implications in medical science but beauty as a cultural phenomenon should be treated as such first rather than fallaciously reified.

Marquadt needed a definite method of treating his patients. He was inspired by da Vinci.
da Vinci tried to apply mathematical ratios to beauty, and that intrigues me.


In John Cleese's documentary, he mentions that babies are more inclined to beautiful faces. I'm not sure if it's true, but if it is then there may be a biological basis.

jobyts and edward brought up some biological examples too, but those aren't well verified.


Lastly, society does play a major role, just look at all the super skinny catwalk models these days.

 

[Ryan_m_b]

This may make me appear callous, but I did not view those subtexts as particularly hideous.

To me, I just accepted this simple fact of life: some people are more beautiful than others.
Most of it is beyond our control.Perhaps you attach greater emotional value to those subtexts.

You miss my point. Beauty is a complex and multifaceted phenomenon, there is no evidence to suggest it is an objective spectrum which proposals like this thread would imply. There are negative consequences for individuals and society at large if we start adopting "you're either look like this and are beautiful or you're not" standards. You display a large privilege here, you're coming across as this not being an issue for you so therefore it isn't an issue or the issue lies with those who do find fault with it.

It is often said that men care more about the looks of their partner compared to women. I think I'm quite impartial, I don't place large significance on beauty.

Rather than often said perhaps it would be best to look into these things to see if they even make sense. I.e. is the difference between men and women so discrete or is this another example of cultural bias?

But everyone has different opinions. To each his own.

If only this topic was as whimsical as to leave each to their own we wouldn't have a host of problems because of it's poor exploration.

Marquadt needed a definite method of treating his patients. He was inspired by da Vinci.
da Vinci tried to apply mathematical ratios to beauty, and that intrigues me.

Da Vinci is hardly a contemporary authority on this topic.

In John Cleese's documentary, he mentions that babies are more inclined to beautiful faces. I'm not sure if it's true, but if it is then there may be a biological basis.

As babies have poor vision I'm again dubious. Rather than relying on TV documentaries by celebrities it would be best to refer to actual studies. But just to give you an idea of possible shoddy methodology: how is beauty being defined in this sense when one says "babies are attracted to beautiful faces?"

Lastly, society does play a major role, just look at all the super skinny catwalk models these days.

Quite. For a negative follow on to this look at the problems of air brushing and body image.

 

[leroyjenkens]

My girlfriend can be described mathematically; $\sqrt{-1}$