I’ve been collecting faces over the past few days, and what a task that is! I have pretty much been harassing people to send me pictures of their faces so I am able to have enough data to make this actually work. Looking at the faces so far, it is pretty interesting that a lot of girls in the same groups do, in fact, look similar. Of course, that is just to my untrained eye, but still. Pretty cool. While I continue to collect faces and start to take measurements soon, I’ll leave you with some more information about the Golden Ratio and a little bit about how my project works.
Most people have probably read that more symmetrical faces are considered to be more beautiful. The fact that beauty can be quantified is one of the most crucial components of my project. I am, of course, mainly looking at if people choose their friends based on genetic similarities to themselves, but without a quantifiable perception of beauty, there is really no data.
Believe it or not, this idea of perfect proportionality using nature’s own golden ratio can be traced back as far as 500 years ago, with Leonardo DaVinci’s “Vitruvian Man.” We have all seen it and understood how incredible the understanding of the proportionality of the human body was at that time. Many still don’t realize the pure genius of DaVinci’s creation.
Leonardo DaVinci's "Vitruvian Man"
This golden ratio also applies to many things in nature. The ratio is present in everything around us, purposefully made that way to provide the most aesthetic appeal. We won’t go into creationism vs. evolution- that’s another discussion for another time. I would definitely recommend checking out how the golden ratio applies to that argument if you are interested as it is a very interesting debate.
The Golden Ratio in nature (Yosh Jefferson)
There is also evidence of the golden ratio in architecture, art, music, and advertisements.
Architecture (Yosh Jefferson)
Art (Yosh Jefferson)
Music (Yosh Jefferson)
Advertisements (Yosh Jefferson)
As you can see, the golden ratio really is everywhere. Below is how it appears in the human face, my area of study.
The Golden Ratio in the human face (Yosh Jefferson)
Pretty amazing, huh? I don’t know about you, but this stuff makes me go crazy. What does this have to do with math, though? Let’s look at the Fibonacci sequence.
1, 1, 2, 3, 5, 8, 13, 21, 34…
To get the next number in this sequence, we add the previous two numbers in the sequence together. The next numbers in the sequence are:
…55, 89, 144, 233, 377, 610…
There’s more to the pattern than just adding the numbers together, however. The fact that the numbers rely on the previous number in the sequence shows that there is a relation between these two numbers that is far more complicated. If you divide each number by the previous number in the sequence, a strange pattern starts to emerge:
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.666…
8/5 = 1.6
13/8 = 1.625
21/13 = 1.61538…
34/21 = 1.61905…
55/34 = 1.61764…
89/55 = 1.61861…
As we keep dividing, we start approaching 1.6180339887…, or Phi, the Golden Ratio.
This ideal ratio is not presented perfectly in humans and other things in nature all the time. Only the most aesthetically pleasing faces will have this ratio perfectly. What I am looking at is how far peoples’ faces deviate from perfect, and then seeing if people that are the same distance away from the perfect ratio choose to be friends, like little sub-ratio groups, with each group hovering around a similar deviation on either side of the ratio. Soon my numbers will be ready to share and we’ll get more answers to that question.
You ought to consider not only friendships, but alternative relationships as well. I would look at married couples of all ages, as well as employers and their employees. Is there a deep rooted physical reason that one might be more inclined to hire a person with ‘more perfect’ facial qualities? If the data proved thus, you could have a tremendous observation on your hands – is it discrimination if you judge someone based on their appearance but don’t know you’re doing so?
And can it be assumed that facial proportionality “runs in the family”? Do people from the same family possess similar linear facial relationships? It could be very interesting if they don’t- think of the ‘black sheep/ugly duckling’ phenomenon.
This research is…really, really cool. Undoubtedly my favorite of all the abstracts. I’ve definitely seen a lot of the examples of the golden ratio in nature–but I have to wonder, how hard do those who study it have to search to find its existence? I’m sure there are plenty of natural objects that don’t fit the ratio at all. Perhaps it’s something that’s tended to evolve more rapidly in species which rely more on looks to attract mates, rather than those that use scents/dances/etc.
This is a very interesting project. You have a very informative blog post, and it’s definitely gotten me excited to see your final results! Just wondering–how are you collecting faces and determining groups of friends? I feel like it’s one thing to ask for people to simply give pictures of their own faces, but it must be exceedingly difficult to ask an entire group of friends to do so, especially if you want to reach out to different social groups. Also, how exactly are you measuring the proportions from the photographs–are you measuring them from printouts, or do you have technology that you’re working with?
From what I have found so far, studies show that people are attracted to people similar to themselves. Most have been about personality traits, but if you’ve ever done some research into pheromones and dating you’ll see this goes even further than just facial attractiveness. There is definitely merit to the statement that people choose mates based on predisposed genetic traits (such as pheromones) but it would be interesting to delve into how the golden ratio applies to the choosing of mates.
It would be really interesting to see the link between the golden ratio of facial proportionality and the relationship between employers/employees. I imagine this type of research could be used to examine tons of relationships. Everyone has probably heard that some dog owners look like their dogs- maybe this could have to do with that as well?
I love your argument about judging based on appearance without realizing it- if this goes viral, there could be a lawsuit on my hands with that one. (Just kidding.)
Definitely another good point about facial proportionality running in the family. My argument throughout this project is that people are attracted to each other because of genetic similarities that are uncontrollable, so you have a good point there. Some of the most attractive people I have seen come from attractive families, so you may be on to something with that.
I’m glad you think it is interesting! To answer your question, I am not really sure how difficult it is to find these patterns. I imagine in nature it is pretty hard to find, but once you find one instance it can be applied to many other things. It really all comes down to the Fibonacci sequence. I think the bigger issue, though, is once you find it there’s not really much to do with it. All we know is we instictively are attracted to that ratio. Does a pinecone that has the pattern ward off predators that try to eat it? That’s a more difficult question. So I think actually finding the ratio isn’t as hard as interpreting it in nature. One of the main questions scientists today (and for centuries) are trying to answer is whether the people who created ancient buildings and works of art knew about the ratio or if it is completely instinctive and we just perceive the ratio to be attractive. Even today the ratio is used (purposefully now) by artists, interior designers, architects, and even paper makers (have you ever wondered why legal sized paper looks so strange and out of proportion compared to regular paper, postcards, stationary, etc?) It’s a really interesting debate, actually. Another extremely interesting debate regarding the golden ratio is its involvement in the debate between evolution, creationism, intelligent design, etc. I won’t go into that unless someone is curious and would like to know how the golden ratio fits in.
Something to point out here- the ratio being present in nature and having aesthetic properties does not mean it is used for attracting mates. As I said above, scientists don’t know a whole lot about what it means, just that it exists and when we see it compared to something else similar without the ratio, we will think the object with the ratio looks better. An offshoot of my project would be what you are talking about with attracting mates.
Great question.
When I first thought of this idea, I wondered how I would be able to amass someone’s groups of friends. For example, if I were to use my own friends as an example, I would have to use my friends from high school, college, my hometown, camps, and all their friends. It would be a crazy web. I decided to use our school’s sorority system as a little microcosm of friend groups. I figured that because in the recruitment process you are choosing friends to be in your group and everyone in the sorority is a mutual friend with each other, it is as close as I could get to a control group with the resources I have. This way I would only have to analyze one web of friends that kind of closes in on itself. In my research each sorority is its own group that is being compared to the golden ratio. I am doing this double blind so if anyone tries to ask me which sorority is the most attractive or who is the most attractive person at William & Mary I honestly won’t know and can’t answer. I am using 5 faces per class per sorority, which comes out to 200 faces. (10 sororities x 4 classes x 5 from each class = 200 people.) There are one or two programs out there that will tell you your face’s ratio and the percent error from the golden ratio, but with that I couldn’t tell what part of the face they were measuring or how good their algorithm was. I am doing it by hand, pixel by pixel. I also had to do it myself because I am measuring three different ratios in the face proven to display the golden ratio to see which one works best with what i am trying to study. I wouldn’t want to do one that shows no correlation and have another one be more fitting to my research! So I decided to do all three. (My next blog will go into that.) There are many more lengths of the face that exhibit the golden ratio, however.
It wasn’t to hard to get photos of people to use. I had a few friends in every sorority and asked them to ask around. A lot of people sent me pictures of themselves (it has to be a straight on picture), and others gave me permission to use a Facebook photo to get their ratio. Most people opted for giving me permission because the pictures some people sent were some awkward webcam photos so I guess some people aren’t into that. I only needed about 5 per class, and with about 30 people per class it wasn’t too hard to get people to agree. Also since I take everyone’s names and sororities out before I do the ratios but after I measure no one really had a problem with it.
There are definitely some flaws with this- as with any experiment- but with the time/ resource constraints I think I more than maxed out what I thought I was capable of doing.