December 2, 2013

Video: A Mathematical Breakdown of the Cinematography in 'There Will Be Blood'

Even if (like me) you are one of those souls who are congenitally allergic to mathematics, so much of creating a beautiful image involves numerical principles. Many classic films have made use of the number known as the "Golden Ratio" (1.618), as well as the visual device known as One-Point Perspective (a way to make a two-dimensional plane look three-dimensional), and now Vimeo user Ali Shirazi has put together a visual essay on the use of these, and other visual principles, in Paul Thomas Anderson's There Will Be Blood.

First, a bit of a primer:

The Fibonacci Sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...) is a sequence of numbers that started as a way for 12th century Italian mathematician Leonardo Fibonacci to calculate the breeding habits of rabbits (seriously). Each new number in the sequence is the sum of the two numbers before it, (i.e., 3+5=8, 13+8=21, etc.). Any two of these numbers is an approximation of the Golden Ratio, or 1.618, and the approximation gets more accurate the higher you progress in the sequence.

The Golden Ratio appears countless times in nature and art, and is considered to be the ratio most pleasing to the human eye, though why this is so is a question that has never quite satisfactorily been answered. (Caveat: this is a vast oversimplification.)

This video explains the situation better than I ever could:

Many filmmakers are no doubt familiar with another compositional technique, the Rule of Thirds, which, simply defined, states that "an image is most pleasing when its subjects or regions are composed along imaginary lines which divide the image into thirds — both vertically and horizontally."

Single Point (or One Point) perspective is another visual device that has been used for thousands of years to give a three-dimensional quality to a two-dimensional work of art (whether painting, photograph, or motion picture), essentially by having lines radiate outward from a single vanishing point, giving the illusion of depth.

This video, by Vimeo user Kagonada, demonstrates Single-Point perspective in the works of Stanley Kubrick:

And now, Ali Shirazi has made a study of P.T. Anderson's There Will Be Blood, demonstrating how the film makes use of the Golden Ratio, Single-Point perspective and tracking shots; it is a beautiful and educational visual analysis of the film, and a lesson for any filmmaker (or anyone) interested in the mathematics behind cinema. How are images constructed so as to be pleasing (or jarring, as the case may be) to the eye, and what is the numerical basis behind this phenomenon?

According to the filmmaker, this is the first in his series of series of videos on 'Paul Thomas Anderson's Directing Style,' so look for more videos in the future. In the meantime, check this out and see what Ali found in the images created by P.T. Anderson and DP Robert Elswit.

What do you think? Do you have any favorite examples from film (or other visual art) that can shed light on this fascinating phenomenon? Let us know in the comments!

Links:

Your Comment

28 Comments

Its a tad overblown but very interesting nonetheless. And hey, any reason to look at that gorgeous imagery is fine with me.

December 2, 2013 at 7:07PM, Edited September 4, 11:21AM

2
Reply
marklondon

You can find these ratios anywhere if you look for them. Doesn't mean they a A: Artistically relevant in any particular case or B: Intended by the author.

Lendvai's analysis of Bartok is a good example of where this approach can go somewhat awry.

Don't mean to be critical of this post, it's an interesting topic but it's worth bearing in mind the history and various issues etc.

December 2, 2013 at 7:10PM, Edited September 4, 11:21AM

9
Reply

Goofy. The There WIll Be Blood video doesn't break anything down, it just puts graphic garbage up that has very little relation to what's actually going on onscreen. All the one point perspective shots weren't one point perspective. The golden ratios seemed to be floating, not relating to anything with any golden ratio on screen. Pretty silly.

December 2, 2013 at 7:32PM, Edited September 4, 11:21AM

7
Reply
Adam

Agreed with above comments. I love the topic and do believe some people implement the Fibonacci sequence into their art knowingly, but this seems to be unintended. I have used it in music from time to time (even down to individual instruments and notes) but I find, more often than not, it shows up without me intending it to.

December 2, 2013 at 7:41PM, Edited September 4, 11:21AM

3
Reply

Well, people day trade based on Fibonacci numbers - among another dozen formulas - but this is more of a geometric post scriptum analysis of a fly-by-the-seat-of-the-pants auteur. One could just as easily find more asymmetric "rule breaking" shots in other films. Conrad Hill once said visavis "Butch Cassidy and the Sundance Kid", ~ "We took the prescribed rules and threw them out of the window. Bokeh, sun flares, everything we were told to avoid in the past was used and then became the new norm". As to PT personally, Kalatozov and Tarkovsky had these long tracking shots long before him. Kalatozov also knew when to yell, "Cut".

December 2, 2013 at 8:20PM, Edited September 4, 11:21AM

4
Reply
DLD

I enjoed very much the one about The Good, the bad & the ugly

December 2, 2013 at 8:30PM, Edited September 4, 11:21AM

1
Reply
maghoxfr

Yeah . . . this is what I would call a stretch.

December 2, 2013 at 8:38PM, Edited September 4, 11:21AM

2
Reply

"A Mathematical Breakdown of the Cinematography in ‘There Will Be Blood’?"

nope. just a misleading post not containing anything of the sort.

December 5, 2013 at 11:51AM, Edited September 4, 11:21AM

0
Reply
Fred Pays

PTA, as a filmmaker, is just so damn good that it sometimes makes you feel inferior.

December 2, 2013 at 8:47PM, Edited September 4, 11:21AM

0
Reply

Nice lesson. But I thought that movie was dreary.

December 2, 2013 at 10:29PM, Edited September 4, 11:21AM

3
Reply
Gene

Oh what utter rubbish that 'there will be blood mathematics' is. :3

December 3, 2013 at 2:06AM, Edited September 4, 11:21AM

3
Reply

Did P.T. Anderson direct this movie with protractor in hand? Probably not. Did he follow certain compositional rules that happened to result in images that corresponded with universal visual rules that appear over and over? Maybe. Is it interesting? I think so.

December 3, 2013 at 2:41AM, Edited September 4, 11:21AM

0
Reply
avatar
Justin Morrow
Writer
Writer/Director

A Mathematical Breakdown of the Cinematography in 'There Will Be Blood'? Not even close.

December 3, 2013 at 4:42PM, Edited September 4, 11:21AM

0
Reply
Adam

Justin

I, for one, wasn't trying to sound negative on your post.

I did think there was something interesting about the math framing.

I was only saying the movie was dreary, the color, sets, everything. I can't find it in myself to model something I do in the future from what I saw in that movie. Maybe it was the intended dreary outlook of the movie---maybe I want to forget I ever saw it. Daniel Day Lewis' acting was pretty good, not his best ever. But the politics on a soap box left a very bad taste in my mouth.

It may have put a bad vibe in my first comment. My bad.

December 3, 2013 at 7:29PM, Edited September 4, 11:21AM

0
Reply
Gene

definitely interesting and great to have a director focussed post...

December 3, 2013 at 5:03AM, Edited September 4, 11:21AM

1
Reply
jojo

This seems like a clear case of the DP and director's inate sensibility for composition, space and storytelling happening to create images that fall into the golden ratio etc. Very interesting none the less. I think it's equaly interesting how bumpy and handheld the tracking shots are. It gives it a very unsettling feeling and also makes the film feel like it was created in long past era. It's always refreshing to see that great work is often made with very old tools. I love all the new tech but it puts it in perspective.

December 3, 2013 at 1:43PM, Edited September 4, 11:21AM

6
Reply
Matthew

IMO, the "old time feel" was very well done but that's to the set lighting and the choice of colors. It's like "SPR" captured the feel of Normandy on a dreary, mist filled morning with the subsequent physical treatment of the film used on the shoot. Someone like Lelouche used the same morning mist to make everything appear romantic.

December 3, 2013 at 10:32PM, Edited September 4, 11:21AM

0
Reply
DLD

It's fun and well made, but I'd hardly call this a mathematical breakdown. Many of the 'one-point perspectives' are actually zero, two, or three point perspectives, and the strongest one-point perspective shown in the video (the sermon scene) is ignored and labelled as a golden rectangle instead. Out of all the examples shown, I would say maybe four or five of the perspectives/rules of thirds were correctly labeled.

I'd say this is closer to what Harold Crick sees in Stranger than Fiction than a true mathematical/compositional breakdown of There will be Blood. It was pretty, and well executed, but hardly relevant to what was being shown on screen.

December 4, 2013 at 10:22PM, Edited September 4, 11:21AM

0
Reply
Christopher Siler

The golden ratio does lend itself to be very pleasing to the eye. If anything I do not think it was a conscience decision, but rather we do it from more of a sub-conscience level. We will always try to capture what is pleasing to the eye and most of the time it ends up getting close to the ratio.

December 5, 2013 at 9:28AM, Edited September 4, 11:21AM

0
Reply
Terry Jun

great video nice work BUT this is a stretch. you can superimpose anything over anything. the 'maths' are in no way relevant what so ever to the imagery.

surely this is quite obvious?

December 5, 2013 at 11:49AM, Edited September 4, 11:21AM

2
Reply
Fred Pays

^ What Fred Pays and Terry Jun said ^
This video might be interesting for a compositionally-challenged eye but, if you need this to shoot your film, you're in the wrong business.

December 5, 2013 at 1:06PM, Edited September 4, 11:21AM

0
Reply

As a gentle reminder, please bear in mind that not everyone on the internet is an Oscar-winning director like you.

December 6, 2013 at 5:58PM, Edited September 4, 11:21AM

2
Reply
Zan Shin

I agree with everyone that says it doesn't really show anything, the spirals don't line up really, if you have decent composition it tends to show up as spacing between things, as they said the human body has the spiral, I see a few human bodies in PTA movies...Obviously they're going to be there.

PTA doesn't sit there with a spiral overlay on his view finder checking.

Seems like a video of someone breaking down a PTA film that has no idea of the process or what they're even talking about, just trying to act like they found a secret.

December 8, 2013 at 5:51PM, Edited September 4, 11:21AM

0
Reply

Don't be so harsh on Justin dudes. While it s true that the mathematical bAsis of art was long ago debunked, Tools like the golden ratio are very useful in teaching beginners how to understand concepts such as negative space and visual balance, and give them a little bit of a head start in creating worthwhile images.

April 15, 2014 at 5:44PM, Edited September 4, 11:56AM

0
Reply
Bigeater

Loved this. You have a definite passion for film. Thank you for creating and posting.

July 15, 2014 at 5:07PM, Edited September 4, 11:56AM

4
Reply
Jacob Boone

Thanks NFS for sharing and doing write ups, this is my #1 site, love it.

However, this video reminds me of those pictures where people find the Illuminati triangles, a bit of a stretch IMO.

http://static.fjcdn.com/pictures/Illuminati_d25092_4913923.png

July 23, 2014 at 5:18AM, Edited September 4, 11:56AM

3
Reply
Reggie

Oh and have you seen all those Hipster triangles they are actually Freemason symbols to convince you of their alien over power. Plus all the round objects where circle like because the Templars wont to tell you that:"No men has ever bin on the moon" and "the earth is actually flat" and " 500yrs old"

Bullshit we call it god Framing that's it

July 23, 2014 at 5:52AM, Edited September 4, 11:56AM

0
Reply

Thanks for the post Justin, really interesting and very informative, one of the best pages on the net for helping to explain these certain composition laws. The first three videos are great however I have to echo a lot of others here in that the PTA video seems a massive stretch. Yes it looks fantastic and the author has spent a lot of time but on the whole it confuses and some of the attempts to define certain shots are just silly and not helpful at all for anyone learning this subject. I'd go so far as to say it really wipes out any of the three previous videos very helpful attempts to explain these composition matters.

July 26, 2014 at 7:04AM, Edited September 4, 11:56AM

0
Reply
Andy