Requiem
How long is the coast of Britain? asks Benoît Mandelbrot, mathematician and recently deceased* conquistador of fractal geometry. The answer, surprisingly, depends upon how closely you’re able to look.
Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line, Mandelbrot writes in the introduction to an iteration on his seminal work. Look close enough and one begins to see that “coast” and “length” are merely convenient abstractions of an ever-receding horizon of unseen complexity. Our words simply refer to that which we can see without looking closely.
There is madness where Mandelbrot goes. Unspeakable, beautiful madness.
Seeing is Perceiving
Speaking of madness, there is much of it in the perception of what we see. An article in this month’s issue of Psychological Science explores the perceptions that arise from seeing what only appears on a political map:
By perceiving state borders to be physical barriers that keep disaster at bay, people underestimate the severity of a disaster spreading from a different state, but not the severity of an equally distant disaster approaching from within a state. We call this bias in risk assessment the border bias.
Marginal Revolution’s Alex Tabarrk quips, amusingly, the authors show that making the border more salient by darkening the border lines on a map can make people feel even more protected.
Of course, not all is madness, but this bit of madness is a poignant example of seeing forming the basis of perception.
Seeing is Conceiving
I looked into my wife Laurie’s eyes some years ago and saw something that led to a thought — a fascination and an obsession which grew into a romance to power a lifetime companionship. Other conceptions followed and what was seen in a moment has developed into another generation of humankind and unfathomably rich experiences.
Along with the hyper-stereoscopics of a full complement of senses, seeing feeds the mind with conceptual nutrients. Seeing provides the feedback from which the mind builds a virtual representation of our environment, upon which we can play-out our war games and love affairs in anticipation of, in preparation, for real events. Seeing truly is simultaneously an assessment of the moment and a vision of the future, for the mind was formed on the patterns depicted in a Mandelbrot set. Each moment being, to borrow Madelbrot’s words, a reduced scale image of the whole — a vision of past, present, and future in one.
Seeing puts us in touch with the concept of “our world.”
Seeing is …
… as seeing does. Our eyes gulp up an extremely narrow slice of light spectrum as it bounces off the elements around us. The data captured is only that which our eyes have been tuned to collect — tuned by aeons of exposure to our world’s evolutionary forces. The same forces work on the mind, which seeks to interpret the meaning of electrical impulses trigged with each spray of light to the eye. In fact, most of what we know as “seeing” takes place in the mind where images are formed, gaps are filled, associations are made and meaning attached. The mind does not even require feedback from the eyes to see, as each thought may form a vision independent from what the eyes have seen, and every dream is a holistic worldview, while the eyes flutter unseeing with REM syncopation. When we understand we may say, “I see.” When the mind sees, it interprets and tests, succeeds or fails, sees further then expands its range of vision, takes pleasure while learning from pain. Iterate. Iterate.
We have fashioned tools to extend our vision, devised conceptual frameworks and mathematical constructs to expand our view, and there is always a limit, a horizon, a frontier. What lies beyond we can only glimpse at its vanishing edge; where visions branch out of visions past, at once familiar and haltingly bizarre.
Seeing further, seeing deeper. Giving way to the next iteration.
Seeing is believing that, though one life may end, another will begin.
— —
*Benoît B. Mandelbrot, 20 November 1924 — 14 October 2010
NOTES:
- The Image – Galaxy of Galaxies is a computer-generated graphical representation of a partial Mandelbrot set. Featured at Wikimedia Commons, it sits among a large and fascinating collection of fractal images.
- Resources – Special thanks to Wikipeda with its wonderfully detailed and link-rich articles, and to the New York Times, and the UK’s Telegraph whose beautifully written tribute obituaries fed my mind. To the many bloggers in my feed who celebrated Mandelbrot’s life and the beauty of his achievements this past week, among them: Planet Money’s Jacob Goldstein and kottke.org’s Jason Kottke. Your posts were fractal events for my own. Also to Jeremi whose Through a Glass, Textured Seasons coincides my post with fractal beauty all their own. Finally to all of my colleagues here on Doves & Serpents: your phenomenal abilities as writers and editors are an inspiration to me.
- About – Cipher on a Wall is a weekly column and forum here on Doves & Serpents which explores the realm of mind, memories, and dreams. You can find an introductory post for Cipher on a Wall here and a full archive of posts here. My name is Matt, and I’ll be your host for the duration.
- Updates – the approach we’ll be taking with Cipher on a Wall is to encourage lively and ongoing discussion throughout the week between each Saturday edition. To help with this I’ll be returning to each post and adding updates in the form of additional thoughts, observations, related news, elevation of comments, links, additional resources. etc. Just know there will be updates so it’ll be worth checking back occasionally throughout the week.
Update 1
MoMA curator Paola Antonelli interviews Benoît Mandelbrot. Posting mostly as an opportunity to see that man behind the notion. (via SEED Magazine) …
Fascinating post. My husband and I watched a four-part documentary about Mathematics early this year — more his choice than mine I’ll admit, although, I found it really interesting in the end. One of the parts was about Mandelbrot and fractal geometry. Honestly, I found the mathematics difficult to grasp, but the subject of this post — the difficulty of seeing clearly and the way abstractions, such as maths and language, are useful, but limited, mostly by our perspective and how close we are willing to look — made a huge impression on me.
I’m not the math mind in my house, but geometry was one of my favorite subjects. I get a special thrill when I “see” patterns and symmetry in nature and the order helps with my perception of the natural, physical world. This was a beautiful post to read.
Heidi, Corktree, you both made me smile. Thanks!
I think it’s totally human to thrill at patterns and symmetry. It’s so beautiful to us, I think, because it’s part of us and among our most ancient memories — comfort food for the senses of all living beings if you will. :D
A recent edition of the BBC Science programme Horizon was entitled Is Seeing Believing?.
I liked the Inattention Blindness and the Sheppard’s Table illusions
Thanks, Steve. Right now I’m getting an error: “not available in your area.” I’ll try again later tonight but could it be that some programming is UK-only?
I’ve been thinking about this post Seeing, and how it relates to your post of a couple of weeks ago titled Forgotten. I think my memories are frequently a bit like images from an old filmstrip. Brief flashes of things, or even just a single scene frozen in time. Often visual. Flickering, and sometimes a bit stuck. Like old celluloid in the projector, a part of some fifth grade science lesson. The more recent events of my life are less like the filmstrip’s halting frames. They are more continuous. The frames of the filmstrip moving so fast now that the motions are smooth and seamless. Sometimes the events are flying by at such high speeds, it becomes a blur.
I love this series you are doing. The jump you make in your post from perception to conception is really nice. This sort of thing makes me want to write some poetry.
Oh, and nice to see you over in our little corner of the ‘nacle too.
Rebecca! I’m listening-in on the exponent feed. I’ll try not to cause a commotion. :D Love your description of how memories are experienced. I hope you decide to write some poetry and cross-post it here at D&S!
I agree with Rebecca – the posts in your column, Matt, flow and stretch the mind like poetry. I really enjoy reading them.
The idea of the horizon or frontier, that you end with, is an interesting one, because that frontier can always recede, when we travel towards it. Tools for extending sight are useful if we cannot travel from our spot (eg. telescopes for the earth-bound astronomer)… but the edges of sight will always inspire humankind to travel into the distance, to see further into the fractal’s depth.
When do we extend our vision by device – and when do we put down our machines, and walk? These metaphors have connection to our tasks of understanding and experience in our lives, I think.
Nice! I’d sure like to get up and do more exploration. It’s too easy to get into a ‘the world is a small place’ rut with this internet thingy. At the same time, look at me here chatting with you across time and space. What a head-trip.
On Saturday night, my husband and I watched a show about Hieronymus Bosch’s triptych “The Garden of Earthly Delights.” This is one of my husband’s favorite paintings. For years and years, we had a print of the middle panel hanging on our wall — I’d looked at this abstraction of the actual painting every day. The show, which was narrated by some art historian, kept focusing on different corners of the painting and I realized how little I had ever seen of it and how much I missed. Then, it showed the presenter standing next to the tryptych and I realized how I’d never understood the scale or size of it. It made me think of this post and how my seeing would change, yet again, if I were able to go to the Prado and see it in person (which I’m now dying to do).
I’ve seen it in the Prado. I’m no art critic, so I can’t speak intelligently about it, but it was definitely memorable. That and Picasso’s Guernica–not at the Prado, but still huge and mind blowing.
Both paintings are on my bucket list. I’d also love to see some Frieda Kahlo’s in person, but I think I have a better chance of getting to Madrid than Mexico City these days.
One other thing I forgot to mention is that I’ve studied Bosch’s work in a number of humanities/art history classes (I was an art history major for a few minutes) and I had never seen the panel closed until I watched the program the other night. When the triptych closes, there is a painting of the world in black and greys and a small painting of God in a dimly-lit cave, peeking in on his creations. Amazing.
Heidi, that’s amazing. I’d never really looked at all. Here’s a link to “The Garden of Earthly Delights” — and I’m curious about what part you had hanging in your living room? I hope you get a chance to go and see it in person.
We had this painting in an art book growing up (my dad is a painter and art professor). I spent time poring over it. I’ll admit the flowers popping out of someone’s rear end was always a draw :-)
Yeah — gotta say that I never noticed quite how subversive it was. It truly looks like a surrealist painting, but it was done roughly 400 years before.
Matt — it was a print of the center panel (not the Garden of Eden with the sad Jesus or Hell with the bird-head Satan).
Crazy, amazing, beautiful image… reminds me of Dali! His brand of Surrealism does have a strong connection with Catholic mythologies.
I like the idea of the new meaning and context a painting takes on when it hangs in a person’s home. Seeing an artwork in a gallery is something amazing, to be sure… especially when the scale of a large painting is involved. Have you been to the New Tate Modern, Heidi – they have a space for artwork in the turbine hall there that allows for a really incredible experience of magnitude.
What’s Jared’s take on the painting? Would he have preferred to have the whole image on the wall, or is the central panel best for that? :)