My Dominant Hemisphere

The Official Weblog of 'The Basilic Insula'

On The Impact Of Thinking Visually

with 5 comments

Romanesco broccoli - One of many examples of fractals in nature. (Wikipedia)

Romanesco broccoli - One of many examples of fractals in nature. (Wikipedia)

What do Mandelbrot and Einstein have in common?

They were/are both math aficionados. But more importantly, they both laid down the foundations for thinking about abstract natural phenomena in a geometrical way. The impact was reverberating.

Before Einstein came along, people had no real sense of gravity at all. Yea sure, there was Newton’s universal law of gravitation. But no one really could make any sense whatsoever of how exactly gravity might operate. Was it a wave? If so, at what speed could it act? Was there something particulate about it? Gravity was so mystical. And as always, so have been the concepts of time and space. Einstein’s greatest achievement in my view is that not only was he able to lay out the underpinnings of such phenomena in the form of a couple of abstract equations, but perhaps more importantly, that he devised a method to think about them visually. In developing his theories of special and general relativity, Einstein proposed the idea of the space-time fabric. It has a 3-D structure, yet represents four dimensions – 3 in space and 1 in time. Gravity would result from distortions in this fabric. The speed with which gravity could influence an object would depend on how fast these distortions could travel. And this central notion of ‘distortions in a fabric’ would also influence our understanding of the more difficult to grasp concepts of time and space. Time and space could mean different things to different observers depending on how this fabric was warped or sliced.

Mandelbrot achieved the same thing with his theory of fractals. How can complex natural structures and phenomena be represented mathematically? How to mathematically model a plant, the form of a human or a mountain range? In spite of how incredibly difficult it all sounds, these complex shapes could all be simplified into repeating units of tiny yet geometrically simple components – fractals. Mandelbrot went on to write his epic, “The Fractal Geometry Of Nature” and there was no turning back. Suddenly so many of nature’s workings could now be analyzed mathematically. An immensely significant step for mankind indeed. What I find absolutely fascinating about fractals, is the discovery that many intangible natural phenomena also contain a fractal component. Dr. Ary Goldberger and his team of researchers at Harvard Medical School have been working on applying fractal theory to medicine and biology. For those of you who might not be familiar with Dr. Goldberger, the name might ring a bell if you’ve read his books on electrocardiography. For Dr. Goldberger, interest in electrocardiography runs in the family, his father having invented the augmented limb leads back in the day. Among some of the things I learned about his work on electrocardiography, is that his team has shown that there is a fractal nature to ECG waveforms! This isn’t something like representing the heart itself in fractal form. It’s the activities of the heart that we are talking about here. Something really quite abstract. By looking at these fractal patterns, one could potentially detect pathology at a much earlier stage. Fractal patterns and their aberrations could help detect diseases in ways that no one had ever imagined! If you want to dig what’s cool, check out what’s been going on in the world of fractals in medicine – from human vasculature, to the brain and beyond. A quick PubMed query would lead you to a lot of riveting literature on the topic. Don’t forget to also take a look at the excellent documentary on fractal theory from PBS NOVA, “Hunting The Hidden Dimensions“.

Copyright © Firas MR. All rights reserved.

Readability grades for this post:

Flesch reading ease score: 61.1
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Flesch-Kincaid grade level: 8.2
Coleman-Liau index: 10.8
Gunning fog index: 11.6
SMOG index: 11


Written by Firas MR

August 18, 2009 at 11:48 pm

5 Responses

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  1. Wow ! Is that broccoli real ?! I’ve never seen one like that !
    The theories of relativity still fascinate me because time and again I find myself understanding it and chin-wagging but I go back to read it again only to forget !

    I haven’t had much exposure to the application of fractals but they are so neat to create and admire 😉


    August 19, 2009 at 12:49 am

    • Thanks for dropping by Jaffer 🙂 ! You know, I’ve been inspired to read James Gleick’s “Chaos: Making a New Science” after having learned some of the things about fractals. Another book to put on my to-read shelf 🙂 . Should make for some interesting blogging material later!

      Firas MR

      August 19, 2009 at 1:37 am

  2. Hi there!

    Thanks for this fascinating post. I’ve been participating in a photo-a-day project with Jaffer and this was my pic of today: I had no idea what it was when I saw it, I’d never seen such a strange vegetable before. As the discussion on Frapto deepened, Jaffer pointed me to your post and I must say, that is one fascinating broccoli! I’m not so science-minded, but I really enjoyed reading your post. Best of luck to you!



    January 6, 2010 at 6:23 pm

    • Hey Sezin! Thanks for dropping by 🙂 . I hope to see you visiting again 🙂 !

      Firas MR

      January 6, 2010 at 6:45 pm

  3. […] On The Impact Of Thinking Visually […]

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