Sense of Harmonious Proportionality
Tribute to Mandelbroth for the Magic of Symmetry and Fractals

Purpose of the Article
In this article, I reflect on my thoughts, experiences, and memories of harmonious proportionality as a secret of life energy and underlying universal mechanism.
I believe that art and science are strongly interrelated, and philosophy fills in the gaps and provides essential connectivity.
Technology and engineering make the relationships tangible and concrete. I am not sure about politics and religion though hence need to explore the relationship from the body of knowledge.
What is the sense of harmonious proportionality?
The answer is symmetry.
There is symmetry in objects in various ratios.
Nature is the prime example.
Symmetry is an indistinct sense of harmonious and aesthetically pleasing proportionality.
Symmetry creates balance such that it can reflect beauty and excellence.
Some even call it perfect but I removed this word from my vocabulary.
Introduction to Fractals
There are various types of symmetry; for example, reflection, rotational, translational, helical, and most prominently fractals.
Fractals have a special meaning for me.

When I see fractals many fond memories arise: some joyful, some uplifting, and some sad.
Fractals were invented and created by one of my distinguished mentors at IBM.
I learned a lot from Benoit Mandelbrot when he was consulting in our research department.

The key concepts in his distinguished theories were the art of roughness, self-similarity in nature, and the uncontrolled element in life.
In some ways, his theories attempted to explain the secrets of life energy and the secrets of the mysterious universe but he did not get a chance to articulate it. Only a few understood his messages though! Fortunately, some mathematicians and scientists, including quantum physicists continued further studies on fractal geometry in various established research organisations.
He was elderly when I met him, close to his 80s but he was still working as an IBM fellow consulting passionate researchers with a sharp mind and excellent vision.
Mandelbrot was ahead of his time; much ahead!
In those days, his famous statement was quoted in the press: “Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.”
He had a strong academic background but initially, he preferred to work in industry labs. When I asked his advice, he was an ardent supporter of my choice for working in the industry rather than in academic institutions.
I followed his path and advice. His confession on this point was also quoted in the leadership literature when he famously said “I was in an industrial laboratory because academia found me unsuitable”.
Even though initially, he did not work as an academic, he was still passing on his knowledge, for example, teaching at Harvard University during his recreational leaves in his IBM tenure.
Then, he was offered as a sterling professor of mathematical sciences at Yale.
We sadly lost him, over a decade ago, on 14 October 2010.

He left a fascinating legacy of fractals for symmetry lovers in art and science.
Mathematicians and many scientists adored Mandelbrot and recognized him as “fractalist”.
Many artists used fractals to express universal emotions.
His theories contributed to many disciplines such as physics, medicine, geomorphology, anatomy, neurology, hydrology, computer science, engineering, and cosmology.

Mandelbrot taught us that things typically considered to be rough, messy, and chaotic such as clouds and shorelines, had a degree of order.
This exquisite and insightful learning helped the scientists and philosophers to redefine the mechanics of life energy and the underlying universal mechanisms.
Rather than delving into deep scientific and philosophical aspects in this short article, let me give you a taste of Mandelbrot’s famous fractals animated in the attached Youtube video to appease your symmetry sense.
Please don’t stand up immediately after watching this. Ensure your eyes are adjusted back to reality and you don’t feel dizzy.