Today’s guest blogger is Judith K. Boyd. Boyd is a Senior Fellow at the Long Island University’s Homeland Security Management Institute.
Nature has been using fractal geometry to solve complex problems since the beginning of time. Perhaps it is time for homeland security professionals to tap into this mechanism to solve those nagging problems that don’t seem to be going away, such as, what causes a seemingly normal person to want to put a bomb in Times Square?
In his 1975 ground breaking book, “Fractals: Form, Chance, and Dimension,” Dr. Benoit Mandelbrot asserted that many forms in nature can be described mathematically as fractals, shapes that appear to be jagged and broken.
A fractal is created by taking a smooth looking shape, such as a triangle, and breaking it into pieces, over and over again. Through the application of this simple principal, you are able to to transform that simple shape into a figure rich with complexity and texture.
The inverse of the fractal principle is that you can take something that appears to be complex and break it down into the repeating patterns that build upon each other to create the larger whole.
We can see this demonstrated graphically in the well-known woodcut, “The Great Wave off Kanagawa,” produced by the Japanese artist Hokusai in 1832. From afar, we see an image of a large wave about to crash over a small fishing vessel. And yet, if we look closer, we can see that the large wave is actually comprised of a repeating pattern of smaller waves.
The curves that repeat over and over are not random but rather, according to Mandelbrot, predictable shapes that can be described in mathematical terms.
How to apply this new language, especially in this age of nearly unlimited computing ability, is yet to be fully realized. However, it is clear there is tremendous potential for solving what have been seen, up until now, as unsolvable problems.
For example, when you plot the intervals between heartbeats and expand them, healthy heartbeats have an interval that may be measured through a distinctive fractal pattern. Scientists such as Dr. Ary Goldberger at the Harvard Medical School have been analyzing how this signature may allow cardiologists to discover when a patient has a heart problem long before the heart attack occurs.
Another scientist, biophysicist Dr. Peter Burns in Toronto, Canada, has been studying how to develop mathematical models to detect small tumors. Conventional technology, such as ultrasounds, do not have the capability to show the network blood vessels that grow around tumors as small as few tenths of a millimeter across in diameter. But an ultrasound does provide a very good image of the movement of blood. Burns and his colleagues used the simple rules of fractals to create models of “normal” blood vessel activity — a well-organized network of vessels not unlike the branches of an elm tree. This model may then be compared to an ultrasound image of a patient who might have a tumor. Analyzing the image with fractal geometry principals reveals a pattern of blood flow not like a strong limbed tree but rather, a tangled mess of shrubbery.
This approach turns on its head the conventional wisdom that technology must get more and more precise in order to inform the doctor. What fractal geometry allows us to do is analyze information available today in the absence of far more precise and intrusive technology. The reason for this is because the human body, like nature, repeatedly demonstrates a tendency to naturally select those features and activities that are the most efficient and most productive. Hence, the potential to understand what is “normal” and through comparison, identify what is not.
What else can we “see” through the application of fractal geometry?
If we view humans and societies as machines, the potential to apply these rules begins to emerge. If the ideas of al Queda are viewed as a network that is self-sustaining, what is the relationship between mass and energy use? How much energy does the movement require to grow and branch off? What are the trigger points for a new branch or offshoot to develop? According to fractal code, there are rules that identify the pre-defined trigger points that will lead to a new branch off-shoot. Hence, what appears to be a complex network is in reality, a repeatable process. If you understand what makes the tree grow, you will understand how the rainforest is sustained. Taken to its logical end, we should be able to understand the sum by analyzing just a few of its parts. It may not be coincidence that Faisal Shahzad and Najibullah Zazi had roots in working or middle-class society, some college education and no previous criminal record.
Note to all Intelligence Community recruiters: hire more mathematicians!
Note: If you are interested in learning more about fractals, here is a link to a 1 hour video from NOVA, called Hunting the Hidden Dimension