Complexity Is Simple

By J. Peder Zane

Occam’s razor suggests that simpler explanations are, other things being equal, generally better than more complex ones. Given the world’s complexity, this would also suggest that immensely complex structures can derive from relatively simple ones.

I thought about this while reading an article in The New York Review of Books on George Dyson’s new book, “Turing’s Cathedral: The Origins of the Digital Universe.”

It focuses on the period in from the late 1930s to the early 1950s when researchers were trying to develop a universal machine, one that did not just perform mathematical calculations but a wide range of functions. The idea was to invent a language that would empower the machine to perform many functions – to be a calculator, a word processor, a gaming device and so on. The answer, first suggested by the English genius Alan Turing,” was a simple pattern of 0s and 1s. Reviewer Jim Holt writes:

“The genius of Turing’s imaginary machine, as Dyson makes clear, lay in its stunning simplicity. (“Let us praise the uncluttered mind,” exulted one of Turing’s colleagues.) It consisted of a scanner that moved back and forth over an infinite tape reading and writing 0s and 1s according to a certain set of instructions—0s and 1s being capable of expressing all letters and numerals. A Turing machine designed for some special purpose—like adding two numbers together—could itself be described by a single number that coded its action. The code number of one special-purpose Turing machine could even be fed as an input onto the tape of another Turing machine.

“The boldest of Turing’s ideas was that of a universal machine: one that, if fed the code number of any special-purpose Turing machine, would perfectly mimic its behavior. For instance, if a universal Turing machine were fed the code number of the Turing machine that performed addition, the universal machine would temporarily turn into an adding machine. In effect, the “hardware” of a special-purpose machine could be translated into “software” (the machine’s code number) and then entered like data into the universal machine, where it would run as a program. That is exactly what happens when your laptop, which is a physical embodiment of Turing’s universal machine, runs a word-processing program, or when your smartphone runs an app.”

Most intriguing was the fact that another entirely different but eerily similar breakthrough was made around the same time – Watson and Crick’s discovery of the structure of DNA in 1954. I am not a geneticist, but as I understand it just about all of life is based on the patterns created by the four bases found in DNA: adenine (abbreviated A), cytosine (C), guanine (G) and thymine (T). Through this, Holt writes,” the digital basis of heredity became apparent.”

That is, while our world may appear to be supremely complicated, it rests on workings of sublimely simple patterns – the permutations created by 0s and 1s and the four bases of DNA.

I am particularly drawn to this idea because my new book, “Design in Nature,” shows how all the structural patterns we see in nature can be predicted by a single principle discovered by Adrian Bejan, the constructal law. It holds that all design (all shape and structure) emerges and evolves to facilitate flow. If you want to know why something looks the way it does, ask what flows through it. A river basin, for example, is a design to move water, a lightning bolt moves electricity, your body moves your mass. This is the paradox of life: everything is unique and complex; just about everything results from simple pattern.

I will add that my love of literature is what attracted me to Bejan’s science. In giving meaning to experience, literature finds the common ground among us; it helps us connect the dots between our unique experiences and those of all around us. At its best, it cuts through the transient to help us see the (semi) enduring fundamentals. It reveals the simple ideas that are the foundation of our complex world, of everything from the biology of single cells to the mysteries of the human heart.

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