The Mind-Expanding Power of Complementarity

In his Pensees (“Thoughts”), Blaise Pascal wrote: “By space the universe encompasses and swallows me up like an atom.” In Leaves of Grass Walt Whitman wrote: “I contain multitudes.” On the surface, Pascal and Whitman seem to be saying very different things. Pascal says we are small; Whitman says we are large.

Yet both are profoundly correct. Science not only supports but amplifies their famous declarations. Modern cosmology has revealed a universe vastly larger than Pascal could have conceived in 1660. And today we can appreciate the true complexity of Whitman’s brain, which incorporates tens of billions of vibrant, interconnected neurons, more clearly than Whitman himself could in 1855.

Complementarity is the realization that a single thing, when considered from different perspectives, can appear to have different, or even contradictory, properties. Complementarity alerts us that answering different kinds of questions can require radically different approaches.

My goal in writing Fundamentals: Ten Keys to Reality was to unlock the treasure of what everyone can know about the physical world. That treasure is not an attic crammed with dusty facts—though it contains many surprising facts—but a broad vista including our best current understanding, the reasons why we trust it, its limits, its meaning—and some guesses about its future.

As a discipline to myself, and to make things easily digestible and memorable for my readers, I decided to follow a long tradition, inspired by the Ten Commandments and the tenfold lists you find in many modern self-help books, by organizing the presentation around 10 powerful statements: the “Keys to Reality” promised in the subtitle.

My first key to reality, “There’s Plenty of Space,” goes deep into the issues raised by Pascal and Whitman, mentioned above. That was an obvious starting point. Later choices were not always so obvious, but I settled on a list of nine fairly easily. I hoped that thinking and writing about those nine would suggest another.

And that is what happened. My 10th key to reality, which emerges from but in some ways transcends science, turned out to be “Complementarity is Mind-Expanding.” Complementarity is an attitude toward life that I’ve found eye-opening and extremely helpful. It has, literally, changed my mind. Through it, I’ve become larger: more open to imagination, and more tolerant.

Let me give two important examples of complementarity in action. The first is the complementarity between analysis and synthesis; or, in popular jargon, “reductionism” and “holism.”

There is immense satisfaction to be had in describing the world in terms of its most elementary building blocks. It is tempting to say that this is the ideal description, while other, high-level descriptions are mere approximations—compromises, that reflect weakness in understanding. That attitude, which makes the perfect the enemy of the good, is superficially deep, but deeply superficial.

In order to answer questions of interest, we often need to change focus. To discover (or invent) new concepts, and new ways of working with them, is an open-ended, creative activity. Computer scientists and software engineers are well aware that in designing useful algorithms it is important to pay attention to how knowledge is represented. A good representation can make the difference between usable knowledge and knowledge that is there “in principle,” but not really available, because it takes too long, and too much trouble, to locate and process. It’s like the difference between owning bars of gold and knowing that in principle there are vast stores of gold atoms floating dissolved in the ocean.

For that reason, complete understanding of the fundamental laws, if we ever achieved it, would be neither “The Theory of Everything” nor “The End of Science.” To do decent justice to reality, we would still need new ideas and complementary descriptions. There would still be plenty of great questions left unanswered, and plenty of great scientific work left to do. There always will be.

The complementarity between humility and self-respect is, I believe, the central message of Fundamentals as a whole. It recurs as a theme in many variations. The vastness of space dwarfs us, but we contain multitudes of neurons, and of course vastly more of the atoms of which neurons are made. The vastness of cosmic history far exceeds a human lifetime, but we have time for immense numbers of thoughts. Cosmic energies outstrip what any human, or even humanity as a whole, commands, but we have ample power to sculpt our local environment and participate actively in life, love and adventures among other humans. The world is complex beyond our ability to grasp, and rich in mysteries, but we know a lot, and are learning more. In each case humility is in order, but so is self-respect.

The word “complementarity” was introduced into scientific and philosophical discourse by Niels Bohr, a founder of modern quantum theory. Within quantum theory, complementarity is not merely helpful but essential. It arises in the interpretation of Heisenberg’s uncertainty principle, according to which it is impossible to predict both the position and velocity of a particle simultaneously.

In quantum theory, the fundamental description of a particle is given by its wave function. Theoretically, the particle’s wave function supplies the answer to any question about the particle that it makes sense to ask. We do not have empirical access to the wave function itself, however, but only to processed versions of it. One way of processing gives us predictions about the particle’s position; another way of processing gives us predictions about its velocity. Sadly, those two ways of processing are mathematically incompatible. In this setting, complementarity is a theorem: different questions correspond to different aspects of reality, which do not yield to a single description.

Though Bohr first articulated complementarity in the 20th century, once you’re alert to it, you can find many traces of it in the science, literature and art of earlier times. Pascal’s quote concludes: “Through space the universe grasps me and swallows me up like a speck; but through thought I grasp it.” And Whitman’s, in context, is a wonderfully poetic celebration of complementarity:

Do I contradict myself?

Very well then I contradict myself,

(I am large, I contain multitudes.)

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