Nur die Fulle fuhrt zur Klarheit (only wholeness leads to clarity)

"At Como[1] in pleasant September Bohr[2] began with a polite reference to Volta, "the great genius whom we are here assembled to commemorate," then plunged in. He proposed to try to develop "a certain general point of view" which might help "to harmonize the apparently conflicting views taken by different scientists." The problem, Bohr said, was that quantum conditions ruled on the atomic scale but our instruments for measuring those conditions---our senses, ultimately-worked in classical ways. That inadequacy imposed necessary limitations on what we could know. An experiment that demonstrates that light travels in photons is valid within the limits of its terms. An experiment that demonstrates that light travels in waves is equally valid within its limits. The same is true of particles and waves of matter. The reason both could be accepted as valid is that "particles" and "waves" are words, are abstractions. What we know is not particles and waves but the equipment of our experiments and how that equipment changes in experimental use. The equipment is large, the interiors of atoms small, and between the two must be interposed a necessary and limiting translation. 

The solution, Bohr went on, is to accept the different and mutually exclusive results as equally valid and stand them side by side to build up a composite picture of the atomic domain. Nur die Fulle fuhrt zur Klarheit: only wholeness leads to clarity. Bohr was never interested in an arrogant reductionism. He called instead-the word appears repeatedly in his Como lecture for "renunciation," renunciation of the- godlike determinism of classical physics where the intimate scale of the atomic interior was concerned. The name he chose for this "general point of view" was complementarity, a word that derives from the Latin complementum, "that which fills up or completes." Light as particle and light as wave, matter as particle and matter as wave, were mutually exclusive abstractions that complemented each other. They could not be merged or resolved; they had to stand side by side in their seeming paradox and contradiction; but accepting that uncomfortably non-Aristotelian condition meant physics could know more than it otherwise knew. And furthermore, as Heisenberg's recently published uncertainty principle demonstrated within its limited context, the universe appeared to be arranged that way as far down as human senses would ever be able to see. 

Emilio Segre[3], who heard Bohr lecture at Como in 1927 as a young engineering student, explains complementarity simply and clearly in a history of modern physics he wrote in retirement: "Two magnitudes are complementary when the measurement of one of them prevents the accurate simultaneous measurement of the other. Similarly, two concepts are complementary when one imposes limitations on the other." 

Carefully Bohr then examined the conflicts of classical and quantum physics one at a time and showed how complementarity clarified them. In conclusion he briefly pointed to complementarity's connection to philosophy. The situation in physics, he said, "bears a deep-going analogy to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object." That reached back all the way to the licentiate's[4] dilemma in Adventures of a Danish Student[5], and resolved it: the I who thinks and the I who acts are different, mutually exclusive, but complementary abstractions of the self. 

In the years to come Bohr would extend the compass of his "certain general point of view" far into the world. It would serve him as a guide not only in questions of physics but in the largest questions of statesmanship as well. But it never commanded the central place in physics he hoped it would."

Richard Rhodes, The Making of the Atomic Bomb

Perhaps we need a concept like complentarity to help explain how a system can appear simple, complicated or complex at the same time.

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[1] a city and comune in Lombardy, Italy. It is the administrative capital of the Province of Como.

[2] a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922.

[3] an Italian physicist and Nobel laureate in physics, who with Owen Chamberlain, discovered antiprotons, a sub-atomic antiparticle.

[4] the title of a person who holds an academic degree known as a licence or a licentiate.

[5] A novel by Pohl Moller that gained lasting fame. It tells the comedic story of the romantic escapades of an eccentric student and his philosophical musings. Years later it became a favorite book of the Danish physicist and thinker Niels Bohr, who often quoted it during lectures