It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature. – Neils Bohr.
Neils Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory. Although his model of the atom - a nucleus surrounded by orbiting electrons in discrete energy levels - has been supplanted by other models, another of his principles, complementarity, remains valid.
Complementarity is the idea that certain events can be analyzed into two different and opposite descriptions. For example, depending upon how the physicist is viewing light, it can be thought of either as a wave or as a stream of particles.
This situation occurs because we have no word to describe a single event which exhibits apparently mutually exclusive characteristics, consequently, we have a difficult time imagining how such an event can be possible. As Bohr stated it, “If anybody says he can think about quantum physics without getting giddy, that only shows he has not understood the first thing about them.”
Complementarity is not limited to the world of quantum physics; we frequently experience it in the macro world. Suppose you suddenly find yourself unemployed because of downsizing. After getting over the shock you can view this situation in one of two ways:
a) A calamity - What will I do without income? How will I eat? Where will I live?
b) An opportunity - I can go back to school or hitchhike across Europe or write the great American novel.
As in the example of the dual qualities of light, the interpretation is dependent upon how you view the situation. You might even change from one viewpoint to the other at different times.
Another example, this time from Mark Twain’s The Adventures of Tom Sawyer, is the situation in which Tom sees Becky Thatcher accidentally tear the schoolmaster’s anatomy book. Although he was upset with Becky for her refusal to accept his apology for an earlier indiscretion, Tom’s desire to see her punished was in direct conflict with the secret love he felt for her. (Love won out).
For other examples see any “horns of a dilemma” situation.
The point of this discussion is to show that there are some things in the world to which the rules of logic do not apply. Because the basis of our logic is the English language, it is limited to the rules of that language. In particular, two of the basic logical rules of English are:
1.) The Law of Identity says that entity A is A and not non-A. In other words a dog is a dog and not a cat, a tree is a tree and not a mouse, and in the case of quantum physics, a wave is a wave and not a particle.
2.) The Law of the Excluded Middle says if proposition A is true, the opposite proposition cannot be true, i.e. if it’s true that entity A is a wave, the proposition that A is a particle cannot be true.
In this age of “reality,” we are beginning to realize that under certain conditions the line from A to non-A, as well as the line from true to false, can be a continuum. Perhaps the ideal resolution of a problem is neither A nor non-A, neither true nor false, but somewhere in between. It’s the next step up from complementarity, and it’s called “fuzzy logic.” It should probably be called “reality logic.”
Another of Bohr’s quotations was, “No, no, you're not thinking; you're just being logical.” Now we know what he meant. Reality reminds me of a prairie dog community: the deeper we dig, the more complicated it becomes.
It boils down to this: Each of us tries to make sense of the world outside our heads by creating a matching logical world inside our heads. As we have seen, the logical world does not always match the real world, which on occasion can get us into trouble.
The same was true 2,000+ years ago; the early biblical writers were trying to understand what they were seeing in the “outside” world. They truly were the scientists of their day. However, they were saddled with two serious problems:
1.) Their language was mired in the laws of logic.
2.) They were the recipients of an age old tradition which attributed the workings of the world to the activities of gods, and while they managed to eliminate thousands of them by inventing monotheism, their progress reached a standstill at that point.
Entities were generally placed in either/or categories. From fig trees to individuals, an object was either good or evil, and a proposition was either true or false. There was no differentiation between a greater or lesser good; there were no shades of gray. The authority for such discrimination was God himself. It’s unfortunate they didn’t realize that God’s logic is the “fuzzy” type.
Don’t misunderstand me, traditional logic still applies to many, if not most, situations faced by people today. But we should always be aware that for any given event, complementarity, or even fuzzy logic may be apropos.