Some areas are built on foundations of fundamental principals that can be built upon. For example many of the world's religions have a form of the golden rule in their bedrock. Physics has a few of these cornerstones that are so deep they're considered beautiful and have become guides. I've been thinking about one of them - complementarity - a lot recently. Particularly as it appears outside of physics in many areas probably including some you're used to thinking about.
Neils Bohr and Albert Einstein were contemporaries - peers actually. Both were great sources of quotes. Einstein's fame is such that it's difficult to figure out exactly what he did say without original sources. Bohr's lack of fame outside of physics makes it easier. Here are a few:
“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough.”
“Never express yourself more clearly than you are able to think”
“A physicist is just an atom's way of looking at itself.”
“There are trivial truths and there are great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true.”
None were meant to be flippant and the last one is one of the richest quotes I know. Really deep ideas have meanings that go beyond the surface. As an example consider this question
"is light a particle or a wave?"
It turns out it's both, but sometimes it's most useful to describe it as a wave while other times you treat it as a particle. It's impossible to apply both descriptions at the same time. The essence of complementarity is there are different ways of looking at the world and each can have its own language and domain where it's true.
You can step back a bit and look at a satellite in orbit. Physics developed by Newton are good enough to put it there and predicting where it is to good precision, but if you're worried about the accuracy of its clock you need to bring in relativity. Einstein and Newton offer very different theories that describe orbital motion and how clocks keep time. Relatively turns out to be richer, but Newton's ideas are good enough for almost everything people normally do - that and I'd hate to describe the motion of a volleyball using special and general relativity.
I won't go into quantum mechanics, but complementarity is at the core how you think about things. That and like Newton and Einstein's models, there are boundaries where one is more useful than the other. The trick is knowing both and where the boundary lies. It's for another discussion, but I think complementarity is a good basis for talking about the concept of free will.
Bohr was so taken with the idea of complementarity that he made it part of his coat of arms with a nod to Eastern religious philosophies and the Order of the Elephant. (how's that for clickbait?)
Light offers another example. Newton used a prism to break whiteish sunlight into a spectrum of colors. Later Keats objected to the beauty of science claiming Newton unwove the rainbow.
Do not all charms fly/at the mere touch of cold philosophy?/There was an awful Rainbow once in heaven.
In reality something deeper is afoot.
Consider a yellow light on your desk. The wavelength of the light makes it look yellow, but if you are moving towards at a constant velocity you observe a shorter wavelength. If you're moving fast enough it looks blue. Faster still and it's ultraviolet. If you're moving away the wavelength lengthens and it shifts towards the red. In fact by selecting your velocity with respect to the light, the wavelength can be anything you want. In this view of nature the color of light only depends on your velocity relative to it. It may not seem useful, but it turns out to be one of the most important tools for measuring the size and age of the Universe.
Complementarity appears all over physics and turns out to be a useful way of thinking about new phenomena. Over time I've come to think of it in areas outside of physics. The spoken word and a television show can both get across their own versions of something. Neither is complete and understanding both can lead to a deeper appreciation. Picasso and Rembrandt had very different portrait styles and both tell us something deep about their subjects in very different ways. Mix different forms of art - a piece of music might describe the feeling of Winter quite differently from a painting, but both can offer deep if incomplete views of the feeling of the season. Sports are offer many examples. Movement in a sport can make statements that added with the emotion of the crowd give a more complete picture.
You can't use a flat Earth, geocentric universe, or being able to turn off gravity for an hour tomorrow. The descriptions have to be valid in some domain in the first place. But having two good but very different representations of something in your head at the same time may just lead to a deeper understanding. Usually you're not thinking about deep truths, but that's fine. This doesn't come easily, at least not to me, but it's a lot of fun once you get the hang of it.
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