Friday, February 11, 2011

"Explanation" between concrete and abstract

I realized that an apparently well-understood word, "explanation", may lead to controversies in discussions about the foundations of physics. The foundations are already controversial enough, but this adds even more to the confusion. It gives you a double featured feeling: on the one hand, of being misunderstood, and on the other hand, that you don't understand where the interlocutor is going on.

What is an "explanation"? Probably the most usual meaning is that explanation is to reduce the unknown to the known, the unfamiliar to the familiar. When this happens, we get the sense of understanding.

Even since childhood, we had so many questions, and the grown ups explained them - reduced the unfamiliar to more familiar notions. In school, the teachers continued to provide us explanations, and we appreciated most the teachers who managed to make the unclear things more intuitive for us. When reading about the foundations of physics, we usually start with popular physics books. The most recommended such books are those providing the feeling of understanding, appealing to our intuition. When we try to read something more advanced, even if it is recommended by our favorite pop-sci books, we find ourselves in a totally different situation. Instead of finding the deeper explanations we are looking for, we find ourselves thrown in the turbulent torrents of the abstract mathematics, drifting without an apparent purpose. And what is most annoying, these textbooks and articles full of equations actually claim to explain things!

Why is this happening? I think that they are guided by another meaning of the term "explanation": "to give an explanation to a phenomenon is to deduce the existence of that phenomenon from hypotheses considered more fundamental. For example, when from the principles of General Relativity was deduced the correct value from the perihelion precession of Mercury, it was considered that GR explained this precession. On the other hand, the deflection of light by the Sun was considered a prediction. After the full experimental confirmation, it became an explanation. I consider that "prediction" is just a temporary status of a scientific explanation, and that the fact that many explanations are first predictions is a historical accident.

There seem to be a similarity between principles/phenomena and axioms/theorems. This similarity suggests the reason why mathematics plays such an important role in the explanation of phenomena. To deduce more from less, complicated from simple, diverse from universal, this means to use logic and mathematics. And there is no limit of the difficulty of the needed mathematics, even if the principles are not that difficult.

This notion of explanation, I understand now, it is not shared by all of us. The reason is simple: because "explanation" usually means to reduce the unfamiliar to familiar. When somebody claimed to explain a phenomenon, we expect him to show how this strange phenomenon can be described in more familiar, concrete terms. Instead, we find that he or she starts describing it in more abstract terms. How come that such more and more abstract terms are shamelessly named "more basic principles", "more elementary principles" and so on? Isn't this a lie?

Maybe the explanation by "reducing to concrete things" has pedagogical reasons, and the explanation by "reducing to universal principles" is in fact foundational research. But does this means that the gap between pedagogical and scientific explanation should grow as it does nowadays? Wouldn't be much, much better to have a mechanistic explanation? After all, Maxwell sought for such an explanation of the electromagnetic waves, even though he had the equations! The ether theorists of the XIXth century tried to reduce electromagnetism to vibrations in a medium. This tradition still continues, and we encounter on a daily basis renowned scientists trying to explain things which other renowned scientists consider to be already explained: electromagnetism, wave-particle duality, gravity, entropy, the Unruh effect, spacetime, time, black holes and so on.

Probably it would be better to have a mechanistic explanation of everything. This would definitely help the public outreach of physics, and will help physics to advance faster. This may have a huge impact on technology, and on our lives. But who can bet that God, when created the world, bothered about our need to reduce the things to what we know? Why would the universe care about our limited understanding, when decided what principles to follow? Who are we, why would we be so important? I think that, although it would be desirable to find concrete, familiar universal principles behind this complex and diverse world, we have no guarantee that this will ever happen. "You shall not make for yourself a carved image, or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth."

The definition of "explanation" as a reduction to universal principles has its own advantages, given that we do not take these principles as ultimate truths, but just as hypotheses. One of these advantages is that it allows us to equally appreciate theories which seem to contradict each other. We can appreciate its explanatory power in the sense stated above: as its efficient encapsulation of a wide variety of phenomena in fewer, simpler, and more general principles. This doesn't mean that we should consider these principles as being "true". It is not about being "true", just about encapsulating as much phenomena as possible in as few principles as possible, even if these principles are more abstract. If we insist to become fans of one theory or another as the ultimate "truth", we may reduce our capacity to grasp other explanations. This would not be a problem, if we could prove our theories beyond any doubt, but the truth is that we cannot, no matter how convincing they may look to us.

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