Now that I have, ahem, explained my take on explanations, Uncertainty Wednesday can move on to examine what limits them. Again, as a reminder, the whole point here is that limits to explanations and to observations are what results in uncertainty (we will soon also talk about whether there is anything such as inherent randomness in underlying reality).

The fundamental limit on explanations is the same thing that gives them power in the first place: they are abstractions, meaning they are more general than a specific set of observations. Let’s stick with the example I used when introducing explanations: the relative motion of the Earth and the Sun. I defined an explanation as a “relational story about reality” – such as the Sun revolves around the Earth (as we first thought). In retrospect I should have maybe added the word “abstract” to this description. Because the following is *not* an explanation: “At 8am the Sun was at an angle of 20 degrees, at 10am the Sun was at an angle of 40 degrees, at noon it was at an angle of 80 degrees …” – this is simply a set of observations! No matter how detailed I make this, it is not an explanation of the motion of these two objects.

As a great comment on last week’s post pointed out, the nature of an explanation requires that it is more general (more abstract) than a specific set of observations. So let us consider some possibilities for abstract motions of the Earth and the Sun. In the original geocentric model, the Sun and the planets were believed to have a perfectly circular orbit around Earth. It turned out to be difficult to reconcile this with observations and ever more elaborate geocentric explanations involving so-called epicycles were proposed. Then came an explanatory breakthrough with Copernicus’s publication of the heliocentric model. But Copernicus still used perfectly circular paths as his abstraction. It was not until Kepler that the abstraction was shifted to an elliptic path which fit much better with Tycho Brahe’s extensive observations.

Throughout the series this will turn out to be a fundamental idea: there is an interaction between observations and explanations through which both of them get better over time which in turn reduces uncertainty. But that’s not the main point of today. Today’s main point is that even an elliptic path is still an abstraction. It is not the same thing as the actual path taken by a planet (which is what I call reality) and it is not the same thing as a series of observations of that reality. Or to state it positively: reality are the actual paths of the planets, Tycho Brahe provided us with extensive observations and Kepler gave us an explanation.

Being abstract and general is what gives an explanation its power. We can apply it to any planet or even man-made space object. We can apply it to planets in other solar systems. But it is also a limiting factor. Any one specific orbit may or may not correspond to it. That results in uncertainty about that orbit! And when it doesn’t correspond that winds up being an important source of information. For a fascinating example of exactly that happening, you can read up on the so-called Pioneer Anomaly.

Before wrapping up today here is another important point about explanations. Kepler’s elliptical orbit is in my terminology an explanation, even though he did not say *why* planets are on this orbit. It was Newton some 80 years later who provided his theory of gravity, which was later superseded by Einstein’s. So an explanation in my terminology does not necessarily need to speak to causality or “explain” why something is happening, it just needs to express an abstracted relationship about real entities (see also my reply here).