What is a short theory, anyway?


(filling in a detail that arises in the last few entries)

Short theories are to be preferred. What is a short theory?

It may be that there happens to be a short theory that exactly matches the data in every detail. But rather more commonly a short theory will only match the data to within some margin of error. When talking about short and long theories, we will most often be talking about probabilistic theories.

Now in this case it will almost certainly be wrong to say that those details a short theory does not explain are some sort of pure quantum randomness. Far more likely is that the randomness is pseudo-randomness, arising from details that we simply don't know or don't have the computing power to analyse.

So, generally, a short theory is an incomplete theory. It's a small fragment of the true reality. This would be similar to an incomplete assembliage in Ghost Diagrams containing only a small number of tiles.

A short incomplete theory has two advantages over a long incomplete theory. Firstly, it stands for all complete theories of which it can be a part, and the total likelihood of all those theories is likely to exceed the total likelihood of all theories containing a larger fragment. But even if we divide out this factor, assessing the average rather than total likelihood of all theories it could stand for [1], there is still the hope that it has been produced by performing a thorough survey of all small fragments. Such a survey quickly becomes impossible for larger theories, so any proposal of a longer theory is almost certainly biassed.

[1] This is actually the normal English usage of the word likelihood. For example, which is more likely: that I die before I reach the age of forty, or that I die at age 83 from a heart-attack while eating spaghetti? And so this is the usage of "likely" that is intended when asking the question "which of these theories is most likely?"