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And indeed in the literature of traditional science I have quite often seen models which were taken very seriously because they could be made to reproduce a few specific numbers, but which are shown up as completely wrong if one works out the overall behavior that they imply. And in my experience by far the best first step in assessing a model is not to look at numbers or other details, but rather just to use one's eyes, and to compare overall pictures of a system with pictures from the model.

If there are almost no similarities then one can reasonably conclude that the model is wrong. But if there are some similarities and some differences, then one must decide whether or not the differences are crucial. Quite often this will depend, at least in part, on how one intends to use the model. But with appropriate judgement it is usually not too difficult from looking at overall behavior to get at least some sense of whether a particular model is on the right track.

Typically it is not a good sign if the model ends up being almost as complicated as the phenomenon it purports to describe. And it is an even worse sign if when new observations are made the model constantly needs to be patched in order to account for them.

It is usually a good sign on the other hand if a model is simple, yet still manages to reproduce, even quite roughly, a large number of features of a particular system. And it is an even better sign if a fair fraction of these features are ones that were not known, or at least not explicitly considered, when the model was first constructed.

One might perhaps think that in the end one could always tell whether a model was correct by explicitly looking at sufficiently low-level underlying elements in a system and comparing them with elements in the model. But one must realize that a model is only ever supposed to provide an abstract representation of a system—and there is nothing to say that the various elements in this representation need have any direct correspondence with the elements of the system itself.

Thus, for example, a traditional mathematical model might say that the motion of a planet is governed by a set of differential equations. But one does not imagine that this means that the planet itself contains a device that explicitly solves such equations. Rather, the idea is that

From Stephen Wolfram: A New Kind of Science [citation]