theory

Those who are enamoured of practice without science are like a pilot who goes into a ship without rudder or compass and never has any certainty of where he is going. Practice should always be based upon a sound knowledge of theory.

He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may cast.

If Darwin's theory of evolution was correct, cats would be able to operate a can opener by now.

There is nothing so practical as a good theory.

Of course, we knew that the official reports were sketchy, if not falsified. But, in terms of information theory, this is precisely where the problem lay: How were we to reconstruct reality from incomplete or false reports? It is not true that virtually all news in a totalitarian state is false. On the contrary, most news is completely correct, albeit tendentiously slanded; it is just that certain information is suppressed. One can adjust for the political slanting of the news, but there is virtually no way to fill in the omissions.

The hard part is keeping it simple. Says Farmer, "The more complex the problem is, the simpler the models that you end up having to use. It's easy to fit the data perfectly, but if you do that, you invariably end up just fitting to the flukes. The key is to generalize." Prediction machinery is ultimately theory-making machinery -- devices for generating abstractions and generalizations. Prediction machinery chews on the mess of seemingly random chicken-scratch data produced by complex and living things. If there is a sufficiently large stream of data over time, the device can discern a small bit of pattern. Slowly, the technology shapes an internal ad hoc model of how the data might be produced. The apparatus shuns "overfitting" the pattern on specific data and leans to the fuzzy fit of a somewhat imprecise generalization. Once it has a general fit -- a theory -- it can make a prediction. In fact, prediction is the whole point of theories. "Prediction is the most useful, the most tangible, and, in many respects, the most important consequence of having a scientific theory," Farmer declares.

Do not use more precision in your theories than is necessary.

Why do I think that we, the intellectuals, are able to help? Simply because we, the intellectuals, have done the most terrible harm for thousands of years. Mass murder in the name of an idea, a doctrine, a theory, a religion - that is all "our" doing, "our" invention: the invention of the intellectuals. If only we would stop setting man against man - often with the best intentions - much would be gained. Nobody can say that it is impossible for us to stop doing this.

Theory attracts practice as the magnet attracts iron.

A great part of its [higher arithmetic] theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.