March 16, 2017

What makes good rules?


One way to obtain knowledge in this world is to find a pattern. When we observe a pattern, we make a heuristic or a rule for future reference. A great example of this is science. This set of rules explains how universe work.

Why we need rules? First, it makes a lot of explanations for us, since explanation is just a set of rules that leads to an observation. Human always seeks for reason. Even when we can’t find an explanation, we make one up. Second, when a rule is strong enough, it also serves as a prediction, making future more deterministic and convenient. Science makes both advantages obvious.

Now we all know the importance of good rules and are ready to find them. However, we can’t find what is not sufficiently defined, so here comes the main question: What makes good rules?

Good is subjective. Let’s define it as useful. Something useful can help us achieve some goal. So, good rule should give us many accurate explanations as many as possible.

Here are two characteristics of good rules:

  1.  Predict future consistently
  2. General enough

The first one is quite obvious. Those that can predict future events accurately gives us more control over our surroundings. Physics, even a classical one, are good enough to predict next action of an object. Without the ability to predict, it’s just a statement that will be disproved sooner or later.

As an example. When we let go of an apple from our hand, it fell. We tried with few more apples and they all fell. Now we have a rule, that if we let go any apples, it will fell. Now we can give an explanation to people (and to ourselves), that there’s this rule in the world, that when we drop any apple, it will fall.

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Secondly, a rule should be general. General enough to be able to apply to similar circumstances that are in the scope of an event.
We can improve our “apple-fall-when-it-is-let-go” theory to make it more general. First, we looking around for something looking different from an apple, like a stone. Hold it in our hand, then try to let go. Unsurprisingly. It also fell.

Now we have an urge to make the previous theory more general, and more useful. So we step back from “apple” that is so specific. We define a new word that can represent both apple and stone, and anything else that we could hold in our hand. Suppose that we come up with a concept of “holdable object”. Our new theory is that if we let go a holdable object, it will fell. Congrats, our rule is now more general.

Of course, not only our new rule is so limited, it’s not even valid. If we hold a balloon and let go, it floats away. We now come to notice limits of our rule. To improve it further, we may invent physics. It predicts well and general enough to cover a wider range of objects.

Conclusion

Every time we come up with a rule or theory to explain an observation, we can assure that it is good by (1) prediction test: testing out again with the same or a similar object few more times if it gives the same result. Then, improve it with (2) generalization test: pick something else and do the same prediction test on it.

It a rule passes these two tests, it is good.