Why are some clues more specific than others?

In crime investigations fingerprints and DNA samples can provide important clues. Since no two people have the same set of fingerprints nor exactly the same DNA they identify individuals unambiguously. On the other hand, if a witness of a crime says the person running away has two arms and two legs, no one will marvel except perhaps at the naivete of this particular witness. Most people have two arms and two legs. Knowing that the suspect has two arms and two legs will not help us locate this person.

Why are some clues more specific than others? DNA is a specific clue; having two arms and two legs is not. (Indeed, having two arms and two legs is so useless as a clue that we might not want to call it a clue at all!) Now clues are the characteristics of structures, so one way to answer our question is to say, a clue is more specific if it is a characteristic found in a smaller number of structures. A particular DNA is the characteristic of just one person. Having two arms and two legs is a characteristic common to most human beings. DNA is a more specific clue than having two arms and two legs.

But this does not seem to be totally satisfactory. Consider the following. A murder investigation is nearing an end. Only two suspects are left: all the others have been ruled out. Of the two left only one is responsible for the crime; the other is innocent. So, who is the murderer? Which of the two?

Naturally, the thing to do at this point is look for more clues. Unfortunately in this case, none can be found. At the moment, everyone is still scratching their heads .... Then someone remembers: the person running away from the scene of the crime has two arms and two legs!

This wraps up the case. Why? Because of the two remaining suspects, one has lost a leg in an accident not so long ago.

Ordinarily, having two arms and two legs is not a specific clue but situations can arise in which it can become highly specific. In our example it is so specific that it points out who the guilty party is.

We have to re-think our question why some clues are more specific than others. We cannot say any more a clue is more specific if it is a characteristic shared by fewer structures. Most people have two arms and two legs; yet in our example having two arms and two legs became a significant clue!

It seems how specific a clue is depends on what stage of an investigation we have arrived at. In our example, at the beginning of the investigation having two arms and two legs is far from specific. Close to the end, it becomes highly specific. Why? What is going on?

I think what goes on is the following. We follow clues to reconstruct structures. Clues are the characteristics of structures but we do not gather all the characteristics first and then rebuild the structure. We do not ask, what are the characteristics of this crime? Then, after finding all of them, start to reconstruct the crime. Following clues is a narrowing-down process; we look for clues as we go along, to help us narrow down. In a murder investigation we do not start by suspecting everybody in the universe; we suspect only a tiny portion. As the investigation continues, as more clues are found, the number of suspects is whittled down until at the end the culprit is caught. But this is not yet the whole story. In order to pin down the murderer; in order to reconstruct the crime; we have to pin down the other players as well. Who are they? Where can we find them? What were they doing? What can they tell us? Are they telling the truth? In an investigation there are many things to pin down. A crime has many details (characteristics). The more of these details we can nail down, the clearer we will be as to who is responsible. Clues may not help us nail down all these details right away but they should at least help us converge on them.

What do we mean by 'converge on them'?

We mean having fewer interpretations ... We are converging on the things we want to know if our clues have fewer and fewer interpretations. If a clue tells us that the butler has to be in the room when the murder happened, we say this clue has nailed down the location of the butler: the clue has at this point only one interpretation. But sometimes a clue is not this specific. For example, it may only tell us that the butler is either in the room or the one next door. Clues are open to interpretations. The fewer interpretations a clue is open to, the closer it brings us to the truth. The more specific clues therefore are those that do not allow for much room in our interpretation. We have to remember, a clue is a characteristic of a structure, disguised. When the disguise is light it is easy to tell what it means. But when the disguise is heavy more than one interpretation of the clue will be possible. A characteristic under heavy disguise is a vague clue; a characteristic thinly disguised is more specific. But disguise is gradually removed as the investigation advances (things become clearer and clearer). At the beginning of an investigation knowing that the murderer has two arms and two legs would not help us but by the time the number of suspects is narrowed down to two this originally vague clue becomes highly specific.