This post is inspired by a series of Facebook discussions.
In this blog post I shall assume importance, interest and notability to mean the same thing. I shall also assume that lists are always well-ordered — that is, of any two elements in the list, one must come before the other.
Claim 1. It is not possible to rank the world’s people by importance.
Proof. Suppose the contrary, that there is a list of all of the world’s people ranked by importance. Then there must be some person at the end of the list (ie, the least interesting person). But this person is at the end of a list, which must give him some notability. Hence this person is no longer the least important person in the world. By contradiction, the list cannot exist.
Claim 2. It is indeed possible to rank the world’s people according to importance.
Proof. We show this by counterexample. Suppose the world has one person. Then there is only one possible list.
Objection 1. Then the list is impossible if the world has more than one person.
Reply. This is untrue. Suppose the world has two people: one person of very high importance, and the other of far less importance. Now we put them in a list. Clearly it does not matter that the less important person is at the end of the list. The same can apply if the world contained 3 people: two people of high importance and one person of low importance: nobody cares that the person is at the end of the list: it is true but that does not remove him from being at the end of the list. This works for 4 people, 5 people, n people, n+1 people.
Objection 2. You have not defined what importance means.
Reply. Importance is usually defined as a combination of wealth, power, achievements, and such. But it does not matter how we define importance. The only requirement is that the definition of importance of a person is affected at least partially by his position on the list: otherwise there is no contradiction.
Objection 3. How is the list constructed, then, if to give a person a rank on the list, one has to already know his position on the list?
Reply. The list can be constructed sequentially – that is, constructed using all factors but the list factor (the position on the list affecting notability). Then the list is rearranged when the list factor comes in and affects the notability. This is repeated until no more conflicts occur.
Objection 4. This is wrong. Suppose that there are three people in the world: one of great importance and two equally boring people. Of the second and third people (the two boring people), one has to be at the end of the list and the other at the middle. Then by the fact that the third person is at the end of the list, he is more notable than the second person, thus going up a place in the list. Then the situation plays out in reverse, forever vibrating between the two states. The list cannot exist.
Reply. Then the list can be constructed declaratively instead of procedurally – like solving a system of equations. If you put the person of great importance in the middle and the boring people at the two ends, then the list no longer vibrates.
Objection 5. But the point is that one person has greater importance than the other two, thus it doesn’t make sense to put him in the middle of the list.
Reply. Then we redefine the definition of importance and notability to be affected only by a person’s position in the list. This way, the list is stable.
Concluding objection. What is the point of such a list then?