Ranking (part 6): Randomness and lists

In the last post I have stated that random lists are boundary objects: They include a low level of list-ness, and can therefore often better be described as sets or groups (I used these two terms quite carelessly as interchangeable - I will stay with the term 'set'), which have a certain degree of list-ness. Now I want to look into this a bit more thoroughly. To look at boundary objects such as random lists can teach me more about lists in general.

My question is: What is the random in random lists? I pose that it can be threefold.

The first kind of randomness is given, when a list contains randomly selected elements. What we can see here is that all lists are sets (but they are of course also more than sets, as I will develop later). In a way you could say: Such a list/set is based on no selection criteria. However, to say this is true and not true. It is only true in the sense that there are little logic criteria for inclusion: It is not based on significant traits of the elements.

So why is it untrue? A list based on random selection still contains elements (otherwise it would be no list/set at all). The element happened to be included in a moment of random selection. The criterion is the random inclusion of the elements in a past event. To take an obvious example: A, B and C can be part of a list/set, because Joe decided by drawing lots that A, B and C are members of his team. But even if in such a situation, such a list/set is still defined by this random decision. As soon as Joe has made it, the inclusion in this event becomes a character trait of the elements of this list/set: This is the list of members of the team, about which Joe has made a decision through drawing lots.

It is also not true, because a total randomness of selection is hardly ever given. Even if you choose 3 random objects, you normally choose them from objects of a kind (three randomly selected videos out of a pool of videos, three football players out of a pool of football players, for example). So there was a larger pre-selection, and then a random selection out of this larger set.

What can we learn from this? Two things. Firstly, randomness is already relative on the level of the list as set. Yes, a randomly selected list includes randomness, but no, it is not fully random. Secondly, the inclusion in any list/set does something to its elements. It ads a trait to them, at least for the time as they are included in this list/set in a context, where such a membership is of relevance.

Now to the second form of randomness. This form starts at the other end. List can be of random order. The position of the element is not determined by some of its former traits. It is contingent. This is a totally different form of randomness. Indeed, many lists of random order are not lists of random selection.

However, just as in the first case, it is once again true and untrue, if you say that a list has a random order. If the order is totally random, it is not a list, but only a set. I have put forward in the last post the definition of lists as a form of assemblage, whose internal order can be potentially expressed by ordinal numbers. This means: Even a list of random order still orders its elements along a line. Even a non-signifying order is an order. But of course it is an order of lesser importance. This is why a list of random order is on second level a list, and on a first level a group or set. Inside the list, there is no escaping of this order. On this line, each element has it precise place. This place is always defined through two other elements: One is before, the one is after, and the element is in between.

If you look at what I just said a bit more closely, you will notice that I was arguing quite imprecise. To increment more accuracy into my argument, I have to introduce a further division: element versus position. A position is indeed part of the form of the list. A position is the specific form that multiplicity takes in lists. An element finds it place on a position. A position A is defined by its relationship to one or two other positions. If the position A is in the middle of the list, it is defined by two other positions, if the position is at the beginning or the end of the list, there is only one other position that defines it (and I will look at what else there is needed to define this later). It is also indirectly defined by other elements of the multiplicity: It makes a difference whether I am placed on a short list or a long list or an open ended list. Once again we can see, that a list ads traits to its elements.

Lets finally look at the third kind of randomness in random list: Lists, which express randomness. Their message is: ‘This might look like a list, and therefore imply some kind of significant order, but in fact this is not the case, in fact this is a total random order’. They try to break with the effect that all elements get ordered simply by the inclusion in the list. They try to undermine the ordinal numbers, which are added by any list.

The interesting thing now is, that lists can only do that, if they suggest a different order. The most prominent form how we do this is the alphabetically ordered list. An alphabetical order means: This is no ordinal order of significance. Take a phone book: It orders all owners of phone numbers after each other, and can thus be defined as a list that is based on ordinal numbers. However, the elements are placed on this list by a second order: The order of the alphabet. This is done to enable us to find a name quickly. But it is also done to express: This order is otherwise totally arbitrary. We therefore use alphabetical lists in general, if we want to say: This order means nothing. It is only a tool to find its elements quickly.

If you now look at such alphabetically ordered lists more closely, you soon see, that the alphabet is in this case just another form of expressing ordinal numbers. It is not based on the "Base ten" (0-9), but on 27 graphemes (this is of course the Latin alphabet, and there are even here further regional differences). "Ice" is turned into "Eighth-Third-Fifth". A position through alphabetical order is another form of expressing a position of ordinal numbers.

But the difference is of course crucial. A position based on the alphabet is one that is based on an insignificant or random trait of the element: The form of the signifier is arbitrary (at least in most cases). So there we are: An alphabetical list imposes an order on its elements, to make clear, that there are no other criteria of order at play.

The significance of this move becomes clear, if we look at another form, how we sometimes try to express random order of lists: The bullet point. The bullet point says: Each of these elements is separate, and because they are not numbered, they are neither ranked nor otherwise ordered. However, this is a much weaker form of breaking the order. It hardly ever succeeds fully, because t does not impose an alternative order. It just say there is none, which we then are inclined not to believe, and rightly so. I will look at the bullet point more closely, when I write about the relationship of lists and text.

To sum up: There are three kinds of randomness in random lists: Firstly the randomness of selection. Secondly: The random placement of elements on its internal order. Thirdly: Orders that express randomness. These three forms of randomness do not have to occur at the same time and all are random only to a certain degree.

In the next post I will look at open and closed lists and thus, amongst other things, at the relationship of lists to infinity.