counted. In this manner, for a brief instant while each apple is between boxes and while we have a unique number associated with it, we have established that apple’s differential identity within the set comprised of the original box of apples. When the first box is empty, we’re through counting the apples and we know how many apples were in it. We do not, however, know the differential identity of any of the apples in the second box. Thus, we have established the most basic facet of identity and we have preserved it only long enough to use it for its intended purpose, to count. Unfortunately, in social ecosystems, we rarely want to establish any facet of identity for such a tenuous purpose. The form and structure of interactions, including their consequences, often demand a more enduring approach. However, we can at least be aware of when we have gone beyond the original concept of differential identity and in designing identification systems we can attempt to minimize this extension if we wish.

Now, suppose that we did want to preserve the differential identities of all the apples in the second box. We could do so by simply writing the number of the count (the one-to-one correspondence between each apple and a positive integer) on each apple as we put it into the already counted box. Then, after we have completed our counting, we could re-examine specific apples; we could even duplicate the process of our count exactly if we wanted to. We just find the apple with a 1 on it, then the apple with a 2 and so on. We could even locate apple 23 and hold it up to the light. In this example, these numbers that we write on the apples we will call markers through which we can authenticate the differential identity of each individual apple. These markers are quite interesting because they are unique within the box of apples that we’re counting, and each marker is indelibly attached to the entity that it represents. Thus, to authenticate the fact that I’m holding apple 17, I merely need to look at the number 17 written on the apple. This all seems rather trivial, but we’re establishing concepts that we want to subsequently extend to larger groups than just a box of apples. In particular, we’re creating a record of the counting operation, a transaction log if you will that we can subsequently use to enhance our trust regarding an assessment that the count is correct.

It should be noted that even in this very simple illustration, we’ve already bumped into the very distinct demarcation line between establishing the differential identity of an entity and using that differential identity to track information about that entity. That is, we’ve taken the differential identity marker of an apple (e.g. the number 23) and we’ve indexed some potentially private information with that marker. That’s what we did when we noted that apple 23 looks like Thomas Jefferson. So, we have now intertwined the concepts of identity and privacy. Since we are not ordinarily concerned with privacy considerations relative to apples, let’s consider a different simple example dealing with people. Let’s divine an approach to counting the children in an elementary school. After all, it is rather common for a state to provide some level of financial support for local schools and it typically does so by providing some fixed amount of money for each child in the school. So, it is useful to count the number of children in a school because that will translate into actual money for the school.

Let us posit an example in which we have a school with five grades and we have three classes in each grade. So, in total we have 15 classrooms in our school, each with a collection of students. The Grade 1 students are in classrooms 1, 2 and 3. The Grade 2 students are in classrooms 4, 5 and 6 and so on for all the grades located in classrooms through number 15. We want to allow the teacher in each of these fifteen classrooms to perform the count, and at the end we want to be able to confirm that every student has been counted. We will perform the count by asking each teacher to prepare a class roll, or as we will refer to it, an identity registry for each classroom. In each room, the teacher counts each student, making a list with the student’s name followed by a number comprised of the room number, a dash and the count of the student; a number that might

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