The first part of our research program is to hypothesize a model and explore this model in a simulated setting where we can develop the best statistical methodology to detect whether in fact this model is present in real data. Our first simulations will be in a setting having nothing to do with texts, ELSs, cylinder sizes, or ELS compactness measures. It will be in an entirely geometric setting where we have some possibility of understanding everything that is going on. Our second setting will be with ELSs where we will repeat to the extent possible the same investigation.

The investigations are motivated at three levels: An ELS set coming from a key word pair; A set of key word pairs corresponding to an event, each associated with the event; A set of events, each having a set of key word pairs associated with the event.

Any key word pair has a set of ELSs for each of the key words. The compactness of the meeting of the ELSs of the one key word pair with the ELSs of the other key word pair is the basic measurement. An encoding corresponds to a compactness measurement which is more compact than expected by chance. At least one of the key word pairs associated with an event is hypothesized to be encoded. The key word pair that is encoded will have its ELSs in a relatively compact meeting. The key word pairs that are not encoded will have its ELSs in meetings with random compactnesses. Most of the events in the event list are hypothesized to be encoded. These three levels must be reflected in the statement of the Alternative hypothesis and in the associated test statistic. Therefore, our simulations will cover these three levels as well.