One of the most vital cognitive skills to possess is the ability to make sense of objects, events, and situations in the world. In the current paper, we offer an approach for creating artificially intelligent agents with the capacity for sensemaking in novel environments. Objectives: to present several key ideas: (1) a novel unified conceptual framework for sensemaking (which includes the existence of sign relations embedded within and across frames); (2) interaction among various content-addressable, distributed-knowledge structures via shared attributes (whose net response would represent a synthesized object, event, or situation serving as a sign for sensemaking in a novel environment). Findings: we suggest that attributes across memories can be shared and recombined in novel ways to create synthesized signs, which can denote certain outcomes in novel environments (i.e., sensemaking).

We describe the current state of world-class memory competitions, including the methods used to prepare for and compete in memory competitions, based on the subjective report of World Memory Championship Grandmaster and co-author Nelson Dellis. We then explore the reported experiences through the lens of the Simulated, Situated, and Structurally coherent Qualia (S3Q) theory of consciousness, in order to propose a set of experiments to help further understand the boundaries of expert memory performance.

This work draws its inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and Memoli to partition-based clustering, and the Isbell/Dress school's study of injective envelopes. Carlsson and Memoli introduce the idea of viewing clustering methods as functors from a category of metric spaces to a category of clusters, with functoriality subsuming many desirable properties. Our first series of results extends their theory of functorial clustering schemes to methods that allow overlapping clusters in the spirit of Jardine and Sibson. This obviates some of the unpleasant effects of chaining that occur, for example with single-linkage clustering. We prove an equivalence between these general overlapping clustering functors and projections of weight spaces to what we term clustering domains, by focusing on the order structure determined by the morphisms. As a specific application of this machinery, we are able to prove that there are no functorial projections to cut metrics, or even to tree metrics. Finally, although we focus less on the construction of clustering methods (clustering domains) derived from injective envelopes, we lay out some preliminary results, that hopefully will give a feel for how the third leg of the stool comes into play.

We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering functor is naturally constrained to refine single-linkage clusters and be refined by maximal-linkage clusters. We work in the context of metric spaces with non-expansive maps, which is appropriate for modeling data processing which does not increase information content.