Making Spaces Phase One Impact Summary

This infographic presents a summary of impact from the first phase of the Making Spaces Project (2020-2022)

Domestic spaces in unhomely places : Oikos and ethics in McCarthy’s the Road

Spatially, Cormac McCarthy‟s The Road is starkly simple. Although the basic schema permits many variations, I would argue that there are qualitatively only three spaces in the entire novel. These are the road itself, the sea, and chanced-upon, variously manifested domestic space. These closely interdependent spaces structure the narrative and allow for the staging of an exploration of memory and childhood, as well as providing the context for a compelling but never fully articulated ethical demand to emerge. The road is a threateningly exposed and entirely desperate place that offers no refuge or sustenance. Roving gangs of half-starved cannibals travel the road, as does their food, the last remaining, pitiful detritus of humanity, aimlessly and hopelessly wandering. Chronotopically, the road exists in the pitiless zero hour of a present bereft of past and future [there is no past, 55; the hour. There is no later. This is later, 56].peer-reviewe

Knowledge Spaces and Learning Spaces

How to design automated procedures which (i) accurately assess the knowledge of a student, and (ii) efficiently provide advices for further study? To produce well-founded answers, Knowledge Space Theory relies on a combinatorial viewpoint on the assessment of knowledge, and thus departs from common, numerical evaluation. Its assessment procedures fundamentally differ from other current ones (such as those of S.A.T. and A.C.T.). They are adaptative (taking into account the possible correctness of previous answers from the student) and they produce an outcome which is far more informative than a crude numerical mark. This chapter recapitulates the main concepts underlying Knowledge Space Theory and its special case, Learning Space Theory. We begin by describing the combinatorial core of the theory, in the form of two basic axioms and the main ensuing results (most of which we give without proofs). In practical applications, learning spaces are huge combinatorial structures which may be difficult to manage. We outline methods providing efficient and comprehensive summaries of such large structures. We then describe the probabilistic part of the theory, especially the Markovian type processes which are instrumental in uncovering the knowledge states of individuals. In the guise of the ALEKS system, which includes a teaching component, these methods have been used by millions of students in schools and colleges, and by home schooled students. We summarize some of the results of these applications

Mapping spaces from projective spaces

We denote the $n$-th projective space of a topological monoid $G$ by $B_nG$ and the classifying space by $BG$. Let $G$ be a well-pointed topological monoid of the homotopy type of a CW complex and $G'$ a well-pointed grouplike topological monoid. We prove the weak equivalence between the pointed mapping space $\mathrm{Map}_0(B_nG,BG)$ and the space of all $A_n$-maps from $G$ to $G'$. This fact has several applications. As the first application, we show that the connecting map $G\rightarrow\mathrm{Map}_0(B_nG,BG)$ of the evaluation fiber sequence $\mathrm{Map}_0(B_nG,BG)\rightarrow\mathrm{Map}(B_nG,BG)\rightarrow BG$ is delooped. As other applications, we consider higher homotopy commutativity, $A_n$-types of gauge groups, $T_k^f$-spaces by Iwase--Mimura--Oda--Yoon and homotopy pullback of $A_n$-maps. In particular, we show that the $T_k^f$-space and the $C_k^f$-space are exactly the same concept and give some new examples of $T_k^f$-spaces.Comment: 26 pages, 3 figures; the appendix in v3 is deleted since its argument was incomplet