Transreal limits and elementary functions

We extend all elementary functions from the real to the transreal domain so that they are defined on division by zero. Our method applies to a much wider class of functions so may be of general interest.

Typographic meaning: readers’ impressions of patterns of typographic differentiation

This research explores whether patterns of typographic differentiation influence readers’ impressions of documents. It develops a systematic approach to typographic investigation that considers relationships between different kinds of typographic attributes, rather than testing the influence of isolated variables. An exploratory study using multiple sort tasks and semantic differential scales identifies that readers form a variety of impressions in relation to how typographic elements are differentiated in document design. Building on the findings of the exploratory study and analysis of a sample of magazines, the research describes three patterns of typographic differentiation: high, moderate, and low. Each pattern comprises clusters of typographic attributes and organisational principles that are articulated in relation to a specified level of typographic differentiation (amplified, medium, or subtle). The patterns are applied to two sets of controlled test material. Using this purposely-designed material, the influence of patterns of typographic differentiation on readers’ impressions of documents is explored in a repertory grid analysis and a paired comparison procedure. The results of these studies indicate that patterns of typographic differentiation consistently shape readers’ impressions of documents, influencing judgments of credibility, document address, and intended readership; and suggesting particular kinds of engagement and genre associations. For example, high differentiation documents are likely to be considered casual, sensationalist, and young; moderate differentiation documents are most likely to be seen as formal and serious; and low differentiation examples are considered calm. Typographic meaning is shown to be created through complex, yet systematic, interrelationships rather than reduced to a linear model of increasing or decreasing variation. The research provides a way of describing typographic articulation that has application across a variety of disciplines and design practice. In particular, it illuminates the ways in which typographic presentation is meaningful to readers, providing knowledge that document producers can use to communicate more effectively.

Investigating readers’ impressions of typographic differentiation using repertory grids

Document designers combine a range of stylistic and structural typographic attributes to articulate and differentiate information for readers. This paper explores how the kind of typographic differentiation used in a document influences readers’ impressions of documents. A preliminary study indicated that three patterns of typographic differentiation (high, moderate and low) might underlie participants’ impressions of magazine design. Subsequently, a set of nine magazine layouts with controlled content was purposefully developed to systematically examine the impact of high, moderate and low patterns of typographic differentiation on participants’ impressions of documents. These documents were used in a repertory grid procedure to investigate the kind of impressions readers articulate in relation to typographic presentation and whether readers are likely to formulate similar or differing impressions from high, moderate, and low patterns of typographic differentiation. The results suggest that typographic differentiation influences a range of rhetorical and experiential judgments. For example, participants described high differentiation documents as the most attention-grabbing and easy to skim-read, while they considered moderate and low differentiation documents to require deeper reading strategies. In addition, participants assumed high differentiation documents to be much more sensationalist than moderate or low differentiation documents, which they generally perceived as authoritative and credible.