Foundations for Spread Page: review of existing concepts, solutions, technologies capabile of improving effectiveness of conveying knowledge

fields are usually pure conventions composed of arbitrarily chosen symbols and spatial layout rules – often based on relatively random connotations with real-life objects (e.g. danger having the shape of a yellow triangle). Secondly: due to multitude of aspects and dependencies within such entities (think of complex computer systems or national economy) they simply cannot be completely (and readably) depicted with just one graphical representation. Hence, many perspectives drawn on diagrams of different kinds are necessary to show all the various aspects of the same thing. Without much exaggeration, it may be stated that there is almost a whole branch of science dealing with abstract graphical notations (outstandingly reviewed in [2]) whose generally agreed goal (at least in theory) is cognitive effectiveness – defined as “the speed, ease and accuracy with which a representation can be processed by the human mind” ([24]). It turns out, however, that in many cases practice hardly COMPUTER SCIENCE AND MATHEMATICAL MODELLING 6 33−44 (2017) 37 follows the enlightened theory – numerous notations are based on intuition and aesthetics rather than proven effectiveness (topic discussed in depth in [2] with respect to notations used in software engineering). This way numerous fields ended up with notations where out of a number of visual variables (six, according to [25]: shape, size, color, brightness, orientation, texture) only shape is really used to convey actual semantics. And even that is done poorly – the shapes are overly simple and with little variability (mostly rectangles, sometimes with decorated or rounded corners, and ellipses). Such notations are extensively used in a wide range of fields, with good examples being: • software engineering, as already mentioned, currently dominated by UML – “a visual language for visualizing, specifying, constructing and documenting software intensive systems” [26], although several alternative notations are also in use e.g. in Data Flow or Entity Relationship Diagrams; • systems and control theory, in which dynamical systems (with or without control) can be graphically represented in a number of alternative notations: traditional Block Diagrams, Causal Loop Diagrams and Stock-and-Flow Diagrams within the System Dynamics methodology, or ModelicaML (derived from UML/SysML and mapped to model’s textual representation in Modelica), etc. • management, with such key areas as modeling of business process (with BPMN or similar notations) or representing and tracking projects (e.g. with PERT/CPM or Gantt charts). Another important area in management control is Business Intelligence – Visual Analytics which aims to optimize presentations of massive, complex data through novel visualization techniques (e.g. treemaps, [28], for displaying non-spatial, attributed data with hierarchical structure). The great majority of notations, including the relatively modern ones, are still deeply rooted in 2D, paper-centered mindset – flat, simple and static. Many of them were designed for drawing models with pen-and-paper, and hence cognitive effectiveness was subordinate to the ease of sketching by hand. But today no one needs to do that anymore and it is actually more likely that a person has in his packet an electronic device with touchscreen, than a pen and a paper notebook (an IT person, at least – the authors have verified this claim on themselves, on numerous occasions). Sticking to flat notations seems to be mainly a matter of inertia, as there are already numerous proposals to introduce 3D spatial diagrams. One interesting example discusses ways of extending treemap into the third dimension to enhance its informational capacity – not only due to the plain use of the extra dimension but also thanks to new opening possibilities to use shape, shading, transparency, texture, shadowing, silhouette enhancement techniques, etc. to fit more facts on the same graph (see e.g. [14], [15]). Similarly, a number of authors postulate to move towards 3D diagrams in software engineering practice (e.g. in [16], [17], [20]; see also an interesting animation at [19] demonstrating the potential of animated 3D UML). Further examples could easily be given; the ideas are already out there. In that light, we believe that it is both viable and desirable for abstract notations to catch up with the ways currently specific to 3D modeling of physical objects. Then, as a next step, we see it as a possibility to apply one, uniform way of perceiving and modeling all constructs: physical, abstract or hybrid (i.e. having both aspects). Such modeled entity could be defined as a set of inter-related elements residing in a multidimensional space, of spatial, temporal and logical dimensions. The internal relations among components could, again, have spatial, temporal, abstract or, possibly, mixed nature. Assuming, that all dimensions could be treated uniformly, at least to a degree, it should be feasible to render visually meaningful views build for arbitrarily chosen dimensions, even with mixing-and-matching spatial, temporal and abstract aspects. With such modeling framework, it could become more natural to use graphical notations in areas today dominated by text, like law, political science, philosophy etc. Although today we neither have adequate notations and standards nor experiences and practice needed to construct multidimensional, graphical representation of, say, international treaties, scientific theories or national economies, our intuition suggests that, in principle, this is possible. And it is also desirable, as today these domains really start to groan under the weight of countless pages of text. 4. Technical aspects: current tools and technologies The numbers of available computer applications are vast and rapidly growing, making the field hard to embrace. Even if we put aside computer Tomasz Tarnawski, Rafał Kasprzyk, Robert Waszkowski, Foundations for Spread Page... 38 gaming and concentrate on tools dealing clearly with creating, editing and presenting information (plus persisting it with specifically formatted disk files – “content containers”) it is still an abundant area. Without claiming, that it is the best ever classification, we propose the following as on serving well our needs. For our purpose we divide available computer tools into three rough groups, where the mode of presentation is predominantly: • linear, text based – being the closest relative of traditional books and articles; • (up to) three-dimensional – dealing with models of real-world, physical objects; • in abstract “space” defined by arbitrary, logical dimensions and relations – for modeling abstract constructs; bearing in mind that the division and distinction might at times be far from clear or obvious. Text-based form In this category, the presentation of electronic content most closely resembles the traditional, paper-based approach. Even today, in typical uses of the most popular applications (Microsoft Word or Power Point, Adobe Acrobat Reader, a web browser displaying static webpage) the displayed content (of a doc, pdf, html or other such file) could almost just as well be read off a piece of paper. Fortunately, we already are moving away from static text, towards content experienceable in live, interactive and multidimensional ways. One key feature is enhanced, interactive browsing through the content’s structure. Most commonly, the structure is hierarchical (i.e. based on the composition, or “whole-part” relationship) and one-dimensional – constructed as linear narration divided into chapters, which are composed of subchapters (which are then composed of sections, etc.). A reader can fold– unfold chapters and sections and quickly navigate to the interesting part (a word processor in outline view, PDF reader showing navigable table of content, foldable elements and hyperlinks within webpages). Noteworthy, in some presentation applications (e.g. Prezi, Sozi or Impress.js) the hierarchy is not linear, but planar, therefore reading and presenting the content uses two-dimensional navigation plus zooming-in and out. Two dimensions is, however, as far as it currently gets – the presented content is confined to a planar page that does not spread into higher dimensions (as in categories described later on). In addition to composition, also other relations between document’s elements may be present and important which in effect defines a complex, network-like structure of interlinked, cross-referenced parts (think: Wikipedia). Another enhancement in interaction with information, unavailable on cellulose, is present in “computable documents” going much farther than automatic text formatting or autonumbering of chapters and lists (although that also requires some computation). In such documents, the information presented is calculated on the fly, based on mathematical formulas or logical rules defined by the user. The generated results may have numerical or textual forms but also graphical and/or animated. Simple mathematical functions (such as summation) are actually available in tables in most popular word processors (e.g. Microsoft Word or OpenOffice Writer) but better examples of computable content provide spreadsheets (Excel, Calc) or scientific computing environments such as Wolfram Mathematica or MathCad. Also, similar end can be achieved with embedding appropriate active controls within html pages. Finally, numerous applications in this category allow the user to embed almost any kind of rich media, such as sound clips, animations or other interactive controls (example technologies include ActiveX, AJAX, SilverLight, Flash, etc.). Such documents are not created with printing in mind, anymore, but for viewing on electronic devices. Paper deprives them of their key features. Physical-(3D) space-based realm Graphical representation of knowledge about real-world objects was already touched on in the previous section. The notations a