Propositional density

Let us start with the notion of a proposition: in this context, a proposition is simply an elementary, atomic statement about the object at hand. “The FedEx logotype is purple” and “The FedEx logotype is set in a sans-serif font” are propositions, and because they describe salient, perceptible properties of the design, they are referred to as surface propositions.

Now, the FedEx logo became famous for a perceptual trick: The white space between the E and the x creates an arrow. This arrow induces, by its semiotic reading, a number of additional associations and readings of the design: “FedEx is on the go”, “FedEx is forward-thinking”, etc. Note that these propositions, unlike the surface propositions, are much harder to enumerate as they depend on the meaning that the observer ascribes to the arrow. These are called deep propositions as they describe underlying and often hidden meanings of the design. You can think of an iceberg, where the surface propositions are over the water — easy to see and clear cut — but the much larger part is under water.

Now we have all elements together to define propositional density more precisely:

The propositional density of an object is the number of deep propositions divided by the number of surface propositions it conveys.

Note that there are two ways of increasing propositional density: Using fewer surface elements to convey the same number of deep propositions, or increasing the number of deep propositions per surface element. Also, we can see now why the FedEx arrow is so effective: It adds a high number of deep propositions without adding surface elements. It just emerges by clever arrangement of the surface elements; in fact, any Gestalt law has a great potential in this respect.

Generally speaking, good design usually has a high propositional density. On the other hand, if your propositional density is below one, you probably have superfluous, merely decorative elements in your design, which do not add to the deep reading.

Example: High altitude

We can use the image series “High Altitude” by Michael Najjar to illustrate some of these concepts. For this series of photographic montages, the artist used self-shot photos to assemble images of what seem to be natural mountain scapes on first glance…

… yet the sky lines are carefully crafted to match the development of major stocks and and indices. See for instance, the “dax_80-09″ image with an overlay of the DAX index development I added:

Clearly, a high number of surface features (and visual efforts) to express this simple type of data (one measure over time). Yet, I would claim that the high number of deep propositions associated with this imagery justify these efforts, and make the work an extremely rich type of visualization; possible associations include thin air, the borderline between earth and sky, the manifested history of processes, monumentality, man-made vs. natural objects etc.

Other works, like the “Global emissions” graphic published in GOOD magazine manage to establish a strong visual impression suited to the topic with simple visual means:

Finally, also a very sober visual style can yield rich experience by a clever combination of chart style and content; see for instance “Miracles in nature and Science”, a chart of the number of mentions of the word “miracle” in the renowned scientific journals “Nature journal” and “Science magazine”.

Note how the deep reading of the piece arises not only from the selection of data sources (and thus the title pun), but also subtle design choices like the chart axis ratio.

What does this mean for visualization?

A common truism about information visualization is that it is primarily about “showing the data”. I would like to challenge this view. While this might be true for scientific (or financial, or many other) application fields, there are many good uses of visualization that go beyond a precise, “neutral” display of data. In fact, most people I know are much less interested in data than they are in information. Information can be conveyed in many ways, and we have a rich tradition and cultural contexts that allows us to communicate beyond the surface level. For instance, in linguistics, there is a whole subfield called pragmatics that investigates what is said beyond the “surface meaning” of the sentence, based on the context, connotations, the inferred intent of the speaker etc.

Bottom line

Every designed object invokes multiple layers of interpretations and associations. It is not possible to produce a neutral design. In other words, there are always deep propositions involved. The shapes, the colors, the presentation form you use will always invoke associations. This has nothing to do with art, or “dressing up” data — the question is if you ignore this fact (and thus leave it to chance, if the deep propositions serve or contradict the intended reading) or acknowledge their existence and use them consciously. In my view, traditional infovis research has explored the surface propositions quite well — the next big challenge is to understand the associative, evocative character of our visual information vocabulary and use it effectively.

Addendum: While I have been pondering and editing this article, a first empirical analysis of implied dynamics in visualization has been published. Great!

“Beautiful Visualization – Looking at data through the eyes of experts” is out (at least the ebook edition). I am proud to be among the authors, along with giants like Aaron Koblin, Fernanda Viega and Martin Wattenberg, Jer Thorp or Jessica Hagy. I mostly flipped through the book up to now, but from what I can see, it comprises a great collection of case studies and reflections by practitioners from the field. So if you always wondered about the stories and considerations behind great visualizations, this could be a very useful resource. My chapter deals with the process behind X by Y, and is available as a pre-print download (2.3MB pdf). I would love to see this book printed, too — if you feel the same, why not pre-order the print edition to speed up the process?

Also noteworthy: All royalties from this book will be donated to Architecture for Humanity.

So, we agreed on it and shipped it. Seeing it with the real data, however, made me wonder if I should have looked into typical rating statistics a bit more :)

Well. Lesson learnt. It is a nice little visualization nevertheless.

Which reminds me of an excellent article about how to prevent to uniform votes already in the interface.

As a bonus, here is a little remake using protovis with again, ridiculously few lines of code:

var data=[ ["05.11.09 17:01", 10, 10, 10, 10, 10, 10, 10, 10, 10] // .. etc .., see page source for full data ]; // pre-process data var processedData = []; data.forEach(function(d) { var o={}; o.date = Date.parse(d[0], "%d.%m.%y %H:%M"); o.dayDate = new Date(o.date.getFullYear(), o.date.getMonth(), o.date.getDate()); o.dayTime = o.date.getHours(); d.shift(); o.ratings = d; o.mean = pv.mean(d); processedData.push(o); }); // sort by rating processedData = processedData.sort(function(a,b) a.mean - b.mean); // result: // [{date:..., ratings:[10,2,3,4...], mean:6.7}, ... // set up visualization var w = 440, h =440; var vis = new pv.Panel() .width(w) .height(h) .left(20) .top(20) ; // encoders var color = pv.Scale.linear(0, 5, 10).range("rgba(255,0,0,.3)", "rgba(200,200,0,.3)", "rgba(0,90,0,.3)"); var angle = pv.Scale.linear(0, processedData.length).range(Math.PI1.5, Math.PI3.5); var radius = pv.Scale.linear(0, 10).range(100, 200); // A panel for each rating event var panel = vis.add(pv.Panel) .data(processedData) .left(function() w.5)
.top(function() h.5) ; // a wedge for each rating value panel.add(pv.Wedge) .data(function(d) d.ratings) .startAngle(function() angle(this.parent.index)) .endAngle (function() angle(this.parent.index+1)) .innerRadius(function(d) radius(d) ) .outerRadius(function(d) radius(d+1)) .fillStyle(function(d) color(d)) ; panel.add(pv.Wedge) .data(function(d) [d.mean]) .startAngle(function() angle(this.parent.index)) .endAngle (function() angle(this.parent.index+1)) .innerRadius(function(d) radius(d+.5) ) .outerRadius(function(d) radius(d+.7)) .fillStyle(function(d) "#000") ; vis.render();

On the occasion of the recent fifth birthday of infosthetics.com blog, your premier source for fresh projects from visualization and information aesthetics, I made a custom adaptation of the elastic lists principle for the – up to now – 1950 posts of the site. Try it out, and read more about it here.

Happy birthday infosthetics!

Andrew Vande Moere from FHP Interface Design on Vimeo.

Paolo Ciuccarelli from FHP Interface Design on Vimeo.

Find the whole album here.

I contributed to the user interface design chapter in the recent Springer book “Dynamic Taxonomies and Faceted Search – Theory, Practice, and Experience” (online version) edited by Giovanni Maria Sacco and Yannis Tzitzikas. Based on a definition of core principles and challenges, the chapter presents a taxonomy of navigation modes observed in existing applications. On that basis, design patterns for enabling these navigation modes in user interfaces as well as extensions and related approaches are discussed. The chapter closes with a section on personalizing faceted search.

The book itself covers a wide range of topics and current research questions related to Dynamic Taxonomies and Faceted Search from an academic point of view.

You can find a pre-print version of the User Interface Design chapter here. Thanks also to my co–authors Sébastian Ferré, Saverio Perugini, Jonathan Koren and Yi Zhang!

Together with my colleagues in Seattle and Umea, I modified the “change over time” visualization to tell a specific story: The formation of neuroscience as a field of its own right over the last decade. Originally scattered across related disciplines (such as medicine, molecular and cell biology or neurology), the neuroscientific journals start to define a niche of their own, reflected in the dense cluster emerging in 2005.

Download a larger version with full explanatory text here: png (1MB) pdf (4MB)

And here is some more in depth info: First, almost 8000 scientific journals are clustered into groups, based on their citation patterns, and using the map equation (demo, paper). In short, for a network partitioned into groups, the map equation specifies the theoretical limit of how concisely we can describe a trajectory of a random walker on the network. Therefore, minimizing the map equation over all possible network partitions reveals regularities of information flow across directed and weighted networks or, in our case, the structure of how citations flow through science.

Second, using the Eigenfactor™ Score, the journals are assigned a measure of importance – much as Google’s PageRank algorithm ranks the importance of web pages. The Eigenfactor™ Score measures the percentage of time that researchers would spend with the respective journal, if they were to move through the network by randomly following citations in the journals.

This process is repeated in two-year chunks from 1999–2007, in order to capture changes in clustering and shifts in importance over the years. For this diagram, we picked only the clusters relevant to the formation of neuroscience.

In the visualization, each cluster occupies a vertical column block in the respective year’s column, further subdivided into a block for each journal. Each journal is connected with a horizontal band over the years. The height of each journal reflects the Eigenfactor Score. All journals in the cluster that corresponds to the field of neuroscience in year 2007 are highlighted to tell the story of the formation of this field of science. The coloring is based on the cluster assignments in the first year, 1999.

We use a subset of the citation data from Thomson Reuters’ Journal Citation Reports 1999–2007. The complete data aggregate, at the journal level, approximately 35,000,000 citations from almost 8000 journals over the past decade, but here we only display journals relevant to the formation of neuroscience.

X by Y visualizes all submissions to the prix ars electronica, from the early beginnings in 1987 up to 2009. The goal is to characterize the “ars world” in quantitative terms. A series of diagrams groups and juxtaposes the submissions by years, categories, prizes and countries. The graphics are composed of little dots (each representing a single submission) to provide a visual scale for the statistical statements and thematize the relation of the totality and the individual.

Their placement is computed with a Fibonacci series, imitating the arrangement of sunflower seeds – a very efficient and visually mesmerizing way of packing small elements into a large circle. Color distinguishes the submission categories, and a diamond shape marks submission that have been awarded a prize. The numbers in the center of the diagram elements are constructed by skipping points in the pattern – establishing a tight connection between the number and the individuals, but also demonstrating the duality of the two concepts.

The project is currently at display at the history lounge of ars electronica 09.

The project was done in cooperation with the Ludwig Boltzmann Institute for media.art.research. Find all diagrams and some more info here: X by Y. Also, don’t miss the other works on the poster over at vis.mediaartresearch.at.