From putting data in statistics to controlling conclusions

Decision making with your eyes only

Past and future of the presentation of quantitative data. Paper based traditional line graphics versus graphs using today's technology to fit human perception, memory and thinking.

AbstractThis article describes an evolution of the presentation of quantitative data. Technology driven alphanumerical presentations (paper, pencil, ruler, typewriter) are replaced by graphics meeting perceptual and cognitive psychological requirements.Discussed are single variable presentations such as a number in an alphanumerical or analogue way, multi variable presentations (tables, Isotype, x-y graphs, Gapminder) and the presentation of interacting multidimensional variables. This evolution is general and the examples given are from several domains (traveling, train driving and population statistics). The future of information presentation is not in a black box but in the psychology of the user.

1. From alphanumerical to…Human visual performance with alphanumerical presentations is low. Small visual differences like between the characters 1 and 7 are difficult to perceive. In nature such small differences are not relevant for survival. Leading zeros, as in 007, obscure compatibility between visual and conceptual quantity. Nevertheless, leading zeros are common practice in information presentation (See the figure at the right).

Alphanumerical presentations also lack compatibility with cognitive human performance. These forms provide little information on the content. Visually 2345 has more types of figures than 11111 but the latter one represents a larger quantity.
Some domains are in the alphanumerical phase and present variables not meeting the perceptual requirements. Not meeting psychological requirements increases reading time, search time and errors ( , ,
Beldie et al., 1983

Beldie et al., 1983
). Typical examples are the information banks present their customers.

No link.

Typical examples are the information banks present their customers. but the characters used to present information meet perceptual requirements much more than in the financial world.
public transport times of departure dynamic panelFigure 1. Leading zeros

Minutes to departure for metros is presented using leading zeros (bottom right).

Source: Train and bus station Amsterdam Arena, 2009.
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2 …analogue An arc of approximately 5 degrees is the visual focus area on the retina. The circular form of the focus area is compatible with circular scales like clocks. The hand on a clock is a straight line of which small changes in angle are easier to perceive than the details of an alphanumerical character.The traditional ergonomic rule is that digits are to be used when accuracy of perception is needed and an analogue presentation when speed of perception is needed. This rule of the thumb does not account for the use of scales having more than one hand and modern scale technologies that can meet both, the speed and the accuracy requirement (See the figure at the right and figure 5 below). ermts driver interface mmiFigure 2. Three values in a scale but only one presented by a hand

 In addition, scales can present more than the value of a variable. They can show more parameters of the value such as the speed of change, the distance of the current value to the minimum and to the maximum value. All these parameters can be perceived at one glance.An analogue presentation can be more compatible with the content to be presented and that is what we need (See the figure below).

 ermts experimental driver interface mmiFigure 3. Visual – content compatibility of digital and analogue presentations
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2.1 Present user’s targetHumans can be seen as black boxes reacting in some incomprehensible way to stimuli. Humans also can be seen as intrinsically goal-directed systems ( Making the goal parameter clear, is the first step in understanding behaviour, especially today when the number of goals increases (economics, safety, comfort and all kinds of friendlinesses).In addition, today, goals are hidden for political, management or marketing reasons. However, when no targets are set, human cognition cannot control a process and solve a problem. Targets are landmarks for cognitive activities.Educational psychology, for instance, developed a target-based methodology, called formative evaluation ( Domains dealing with quick responding, dangerous processes obeying the laws of Mother Nature, taught that planes crash and nuclear power plants explode when no target parameter (called set point) is presented to the operator.
 dispays pointer directionFigure 4. Clock scale, presentation of static targets

All dials are positioned having the target value at the top. The effect of this implicit static target is that an off target value is conspicuous.

Source: Holslag & Verhoef, experimental demo design.
ermtc experimental driver interface mmiFigure 5. Clock scale, speedometer for high speed trains with two targets

Train speed: 192.
Maximum permitted speed 200.
Next target permitted speed 40.


 scale designFigure 6. Scale with the target value positioned in the middle

s point zero (OK) in the middle of the scale.
The distance between the middle of the scale (the target, OK) and the current value (the pointer, not shown here) is the cognitive focus of the user.

Source: Holslag & Verhoef, experimental demo design.
 In 1992 development started of the train driver interface for the European Train Control System (ETCS-dmi, note 2). The need to test the benefits of the presentation of a target speed (maximum speed permitted) was considered evident by the European train control experts involved and not tested. Recently this was confirmed by who presented schedule and energy targets to drivers and observed a 7% reduction of driving time and a 14% reduction of energy.
Note 2:
European Train Control System driver machine interface (ETCS-dmi), a European safety system to prevent high speed trains driving too fast. Forty European train safety experts and 101 European train drivers participated in this project. This MMI is now being implemented.
 In non-physical and non-technical domains, targets might be less explicit and hidden for marketing or political reasons. The OECD (note 3) Quarterly growth table is a typical descriptive target-less presentation. (See the figure at the right).
Note 3:
OECD (Organisation for economic co-operation and development. OECD brings together the governments of countries committed to democracy and the market economy from around the world to support economic growth.
oecd presentation design of tableFigure 7. OECD quarterly growth table

No targets presented.

 If no target is available for the designer, the first quarter of the year or some mean could be used as a target. See the figure at the right. Content related targets in this domain might be Millennium Development Goals or the number of votes associated with a value.oecd presentation design of tableFigure 8. Target based table

Quarter two is set as target; next quarters are presented in proportion to the target.

Source: OECD, adapted by Holslag & Verhoef.
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2.2 Present user’s point zero

Technical scales have a minimum, a maximum, and a current value somewhere in between. This three point scale model is not compatible with the visual system. When the left eye focuses left on zero, the right eye should focus right on maximum. That is impossible.In addition, there is no eye left for the information in between: the current value. Of course, we can switch to peripheral perception but in that case, we will miss details. The three values on the scale have to be inspected individually and the information has to be stored in short term memory in order to allow interpretation.

In addition, the cognitive focus of the user should not be on the total scale but on the difference between target value and current value. This difference should be the focus of the scale as well. The rest of the scale could be deleted.

present experimental evidence that relative information is perceived as clearer than absolute.

 Daily conversation provides insight in this debate on the point zero parameter of a variable.

  • When humans are not constrained by technology or bureaucrats, they use a relative indication in which the current position is point zero. We usually do not say June 20th 2009 but yesterday, today or tomorrow.
  • Computers and bureaucrats interpret last year as the last calendar year, e.g. 2008. From a cognitive point of view the last year is the previous 365 days. That is what dynamic presentations can and should show.

  • The difference between 31-12-2009, 23:59 and 1-1-2010, 0:01 is large in a calendar clock system but these two seconds are irrelevant in most processes on earth. Categorizing data in months gives a delay up to 30 days and the year or month mean, obscures the moment and the cause of changes.
  •  The unit in the OECD population statistics in figure 7 above is a quarter. The units of a content based time scale might be a change of a law, presidency or a national disaster. Categorizing the time variable in quarters makes the task for the OECD designers and data collectors easy and the interpretation task for the users more difficult.A technical problem, of course, is that the resolution of the database and the underlying system is year, quarter or month based. Once, this should be at day-level. An in between option is to set periods selected by users.

     scale design use of coloursFigure 9. Scale with several cognitive psychological parameters of the value to be presented.

    The focus is on the discrepancy current value and target value.

    Source: Holslag & Verhoef, experimental demo design.
     In public transport there are two strategies for presenting point zero. One strategy is a point zero based on the position of the earth and the sun. In this case midnight is point zero and time of departure is presented.The other strategy is a point zero based on the position of the passenger in relation to time of departure. In this case time of departure is point zero and time to departure is presented. (See the figure at the right and public transport times of departure amsterdam arenaFigure 10. One trains indicator, two point zeros

    For Amsterdam Public Transport (metros at the bottom)
    time of departure is point zero. Count down time is presented.
    For Netherlands Railways (trains at the top) midnight is point zero.

    Source: Train and bus station Amsterdam Arena, 2009.
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    2.3 Present interpretationWhen there is a target, then there is an interpretation parameter indicating the distance between the current value and the target value. This single parameter saves the user searching for the current value, the target value, the norms, performing calculations and interpretations. For a monitoring task, the interpretation parameter has four levels:

    a) No action needed.
    b) Action needed shortly.
    c) Action needed now!
    d) Action needed is not performed, game over, disaster occurred, target will never be reached.

    These levels are general and can be applied to cognitive tasks like teaching, train driving, traveling and piloting to the planet Mars. The levels are elaborated in and briefly shown in the figure below.
     scale use of coloursFigure 11. Interpretation of car speed using colour

  • Dangerous, orange: driving too slowly for this (high) way.
  • OK, white: mean speed for this road (maximum speed in most cases).
  • Too fast, yellow: too fast but within limits for over speeding.
  • Too fast, orange: too fast, you might get a fine.
  • Far too fast, red: You will lose your driving license when caught.
  • Source: Holslag & Verhoef, experimental demo design.
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    2.4 Present trend , so that is what human cognition does. However, predicting future values of variables imposes a load on working memory (What were the recent values?); on learning (What were the values in the past? Are there interaction effects between variables?); and on cognition (Calculations, e.g. How steep is the curve?). Today's technology can memorise, learn and process the information needed to establish a trend.In tables and graphs, one axis can be used for time and trend. Unfortunately, that axis cannot be used to show the interaction with another variable. Gapminder solves this problem using the play button to visualize changes over time (See the figure at the right).evaluation gabminder graph
    Figure 14. Graph, Gapminder

    Five dimensions in a x-y model. X and y for population characteristics, the area
    s (circles) for continent, play for time/trend/history and circle size for quantity.

     In quick responding processes the speed and the direction of the change show a short term trend parameter. A car driver can see that his speed is increasing or decreasing. The planning area of ETCS train driver interface provides several trends (See the two figures at the right).ermts experimental driver display mmi
    Figure 15. Long term speed trend presentation for a high speed train driver

    At the right of this screen maximum train speed profile ahead.
    Lower maximum speed at 1000 m.

    ermts experimental driver display mmi
    Figure 16. Short term speed trend presentation for a high speed train driver

    At the top left of this screen a growing white square indicates: take care you are close to over speeding, the system might intervene.


    The speedometer at the right enables the driver to anticipate while he is supervising the speed of his selfdriving car.
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    2.5 Present reliabilityIn public debate implicitly 100% reliability is required. It is not accepted that planes are delayed or crash. Professionals know that 100% reliability is impossible and too expensive. They take into account that there is unreliability and a mean time between failure. Reliability should not be avoided and hidden but should be accepted and presented. Reliability information enables the user to select the best option. (See the two figures below).

     presentation in graphs of reliabilityFigure 17. Shading for reliability

    Reliability presented using shading, e.g. less shading less uncertainty, much shading much unreliability.

    Source: Holslag & Verhoef, experimental demo design.

     Figure 18. Boldness for reliability

    Darker number means more reliable. The human eye can conclude that reliability of the values at the bottom is lower.

    Source: Holslag & Verhoef, experimental demo design
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    2.6 Present units of the userThere is a tradition of presenting physical, easy to measure and to count technical units such as degrees centigrade, km/h, Euros and months to users.Cognitive task analysis unveils that units for targets and problem solving are different. Consequently, the units of a value should be transformed to a cognitive users unit (See the figure below).

     Figure 19. Scale with several cognitive psychological parameters of the value to be presented.

    Speed is dangerous low.
    Speed is OK.
    Speed is too fast.
    You might get a fine.
    You might looe your driving license.

    Source: Holslag & Verhoef, experimental demo design.
     When train speed is close to maximum speed, ETCS does present current speed and maximum permitted speed to the high speed train driver, of course. However, time to intervention (note 4) becomes more prominent when the driver is close to the maximum permitted speed (See the figure at the right).ermts driver mmi displayFigure 20. A square, showing time to intervention

    Train braking curve is close to safety braking curve. The square top left shows time to intervention of the safety system. Time to intervention depends on maximum permitted speed minus current speed and the traction/brake application.

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    2.7 Graphical figures Alphanumerical forms and line charts are easy to draw with a pencil, ruler and typewriter. The fovea contains many thin cones, tightly packed together, however, not line-wise organized. Visual acuity and hue discrimination is best in the fovea and becomes poorer more eccentrically The shape of the fovea is a 5 degrees circle. The retina is not a relay station for isolated photosensitive visual elements; it is capable of extensive and complex interactions and integration These characteristics of the visual system have direct consequences for the design of information.

    It is supposed that 5 degrees filled figures projected in the fovea, such as the figure at the right, take more advantage of these foveal characteristics than line figures, such as traditional line graphs that spread out the information over the retina. The 5 degrees filled figures also should perform better than presenting the information alphanumerical. From a graphical point of view, it is easier to design a presentation for a value and its six parameters using a filled figure than using a line figure. multi dimensional display of variables in a graph
    Figure 21. A triangle, presenting five parameters of a value, e.g. car speed

    One value and its parameters:
  • Current value: the middle of the triangle, at the OK position.
  • Target value: thick vertical line, current value is target value.
  • Trend: slope to the right, value is decreasing.
  • Interpretation: yellow; attention is needed.
  • Reliability: shading, current value most probable at target value.
  • Source: Holslag & Verhoef, experimental demo design.

      However, this triangle shaped speedometer still is traditional x-axis and y axis graphs based. The speedometer at the right goes one step further.
     Written text, for instance, consists of line shaped forms (letters) and line shaped sentences. Incompatibility between the form of text and the fovea makes that while reading we perfectly perceive text of the previous line, which we have read, and text of the next line, which we should not read yet. Most of the text we can see we should not read at the moment we see it. That is not efficient.Characteristics of the cognitive activities of users also have consequences for the presentation of parameters of values. So far, it was suggested to present a figure for a variable.We can go one step further. In many cases, the values of two variables of a system interact and the potential conflict is the focus of the user. Consequently, it might be better not to present the two conflicting values independently but to integrate the space between them. Calculation and presentation of the space between variables reduces psychological load substantially. The conclusion can be in the fovea from a large distance as the three the figures below show.
     ermts experimental driver display mmi
    Figure 22. A square, showing time to intervention

    Train braking curve is close to safety braking curve. The square top left shows time to intervention of the safety system. Time to intervention depends on maximum permitted speed minus current speed and the traction/brake application. Figure 8 shows a smaller square, meaning more time to intervention.

    Figure 23. Train indicator, space between time variables

    Platform train indicator. The triangle presents minutes to departure.
  • Left long leg: position of the minutes hand at time of departure.
    In this case the 31 minutes position.
  • Right long leg: position of the minutes hand at current time.
    In this case the 19 minutes position.
  • The conclusion is in the fovea, even from a large distance.

    Source: NS, Amersfoort 2008, adapted Verhoef, experimental demo design.
    One more step further:

      Another cognitive advantage of presenting space between variables and not the space between the two variables, is the effect of simultaneous changes. When two changes each make the situation worse, the graphical change is double. When two changes compensate one another there is no graphical change. When a train starts going uphill and the train slows down while the driver increases traction that speeds up the train, the time to intervention square will not change (See the figure immediately below left.). When a train departure delay increases because the signal does not turn to green and the passenger decreases walking speed, the train indicators the passenger passes while walking to his train, will not change the walking speed needed to catch the train.

     ermts experimental driver mmi displayFigure 25. Integrated presentation of interacting variables

    Train braking curve is close to safety braking curve. The square top left shows time to intervention of the safety system. Time to intervention depends on maximum permitted speed minus current speed and the traction/brake application. Figure 8 shows a smaller square, meaning more time to intervention.

      display of reliability in a graph Figure 24. Rectangles presenting reliability between conflicting variables

    Each line shows a value left and a value right.
    Unreliability indicated by shading.
  • A: values close separation is sufficient no problem.
  • B: values distant separation very large no problem at all.
  • C: values close separation small take care!
  • D: values distant separation large no problem.
  • In case of a conflict the control of attention colours can be used (see section 2.3).

  • Source: Holslag & Verhoef, experimental demo design.
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    3 From formal tables to…So far, we discussed how to present six parameters of the value of one variable. Real life is a synthesis and much more complex. For performing today's tasks, more than one variable is relevant. A common option to present more variables is a table.The design of tables on dynamic screens can be similar to the design of tables presented on paper. These paper-screen tables meet the restrictions of old technology and do not use the options of new dynamic technology.
    Lines to position data

    Tables with borders for cells are evident with old mechanical type writing technology (See the figure at the right). The lines are a visual scaffolding to position the numbers aligned.
    Once set for the typist, erasing the lines was not possible. The reader had to read a scaffolded text. Figure 26. Lines for the designer

    The lines help the designer to position the data. Like a scaffolding they should be removed after construction.

     Superfluous heading

    The design team needs headings to discuss and know where to put the values in the table. When the meaning of the value of the cell is obvious, there is no need for an explanation in the heading for the user.

    In the figure at the right it is unlikely that a passenger will read that his train departs at 30B hours from platform 15:15.
    public transport departure times on a dynamic displayFigure 27. Superfluous heading

    Source: Train and bus station Amsterdam Arena, 2009.
     Fixed column size

    Printing headings on the frame of a passenger information screen as on the panel immediate above, fixes the columns on the screen to a general maximum width. Selecting a column width, appropriate to the space the values on the screen need, is not possible.

    On dynamic panels floating widths are possible, enabling to present more information on smaller (cheaper) panels.

    In figure 27, immediate above, the heading minutes to departure causes its column to occupy half the space of the indicator whereas for time to departure only two positions are needed.
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    4 …content tables

    Graphics can be used for aesthetic reasons as in the figure to the right. With new technologies, it is possible to present content using colours and bold type for text. For the cells of a table background colours and borders can be used. All these options can be used in dynamic way.Figure 28. Graphics for aesthetics

    A landscape that is not compatible with the contents of the table

     When graphics are used to guide the reader, this will improve the exploration of data. Without reading the numbers, the eye can understand the parameters of the values such as distance to target, reliability and trend.In population statistics there is an unnecessary load to find out which countries have a too high birth/death ratio and need health support. Using norms, the interface should interpret the value of the variable, e.g. colouring the values. The result might be a table in which the eye only can find the cells of the table that show where the problems are. Human cognition can be used for fine tuning of laws and rules. (See the figure at the right).

    Figure 29. Table with graphics for content

    Source: OECD, adapted by Holslag & Verhoef for demo purposes.

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    5. From x-y forms to…
    5.1 Visual perception
    Line charts are not compatible with the characteristics of human perception (See section 2.7). The visual distance between current value and target value of a variable can be too large. When the scales have a large range and the units on the scale are equal, then the resolution of these most interesting parts might be not legible (e.g. where two lines cross). Some kind of zooming is needed.experimental graph designFigure 30. Traditional x–y line chart

    Source: Holslag & Verhoef, experimental demo design.
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    5.2 Visual routing

    For reading text in the West there is an eye routing convention: from top left to bottom right. Line charts spread information out over an area larger than the fovea. Nevertheless, there are no conventions for eye routing reading graphs.The icons of Isotype (note 5) are attractive and eye catching (See the figure at the right). At the time of their invention attractiveness was an important requirement. However, attention should be at the position just after the last icon. That position indicates the value presented. The icons obscure the visual route to go.
    Note 5:
    Isotype is a system of pictograms designed by the Austrian educator and philosopher Otto Neurath, to communicate quantitative information with social consequences in a simple way.
    Figure 31. Isotype

    Isotype is a system of pictograms designed by the Austrian educator and philosopher Otto Neurath, to communicate values of variables with social consequences in a simple way.

    Source: Holslag, inspired by Neurath.
     Gapminder (See the figure at the right) takes advantages of modern technology in an intelligent way. The basis is a traditional x-y line graph. Gapminder controls eye routing using a man on the stage (note 6) telling where to look. Another solution Gapminder uses is to project the graph on a casino table, again adding a flesh and blood man as a croupier and giving the users tokens to play with. As with the Isotype graphs, attractiveness is beyond doubt.

    As with the Isotype there is a danger that making statistics attractive distracts designers from the problem: how to make statistics understandable.

    A compromise might be story telling. Story telling has exactly what graphs are missing: a strong linear structure. The route in a graph could be presented using numbered text balloons in graphs

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    5.3 Short term memory

    To read the graph in the figure at the right short term memory is loaded with the meaning and the positions of four lines in the graph. Even for this simple graph several seconds are needed to inspect and to retain all values.This might not be a problem for experienced professional graph readers interested in the data. In graphs for public information several seconds might be too long. Designers who do not understand short term memory of graph readers, might interpret this as graph users who do not understand the graph. To solve this problem the graph may be made more attractive. Figure 33. Traditional x–y line chart

    With four variables the short term memory load is rather high.
    Little space is left for problem solving.

    Source: Holslag & Verhoef, experimental demo design.
     The effect of spreading out information as in traditional line graphs can be understood with impossible figures (see the figure at the right.)Figure 34. Impossible figure

    Details of the left part and details of the right part cannot be visually inspected simultaneously. There is an overview only in short term memory. In short term memory details are lost and details unavailable are reconstructed to form a sensible interpretation.

     Research indicates that cues for the correct interpretations of these kinds of figures only have effect when presented near the attended area ( . When an impossible figure is positioned in the fovea, the eye only can see the impossibilities as the figure at the right shows.Figure 35. Impossibility made visible

    Details of the left part and details of the right part fit in the fovea. There is an overview within the eye. The eye only can see the impossibilities.

    Source: Holslag & Verhoef, experimental demo design.
    Reminding meaning of lines

    The Isotype icons provide a perfect solution for the short term memory problem. Where ever the focus is, the icons show the meaning of the content. There might be some memory load to learn the meaning of the icons, but being very self-evident and concrete, once read, the meaning will not impose a load on memory. Short term memory load is far less than commonly used arbitrary coding with line types. This Isotype advantage is applied in the figure at the right by replacing line types by meaningful icons.
    Reminding values of axis

    Traditionally axes are presented as straight lines in the periphery of the graph. Consequently, the values have to be stored in short term memory. This memory load could be reduced using floating axes. The effect should be that on interesting spots in the graph all values and their labels are present and within the fovea (x value, y value, variable 1 score, variable 2 score). See the figure at the right.
    Figure 36. Line graph, low working memory load

    The labels of the axes follow the data.
    On the interesting spots all values are available in the fovea.
    Fixating on the top right, the details and the conclusion are available at a glance: in the year 2025 the income of man and women is almost equal.

    Source: Holslag & Verhoef, experimental demo design.
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    5.4 UnderstandingSuppose the graph meets all requirements for perception and memory. Can the user understand the information?
     Understanding proportions

    Isotype makes a value concrete, filling up the bar with icons each representing a proportion of the number to be presented

     Research from developmental cognitive psychologist Jean Piaget clearly indicates that for five year olds there is no need to subdivide a number. For a five year old the question: What is the height of the pile of pancakes you want? is no problem at all. He will point with his hands as high as he can to indicate an imaginary pile. There is much empirical data supporting this hypothesis: +Piaget +conservation gives today 182.000 hits on Google. Piaget (1896-1980) was a contemporary of Neurath.Young children do not find the spatial demands of graphs at all difficult is a recent experimental finding of

    Using concrete piles, Isotype intended to provide insight for schoolchildren ( and workers. Cognitive psychological theories and experimental data suggests that Isotype solves an understanding problem that does not exist.
     More complex reality

    In the twenties, time of departure and platform number was sufficient for a passenger. Today's passengers have to be informed in a split second to be able to choose between trips that differ in price, travel time, comfort, environmental load and reliability of these variables. For the train drivers in the twenties, the physical red lights beside the track were the focus of their attention.

    Today's high speed train drivers have to understand that they drive in three electronic dynamic cocoons at the same time. Each the safety, the schedule and the energy cocoon has its own current and target speeds and its own control of attention curves. It is impossible to present all these values using piles of icons for red lights, green trees and shouting delayed passengers. Using piles of concrete icons does not solve the problem of today's train driver and tomorrows passenger.

    The recent Neurath-revival ( ) is deserved but cannot solve today's information presentation problems. Going backwards to finger counting is not the way to go for information design to present multivariate interactions. We have to go forward, find parameters of values (e.g. reliability, trend, point zero, etc.), find the abstract cognitive variables that are relevant for a task, find their interactions and find out how to present all this. What is beyond Isotype?
      More complex graphics

    Isotype focuses on proportional relations of a few variables. Gapminder focuses on interactions between five variables. That is closer to today's problems. Using modern technology, Gapminder cleverly added three dimensions to the x-y-model: (1) time using a play function, (2) location/continent using colour and (3) circle diameter. However, the presentation is the traditional x-y model as is used on paper graphs.

    The visual inconsistencies and the inconsistent behaviour of the scales of the five Gapminder variables are the bottleneck for this five dimensional presentation. The inconsistencies increase psychological load and impair the visual identification of specific situations and interactions. This specific combination of five values might not produce an easy to identify and to remember picture. What is beyond Gapminder?
     Below some static graphics that show the relations between more than 3 quantitative interacting variables. The human visual system can process these figures at a glance. The human brains can interpret these figures at a glance as well.
      presentation evaluated interacting quantitative numerical variables presentation evaluated interacting quantitative numerical variables
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    6. … a solution

    The x-y model is perfect for the traditional empirical analytic two variable approach. For cognitive psychologists educated in this tradition it might be difficult to find new synthetic presentations. They might know that there are other traditions, such as the Unfortunately a new more chaotic synthetic methodology was never elaborated in statistics for the social sciences. This gives cognitive psychologists a blind spot for the synthetic character of reality and design where all variables are active at the same time. Cognitive psychologists working in practice will have to solve that huge methodological problem.
      One solution is more than one hundred years old. Mendeleyevs periodic table of the elements for chemistry is a scientific synthesis of a body of knowledge that up to that moment was analytic, chaotic and anarchistic. That sounds familiar. A multidimensional model might solve the problem for today's chaotic usability science and interface design theory ( Multidimensional orthogonal structures might also be applicable to the presentation of interacting multidimensional variables. That is exactly what Did on paper for the presentation of demographic information.How to elaborate this solution for information presentation? The traditional model has two axes, one vertical axis, one horizontal axis, and they meet at the bottom left in an absolute point zero. Why not have more axes, not meeting at point zero? No piles of icons, bars and pies, but positions only. In addition, of course, to reduce short term memory load the presentation should fit in the fovea. The scales should present the six parameters specified in section 2.1-2.6. For several of our clients we elaborated these kinds of presentations.
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