Representations of Temporal Relations:
Descriptive captions from the original sources have been maintained. The captions we have added name the features of the images that will form the standard graphical vocabulary for temporal modelling in our project templates.
- The basic categories are linear, planar, spatial representations.
- These may contain bivariate or multivariate information axes.
- Temporal direction is almost always unidirectional/asymmetric.
- Reference frames are either extrinsic to the system (assuming an objective time framework) or intrinsic to it (based on relations) or some combination of these.
- Notation systems contain markers for points (discrete moments), intervals (segments of time), and events (occurrences in time).
- Grand Canyon, John David Miller (Intel) and John Maeda (MIT)
- (Spectrum of biological cycles, from Fraser)
Linear, unidirectional/asymmetrical timeline with extrinsic time frame and multiple granularity scales.
- (Hydrocarbons from Tufte)
Linear time line in 2.5 dimensions (orthographic). Data shown in continuous display cut snapshot mode. Information is mapped onto a topographic plane. Extrinsic time frame.
- (Schreiber - last diagram in the article)
Linear, unidirectional/asymmetrical timeline with cyclic time progession/repetition wrapped around it for correlation. No time frame indicated.
- Bronstein (time lines with Judeo-Christian emphasis, also, the Karl Jasper's axial timeline)
Linear time, 2-dimensional, but inflected by ideological considerations. Time frame is largely event driven.
- Calendar - an idiosyncratic planar graphical schema
- (Mayan/Julian from Fraser) Planar convention, implies unidirectional asymmetry but accessed topographically. Two extrinsic time frames (Mayan/Julian) put into correspondence. Uniform but non-specific granularity (metric of the table has arbitary semantic value).
- Bivariate and Mulitvariate Tables
- Marey (from Tufte) Bivariate table with discrete data points (place names on vertical axis) and continuous data (time progression on horizontal axis). The metric of the diagonal lines allows differences in speed to register (though this feature is not taken advantage of here) - presumably these trains travelled at more or less the same speed.) Extrinsic time frame. Uniform granularity.
- Circadian Rhythm (Fraser)
Bivariate table with both extrinsic (days/hours) and intrinsic (periods of wakefulness/sleep) time frames. Notation system marks intervals as well as points but within a uniform granularity.
- Biological cycles (Fraser)
Multivariate table with five data types mapped on two temporal axes, extrinsic time frames, uniform granularity.
- NY Times weather image (Tufte)
Multivariate table using one axis for correspondences (horizontal) and multiple values on horizontal axis for precipitation, temperature, humidity data. Precipitation indicated in discrete units, temperature and humidity in continuous mode. Extrinsic time frame.
- Bar Graphs
- Life line (from Lifeline article)
Multivariate table, uses intervals and events, extrinsic timeframe.
- Reigns of Kings (Tufte)
Bivariate table, uses intervals, and embodies the "dividing instant" problem.
Dials seem most useful when multiple variables need to be calculated in relation to each other, as in the case of the astronomical/astrological volvelles shown in the second image here, where correspondences can be visually demonstrated through rotation. Otherwise, the dial serves a metaphoric purpose, as in the first image.
- Cyclic representation of timeless, universal cycles (Thames and Hudson)
Hiearchical structure internal to the cycles
- Calculation tools (1 and 2)
Multiple sidereal/astronomical/astrological cycles graphed against each other for calculation. Multivariate, interval-based, multiple granularities, and extrinsic time frames.
- March of Napoleon (Tufte)
Spatial-temporal date integrated into single narrative made into topographic image. Extrinsic time-frame. Single granularity. Topographic template serves both literal (geographic advance) and metaphoric (size of army) purposes.
- Chris Ware (1 and 2)
Multiple time-lines in tree/branching flow-chart capable of inidicating several sequences of events simultaneously. No extrinsic time frame indicated in this example. Intrinsic relations determined by linking.
- Temporal Relations Diagrams
The issue here is not the linear/planar distinction, but the graphing of relations within an assumed assymetric temporal experience.
- Allen's diagrams are standards in the field for showing logical relations. (1 and 2)
- Steedman's images from The Productions of Time (derived from Reichenbach) add a useful notation system for discourse analysis.
- Minkowski Diagram
This description is taken from Schreiber:
"First, time looses its privileged position as the independent variable for describing natural phenomena, while only a four co-ordinate space-time continuum is used to express the physical laws; second, each event (a point in space-time) is the vertex of a twofold cone which contains the past and the future of the event itself. Points which belong to trajectories (world lines) lying within the cone are related to the vertex event by a precedent relation, which expresses causality. Points outside the cone are simply "elsewhere" and cannot be causally related to the event; they are independent of the event or concurrent with it. Therefore, any interaction between two events can only occur within the intersection of their light cones."
- Fraser - Time Dilation images from Time, the Familiar Stranger