The Revival of Time Geography
Time geography was presented by Torsten Hägerstrand in his 1970 paper What about people in regional science? For the first time, a scientist was looking at movement in space on an individual level. Until then, regional scientists were merely looking at the movement of big groups of people. His basic idea was to create space-time paths in a 3D space where horizontal axis represent geograhpic space and the vertical axis represents time. An example for a space time path looks like this:

This might be considered as a typical path for a working person. The path starts at home, indicated by the lowest vertical line. Vertical lines stand for stays at a certain location. The first line segment with a slope indicates that our example person moves to his work place, where he stays for some hourse (the second vertical line segment). Actually, our example person seems to have quite short working hours, as that line segment is pretty short compared to the other segments. However, after work, he moves to a supermarket to go shopping (the third vertical segment), and back home afterwards. Note that the rectilinearity of the movement line segments assume that the person is travelling with constant speed, which is usually just an approximation of the real behaviour. The dotted lines have been added to the figure to show his movement in geographic space.
Note that the workplace is an exmaple of a station, that is a place where people meet for a certain activity. Beyond that, a station might be available only for a limited period of time, e.g. supermarkets usually have limited operating hours, which can be symbolized as in this revised version of the first figure:

Another central object in time geography is the space-time prism, which gives a 3D representation of the locations a person can reach between two fixed appointments. If we take our previous example again, let’s say, the next day, our example person quits work at the same time, but there is no shopping to do. He just needs to be home at 6 p.m. For this example, the following prism delimits the places he can reach within that time given a certain maximum travel speed (e.g. for going by car).

Going to the limits of the prism does not make much sense in most cases, as it means that one has no time at the destination to do anything. Hence, it makes more sense to stay somewhere within the prism, depending on the time one wants or needs to spend at the destination.
The above examples show that time geography is a very powerful way to visualize people’s movement in space. Although Hägerstrand originally developed it mainly to describe individuals’ movements over a long period of time, it got back into focus with the rise of precise tracking technology such as GPS. Researchers realized time geography’s potential to be useful for enhanced routing services which take the user’s different tasks and constraints into account.
However, to make computable what the above figures show, a mathematical therory is required. This aspect was not covered by Hägerstrand’s original work, probably because he saw time geography mainly as a means for analyzing past movements. Harvey Miller from University of Utah has done a lot of research on this theory (have a look at the paper a measurement theory for time geography listed on his website).
I am really curious about the applications evolving from this area in the future. For instance, you could think of geocoded calendars, which help you managing your schedule and managing your travel between them…
15. March 2006 um 13:10
Good read. I am not quite sure about the visualisation though. As long as you just want to show the path of one individual its good, but integrating more paths or displaying longer time periods makes it pretty complex. Claus Rinner implemented a nice VRML application [1], which allowed dynamic interaction with the mapviewer to assist the user in this aspect.
I think these two visualisations methods should be better taken as models, which you should reconsider if you have to implement time-dependent GIS applications. Especially if you are developing for mobile hardware.
[1] Claus Rinner (2004): Three-Dimensional Visualization of Activity-Travel Patterns
15. March 2006 um 13:20
You are right - the model behind time geography is what it makes particularly interesting for mobile applications. But it is not yet fully understood how to treat the model mathematically. Miller has done a good part of the work in the paper mentioned above.
Concerning visualisation over a longer period of time, you would certainly have a lower spatial granularity. If you look at a person’s path for, let’s say, a year, you are probably interested in longer trips. And once you want to visualise more than just a few paths, it becomes pretty confusing, of course. But as this was designed for the individual level, I don’t think this is a real problem.
I don’t know the Rinner paper, but I will have a look at it.
25. March 2006 um 23:37
Nice to find something about time geography here - for my thesis I’m currently looking at mapping these concepts to transportation networks. One would think that the lower dimensionality makes life easier: well it doesn’t. When calculating the network analogs (PPT/PNA) of the original concepts you run into serious algorithm complexity issues. For instance calculation of shortest-path based subgraphs for every time interval.
As Miller mentions “[...] for detailed urban-scale applications, especially for real-time applications (such as LBS) or data mining and visualization [...]” more efficient methods must be found.
Nevertheless I think interesting applications are possible and, like you wrote, a mathematical model is available.
P.S.: Nice idea with the gisblog !
19. June 2006 um 01:03
Very interesting ideas and information about the “time prism”. Within this prism you could have decreasing radius as your time at the location increased. A great way to visualize spatial possibilities and planning.
As for the “geocoded calendar”, check out SpeedLimit: http://betimely.com. It ties in your GoogleCalendar, or any iCalendar file with locations to route you to your appointments and alert you when you need to leave.