Spatio-Temporal Maps

Saturday, I looked some of the pages linked to a visualization site I came across over the past week or so. A visualization of the trains out of London and how the trains changed travel times.

Spatio-temporal maps have been a topic of mine for decades. Each of the circles represents a half an hour. Here things are fairly straightforward. But, the realities on the ground are quite different. Yes, the train takes you there quickly. Yet, step off the train, and suddenly it still takes five minutes to cross the street in front of the train station. Things slow down. The 3.5 hours it took to get to Neiuweschans did not deform the map so the physical and temporal, the spatio-temporality, stayed aligned. If you map by time, distance gets deformed. Well, not in this viz. But, try flying to China and then taking the train to your home, several days away via that train. That map would get bent up quite a bit.

Since San Antonio has been my hometown if I ever had one, and having worked in Austin at too very different times, I travelled back and forth a lot. At times I took the Greyhound. Once, on Thanksgivings Day, I blew a hose, popped the hood, opened my trunk, someone pulled over, took a look, dug around in the camper topped-pickup truck found a hose, put it on, filled my car with water, and sent me on my way gratis. Dad didn’t get to tell me off. Thanks. And, I didn’t have to walk 45 minutes to get to a phone in what was at that time ag wilderness. Now it’s convenance stores, burbs, same distance, different mindset. Same spatial, different temporal. Well,  tore up the concrete since then and changed the physical as well. Roads get wider, flatter, and straighter over time.

So here would be something to map and look at the math behind intrinsic curvature. Well, try to if you will. So I pulled the northbound distance and time data for the cities between San Antonio and Austin. I threw away the first attempt. I modified the second. I waffled on how to represent the gaps and lags. Then, I realized that the physical, the miles were continuous, as were the times. I used horizontal bars for each quantity. To get both bars ends to line up meant bending the bars, aka introducing curvature. Except for one thing, I’m working in MS Paint. I know all the tricks. Actually, I learned a few Saturday.

There were four segments. Two of the towns were obvious. The third was just pulled out of necessity. The Greyhound used to pull into Kyle, so I know it’s there, along with DQ and a Wachenhut staffed county jail on the frontage road.

I did not pull the southbound data.

So here’s my spatio-temporal map.

The graphic at the bottom uses spheres to represent each maximum quantity. The minimum quantity is a smaller circle on the maximum quantities sphere. I put the two larger spheres out front and the smaller ones behind them, so both the spatial quantities and the temporal quantities could maintain their continuity. The line charting had gaps. That just isn’t real. The world is seemless, so the spheres let me present that continuity.

The leftmost sphere represents the minutes traveled with the larger circle. The smaller circle represents the miles travelled. The leftmost sphere is blue because travel time trumps distance travelled. That making it a slow segment of the trip. The travel represented by the second sphere is black, because the miles travelled trumps the time travelled. Again, this sphere has a smaller circle on it representing the shorter quantity, time. The two spheres contact each other miles to miles. That would be the smaller circle on the first, and the outer circumference of the sphere on the second. The third sphere is like the second, but they contact each other times to times, aka the small circle on the second sphere to the outer circumference of the third. The fourth sphere contacts the third, miles to miles.

Too complicated, I know. With a better 3D package, it could be clearer.

Each sphere’s rotational axis is shown. The system of spheres are organized along a curve, rather than a plane.

I went on to draw a curvature graph based on the same data, but the formulas didn’t give the correct results. The arc length of the arcs are too long. The red line edits a spike out of the graph, because it too isn’t real. Again, the road is seamless.

I continued my quest for a curvature view with this, the last one.

No explanation for this one. I did manage to get a nice arc, but instead of covering the first three points, it went all the way to the fifth point, to Austin, fitting well, but missing the point.

In these diagrams, I used hard data. Well, hard for the moment. I did go back to get the southbound data and found it at odds with the northbound data. Construction can account for why the trip south took more time. Traffic could do same. I did get to that data later in the day. Escaping the big cities eats up the time on this trip. Still, we can consider the hard data. But, there is a soft component. Back during the dot-com one days, the trip was lit up all night. The convenience stores/gas stations stayed open all night. This shortened the psychological distance. These days the speed limits have been reduced for revenue generation purposes–new speed traps. But, I still remember making the trip from south Austin to north San Antonio in 45 minutes. Forget that. But, yes, the speed limits affect the psychological distance as well.

So tying this to product management? Two things:

• The original train visualization showed a process over geography. Sprints are such a process. And, I’ve talked about product manager geography previously in this blog. For me a roadmap is a map, not a list. Populations are like lakes. Come up with your own analogies. Make your map a real map.
• Consider my maps to be maps of a user experience. When I reach New Braunfels, please don’t make me open a Wal-Mart popup window. I don’t have time to stop. Your features are organized like trips. Different outcomes, different trips. Done again and again, it becomes familiar and routine. The user knows their way until Agile changes something and DevOps thought nothing of injecting a bug into the user’s UX. Click here, then click there is a geography, a series of histograms/long tails, and flow or psychological time.