Maps that show time instead of space

It's called Isochrone map

https://en.wikipedia.org/wiki/Isochrone_map

Yes! This is a less practical but more funky version of isochrone maps.

Not really - you have to wait for the subway, it also takes a finite time to travel, and it frequently stops. It can avoid traffic, but the actual MPH can be slower than a car when you include both those things.

Right, the travel-time metric is not compatible with a Euclidean R² metric. You can imagine three subway stations in a triangle loop, such that it's a shorter trip to do a full loop on the subway then to walk to a point in the interior.

There's no way to continuously deform a map so that it represents travel times as distance in a plane.

Oh yes, unfortunately, you can't do this perfectly. There are some graphs that cannot be embedded in Euclidean space in any number of dimensions, e.g. a 4-cycle with distance measured by path length. It's a good-enough approximation for visualization purposes, though.

This seems to be the article behind the paywall: https://ora.ox.ac.uk/objects/uuid:5c2ebe20-a1c2-44cb-bd71-95...

Cool! I'd love to have a look at that, but the two links in the paper seem to be broken :( http://roadlessforest.eu/map.htm and http://www.map.ox.ac.uk/accessibility_to_cities/

Right. There could be northbound traffic but not southbound for example. The answer is they must be symmetrizing the distances somehow. Alternatively, you could show the travel times _from a source location_ unambiguously, which might be more interesting for the average user (e.g. from home)

Good point.

And hills are rather easier in one direction too.

Indeed, you can't do this perfectly – it's an approximation. I just use one of the two directions as the travel time because if I wanted to symmetrize I'd have to call the Google Maps API twice . Asymmetry aside, it's also not possible to perfectly embed metrics in 2D Euclidean space, or any-dimensional Euclidean space for that matter (see other comment)

Before trying the site I assumed the way they would resolve this is that the distance calculations would be made relative to the point at which you held the map, but what actually happens is that the map is drawn uniformly no matter where you hold it. and of course this is an impossible representation due to the reasons you describe as well as the differences in mappings between a path that is configured to be walked in one direction, but traveled by vehicle in the other.

This is what it is supposed to do. The coordinates in map from one location to another change from distance to how much time it would take to reach there.

IMO, I expected that I could click various places and the map would react to the specific point I clicked.

Instead, it seems to essentially just be an animation between two pre-determined images.

These actually point of a failure mode of the original topic's visualization, at least as it pertains to public transit: https://upload.wikimedia.org/wikipedia/commons/thumb/4/40/Ma...

(I think a previous commenter called this out by referring to subways as "wormholes")

As for car directions, you should be able to create an isochron by drawing circles in the transformed map!

I prefer the typical isochron presentation over the warping. It's unfortunately hard to find free, public isochron maps, though. Some examples I've found:

https://www.targomo.com/developers/apis/isochrone/

https://direkt.bahn.guru/?origin=8503000

https://www.chronotrains.com/en

It would not be representable, since even 1 unreachable point would have to have infinite area.

If you allowed the 2D map to become 3d, I suppose you could have an infinitely high spike or low trough.

What if you want to know how long it's going to take in kilometers?

You can turn on arrows that update as you move your mouse around (assumedly, signifying an origin). Not sure exactly what they do, but they do hint at potentially taking asymmetric distance into account.