§ Whalesong hyperbolic space in detail
We can build a toy model of a space where velocity increases with depth.
Let the x-y axis be: left-to-right (→) is positive x, top-to-bottom (↓) is positive y.
Now let the velocity at a given location (x⋆,y⋆) be (y⋆+1,1).
That is, velocity along y is constant; the velocity along x is an increasing
function of the current depth. The velocity along x increases linearly with depth.
Under such a model, our shortest paths will be 'curved' paths.
§ References