§ 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)(x^\star, y^\star) be (y+1,1)(y^\star+1, 1). That is, velocity along yy is constant; the velocity along xx is an increasing function of the current depth. The velocity along xx increases linearly with depth. Under such a model, our shortest paths will be 'curved' paths.

§ References