English: An overview of the two movies is provided in Text S2. Movie S1 consists of four short segments. It pauses after each one and resumes following a mouse click within the movie window. Pressing the back arrow on the keyboard will play the current segment backwards, returning to the beginning of the segment. Initial condition: The surface of the mountain is denoted by a purple mesh in panel A. The outline of the reward mountain in the plane defined by time allocation and pulse frequency (the variable that controls reward strength) is shown in yellow. Click 1: The mountain slides along the pulse-frequency axis (as denoted by the red arrow). The initial position of the outline is shown in black and the final position in yellow. The space between the black and yellow outlines is colored orange under the purple mesh. Click 2: The mountain returns to its initial position. A little green figure (“Flatman;” Shutterstock Images LLC) drops in from above and stands viewing the mountain from the pulse-frequency axis. This observer perceives the world in only two dimensions. Thus, from Flatman's viewpoint, the price dimension does not exist. Flatman's 2D view is shown in the green bubble (panel B) as a conventional graph of performance (time allocation) versus a reward-strength variable (pulse frequency). This graph is analogous to a plot of data from a conventional “curve-shift” experiment [35], [36], [37]. Click 3: The mountain returns to its initial position and is displayed in 3D in panel C. It then slides along the price axis (as denoted by the blue arrow), moving in an orthogonal direction to the displacement that was shown in panel A following clicks 1 and 2. The face of the mountain includes a diagonally oriented segment. Thus, as the mountain slides along the price axis, its outline (dashed yellow curve) is displaced leftwards along the pulse-frequency axis. Click 4: The mountain returns to its original position in panel C. Flatman then reappears and the mountain again slides along the price axis. What Flatman sees from his 2D viewpoint along the pulse-frequency axis is shown inside the green bubble in panel D. Note that the two orthogonal displacements of the mountain are clearly distinguishable in the 3D views (panels A,C) but are indistinguishable in Flatman's conventional 2D view (panels B,D).