Our understanding of levels is informed by our understanding of directions and dimensions in the physical world. Most of us orient ourselves in terms of cardinal and relative directions. Cardinal refers to the directions of north, south, east, and west. These directions are absolute, compared to the relative directions of forwards, backwards, left, right, up, and down, which vary depending upon an individual’s point of view.
If we match the relative directions to axes of a coordinate system, left-right would be the x-axis, forwards-backwards would be the y-axis, and up-down would be the z-axis. Together, these axes give us the ability to describe movement in a three dimensional space.
Most common uses of the term levels imply an up-down sense of direction (e.g., one thing on top of or below another). However, in the context of emergent phenomena, levels are compositional hierarchies based on scale, and the concept of scale implies an inward-outward sense of direction. This inward-outward ‘axis’ describes movement between smaller and larger scales, from atom to galaxy, from microscopic to macroscopic, from absolute nothing to absolute infinity, and vice versa. The inward direction involves zooming in while the outward direction involves zooming out.
Just as an inward-outward direction cannot be accurately represented by a standard axis, emergence also requires a new way of representing levels. This alternative sense of direction can serve as a reference point for understanding some of the distinctive features of emergence.