We live in a future-forward direction, looking out at the world carrying our left and right along with us. Our left and right are the immediate intersection of our living awareness with the two-dimensional planes of the external universe. Chiral biochemical molecules are also left- or right-handed in the physical world.1 The left, right and forward orientation of all living beings begins with these “handed” biomolecules in cellular metabolism, so we’ll need to examine them at the molecular level as well as the level of the organism as a whole. To do that, we’ll make use of two concepts: a two-dimensional window and a three-dimensional asymmetrical mirror. Here’s what we mean by each of these terms.
A real 3D window lets us look through from one side to the other regardless of which side we’re on. A 2D window requires imagining that both sides of the window merge at the physical plane that is the windowpane, as suggested in Figure 1 above. The result is a “double-sided” two-dimensional plane of interface between the objects on either side of the glass.
A 3D asymmetrical mirror is a more complex idea. Begin by imagining a normal mirror like the one depicted in Figure 2. Here, the surface of the mirror reflects the surface of the object that’s directly in front of it – in this case, the palm of a right hand. Unlike this normal mirror, in which a surface and its reflection are separated by space, a 3D asymmetrical mirror reflects a surface separated in time, as shown in Figure 3. To grasp this idea, imagine that the hand pictured in the foreground of Figure 2 has a “past” side, which is the back of the hand, and a “present” side, which is the palm. If the mirror is a 3D asymmetrical mirror reflecting time, the image it reflects would look like the one in Figure 3, where the “present” palm side reflects its own “past” back side.
Notice that both the window and mirrors are 2D planes at their surface. The image we see through a window resides at the windowpane, regardless of which side of the window we’re looking through. But unlike a 2D photo pressed against the glass, we take the shapes revealed in a window to be real three-dimensional objects that actually exist on the other side. And, like all other real objects, the scene we observe through a window may change with the arrival of each new now moment.2
An important distinction between the window and the mirrors is the left-right (chiral) direction of objects. Unlike the mirror reflection in Figure 2, the two individuals depicted in Figure 1 are independently left- and right-handed. Each of them is displaying her right hand; but from our vantage point on “this side” of the window, the thumb of the person in the black jacket points left and the thumb of the one in the red jacket points right. If we imagine switching sides of the window and standing next to the person in red on the opposite side, we’d see her thumb pointing left and the other person’s thumb pointing right. In other words, each viewer faces the plane of the windowpane with her own left-right spatial orientation. The same is true of the hand in the mirror in Figure 3. If we were looking at it from the “other side” (that is, from the position of the mirror), we’d see the palm of the right hand that’s being reflected with its thumb pointing right.3
1 Three-dimensional chiral objects are any two objects with otherwise identical properties except for their left- or right-handedness. Our two hands are chiral objects. They are symmetrically opposed and their two-dimensional mirror images – whether of the two palms or of the two back sides – cannot be superimposed on one another by any combination of rotations or translations. Objects like our hands, which differ only in handedness, have no plane of symmetry in three-dimensional space. This has implications for two-dimensional surface encounters in three-dimensional space, which we’ll explore later. Our actual hands may have minor differences between them but ideally, they are chiral.
Not all objects are themselves chiral, but our left-right orientation – the way we see things – derives from chirality. In chemistry, chirality and “handedness” are concepts that apply to the structure of molecules.
2 You can also see the window as part of the room you’re in, or as part of a painting that’s in the room you’re looking at. Regardless of the context, the “scene” you see presents itself to awareness as a two-dimensional left-right plane filled with varying shapes in different shades and colors.
3 Notice that a mirror only reverses left and right; it doesn’t reverse up and down. We’ll see how up-down resolves to left-right in next chapter in our discussion of the ideal perpendicular. Whether we turn to face up or down, our left and right orientation remains unchanged
No comments:
Post a Comment