2D Window, 3D Mirror

 

We live in a future-forward direction, looking out at the 3D world carrying our left and right along with us. Our left and right are the immediate intersection of our living awareness with the 2D planes of the external universe. Chiral bio-chemical molecules are also left- or right-handed in the physical world.  The left and right 3D orientation of all living beings begins with these “handed” biomolecules in cellular metabolism, so we’ll need to examine both levels of awareness in detail.

To do that, we’ll make use of two concepts: a “2D window” and a “3D 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 of the window we’re on.  A 2D window simply requires imagining that both sides of the 3D window merge at the physical 2D windowpane, as suggested in Image 1 above.  The result is a “double-sided” 2D 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 2D mirror like the one depicted in Image 2 above.  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 mirror reflects a surface separated in time, as shown in Image 3.  To grasp this idea, imagine that the hand pictured in the foreground of Image 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 reflected in the mirror would look like the one in Image 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 2D windowpane, regardless of which side of the window we’re looking through. ¹ But unlike a 2D photo pressed against the glass, we take the shapes revealed in the 2D plane of a window to be “real” 3D objects that actually exist on the other side.  And, like all other “real” 3D objects, the scene we observe through a window changes with the arrival of each new “now” moment.

Another distinction between the window and the mirrors is the left-right (chiral) direction of objects. ²  Unlike the mirror reflection in Image 2, the two individuals depicted in Image 1 are independently left- and right-handed.  Each viewer is displaying her right hand; but from our vantage point on “this side” of the window, the thumb of the viewer in the black jacket points left and the thumb of the viewer in the red jacket points right.  If we imagine switching sides of the window and standing next to the viewer in the red jacket on the “other side”, we’d see her thumb pointing left and the thumb of the viewer in the black jacket pointing right.  In other words, each viewer faces the 2D plane of the windowpane with her own left-right spatial orientation.  The same is true of the hand in the mirror in Image 3.  If we were looking at it from the “other side”, we’d see the palm of the right hand that’s being reflected in the mirror with its thumb pointing right.

¹  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 2D up-down / left-right plane filled with varying shapes in different shades and colors.

²  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.

3D 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 2D 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 3D space.  This has implications for 2D surface encounters in 3D space, which we will explore later. Our actual hands may have minor differences between them but ideally, they are chiral.