NUMNUM Patterns

“Everything you can imagine is real.”   Pablo Picasso

Unconsciously and without prompting, I “play” an abstract mind game with the geometry of objects and their spatial arrangements wherever I sit or stand. The game is constant and uncontrolled; it is a way in which I see and experience spaces, surfaces, and shapes within them. I rarely talk about it, since it’s a bit odd and embarrasses me. Conscious or not of the geometrical patterns created in my mind, the games’ shapes and lines are always present. Only in high school did it become obsessive, ever present, and insidious.  Self-conscious of the game, I tried to ignore it or shut it out. I never have, though. 

Almost all rooms and buildings contain cubic, rectangular, or rectilinear shapes which are needed for the game. To begin, my mind involuntarily draws imaginary lines from corners and surfaces of all rectangular or cubic objects in a room and projects these lines straight through space in all directions. Lines have no color and are invisible to others. But I see them, or rather, sense them. They have set positions in space and divide a room into zones. More precisely, lines are projected 1) along and parallel to edges of rectangles, 2) in line with diagonals through corners of rectangles, and 3) in line with diagonals through opposing corners of cubic objects. As an illustration of this, figure 1 shows a desk and its associated line projections. Top and sides of the desk are rectangular, and the desk is cubic. Figure 2 shows how each corner of the desk can have as many as seven imaginary lines radiating from each of its corners.

Since objects vary in shape from rectangular or cubic (such as an L-shaped desktop), my mind arbitrarily ignores some lines that are not well-defined.

I refer to the game as a “mnemonic” game, since the relationships between each object in a room and projecting lines from other objects in the room are remembered and recalled each time I enter the room. These relationships identify the spatial arrangement of the room, and I know instinctively if things are moved around. I can recall accurate arrangements for all rooms where I spent time in my life.

The game is also a form of “mapping”, where objects and relationships between them in the room are spatially, and mentally, documented using lines through the space. Of course, usually a tape measure and Cartesian (x, y, z) coordinates are used to measure actual locations of each object to help us draw a 2D or 3D map. But my mind uses these projecting lines to do this.

My mind game is similar to mapping a shoreline using triangulation surveying, such as the early map drawn for part of the U.S. coast surveyed and mapped between 1817 and 1834 (Figure 3). It is not practical to use measured coordinates to draw such a shoreline map. The maze of triangulation lines looks almost random, yet it is based on actual locations of shoreline features.

In a room I orient myself in regard to shapes of objects in a room or building. And the next part of the game begins. The object of this next part is to always be in a zone where few projecting lines exist. Such a zone is “safe”; these safe zones are rarely entirely free from lines. In Figure 1, there is a yellow-shaded area around the chair created by a set of projecting lines. This is the best relative “safe” zone for the chair, since only a few projecting lines and planes across it.

In another simple example of safe zones in the game, Figure 4 shows a room, looking down from the ceiling, with a couch (red) and TV (blue).  A side lamp table (green) and a bookcase (lavender) are other major objects in the room.  Lines projecting from the room’s four objects are shown in corresponding colors. A safe zone for watching TV, a place where few projecting lines occur, is shaded yellow. Red diagonal lines within the couch do not count (…my rules…) against the safe zone, so this is a good place to sit. If the room’s diagonal lines are not counted as part of the game (…my discretion…), the safe zone is extended as shown dull yellow.

The goal of the “game” is to always be completely within a safe zone, which is rarely possible. Frustration in finding a perfect safe zone is important, since it prevents the game from ever ending. The most unsafe zone on the couch for watching TV is clouded in Figure 4; it has numerous projecting lines through it. So, I avoid this area and offer it to others (who don’t care about the game).

The safe zone for watching TV can be greatly increased, as shown in Figure 5, by some simple interior decorating. In this example, it would be better A) turning the bookcase diagonally across the corner, and B) replacing the square lamp table with a round one, which projects no lines.  By rearranging, the couch is almost totally within a safe zone for TV.  Others around me may not realize why I get up sometimes to turn or move a piece of furniture. But I’m only increasing the size of the couch’s safe zone, releasing myself from the game’s obnoxious interference.

A round room with round furniture and round windows and doors may extinguish the game (Figure 6) and lead me to a totally safe zone. But I find it impossible to become securely oriented to my surroundings when there are too many rounded, non-orthogonal forms in a space. Put another way, I may be addicted to the game.

Attending a concert performance in a large, 100-year-old theater recently, I experienced a strong sense of vertigo and anxiety as we climbed curving steps high up to our balcony seats. The theater had no square corners or other familiar frames of reference coordinate systems which are expected inside a building.  All features – ceiling, balcony, stage, and proscenium – were rounded, sloped, or stepped.  The curving, sculpted walls, ceilings, and floors made it difficult to become oriented, and my eyes searched for something either vertical or horizontal. Not finding a reference coordinate system and its familiar stabilizing units of walls, ceilings, and floors, I held onto adjacent seats or walls to keep balanced while ascending stairs.

A room cluttered with too many objects creates too many projected lines and surfaces, resulting in few safe zones. This causes anxiety and unsafe feelings akin to claustrophobia. Okay, that’s my problem. But is there something similar to these feelings of safety and comfort in our homes for all of us? Well, yes, there is. Someday, I’ll do an article on Sheng Fui that is reminiscent of my safe zones. Or perhaps, an article about interior design would be meaningful. We furnish our interior spaces to promote harmony, balance, and calmness at home.