Decoding Distortions On The Plane
In the picture above, a cylindrical mirror, placed in the center of an oil painting, "decodes" the distortions in the seemingly random smears of paint, so that these smears are shown to be an easily understood and rational picture; the clearly defined subject matter easily identified.
The type of transformation created with the cylindrical mirror alters distance, and therefore is not isometric, as are reflections, rotations, and translations, all of which preserve distance.
Anamorphosis: Distorted projection or representation of an image on a plane, or curved surface, which, when viewed from a certain point in a certain manner, as by reflection from a curved mirror, appears regular and in proportion.
Anamorphoscope: An instrument for restoring an image, or picture, distorted by anamorphosis, to its normal proportions. It usually consists of a cylindrical mirror.
An excellent illustration of anamorphosis is the comparison of the relative positions and distance between two points on a flat map of the earth, and those that would appear, for the same points, on a sphere, such as the more accurate portrayal of the earth provided by a globe.
Another example: Try to recall how your face appeared in a fun house mirror. Try to recall the mirror that made your nose look as though it jutted out six inches from your face, and your eyes became tiny dots, pulled in so close to the sides of your nose that they almost merged. Your ears were flattened to the sides of your head and barely visible. Basically, the "front to back" vector of your head had been enlarged, and the "side to side" vector had been diminished. You definitely appeared out of proportion, and distorted. If the reverse had happened to your head, your ears would have been two feet apart, and your nose flattened against the front of your face.
You could accomplish the same alterations by stretching a rubber Halloween mask, the type that fits over your head like a hood. By stretching it one way, and then the other you could almost reproduce what the fun house mirror had done to your face. If you took a picture of the Halloween mask, or your distorted image in the mirror, you would have a difficult time recognizing that the picture represented a human face. If you then viewed the picture’s reflection in a slightly concave/convex mirror, you would probably recognize the original face, or mask.
If you consider that "time" might be 3-dimensional, relative to market movements, then it is understandable why its depiction upon a standard chart, a plane, might not be a true portrayal of the proportional/spatial relationships between various points in time, i.e. the nose, the ears, the eyes.
If the cylindrical mirror shown "decoding" the oil painting in the illustration at the beginning of this section were replaced with a circle, then each point on the plane (oil painting) could be described by locating its image relative to the circle. This transformation is termed an "inversion".
This basic book on Ermanometry will not probe deeply into the restoration of three dimensional forms from their image on the plane. However, inversions themselves will be used extensively to demonstrate proportional relationships. The reader may note a conceptual relationship between this concept and the ability of the same market move to exist simultaneously in different shapes. These chameleon moves (relative to shape, not color), are primarily illustrated in the MacArthur Syndrome.
