Convergence Tautology

A tautology is a repetition. Saying the same thing using different words.

• Rhetorical tautologies occur when additional words are used to convey a meaning that is already expressed or implied.

• A tautological argument is equivalent to circular reasoning.

A tautology is a redundancy. Redundancy can be effective for communication. Redundancy enables errors to be corrected when it is purposefully designed into data streams.

Think of the Rosetta Stone as a clarifying example in the sense in which we use the term. The Rosetta Stone famously proclaimed the same edict in different languages, which allowed the decipherment of the Egyptian Hieroglyphs.

Here, we use the term tautology to refer to expressing the same idea in two different languages, as in different branches of mathematics: Number Theory and Geometry.

Study the figure.

There are two structures.

1. The wireframe is called the KMA.

2. The shaded projection is called the Spire Ostension.

The KMA has been annotated with the magnitudes of its contours.

There is a special significance to the clockwise sequence:

Mathematicians will recognize this as the sequence of convergents of the golden ratio.

The convergents converge to the golden ratio by virtue of a mathematical theorem.

Turn your attention to the shaded region. It is clear that this can be interpreted as a geometric convergence.

Spire Ostension	Geometry
Kma Wireframe	Number Theory

The Kma structure was found to represent a Martian formation. But it was the shaded region that first drew our attention in 1995. The shaded region is an object of pure imagination. It is a cognitive illusion that, in the field of Gestalt perception, goes by several names

The source of the manifestation was not imaginary but physically real. Well-delineated and planar, it rose as a prominence above the Martian surface. This geological feature has never been assigned a proper name. We call it the KMA. It is generally classed as a massif.

A massif is a principal mountain mass, especially one that stands in radical relief from the surrounding topography.

Modal completion of subjective contours. Subjective contours are perceived edges of surfaces in locations where there is no physical contour in the image.

Yet, it was eerily effective in propagating an impalpable beam of pure affect that converged to a point, seemingly in the manner of what might be called the geometric gesture of pointing. In communication theory, this is termed ostension. We call this virtual abstraction The Spire Projection, or Spire for compactness.