We strive to understand by using mathematical tools the phenomena
where the observer can interpret simultaneously opposite situations,
such as the two interpretations of the Necker cube. We present a new
coordinate system that draws a distinction between 0 to +0. The
central theorem is that when divisions and multiplications of 0 are
combined with the real numbers, the Mobius strip provides a model for
nonstandard analysis. We suggest also that the axis 0 is the fifth
dimension extension of the quaternions.
