Abstract
We strive to understand, by using mathematical tools, the phenomena where the observer can interpret simultaneously opposite situations, such as the distinct interpretations of the Necker cube. In this study we present a new coordinate system that draws a distinction between -0 and +0. The central theorem presented here postulates that when divisions and multiplications of 0 are combined with real numbers, the Mobius strip provides a model for non-standard analysis. We also suggest that the axis 0 is the fifth dimension extension of the quaternions. We also propose to add the soft logic capability to humanoid type robots, as a way to overcome the Turing test.
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