Appendix 1: The analogies

This entry is part 12 of 14 in the series A theory of perspective

The first analogy is the pendulum, which is commonly used in Zen or Taoism. The extremes it swings back and forth represent the duality/dichotomy/polarization of the phenomena (me – you, good – bad, right – wrong), and the balance point is somewhere in the middle.

The visual effect of the pendulum comes from its velocity. The pendulum goes fastest at its balance point, and has zero velocity at the extremes. Therefore it can be seen wholly for a moment, before it gets fader to the balance point. The higher velocity the pendulum is, the clearer the extremes and fader the trajectory are. If it goes fast and far enough, the trajectory may completely faded, resulting two seemingly unrelated clear images.

In general, the trajectory of an object that constantly changing its velocity would go from clearness to fadedness:

The second analogy is the moon. It’s not just a symbol of purity or solitude, but also where all the chaos of the world makes sense again. The chaos is the source of all of the sufferings and happiness; transforms what we know unpredictably, brings the familiar to infinity, and the unfamiliar close to us.

I cannot help to realize this is the Riemann sphere:

In mathematics, the Riemann sphere is used to describe the transformation of perspectives. The notion of transformation is important, because it shifts us from the mindset that different perspectives are intrinsically different, to the mindset that they are just distorted versions of each other, and can be transformed back and forth if we know the rule.

In practice, it is easier to imagine how distortion happens under different perspectives with anamorphosis art:

Basically the distortion tells us that although all perspectives are born equal, some of them are more equal than others.

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