It is a known paradoxical illusion that in the apparent observations from the Earth for the motions of all celestial objects, the Earth would appear to be the Centre of the universe as postulated in geocentrism; it could be apparently observed that the motion of all celestial objects are encircling the Earth. This falsified fact was established in a delusion but was undoubtedly accepted independently by the majority of people from all over the world in all walks of life for millenniums.This cognitive paradox fallacy is as a result of a natural delusion; a natural cognitive paradox of relative motion illusion that renders natural negation for its fallacious empirical observation of the natural phenomenon.

Image on right illustrates the basic elements of Ptolemaic astronomy in a geocentric model, showing a planet (orange color object) on an epicycle (smaller dotted circle) with a deferent (larger dotted circle) and an equant (solid black dot •) directly opposite the Earth (purple and white color object) from the center of the deferent (symbol x).

It is a cognitive paradox fallacy that Moon rises in the East and set in the West as it could be apparently observed from Earth in its localized reference frame. Nonetheless, with inductive reasoning based on heliocentric model, it could be empirically observed that Moon revolves around Earth from West to East by tracking the positions of the Moon on a daily basis at a specific time of the day for its celestial coordinates in the celestial sphere over a period of a few days; this qualitative analysis in a transcendental view can resolve this cognitive paradox of relative motion that has paradoxically caused the cognitive paradox fallacy in its delusion.

It was also a known optical motion illusion of a natural cognitive paradox that the Moon apparently appears to be simultaneously following every observer spontaneously, to wherever all these individual observers on Earth who are moving independently to whatever directions. This is a very amazing natural cognitive paradox, and its discernable optical illusion can be easily resolved for understanding its all applicable delusion of passive transformation in local frame of reference.

The apparent retrograde motion of a planet could be solved mathematically with the deferent and epicycle of the planet based on geocentrism. Although epicycle system in a mathematical construct developed through the observation of the apparent planetary motion in the celestial sphere can be fine-tuned to provide workable solutions with accurate quantitative predictions for this peculiar phenomenon that recurs periodically, it is a falsified fact in astrophysics that the planet in apparent retrograde motion is physically moving in the opposite diurnal motion as it could be empirically observed from Earth; the fallacy is caused by a cognitive paradox of relative motion illusion in a passive transformation of celestial coordinate system.

Without the X-ray image to reveal a depth information, the Cartwheel galaxy in a paradoxical effect appears to be facing toward the observer who observe it from Earth. The X-ray image revealed that Cartwheel galaxy is actually facing away from observer; the optical image that shows it in its opposite facing is caused by its cognitive paradox.

The image on near right is an optical view of the Cartwheel galaxy group, the Cartwheel galaxy is the largest galaxy among the group of three galaxies in the image. Image on far right is the X-ray view of a transgalactic phenomenon showing a column structure connecting the Cartwheel galaxy group.