Paradoxical effect
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The resolutions for some paradoxically observed optical illusions


An illustration for an artificial cognitive paradox

The object is not there at all. And instead, the white "tip" is actually pointing away from the viewer.

The illustrated spheroid reveals what appeared as a curved bottom pyramid liked object, is an optical illusion of a hollowed-out segment of the spheroid. When the spheroid is concealed with its depth of field negated in its perception, its cognitive paradox is thus manifested to render its apparent observation with a perception that is delusionally inversed from its actuality.

This is an illustration for how we could be fooled in a topsy-turvy manner with a cognitive negation.


The paradoxical illusion in the apparent layout of the Cartwheel galaxy group

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 apparently shows it in its opposite facing, is a cognitive paradox rendered by its lack of depth perception.

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.

galaxy group

X-ray image of
Cartwheel galaxy


The paradoxical illusion in a SOHO's caption for Comet 96P/Machholz

The approaching of Comet 96P/Machholz as shown in a SOHO's video footage, at times can be apparently seen as coming from behind the Sun and then turns toward the Earth, and at times can be apparently seen as coming from in front of the Sun and then turns away from the Earth.

This amazing cognitive paradox is as a result of its depth information was being negated.

The negation can be revealed by investigating with a 3D trajectory model of Comet 96P/Machholz that shows how this comet relative to the Earth position, was actually turning around the Sun for its rendevous in January 2002. The comet's trajectory path as shown with the 3D orbit diagram, provides the depth resolution, and shows that the 2002 Comet 96P/Machholz was in fact coming into the field of view from in front of the Sun, and then turned around the Sun by moving away from the Earth.


The motion paradox of a spinning 3-D tetrahedron structure

This animation of the spinning tetrahedral as illustrated, is imbued with a motion cognitive paradox for its spinning direction.

Two people seeing the same animation simultaneously, can observe it to be spinning in opposite direction.

To trigger a reversal for the spinning direction of the spinning tetrahedral, look at the image, and take note of the direction of spinning. Then look downward at the image at below for a second, and then look at the spinning tetrahedral image again. Very often, this would trigger the reversal for the spinning direction of the tetrahedral to spin in the opposite direction from what was previously saw.

Close your eyes for one second could also work for triggering the reversal.

This amazing cognitive paradox, is as a result of the depth information of this 3D animation, is negated with its 2D presentation. And without the depth information, it cannot not be conclusive for its spinning direction.

A spinning tetrahedral


The motion paradox in the silhouette of a spinning dancer

See a link to a spinning dancer animation that could appear to be rotating clockwise by a person but could also be observed rotating counter-clockwise by another person looking at a same animation.

Web sites as such listed the functions of left and right brain, and claimed that this is a personality test to tell if the observer uses more of his left or right brain by observing the rotating direction of the spinning dancer animation.

Notwithstandingly, the rotating direction of the dancer can be absolutely controlled by anyone with a simple technique.

And after having mastered the technique, it will always work for controlling the rotating direction of the spinning dancer. Begin by practicing it with a slightly slower spinning dancer animation, and after perfected the skill, it should also work quite easily on the original faster rotating animation.

At a usual observing distance, when the dancer has appeared to be rotating clockwise, focus on the pointed leg until it reaches the left most, then blink your eyes normally and then look at the whole image, it should then change direction and rotate in counter-clockwise direction. When it is rotating in counter-clockwise direction, focus on the pointed leg until it reaches the right most, then blink your eyes normally and then look at the whole image, it should then change direction and rotate in clockwise direction. These are the two places to focus that would change the direction of the rotating dancer at the blink of your eyes, they are optical clues that the motion from these starting positions would set the direction of rotation for anyone focusing there. Take note this method could work well only with a non lagging animation.

To lock into prevailing direction of the rotation, look at the animation focusing on the upper half image following the ponytail. Then whatever the rotating direction appears as, it would thereafter be persistently observed.

For spontaneous change of rotating direction, look at the animation by focusing on the bottom half image following the pointed leg, the apparent rotating direction would then always flip within a moment.

Focus here to lock rotation direction

Focus here to flip rotating direction

However, an unaware observer can always trigger a change in rotating direction of the animation unintentionally in many ways, or get locked in a certain rotating direction in a stereotype manner.

The direction the dancer would appear to be rotating depends on initial optical interception with the animated image, and after a first impression that sets the direction of rotation, this direction would usually prevails in a stereotype manner especially when the observer is staring hard on the upper half image.

There are many other ways without blinking your eyes that can control the rotating direction of this dancer animation, and also make it appeared to be swinging from side to side instead of rotating by focus on the pointed leg when it reaches the extreme end and then quickly focus on the head; this requires some practice playing with peripheral vision. There is also a visualization technique that could work with high success rate in controlling the direction of the spinning image; close your eyes and visualize a specific rotating direction of the spinning dancer in your mind, then open your eyes and look at the stretched out hand, the image would then rotate in the direction you have selected in your mind. This visualization method might not work when the pointed leg is at right end and you have visualized it to rotate in counter-clockwise direction, and also not work when the pointed leg is at the left end and you have visualized it to rotate in clockwise direction.

The standard spinning dancer animation would always start to rotate with the pointed leg at the right most as illustrated on right image, therefore people looking at the animation from this starting point would always see it rotating in clockwise direction with reference to top view when focusing on upper body of the spinning dancer.

Unless the image has lagged on loading when it starts to rotate that causes the observer to lock on the rotating direction with the pointed leg starting to spin from the left most, or for other reasons, such as referencing to the pointed leg therefore assumed bottom view instead of the standing leg that assumes top view, then it should be seen as rotating counter-clockwise persistently.

There are many factors that could contribute to errors for the test result, such as observers reported the direction incorrectly, or only reported a spinning direction that refers to his perferred personality although he had seen it spin in both directions. Without validating the inputs, the collected test results are not qualified for deducing any conclusion. It thus needs to qualify the test results by meticulously weeding out the invalid inputs from a group of observers.

To validate a test result, we can first show the observer a modified animation with depth information that could only be observed to be spinning in clockwise direction, and then follow by another that could only be observed to be spinning in counter-clockwise direction. This could identify a few categories of invalid test results.

Do not let the observer know that the particular spinning dancer animations shown are modified versions with fixed rotating directions, would help if scrutinizing is required. After the first round, then use the standard spinning dancer animation in a second round for further testing. Make it clear to the observer that they have to see it at the moment when the image has just appeared, and the perspective is from a top view of the dancer, thereby eliminating the known ambiguities.

For those who have reported persistence counter-clockwise rotating direction, use a modified animation that spin with a starting position facing left, refresh the animation would always make it start to spin from a fixed position. If odds are still reported, scrutinized these inputs further by making checks and also make sure that the observer have not somehow subconsciously preset the rotating direction in their mind by specifying them to look at the pointed leg at the moment the animation appears.

The size of the preset animations below were reduced to minimize lagging effect. And click on the individual animation to view them one at a time when it starts up.

One could flip the rotating direction of the left pair of the above animations easily by using any of the techniques described above. But for the right pair, one would not be able to easily change the rotating direction. Even if it is done, he would notice the odds that conflict with the observed spinning direction, and the visuals of the spin direction would always be self-correcting when looking at the entire image.

By meticulously using the two modified animations from the above right pair with fixed rotating directions, we could qualify a test result that an observer:

  • Has not made directional reference from bottom view of the dancer that is opposite from top view the majority would have assumed.
  • Has not reported a direction incorrectly.
  • Might be reporting a direction based on the listed personalities he thought he belongs to.
  • Could just be trying to demonstrate a special ability he does not have, can mostly be proven otherwise on a case by case basis in further scrutinizing.
  • Could just be fooling around.

Note: In one interesting test an observer pointed forward his five fingers on the animation from below the image, showing the direction of the spin he has observed as spinning counter-clockwise through rotating his fingers with a animation that only rotates in clockwise direction, it was then realized that he has made the directional reference from a bottom view.

This part of the tests might not work properly if the observer is looking at this smaller size modified animation from more than two feet away from a standard 15" LCD screen, or if he has some kind of visual clarity problems, in such ways that the depth information is lost.

However, these tests were conducted meticulously on a small group of people with careful monitoring and after validated the inputs.

This concludes the optical paradox of the animation is caused by a lack of depth information. This is clearly illustrated by the modified animations as show at far right with its indications for depth.

Image on far right is a modified version with the indications for depth, so the dancer would only appear to be standing on her left leg with her front facing the observer. The smaller image have no depth clues and therefore could be made out with its ambiguous visual effect as her front or back is facing the observer, or standing on left or right leg as could be apparent observed.

With indications of depth.

With the understanding of the motion paradox for this spinning dancer animation, it resolves the fallacious claim that the rotating direction observed by a person, is according to his right or left brain personality.

The cognitive paradox of this animation, is simply caused by the lack of its depth information.


The illusion of a perpetual staircase

The Penrose stairs, also dubbed the impossible staircase, was thought as an impossible object that could not be physically built; this is an abstract mathematical object thought as could not be possible in the objective reality of three spatial dimensions.

See a video clip that illustrates a Penrose stair walker walks down the perpetual stair.

See also a video clip on "Impossible Geometry" that illustrates how the Penrose stairs could be rendered in a type of optical illusion.

The perpetual staircase, can be made possible in objective reality in subliminally negated circusmtances.

Penrose stairs

Nonetheless, the image below illustrates that the perpetual staircase could be physically built. This miniature model was built with plasticine and it demonstrates that a physical structure of this impossible object could exist in the objective reality. This was done by negating a cognitive information to render its paradoxical effect.

To demonstrate the apparent perpetual motion in the objective reality with this perpetual staircase, the staircase could be physically constructed with a clockwise moving conveyer belt carrying a magnet that is hidden just underneath the surface of the stairs, a steel ball on the surface of the stairs drawn by the circulating magnet would thus appear to be perpetually moving down the staircase in clockwise direction.

If a live size model is built with the cognitive information concealed in a well planned architectural landscape, an observer who was unwarily led to any of the given vantage points, could be fooled from his perspective under its delusory circimstances. And therefore would see another person could continuously walk up or down the perpetual staircase in this impossible feat that is counterintuitive and mind-boggling.

See UVS topics on "Delusory inversed illusions", "Significant revolutionary discoveries of UVS", and "Overviews of Universal Vortical Singularity" for more insights.

Watch a video clip on "Nothing is as it seems" that shows some intriguing optical illusions.


The first principle is that you must not fool yourself -- and you are the easiest person to fool. - Richard Feynman




References and links:
Depth of field - From Wikipedia, the free encyclopedia
Rotatating Tetrahedron animation - From Wikipedia, the free encyclopedia
Original spinning dancer animation - by Nobuyuki Kayahara
Peripheral vision - From Wikipedia, the free encyclopedia
Images of X-ray Cartwheel Galaxy - NASA/CXC/A.Wolter & G.Trinchieri et al.
Video clip on "Comet 96P/Machholz (2002)" - Video image credit by ESA/NASA, SOHO spacecraft
Penrose stairs - From Wikipedia, the free encyclopedia
Video clip on "Penrose stair walker" - germafrican, YouTube
Video clip on "Impossible Geometry"
- braincollector, YouTube

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