The Pale Blue Dot? Chapter Twelve: Illusion, Realism, Philosophy of Perception and Visual Space

Written By Thomas Perez. November 10, 2018 at 3:27AM. Copyright 2018. Updated 2020.

What is An Illusion?

By pure definition, an illusion is a thing that is or is likely to be wrongly perceived or interpreted by the senses. A deceptive appearance or impression. A false idea or belief. “An illusion is a distortion of the senses, which can reveal how the human brain normally organizes and interprets sensory stimulation. Though illusions distort our perception of reality, they are generally shared by most people.” (1).

1. Wiki.

A careful analysis of the picture will reveal that square A and square B are the same colors, as the following picture demonstrates…

Hence the two squares are the same color. This can be proven using the following methods:

1. Open the illusion in an image editing program and using the eyedropper tool to verify that the colors are the same.

2. Cut out a cardboard mask. By viewing patches of the squares without the surrounding context, you can remove the effect of the illusion. A piece of cardboard with two circles removed will work as a mask for a computer screen or for a printed piece of paper.

3. Connect the squares with a rectangle of the same color, as seen in the figure to the right.

4. Use a photometer.

5. Print the image and cut out the squares. Cut out each square along the edges. Remove them. Hold them side by side.

6. Isolate the squares. Without the surrounding context, the effect of the illusion is dispelled. This can be done by using the eyedropper tool in image editing programs such as Gimp to sample the values of A & B, and to color in the newly adjacent rectangles using the paint bucket tool.

Here is another example of a perceived illusion. At first glance, both tables look like they have different shapes. But they do not. They are the same size

But what does this have to do with the shape of Earth, you may ask? The answer to that question falls under the category called “Philosophy of Perception.” Yes, that is a field of philosophy, believe it or not. It is also used in the scientific community as well.

What is the Philosophy of Perception?

“The philosophy of perception is concerned with the nature of perceptual experience and the status of perceptual data, in particular how they relate to beliefs about, or knowledge of, the world.” (2). (Or Earth – world – as seen from space; T. Perez).

2. BonJour, Laurence (2007): “Epistemological Problems of Perception.”Stanford Encyclopedia of Philosophy, accessed 1.9.2010.

Philosophy of perception is broken down into three categories…

1. Internal Perception (proprioception): Tells us what is going on in our bodies; where our limbs are, whether we are sitting or standing whether we are depressed, hungry, tired and so forth.

2. External or Sensory Perception (exteroception): Tells us about the world outside our bodies. Using our senses of sight, hearing, touch, smell, and taste, we perceive colors, sounds, textures, etc. of the world at large. There is a growing body of knowledge of the mechanics of sensory processes in cognitive psychology.

3. Mixed Internal and External Perception: is the perception (I.e., emotion and certain moods) that tells us about what is going on in our bodies and about the perceived cause of our bodily perceptions.

The philosophy of perception is mainly concerned with exteroception; most notably neuroscience and cognitive psychology (or cognitive science). And as such, each field falls under the category of the senses, what we; see, hear, small, touch and taste. For the intent and purposes of this chapter, I will be only discussing what we see in relation to space; specifically, visual space between objects and how they relate to realism (what is real and what is not). This category falls under category number two above; “External and Sensory Perception” – which in turn falls under “Visual Space.”

Visual Space and Objects In Between Spaces

What is visual space? “Visual space is the perceptual space housing the visual world being experienced by an aware observer; it is the subjective counterpart of the space of physical objects before an observer’s eyes.” (3).

3. Ibid 1.

Now this is where chapter one concerning a flat geocentric Earth comes once again into play. In order to confirm visual space measurements between objects, observers and their correlating distances between one another, the math of geometry is the discipline needed to achieve this. Geometry is devoted to the study of space and the rules relating the elements to each other within given spaces. For example, in Euclidean space there is the Pythagorean theorem. The Pythagorean theorem was discussed in chapter one in reference to the measurement of distances from an observer, it’s FoV and an object in relation to its two-dimensional equation. “In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and similar spaces of higher dimensions. It is named after the Ancient Greek mathematician Euclid of Alexandria.” (4).

4. Ibid 1.

In a two-dimensional space of constant curvature, like the surface of a sphere, or a globe Earth, the rule is somewhat more complex but applies everywhere. On the two-dimensional surface of a football, the rule is more complex still and has different values depending on location. In well behaved spaces such rules used for measurements and metrics are classically handled by the mathematics invented by Riemann. Object space belongs to that class.

To the extent that an object is reachable by the scientific launching of orbiting probes; visual space as defined is also a candidate for such considerations. Moreover, whether faked or not, anything, if truly launched, that flies into orbit (the firmament), goes up and obviously either the obits within Earths lower orbital plane, or flies vast distances. Since that may be the case, are probes really flying vast distances to places like Mars, Venus and Jupiter? Stellar aberrations and parallax within their relationships regarding distant measurements help to answer this question as covered in chapter three. I will go into depth concerning the Sun and Moon in chapter thirteen; and the planets and stars in chapters fourteen and sixteen. The first, and remarkably prescient analysis, of this observation was published by Ernst Mach in 1901, under the heading “On Physiological as Distinguished from Geometrical Space.” (5).

5. Mach, E. (1906) Space and Geometry. Open Court Publishing: Chicago.

Mach states that “Both spaces are threefold manifoldnesses” but the former is “…neither constituted everywhere and in all directions alike, nor infinite in extent, nor unbounded.” In other words, what Mach is saying is that 2- and 3-dimensional Euclidean space is not infinite or unbounded. And as such the former (2-dimensional space) is not everywhere – but such spaces are all alike. They are not infinite, but yet they remain unbounded. In other words, as discussed in chapter three, the expanding universe just may simply be the expanding firmament and Earth along with it – stellar parallax (the flying away of objects in relation to parallax measurements) explain this, again; “as discussed in chapter two.” (6). Georg Friedrich Bernhard Riemann (1826–1866) was the first to recognize geometry on the surface of a sphere. Spherical geometry is a type of non-Euclidean geometry. This is the reason we name the spherical model for elliptic geometry after him, the Riemann Sphere.” (7). Moreover, Euclidean geometry differs greatly from that of Hyperbolic geometry, of which is discussed a few paragraphs down.

6. Ibid 5.


Rudolf Luneberg, a highly talented mathematician wrote an essay in 1947 demonstrating this. Luneberg’s underlying principles demonstrated that when features are sufficiently singular and distinct, there is no problem about a correspondence between an individual item; for I.e., A in object space and its correlate A’ in visual space. Questions can be asked and answered such as “If visual percepts A, B, and C are correlates of physical objects A, B, and C, and if C lies between A and B, does C (really) – emphasis, T. Perez) lie between A and B?” (8). In this manner, the possibility of visual space being metrical can be approached. If the exercise is successful, a great deal can be said about the nature of the mapping of the physical space on the visual space.

8. Luneburg, R.K. (1947). Mathematical Analysis of Binocular Vision. Princeton, N.J.: Princeton University Press.

Luneburg concluded that visual space was hyperbolic with constant curvature, meaning that elements can be moved throughout the space without changing shape. One of Luneburg’s major arguments is that, in accord with a common observation, the transformation involving hyperbolic space renders infinity into a dome (the sky). The Luneburg proposition gave rise to discussions and attempts at corroborating experiments. The argument actually backs up Mach’s observations and conclusions when you really think about it. It is something that flat Earthers can sink their teeth into. Obviously, Luneberg indicated that space itself is transformed into an infinite dome – the sky (with layers, as discussed in chapter six with reference to the different layers of atmospheric expansions – hence expanding infinitely; T. Perez). (9).

9. Chapter 3 Geometry and Spatial Vision. (2006) In M.R.M. Jenkin and L.R. Harris (Eds) Seeing Spatial Form. Oxford U. Press. pp 35-41

Hyperbolic space became a reality when “The first published works expounding the existence of hyperbolic and other non-Euclidean geometries are those of a Russian mathematician, Nikolay Ivanovich Lobachevsky, who wrote on the subject in 1829, and, independently, the Hungarian mathematicians Farkas and János Bolyai, father and son, in 1831.” (10).


“In hyperbolic geometrythere are two kinds of parallel lines. If two lines do not intersect within a model of hyperbolic geometry but they do intersect on its boundary, then the lines are called asymptotically parallel or hyperparallel.” (11).


The following three pictures illustrate hyperbolic space. All three images wonderfully illustrate the Pythagorean theorem, Euclidean space and non-Euclidean space harmoniously…

Again, let me repeat, more or less; “Euclidean geometry is the study of the geometry of flat surfaces, while non-Euclidean geometries deal with curved surfaces.” (12). “There are two main types of non-Euclidean geometries, spherical (or elliptical) and hyperbolic. They can be viewed either as opposite or complimentary, depending on the aspect we consider.” (13).



It is believed that Luneberg’s discussions and corroborating experiments on the whole did not favor his conclusions. “Basic to the problem and underestimated by Luneburg is the likely success of a mathematically viable formulation of the relationship between objects in physical space and percepts in visual space. Any scientific investigation of visual space is colored by the kind of access we have to it, and the precision, repeatability and generality of measurements. Insightful questions can be asked about the mapping of visual space to object space, but answers are mostly limited in the range of their validity. If the physical setting that satisfies the criterion of, say, apparent parallelism varies from observer to observer, or from day to day, or from context to context, so does the geometrical nature of, and hence mathematical formulation for, visual space.” (14). But Luneberg’s non-favorable conclusions are based upon one concept: the concept of Realism. However, the physicality of realism can be questioned into doubt. In other words, geometrical and mathematical formulations are not constant. They can change depending on what is considered real or Illusion. reality can become illusion, and illusion can become reality. Who is to say what is sense data and what is realism? This reasoning of thought is called; the Argument from Illusion – (T. Perez).

14. Foley, J.M. (1964). Desarguesian property in visual space. Journal of the Optical Society of America, 54.

The Argument from Illusion

The argument from Illusion is an argument for the existence of sense-data. It is posed as a criticism of direct realism (Wiki). Sense-data in the philosophy of perception was a popular view held in the early 20th century by philosophers such as Bertrand Russell, C.D. Broad, H.H. Price, A.J. Ayer, and G.E. Moore. Sense data are taken to be mind-dependent objects whose existence and properties are known directly to us in perception. These objects are unanalyzed experiences inside the mind, which appear to subsequent more advanced mental operations exactly as they are. In philosophy of mind, naive realism, also known as direct realism, common sense realism or perceptual realism, is the idea that the senses provide us with direct awareness of objects as they really are. Objects obey the laws of physics and retain all their properties whether or not there is anyone to observe them.

However, an argument by A.J. Ayer demonstrates a weakness in realism. A wonderful example of this is Ayer’s stick demonstration. “I have a stick, which appears to me to be straight, but when I hold it underwater it seems to bend and distort. I know that the stick is straight and that its apparent flexibility is a result of its being seen through the water, yet I cannot change the mental image I have of the stick as being bent. Since the stick is not in fact bent its appearance can be described as an illusion. Rather than directly perceiving the stick, which would entail our seeing it as it truly is, we must instead perceive it indirectly, by way of an image or “sense-datum” (15).

15. Huemer, M “Sense Data.” Stanford Encyclopedia of Philosophy. Retrieved 11 October 2018.

This mental representation does not tell us anything about the stick’s true properties, which remain inaccessible to us. “With this being the case, however, how can we be said to be certain of the stick’s initial straightness? If all we perceive is sense-data, then the stick’s apparent initial straightness is just as likely to be false as its half-submerged bent appearance. Therefore, the argument runs, we can never gain any knowledge about the stick, as we only ever perceive a sense-datum, and not the stick itself.” (16).

16. Ayer, A.J., The Foundations of Empirical Knowledge. New York: Macmillan, 1940.

J.L. Austin criticized the argument. “Because the stick provides a contrasting surface in the surrounding water, the bent appearance of the stick is evidence of the previously unaccounted for physical properties of the water. It would be a mistake to categorize an optical effect resulting from a physical cause as sensory fallibility because it results from an increase in information from another previously unaccounted-for object or physical property. Unless the water is not taken into consideration, the example in fact reinforces the reliability of our visual sense to gather information accurately.” (17). “Perceptual variation which can be attributed to physical causes does not entail a representational disconnect between sense and reference, owing to an unreasonable segregation of parts from the perceived object.” (18).

17. Austin, J. L. “Sense and Sensibilia,” Oxford: Clarendon. 1962.

18. Putnam, Hilary: The Threefold Cord: Mind, Body, and World. New York: Columbia University Press, 1999.

Ayer’s and Austin’s claims are both valid. But Austin’s criticism of Ayer’s claims is lacking. They are lacking on two accounts. One; he claims that “It would be a mistake to categorize an optical effect resulting from a physical cause as sensory fallibility because it results from an increase in information from another previously unaccounted-for object or physical property. Unless the water is not taken into consideration…” (19). What Austin is saying is that since we have the stick in our hand first, and as such it appears to be straight in reality, then any component added with the stick, thus altering its shape, is to be considered an illusion. The stick is still straight regardless of its altering perception under the added component, in this case water. For Austin, his logic concerning appearances are dependent upon experience (what we know). An experience of knowing things from firsthand experience because we are, or were, there to experience it first. Hence the stick is straight because experience tells us so. Moreover, if we were to put our hands under the water to touch the stick, it will still be straight, and it will also feel straight, regardless of what our eyes (a sense) perceive.

19. Ibid 17

But since his argument is based upon established experience, then I would have ventured to ask him; was he there when, what he refers to as a “second component,” water became a reality? Does water bend? Or is it straight? Is not the stick altering the shape, and even more so, the flow of the water from something straight into something going around the object, in this case, our stick? The answer to that question is, “yes.” The shape of water is changed. Some may argue that water has no shape. Really, how do you know this? Were you there at the beginning of its formations? Objects like sticks, footballs, hockey pucks, and even our own bodies can alter its shape. Land masses can also alter its shape. But we were not there to “experience” its (waters) realities unaltered, and neither was Austin. Hence the stick becomes the secondary component, while the water is the first.

To fish, they will see the stick as a reality that bends. A twisting bending thing. The underworld is their domain. They will also feel the changing currents from the stick altering their little swimming patterns. That is reality to them. Now let us go up, above Ayer’s and Austin’s stick proposals and criticisms, past the skies. From our viewpoint, the Earth seems to bend (curve). Is this due to a spherical (ball) shape, or a circular flat disk; as discussed and demonstrated in the earlier chapters? Putting aside what we discussed and learned in chapters four, five, eight and eleven in reference to green/blue screens, camera lenses, moon landings, the ISS and video feeds; of which can all be altered and faked, what if we were to see the curve appear to actually go under and a round – as in the case of spheres – a continuous curve, like Mach suggested? Would that prove a spherical (ball) Earth? No, it would not. And why, you may ask? Because continuous curves, like Mach claimed, have no end, especially if the ball and/or firmament is expanding like I discussed in chapter three. We can never experience going around a ball – we can never get to the “finish line.” However, some may ask the question, “How do I account for Columbus going around the world?” The answer to that question will be covered in chapter fifteen in regard to circumnavigation, flights paths, Antarctica, and so forth.

Another reason it wouldn’t prove a spherical (ball) Earth is because water alters the shape of sticks and land masses. If NASA is not putting “the hoax” on us, and things are as they seem to be regardless of any fisheye lens, then what we may be seeing is the bending of the firmament above – as it expands – on top and at the bottom (“the waters beneath”). This will account for the bending of the “stick” (land masses). Let us remember, land masses are nothing but bodily formations of the Earth sticking up out from under the first component, water. And as such, land masses, though flat, alters its shape in relation to the bending of the waters surrounding it, giving it a curved illusion.

“And the Earth was without form (non-existent), and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters” Genesis 1:2. (20).

20. Holy Bible; King James Version.

Some might laugh at the Genesis 1:2 quotation, claiming the Earth in its early stages, 4.6 billion years ago, was nothing more than a hot sea of molten land masses until it cooled off, hence producing water, bacterial life, oxygen and so forth. My response would be “That is not considered true anymore by scientific standards.” The verse validates a new chemistry. It indicates that “The Sun, at 4.6 billion years old, predates all the other bodies in our solar system. But it turns out that much of the water we swim in and drink here on Earth is even older. A new model of the chemistry of the early solar system finds that up to half the water now on Earth was inherited from an abundant supply of interstellar ice as our Sun formed. That means our solar system’s moisture wasn’t the result of local conditions in the proto-planetary disk, but rather a regular feature of planetary formation — raising hopes that life could indeed exist elsewhere in the universe.” (21). However, let it be understood that although, I do not agree with the entire citation in reference to “life elsewhere,” and so forth (ages); I do support and agree with the overall citation concerning water always being there.