Perceptual paradox

Last updated May 01, 2019

A perceptual paradox illustrates the failure of a theoretical prediction. Theories of perception are supposed to help a researcher predict what will be perceived when senses are stimulated.

A theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.

Perception Organization, identification, and interpretation of sensory information in order to represent and understand the environment

Perception is the means to see, hear, or become aware of something or someone through our fundamental senses. The term perception derives from the Latin word perceptio, and is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information, or the environment.

A sense is a physiological capacity of organisms that provides data for perception. The senses and their operation, classification, and theory are overlapping topics studied by a variety of fields, most notably neuroscience, cognitive psychology, and philosophy of perception. The nervous system has a specific sensory nervous system, and a sense organ, or sensor, dedicated to each sense.

A theory usually comprises a mathematical model (formula), rules for collecting physical measurements for input into the model, and rules for collecting physical measurements to which model outputs should map. When arbitrarily choosing valid input data, the model should reliably generate output data that is indistinguishable from that which is measured in the system being modeled.

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences and engineering disciplines, as well as in the social sciences.

Although each theory may be useful for some limited predictions, theories of vision, hearing, touch, smell, and taste are not typically reliable for comprehensive modeling of perception based on sensory inputs. A paradox illustrates where a theoretical prediction fails. Sometimes, even in the absence of a predictive theory, the characteristics of perception seem nonsensical.

This page lists some paradoxes and seemingly impossible properties of perception. When an animal is not named in connection with the discussion, human perception should be assumed since the majority of perceptual research data applies to humans.

Terminology

$SUN_{white}$ light: Normal white sunlight is black-body radiation containing a broad and largely featureless spectrum covering the entire range of human vision.
$RGB_{white}$ light: Televisions and computer screens fool the eye by generating photons of three narrow wavelength bands where the proportion of photons from industry standard (but improperly named) R (red), G (green), and B (blue) sources is known to be perceived as white.

Definition

A perceptual paradox, in its purest form is a statement illustrating the failure of a formula to predict what we perceive from what our senses transduce.

Paradox statement that apparently contradicts itself and yet might be true

A paradox is a statement that, despite apparently valid reasoning from true premises, leads to an apparently-self-contradictory or logically unacceptable conclusion. A paradox involves contradictory-yet-interrelated elements that exist simultaneously and persist over time.

A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.

Example: standard information theory limits spatial frequency based hyperacuity to a factor of approximately 4 over the spatial frequency of photoreceptor cells. Yet, reliable scientific journals have published reports of hyperacuity in excess of a factor of 10.

A seemingly nonsensical characteristic is a statement of factual observation that is sufficiently intractable that no theory has been proposed to account for it.

Example: the optical path in an eye, from the cornea to the photoreceptors, goes through a non-spherical cornea and lens that refract and non-circular apertures that diffract such that, in a normal eye, the image on the retina for a point-source is an irregular color-fringed, color-eccentric coaxial bullseye-like pattern with many pathological properties, with the central bright feature covering many photoreceptors.^[1] Yet, the point-source is perceived clearly, and can be discriminated from other such points as little distance away as 1/10 the visual angle of a photoreceptor. According to Roorda, in a "perfect" eye, a foveal cone subtends 30 arcseconds, and the diameter of the central "Airy" disk varies between 10 cones (1mm pupil used for reading) to about 1.5 cones (8mm pupil used during fight/flight response).

Mathematical modeling

One branch of research into perception attempts to explain what we perceive by applying formulae to sensory inputs and expecting outputs similar to that which we perceive. For example: what we measure with our eyes should be predicted by applying formulae to what we measure with instruments that imitate our eye.

Past researchers have made formulae that predict some, but not all, perceptual phenomena from their sensory origins. Modern researchers continue to make formulae to overcome the shortcomings of earlier formulae.

Some formulae are carefully constructed to mimic actual structures and functions of sensory mechanisms. Other formulae are constructed by great leaps of faith about similarity in mathematical curves.

No perceptual formulae have been raised to the status of "natural law" in the way that the laws of gravitation and electrical attraction have. So, perceptual formulae continue to be an active area of development as scientists strive towards the great insight required of a law.

History

Some Nobel laureates have paved the way with clear statements of good practice:

In the preface to his Histology ^[2] Santiago Ramón y Cajal wrote that "Practitioners will only be able to claim that a valid explanation of a histological observation has been provided if three questions can be answered satisfactorily: what is the functional role of the arrangement in the animal; what mechanisms underlie this function; and what sequence of chemical and mechanical events during evolution and development gave rise to these mechanisms?"

Santiago Ramón y Cajal Spanish neuroscientist

Santiago Ramón y Cajal was a Spanish neuroscientist and pathologist, specializing in neuroanatomy, particularly the histology of the central nervous system. He and Camillo Golgi received the Nobel Prize in Physiology or Medicine in 1906, with Ramón y Cajal thereby becoming the first person of Spanish origin who won a scientific Nobel Prize. His original investigations of the microscopic structure of the brain made him a pioneer of modern neuroscience. Hundreds of his drawings illustrating the delicate arborizations of brain cells are still in use for educational and training purposes.

Histology, also microanatomy, is the branch of biology which studies the tissues of animals and plants using microscopy. It is commonly studied using a light microscope or electron microscope, the specimen having been sectioned, stained, and mounted on a microscope slide. Histological studies may be conducted using tissue culture, where live animal cells are isolated and maintained in an artificial environment for various research projects. The ability to visualize or differentially identify microscopic structures is frequently enhanced through the use of staining. Histology is one of the major preclinical subjects in medical school. Medical students are expected to be familiar with the morphological features and function of all cells and tissues of the human body from an early stage of their studies, so histology often stretches over several semesters.

Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes that are passed on from parent to offspring during reproduction. Different characteristics tend to exist within any given population as a result of mutation, genetic recombination and other sources of genetic variation. Evolution occurs when evolutionary processes such as natural selection and genetic drift act on this variation, resulting in certain characteristics becoming more common or rare within a population. It is this process of evolution that has given rise to biodiversity at every level of biological organisation, including the levels of species, individual organisms and molecules.

Allvar Gullstrand described the problems that arise when approaching the optics of the eye as if they were as predictable as camera optics.

Charles Scott Sherrington, considered the brain to be the "crowning achievement of the reflex system", (which can be interpreted as opening all aspects of perception to simple formulae expressed over complex distributions).

Sensory Observations

See:Visual
Hear:Auditory
Touch:Tactile
Smell:Olfactory
Taste:Gustatory
Electric

Perceptual Observations

See:Visual
Hear:Auditory
Touch:Tactile
Smell:Olfactory
Taste:Gustatory
Electric

Statements of Paradox

See:Visual

Contrast Invariance
Boundaries between brighter and darker areas appear to remain of constant relative contrast when the ratio of logarithms of the two intensities remains constant:

 $Contrast\propto {\frac {logI_{a}}{logI_{b}}}$

But the use of logarithms is forbidden for values that can become zero such as $I_{a}\,$ , and division is forbidden by values that can become zero such as $logI_{b}\,$ .

No published neuroanatomical model predicts the perception of contrast invariance.

10 Decade Transduction

Local Contrast

Color Constancy
When observing objects in a scene, colors appears constant. An apple looks red regardless of where it is viewed. In bright direct sunshine, under a blue sky with the sun obscured, during a colorful sunset, under a canopy of green leaves, and even under most man-made light sources, the color of the apple remains unchanging.

Color perception appears to be independent of light wavelength. Edwin Land demonstrated this by illuminating a room with two wavelengths of light of approximately 500 nm and 520 nm (both improperly called "green"). The room was perceived in full color, with all colors appearing unattenuated, like red, orange, yellow, blue, and purple, despite the absence of photons other than two close to 510 nm. Note that $RGB_{white}$ light misuses the terminology RGB since color is a perception and there are no such things as Red, Green, or Blue photons.

Jerome Lettvin wrote an article in the Scientific American ^[3] illustrating the importance of boundaries and vertices in the perception of color.

Yet, no published formula predicts the perceived color of objects in a single image of arbitrary scene illumination.

Transverse Chromatic Deaberration
Light that goes through a simple lens such as found in an eye undergoes refraction, splitting colors. An $RGB_{white}$ point-source that is off-center to the eye projects to a pattern where with color separation along a line radial to the central axis of the eye. The color separation can be many photoreceptors wide.

Yet, an $RGB_{white}$ pixel on a television or computer screen appears white even when seen sidelong.

No published neuroanatomical model predicts the perception of the eccentric white pixel.

Longitudinal Chromatic Deaberration
As in Transverse Chromatic Deaberration, color splitting projects also projects the R, G, and B components of the $RGB_{white}$ pixel to different focal lengths, resulting in a bulls-eye-like color distribution of light even at the center of vision.

No published neuroanatomical model predicts the perception of the centered white pixel.

Spherical Deaberration
Eyes have corneas and lenses that are imperfectly spherical. This inhomogeneous shape results in a non-circular distribution of photons on the retina.

No published neuroanatomical model predicts the perception of the non-circularly distributed white pixel.

Hyperacuity
People report discrimination much finer than can be predicted by interpolating sense data between photosensors. High performing hyperacute vision in some people has been measured to less than a tenth the radius of a single photoreceptor. Among measures of hyperacuity are the vernier discrimination of two adjacent lines and the discrimination of two stars in a night sky.

No published neuroanatomical model predicts the discrimination of the two white pixels closer together than a single photoreceptor.

Pupil Size Inversion
When pupils are narrowed to around 1mm for reading fine print, the size of the central "Airy" disk increases to a diameter of 10 photoreceptors. The so-called "blur" is increased for reading. When pupils are widened for fight/flight response, the size of the central "Airy" disk decreases to a diameter of about 1.5 photoreceptors. The so-called "blur" is decreased in anticipation of large movements.

No published neuroanatomical model predicts that discrimination improves when pupils are narrowed.

Pupil Shape Inversion
Eyes have pupils (apertures) that cause diffraction. A point-source of light is distributed on the retina. The distribution for a perfectly circular aperture is known by the name "Airy rings".

Human pupils are rarely perfectly circular. Cat pupils range from almost circular to a vertical slit. Goat pupils tend to be horizontal rectangular with rounded corners. Gecko pupils range from circular, to a slit, to a series of pinholes. Cuttlefish pupils have complex shapes.

No published neuroanatomical model predicts the perception of the various pupil shape distributed white pixel.

Hear:Auditory

Touch:Tactile

Smell:Olfactory

One paradoxical perception concerning the sense of smell is the theory of one's own ability to smell. Smell is intrinsic to being alive, and is even shown to be a matter of genetics.

Taste:Gustatory

Electric

Conclusion

Related Research Articles

Color, or colour, is the characteristic of human visual perception described through color categories, with names such as red, orange, yellow, green, blue, or purple. This perception of color derives from the stimulation of cone cells in the human eye by electromagnetic radiation in the visible spectrum. Color categories and physical specifications of color are associated with objects through the wavelength of the light that is reflected from them. This reflection is governed by the object's physical properties such as light absorption, emission spectra, etc.

The RGB color model is an additive color model in which red, green and blue light are added together in various ways to reproduce a broad array of colors. The name of the model comes from the initials of the three additive primary colors, red, green, and blue.

In computer graphics, ray tracing is a rendering technique for generating an image by tracing the path of light as pixels in an image plane and simulating the effects of its encounters with virtual objects. The technique is capable of producing a very high degree of visual realism, usually higher than that of typical scanline rendering methods, but at a greater computational cost. This makes ray tracing best suited for applications where taking a relatively long time to render a frame can be tolerated, such as in still images and film and television visual effects, and more poorly suited for real-time applications such as video games where speed is critical. Ray tracing is capable of simulating a wide variety of optical effects, such as reflection and refraction, scattering, and dispersion phenomena.

Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. It is not necessarily proportional to luminance. This is a subjective attribute/property of an object being observed and one of the color appearance parameters of color appearance models. Brightness refers to an absolute term and should not be confused with Lightness.

A set of primary colors is, most tangibly, a set of real colorants or colored lights that can be combined in varying amounts to produce a gamut of colors. This is the essential method used in applications that are intended to elicit the perception of diverse sets of color, e.g. electronic displays, color printing, and paintings. Perceptions associated with a given combination of primary colors are predicted by applying the appropriate mixing model that embodies the underlying physics of how light interacts with the media and ultimately the retina.

Hue is one of the main properties of a color, defined technically, as "the degree to which a stimulus can be described as similar to or different from stimuli that are described as red, green, blue, and yellow",. Hue can typically be represented quantitatively by a single number, often corresponding to an angular position around a central or neutral point or axis on a colorspace coordinate diagram or color wheel, or by its dominant wavelength or that of its complementary color. The other color appearance parameters are colorfulness, saturation, lightness, and brightness.

The Natural Color System (NCS) is a proprietary perceptual color model. It is based on the color opponency hypothesis of color vision, first proposed by German physiologist Ewald Hering. The current version of the NCS was developed by the Swedish Colour Centre Foundation, from 1964 onwards. The research team consisted of Anders Hård, Lars Sivik and Gunnar Tonnquist, who in 1997 received the AIC Judd award for their work. The system is based entirely on the phenomenology of human perception and not on color mixing. It is illustrated by a color atlas, marketed by NCS Colour AB in Stockholm.

YUV is a color encoding system typically used as part of a color image pipeline. It encodes a color image or video taking human perception into account, allowing reduced bandwidth for chrominance components, thereby typically enabling transmission errors or compression artifacts to be more efficiently masked by the human perception than using a "direct" RGB-representation. Other color encodings have similar properties, and the main reason to implement or investigate properties of Y′UV would be for interfacing with analog or digital television or photographic equipment that conforms to certain Y′UV standards.

Additive color, or "additive mixing", is a property of a color model that predicts the appearance of colors made by coincident component lights with distinct colors, i.e. the perceived color can be predicted by summing the numeric representations of the component colors. Modern formulations of Grassmann's laws describe the additivity in the color perception of light mixtures in terms of algebraic equations. It is important note that additive color predicts perception and not any sort of change in the photons of light themselves. These predictions are only applicable in the limited scope of color matching experiments where viewers match small patches of uniform color isolated against a grey or black background.

HSL and HSV are alternative representations of the RGB color model, designed in the 1970s by computer graphics researchers to more closely align with the way human vision perceives color-making attributes. In these models, colors of each hue are arranged in a radial slice, around a central axis of neutral colors which ranges from black at the bottom to white at the top. The HSV representation models the way paints of different colors mix together, with the saturation dimension resembling various shades of brightly colored paint, and the value dimension resembling the mixture of those paints with varying amounts of black or white paint. The HSL model attempts to resemble more perceptual color models such as the Natural Color System (NCS) or Munsell color system, placing fully saturated colors around a circle at a lightness value of ¹⁄₂, where a lightness value of 0 or 1 is fully black or white, respectively.

In the visual arts, color theory or colour theory is a body of practical guidance to color mixing and the visual effects of a specific color combination. There are also definitions of colors based on the color wheel: primary color, secondary color, and tertiary color. Although color theory principles first appeared in the writings of Leone Battista Alberti and the notebooks of Leonardo da Vinci, a tradition of "colory theory" began in the 18th century, initially within a partisan controversy over Isaac Newton's theory of color and the nature of primary colors. From there it developed as an independent artistic tradition with only superficial reference to colorimetry and vision science.

In digital photography, computer-generated imagery, and colorimetry, a grayscale or greyscale image is one in which the value of each pixel is a single sample representing only an amount of light, that is, it carries only intensity information. Grayscale images, a kind of black-and-white or gray monochrome, are composed exclusively of shades of gray. The contrast ranges from black at the weakest intensity to white at the strongest.

The RG or red-green color space is a color space that uses only two colors, red and green. It is an additive format, similar to the RGB color model but without a blue channel. Thus, blue is said to be out of gamut. This format is not in use today, and was only used on two-color Technicolor and other early color processes for films; by comparison to a full spectrum, its poor color reproduction made it undesirable. The system cannot create white naturally, and many colors are distorted.

Colorfulness, chroma and saturation are attributes of perceived color relating to chromatic intensity. As defined formally by the International Commission on Illumination (CIE) they respectively describe three different aspects of chromatic intensity, but the terms are often used loosely and interchangeably in contexts where these aspects are not clearly distinguished.

Color balance adjustment of the intensities of the colors

In photography and image processing, color balance is the global adjustment of the intensities of the colors. An important goal of this adjustment is to render specific colors – particularly neutral colors – correctly. Hence, the general method is sometimes called gray balance, neutral balance, or white balance. Color balance changes the overall mixture of colors in an image and is used for color correction. Generalized versions of color balance are used to correct colors other than neutrals or to deliberately change them for effect.

The CIE 1931 color spaces were the first defined quantitative links between distributions of wavelengths in the electromagnetic visible spectrum, and physiologically perceived colors in human color vision. The mathematical relationships that define these color spaces are essential tools for color management, important when dealing with color inks, illuminated displays, and recording devices such as digital cameras.

In colorimetry and color theory, lightness, also known as value or tone, is a representation of variation in the perception of a color or color space's brightness. It is one of the color appearance parameters of any color appearance model.

A color space is a specific organization of colors. In combination with physical device profiling, it allows for reproducible representations of color, in both analog and digital representations. A color space may be arbitrary, with particular colors assigned to a set of physical color swatches and corresponding assigned color names or numbers such as with the Pantone collection, or structured mathematically as with the NCS System, Adobe RGB and sRGB. A "color model" is an abstract mathematical model describing the way colors can be represented as tuples of numbers ; however, a color model with no associated mapping function to an absolute color space is a more or less arbitrary color system with no connection to any globally understood system of color interpretation. Adding a specific mapping function between a color model and a reference color space establishes within the reference color space a definite "footprint", known as a gamut, and for a given color model this defines a color space. For example, Adobe RGB and sRGB are two different absolute color spaces, both based on the RGB color model. When defining a color space, the usual reference standard is the CIELAB or CIEXYZ color spaces, which were specifically designed to encompass all colors the average human can see.

A color appearance model (CAM) is a mathematical model that seeks to describe the perceptual aspects of human color vision, i.e. viewing conditions under which the appearance of a color does not tally with the corresponding physical measurement of the stimulus source.

HCL (Hue-Chroma-Luminance) is a color space model designed to accord with human perception of color. HCL has been adopted by information visualization practitioners to present data without the bias implicit in using varying saturation.

References

↑ Roorda, A. “A Review of Optics” chapter 2 in Wavefront Customized Visual Correction: The Quest for SuperVision II. (Macrae, S.M., Krueger, R.R., Applegate, R.A., ed). Slack Inc. Thorofare, NJ (2004)
↑ Histology of the Nervous System: Spanish edition
↑ 1986 The colors of things, Scientific American, Vol.255.3, pp. 84-91; (with Brou, Philippe, Sciascia, and Linden)

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[Roorda-1] Roorda, A. “A Review of Optics” chapter 2 in Wavefront Customized Visual Correction: The Quest for SuperVision II. (Macrae, S.M., Krueger, R.R., Applegate, R.A., ed). Slack Inc. Thorofare, NJ (2004)

[Cajal-2] Histology of the Nervous System: Spanish edition

[Lettvin-3] 1986 The colors of things, Scientific American, Vol.255.3, pp. 84-91; (with Brou, Philippe, Sciascia, and Linden)