Sense qualities require intensity, space, and time {intensity and space and sensations}.
Light-wave amplitude has frequency. Sound-wave amplitude has frequency. Touch involves vibrations with frequencies. Smell and taste involve molecule collisions that cause molecule vibrations. For all senses, stimulus intensity fluctuates. Different senses have different vibration types. Perhaps, sense qualities are intensity-fluctuation types {intensity fluctuation type and sensations}. Intensity fluctuation involves frequency modulation and/or amplitude modulation.
People can observe sensations but not physical stimuli. Sensations have observers. Sensations are self-observable {self-observable sensations}.
Sense functions have three parameters {sensation parameters}, making a function family. Different senses have different subfamilies. Within a sense, sense qualities have the same function with different parameter values.
sensation parameters: intensity
Intensity goes from zero to pain. Vision and other senses add receptor inputs to find intensity, and then compare adjacent intensities to find relative intensity. Intensity involves time, distance, momentum, and energy, which are never negative.
sensation parameters: non-opposing quality
Non-opposing quality goes from zero/low through middle to high maximum. Examples are frequency, concentration, polarity, shape, density, and absolute temperature, which are never negative. Light, sound, and vibrations have frequency. Molecules have shape, concentration, and polarity. Materials have temperature and density.
sensation parameters: opposing quality
Opposing quality can go from negative to zero to positive. Examples are charge and spin. Opposing quality can go from below to neutral to above. Examples are acidity and cool to neutral to warm temperatures, as well as compression to equilibrium to tension. Opposing quality can go from left to symmetric to right. Examples are handedness and parity. For opposing qualities, range ends are opposites.
sensations
Sensations always have intensity and have at least one opposing quality and at least one non-opposing quality. Senses combine sensation parameters to make sensations.
Sensations evolve to become best matches to physical information {stimulus matching and sensations}. Brain analyzes inputs to find categories and relations and then synthesizes abstract variables to replace physical variables to make output model the input stream. Output and input integrate to make a unified whole.
Physical processes use gravitational and/or electromagnetic forces and so very short times. Mental processes are about information flows and have arbitrary times. Low-level mental processes occur over 20-millisecond to 200-millisecond intervals {time and sensations}. High-level mental processes occur over hours. 20-millisecond and longer times allow neuron-assembly activity-pattern integration and expression as sensations.
Neuron-assembly activity patterns evolved to become tingles {tingle} {pre-qualities} {semi-qualities}, which later differentiated to become sense qualities. All sensations share an underlying vibrational state.
predecessor
Physical quantities have real-number amounts and have units, such as volts or frequencies, which may have directions. Physical quantities occur at one time and place. Physical intensities use only energy, area, direction, and time. Nerve impulses and neuron-assembly activity patterns involve physical quantities. Sense systems use neuron-assembly activity patterns.
tingles
At first, all senses had only intensities. Evolution then began to work on neuron-assembly activity patterns to make kinetic effects and overall oscillations. These abstract vibrations are tingles. Tingles are non-local. Tingles have intensities. Tingles are the beginnings of sense qualities. Tingles are vibrations of new abstract physiological variables that combine physical quantities. Different senses have different vibration types. Within a sense, different sense qualities have the same vibration type but different frequencies and harmonic ratios.
Tingles derive from neuron transient vibrations after stimuli. Neuron assemblies can combine inputs to make microphonic neuron signals [Saul and Davis, 1932], with frequencies up to 800 Hz.
Semi-qualities are undifferentiated sense qualities and have semi-feeling and semi-meaning. Tingles are between neuron physiology and sense qualities. Like neuron signals, tingles can vary in wavelength, frequency, frequency range, frequency distribution, amplitude, amplitude change rate, amplitude acceleration, intensity, phase, persistence after stimulus, direction, rotation, orientation, pitch, roll, yaw, and wobble. Waves can have different forms, such as longitudinal, transverse, polarized, spherical, and ellipsoidal. Like sense qualities, tingle semi-qualities have semi-time, semi-space, and semi-intensity.
antecessor
As tingles evolved, they differentiated into sense qualities with intensities. Sensations have no real-number amounts and have no units. Rather, sensations have relative amounts and sense qualities. Sensations combine intensity amount and unit into a post-tingle. Tingle frequency, spatial extent, and amplitude differentiated to make different sense types. Within a sense type, post-tingles vary and make sense qualities, such as red.
Animals are Pre-Cambrian invertebrates, Cambrian invertebrates, chordates, vertebrates, fish, lobe-finned fish, freshwater lobe-finned fish, amphibians, reptiles, mammals, primates, Old World monkeys, apes, Home erectus, and Homo sapiens, in order of evolution. Many people believe that mammals have consciousness and sense qualities {animals and sensations}. However, mammal brain parts and functions are similar to other-vertebrate brain parts and functions, so mammals seem to have nothing fundamentally new in brain.
Perception is like behavior in that input triggers output {behavior and perception}. Coordinated switches trigger muscle movements, gland outputs, and perceptions. Perception and behavior have feedback, looping, and exchanging. Muscles, glands, and nerves work together, as do sense receptors and brain. Behavior and perception use whole brain and body.
Sense receptors measure kinetic-energy flow onto their receptive-field area {energy flow and sense intensity}. For example, taste receptors measure salt concentration as salt-to-receptor binding per second, which transfers kinetic energy per second. Kinetic energy flow transforms to potential-energy change. Membrane-potential changes and molecule-potential-energy changes continually transfer stimulus energy to new neurons. Neuron coding represents neuron potential-energy and kinetic-energy transfers. Electrochemical flows are like kinetic energy, and electrochemical states are like potential energy {electrochemical potential and kinetic energy}. Electric circuits have resistances, capacitances, and inductances, and pipes have constrictions and standpipes.
Perhaps, sense qualities arose in humans or mammals from new brain regions or functions {brain evolution and first sensation}. However, human and mammal brain regions and functions are similar to other-vertebrate brain regions and functions, so humans and mammals seem to have nothing fundamentally new in brain.
After sense-region duplication, original region performs original function, so duplicated region can evolve to perform new functions, such as receive from another sense and integrate two senses {brain region duplication and multisense qualities}.
Vision processing {color processing} represents color brightness, hue, and saturation.
photoreceptors
Rods have photopigment with maximum sensitivity at bluish-green 498 nm, to measure light intensity. Cone types have maximum sensitivity at one wavelength and lower sensitivities at other wavelengths.
Non-primate mammals have cones with photopigments with maximum sensitivity at indigo 424 nm to 437 nm (short-wavelength receptor) and yellow-green 555 nm to 564 nm (long-wavelength receptor). Non-primate mammals can distinguish colors over the same light-frequency range as primates. Because they have only one color dimension, they may or may not see subjective colors.
Primates have cones with photopigments with maximum sensitivity at indigo 437 nm (short-wavelength receptor), green 534 nm (middle-wavelength receptor), and yellow-green 564 nm (long-wavelength receptor). Because they have two color dimensions, they may see subjective colors.
neurons
ON-center and OFF-center neurons calculate cone-input sum, which represents intensity, or ratio, which represents light frequency. The first opponent-process ratio was for yellowness and blueness. The second opponent-process ratio was for redness and greenness.
Later processing categorizes colors. Perhaps, whiteness can change to light yellowness, and blackness can change into dark blueness. Perhaps, yellowness split into darker orangeness and lighter greenness, which mixes blueness and yellowness. Perhaps, orangeness becomes redness.
labeled lines and topographic maps
Visual-tract axons carry color-blob opponent-process information from retina to lateral-geniculate-nucleus and primary-visual-cortex topographic maps. Senses have labeled lines because their neurons follow sense-specific pathways and have physiological specializations.
color lightness
The lightness color parameter relates directly to the difference between brightness and short-wavelength-receptor output: M + L - S. In order of increasing color lightness, black causes no response. Blue has small M-receptor and L-receptor outputs and large S-receptor output. Red has middle M-receptor and L-receptor outputs and small S-receptor output. Green has large M-receptor and L-receptor outputs and medium S-receptor output. Yellow has large M-receptor and L-receptor outputs and medium-small S-receptor output. White has very large M-receptor and L-receptor outputs and medium S-receptor output. Therefore, subjective color lightness relates directly to the blue-yellow opponent process.
color temperature
The temperature (warmth and coolness) color parameter relates directly to difference of long-wavelength-receptor and middle-wavelength-receptor outputs: L - M [Hardin, 1988]. In order of increasing color temperature, blue has small L-receptor and medium-small M-receptor outputs. Green has medium L-receptor and large M-receptor outputs. Black causes no response. White has very large L-receptor and M-receptor outputs. Yellow has large L-receptor and large M-receptor outputs. Red has large L-receptor and medium M-receptor outputs. Therefore, subjective color temperature relates directly to the red-green opponent process.
brightness, lightness, temperature
If black has brightness 0, and if blue, red, and green have maximum brightness 1, then brightness ranges from 0 to 3. Magenta adds blue and red to make 2. Cyan adds blue and green to make 2. Yellow adds red and green to make 2. White adds blue, red, and green to make 3.
If blue, red, and green have lightness 1, 2, and 3, respectively, lightness ranges from 0 to 6. Magenta adds blue and red to make 3. Violet adds blue and half red to make 3. Orange adds red and half green to make 3.5. Cyan adds blue and green to make 4. Chartreuse adds half red and green to make 4. Yellow adds red and green to make 5. White adds blue, red, and green to make 6. Blue and yellow, red and cyan, and green and magenta add blue, green, and red to make white 6.
If blue, green, and red have temperature -2, 0, and 2, respectively, temperature ranges from -2 to +2. Cyan averages blue and green to make -1. Magenta averages blue and red to make 0. White averages blue, red, and green to make 0. Blue and yellow, red and cyan, and green and magenta average blue, green, and red to make white 0. Chartreuse averages half red and green to make 0.5. Yellow averages red and green to make 1. Violet averages blue and half red to make 1. Orange averages red and half green to make 1.5.
If brightness is first coordinate, lightness is second coordinate, and temperature is third coordinate, blue is (1,1,-2), red is (1,2,2), and green is (1,3,0). Magenta is (2,3,0). Cyan is (2,4,-1). Yellow is (2,5,1). White is (3,6,0). Black is (0,0,0). Darkest gray is (0.5,1.0,0.0). Dark gray is (1,2,0). Gray is (1.5,3.0,0.0). Light gray is (2,4,0). Lightest gray is (2.5,5.0,0.0).
brightness and blackness
The brightness color property depends on the brightness color parameter, which sums long-wavelength-receptor and middle-wavelength-receptor outputs: L + M. Black has low brightness. Blue wavelength is far from L and M maximum-sensitivity wavelengths, so blue is dim. Red wavelength is closer to L and M maximum-sensitivity wavelengths, so red has average brightness. Green wavelength is close to L and M maximum-sensitivity wavelengths, so green is bright. White adds green, red, and blue and is brightest.
saturation and whiteness
Colors can have whiteness. White adds to primary colors linearly and equally. Any color mixture has red, green, and blue. In any color mixture, red, green, or blue has the lowest brightness, and the other two colors have at least that brightness. Therefore, whiteness is three times the lowest-brightness-primary-color brightness. Subtracting lowest-brightness-primary-color brightness from the other two primary-color brightnesses, and then adding the two results defines hue brightness. Saturation is hue brightness divided by total brightness. Unsaturation is whiteness divided by total brightness. Hue brightness and whiteness add to 100%. Vision processing compares adjacent and overall brightnesses to adjust brightness and so saturation.
hue
Three photoreceptor types and two opponent processes determine color categories [Krauskopf et al., 1982]. Two color-blob-neuron opponent processes detect red-green and blue-yellow ranges [Livingstone and Hubel, 1984].
Retina unit areas have one Long-wavelength, one Middle-wavelength, and one Short-wavelength cone. See Figure 1. Any-wavelength light excites all cones. Retina opponent processes calculate L - M and L + M - S. See Figure 2. Comparing opponent processes, using thresholds to separate continuous frequency-intensity spectra into discrete categories, selects three color-categories. If both opponent-process ranges can be from -1 to +1, blue is (-1,-1), green is (0,0), and red is (+1,+1), where the first value is the L - M range, and the second value is the L + M - S range.
Comparing opponent processes selects four color-categories. Blue is (-1,0), green is (0,+1), yellow is (+1,+1), and red is (+1,0). See Figure 2.
Adding the black-gray-white sense process selects the red, yellow, green, blue, black, gray, and white color categories. See Figure 3.
Vision processing subtracts the smallest primary-color brightness from the other two primary-color brightnesses, and then adds the two results to find hue brightness. Vision processing compares adjacent and overall hue brightnesses to adjust local hue.
opponency pairs
Brightness opponency pairs with darkness opponency. Yellow-blue opponency pairs with blue-yellow opponency. Red-green opponency pairs with green-red opponency. Brain compares opponency pairs for verification and discrimination.
color constancy
Visual-area-V4 neurons account for background illumination, which reflects differentially from local areas, to make color constancy. Spreading excitation, lateral inhibition, and object and object-relation knowledge help make color constancy.
location
A separate visual system finds color spatial locations. The location system finds visual angle (space direction) and distance.
color and location integration
Location system and color system information integrate to specify contrast, color, orientation, shape, location, distance, and time.
Television-screen electron guns excite phosphors that shine until beam returns, so picture persists. Sensory-motor processing exchanges information and interconnects neurons faster than neuron signals decay, making spaces, times, intensities, and sense qualities continuous {continuity and sensations}.
Low-level processing determines high-level processing, and high-level processing sends feedback to low-level processing. However, high-level-processing feedback is not noticeable, because it causes only secondary effects, has complex features, is statistical, uses whole brain, and takes much longer times {high-level processing and sensations}.
Holding all variables, except one, constant can find the derivative with respect to the non-constant variable. Unchanging partial differentials are invariants. Neuron-assembly processing can detect perceptual invariants {invariants and sensations}. Invariants persist and so can become memories.
Perhaps, brain compared before-and-after or adjacent perceptions, and perception changes caused first sensation {perception change and first sensation}. Perhaps, brain compared perception and memory, and sense qualities arose from spatial-gradients, temporal-gradients, differences, or errors. For example, people can realize that motion does not have expected effect. Error can cause punishment or can lower reward. Perhaps, brain detected position differences, and sense qualities arose as movement perception. Perhaps, sense qualities arose as perceptual-process modification, distinction, realization, notice, feeling, or comparison. However, changes, differences, gradients, and errors use same units as original quantities and so are not new things.
Conscious sense qualities have largest combination number and so highest-probability state {probability and sensations}.
Stimuli tend to cause muscular or glandular responses. Perhaps, sense qualities arose as responses became notes, marks, or signals {response internalization and first sensation}. Alternatively, brain processes can inhibit tendencies or internal signals. However, behavior is not sense qualities.
Sensory-motor processes use many parallel processes and storage registers and are statistical {statistics and sensations}. Because many points contribute to results, narrowing to one distribution and average, resolution can be high.
Synchronizing neuron signals increases intensity by causing simultaneous arrival. Synchronous alpha waves cause arousal {synchronization and arousal}.
Topographic maps can have neuron circuits [Gutkin et al., 2003]. Circuit-flow waves and local patterns can represent objects and sense qualities {circuit flows and sensations}. Vibrations, accelerations, jolts, eddies, vortexes, turbulence, and streamlining, with varying dimension, frequency, phase, and amplitude, can represent sense intensities and qualities. Different senses have different flow patterns.
Intensity is kinetic energy flow per area in flow longitudinal direction.
Liquid flows have lateral-pressure patterns, liquid pools have transverse waves from wind and forces, and moving charges have transverse magnetic fields. Sense-quality information is in two transverse potential energy (not distance) coordinates. Circuit flows have cross-sectional shapes, like random stereograms hold stereoscopic patterns.
Reticular-formation input starts and sustains circuit flows. Topographic-map circuit elements control, analyze, and modulate flows, using stimuli, feedback, feedforward, or hormones.
Sense qualities are topographic-map local neuron-activity patterns [Schiffman, 2000] {neuron-array output ratios and sensations}.
Topographic maps have variable-size three-dimensional registers that hold objects with sense qualities {registers and sensations}. Registers work together to represent motions.
Topographic-map neurons can be Off, On, or in between, like a black-and-white TV screen {topographic-map displays and sensations}. Topographic-map neuron activities can make geometric patterns, such as lines, circles, and ellipsoids. Changing neuron activities can make movements, flows, vibrations, orbits, spins, and waves.
Neuron electrochemical processes cause axon impulse instantaneous frequency, average frequency, and frequency changes, and synapse neurotransmitter-packet release rate {coding and sensations}. Impulses and packets are discrete and make digital code. Summing, averaging, synaptic transmission, transmitter binding, feedback, neuron interactions, and neurohormones blur digital code to make essentially analog code.
Stimuli transfer kinetic energy to receptors, which require a minimum (threshold) energy to respond. Light photons collide with, and transfer kinetic energy to, retinal photoreceptors {stimulus energy and receptors}. Photons have energy E that depends on electric-field frequency f: E = h * f, where h is Planck constant. Blue-light-photon-energy to red-light-photon-energy ratio is approximately 1.75. Photoreceptors have maximum-sensitivity wavelength and respond less to higher and lower wavelengths.
To cause one nerve impulse, neuron input must make neuron membrane potential higher than threshold potential. Below threshold, neuron axon has no impulse, equivalent to 0. Above threshold, neuron axon has one impulse, equivalent to 1. Neuron thresholds split instantaneous input-value range into two output opposites, to make intensity categories {thresholds as category boundaries}. Thresholds convert analog signals to digital signals. Neuron series with increasing thresholds can indicate increasing accumulations/intensities and so categories. Thresholds are the lowest level of meaning: yes or no, present or not, true or false.
After receiving sufficient stimulus input, axon-impulse-frequency and synapse-neurotransmitter-packet-release rates typically increase from baseline level, peak, then decrease to baseline, making one wave {neurochemical waves and sensations}, which has 2-millisecond to 20-millisecond time interval. Because they involve few axon impulses, single waves cannot have amplitude or frequency modulation. Neuron-assemblies have coordinated waves that make neuron-assembly activity patterns, to code stimulus intensity, quality, and location.
Hallucinogens distort mental space and sense qualities. Perhaps, normal biochemicals make undistorted mental space and sense qualities {biochemicals and sensations}.
Perhaps, stimuli are like reactants, and perceptions are like products {chemical reactions and sensations}.
Filtering removes values outside a frequency and/or intensity range. Filtering defines a category by specifying boundaries {filtering and sensations}. Neuron assemblies use thresholds to establish boundaries and make categories.
Computers and brains have readers that input data and algorithms, processors that use data and algorithms to make output data, and writers that output data. Computers and brains process information in circuits, transfer information over channels, and store information in structures. Perhaps, mind is dynamic information in brain structures {information processing and sensations}.
Computer operating systems control basic functions, such as file manipulation, gathering input, and sending output. Perhaps, minds are like operating systems {operating system and sensations}.
Analog computers receive continuous voltages or currents and output continuous voltages or currents, so feedback and feedforward simultaneously affect output and input. Simultaneous mutual interaction requires system governors to prevent stops or exponential increases.
Serial digital computers have clocks that step through algorithms in discrete isolated operations that wait for specific input and deliver specific output. Parallel digital computers use clocks and software to deliver inputs and use outputs when appropriate. Digital neural networks step through network layers, so inputs from one layer affect next layer.
Two neurons can exchange information in both directions. One neuron can send excitation directly to other neuron. Other neuron can send excitation directly to third neuron, which sends inhibition directly to first neuron. Brain electrochemical signaling continuously goes through many interconnected circuits simultaneously, so inputs continually affect outputs, and outputs continually affect inputs, unifying and nesting sensation and action and causing continual recursion {simultaneous mutual interactions and sensations}. Perhaps, mind requires simultaneous mutual interactions.
Analog coding is continuous and tracks physical processes directly. Digital coding prevents degradation and other errors and makes categories. Brain uses digital processing for axon impulses and neurotransmitter packets. Perhaps, mind uses analog processing to make continuous sensations {analog coding and sensations}.
Current computers can code numbers and so code sense intensities but cannot code types and meanings and so cannot represent sense qualities {code types and sensations}.
Perhaps, brain is like ink, and mind is like message {coded messages and meaning}.
Computers and brains use data structures, such as files, tables, arrays, and displays. Files have elements, such as bytes, numbers, strings, dates, times, and booleans, separated by tabs, commas, and/or spaces. Files can have rows, with fixed or variable column numbers. Perhaps, mind uses three-dimensional displays {data structures and sensations}.
Computers open and close files to read or write data. Perhaps, brain opens and closes files {file access and sensations}. Opening files is like awakening and becoming conscious, by accessing memory. Closing files is like sleeping, by blocking memory.
To describe object collections, structure files list object types and relative coordinates and distances. For example, to describe molecules, chemical structure files list atoms and relative coordinates and distances [Dalby et al., 1992]. Brains can use structure files to describe visual displays {structure files and sensations}.
Computer-processor programs use binary code. Assembly languages express hardware operations in simple grammar. Human-readable programming languages have sentence-like statements. Programming languages can emphasize procedures that manipulate objects or objects that have procedures. BASIC and C are procedure oriented. Java and C++ are object oriented. High-level code translates unambiguously into low-level code, and vice versa. Brain uses low-level code and/or procedure-oriented programming languages. Perhaps, mind uses object-oriented programming {programming languages and sensations} to represent geometric objects and perform geometric operations.
Ray tracing {ray tracing and sensations} tests light-source and surface-reflection light rays, to see where they land on object-depth-indexed two-dimensional-surface displays. Ray tracing indexes object locations, directions, and distances, as well as shapes, overlaps, shadows, light sources (emissions), absorptions, reflections, refractions, opaqueness, translucency, transparency, and color variations [Glassner, 1989].
Vector graphics {vector graphics and sensations} [Foley et al., 1994] represents scenes using geometric-figure descriptors, such as "circle", which have parameters, such as "color", "radius", and "center", which have values, such as "black" or "2". Descriptors have positions relative to other descriptors or to the display.
Vector graphics represents images using mathematical formulas for volumes, surfaces, and curves (including boundaries) that have parameters, coordinates, orientations, colors, opacities, shading, and surface textures. For example, circle information includes radius, center point, line style, line color, fill style, and fill color. Vector graphics includes translation, rotation, reflection, inversion, scaling, stretching, and skewing. Vector graphics uses logical and set operations and so can extrapolate and interpolate, including filling in.
Complex-number real-number part indicates physical measurement. Imaginary-number part, and interactions between real and imaginary numbers, account for factors affecting solutions or processes. Complex-number multiplication is commutative: (a + b*i) * (c + d*i) = (c + d*i) * (a + b*i). Other complex-number operations can be non-commutative, so complex-number operations can represent all physical interactions. Complex-number functions and series can represent physical states or processes, because they can model translations, rotations, reflections, inversions, and waves, including interference, superposition, resonance, and entanglement. Complex-number operations make complex numbers, not new number types, and so can model physical situations, because physical interactions make only existing physical properties, not new ones.
Perhaps, brain is like real numbers, and mind is like imaginary numbers {complex number analogy}. Like real and imaginary numbers, brain and mind are separate and independent but can interact.
In networks, links and nodes are duals. In two-dimensional projective geometry, points and lines are duals. In three-dimensional projective geometry, planes and points are duals. In three-dimensional space, lines bound surfaces, and surfaces bound lines, so mathematical theorems about lines have corresponding mathematical theorems about surfaces. On n-manifolds, p-forms and (n-p)-forms are duals, so 1-form (covariant tensor, linear function of coordinates, or manifold gradient) and vector field (contravariant tensor, function, or manifold) are duals, and they interact to make scalar products. For vectors, tangent vectors have covector duals. Perhaps, mind and brain are duals, and phenomena and manifolds are duals {duals and sensations}.
From intensity and intensity-change comparisons, brain can build variables that are optimal for describing sensations {principal components, perception}. Different senses have different principal components. Within a sense, different qualities have the same principal components but with different values. Principal components are the same for everybody.
Indefinite spherical harmonics build to make indefinite Fourier three-dimensional waves that model/simulate sensations {spherical harmonics and sensations}.
Algebras have elements, such as integers. Algebras have operations on elements, such as addition. Integer additions result in integers. Integer addition commutes: 13 + 27 = 40 = 27 + 13. Integer addition is associative: (13 + 27) + 5 = 45 = 13 + (27 + 5). Integer identity element adds to integers to make the same integer: 13 + 0 = 13, and 0 + 0 = 0. Integer inverse elements add to integers to make zero: 13 + -13 = 0, and 0 + 0 = 0. Finite or infinite tables can show operation results for all element pairs.
If elements are colors and operation is additive color mixing, adding two colors makes color, by wavelength-space vector addition, following Grassmann's laws {algebra and color}. Order of adding two colors does not matter, so color addition is commutative. Sequence of adding three colors does not matter, so color addition is associative. Colors have complementary additive-inverse colors, and adding both colors makes white, so color addition has inverses. Adding black, white, or gray to color does not change color hue but does change saturation, so black, white, or gray are like identity elements. Unlike integer addition, adding color to itself makes same color.
distributive property
Identity, inverse, commutation, and association work whether colors come from light sources or reflect from pigments. Colors from light sources and colors from pigment reflections can mix. If reflected color mixes with mixture of two source colors, or if reflected color mixes with each of two source colors and then mixtures combine, same color results, like the distributive property.
Tone and color frequencies and wavelengths have harmonic ratios {harmonic ratios, color}.
harmonics
Harmonic ratios have small integers in numerator and denominator. In increasing order of denominator, harmonic ratios are 1:1, 2:1, 3:2, 4:3, 5:3, 5:4, and so on.
color wavelengths
The purest red color is at light wavelength 683 nm, with orange at 608 nm, yellow at 583 nm, green at 543 nm, cyan at 500 nm, blue at 463 nm, and violet at 408 nm. Magenta can be at 380 nm or 760 nm.
color wavelength ratios
Color wavelength ratio for red/yellow, 683/583 = 1.17, and green/blue, 543/463 = 1.17, is 7/6 = 1.17 or 6/5 = 1.20. Color wavelength ratio for red/green, 683/543 = 1.26, and yellow/blue, 583/463 = 1.26, is 5/4 = 1.25. Color wavelength ratio for red/blue, 683/463 = 1.48, is 3/2 = 1.5. Color wavelength ratio for yellow/green, 583/543 = 1.07, is 13/12 = 1.085. Color wavelength ratio for red/violet, 683/408 = 1.67, and magenta/indigo, 725/435 = 1.67, is 5/3 = 1.67. See Figure 1.
color frequency ratios
Color frequency ratio for yellow/red, 518/436 = 1.19, and blue/green, 652/556 = 1.17, is 7/6 or 6/5. Color frequency ratio for green/red, 556/436 = 1.28, and blue/yellow, 652/518 = 1.26, is 5/4. Color frequency ratio for blue/red, 652/436 = 1.50, is 3/2. Color frequency ratio for green/yellow, 556/518 = 1.07, is 13/12. Color frequency ratio for violet/red, 740/436 = 1.70, and indigo/magenta, 694/420 = 1.66, is 5/3.
additive complementary colors
Additive complementary color pairs have same wavelength ratio, 4/3 = 1.33. Red/cyan is 683/500 = 1.37 to 650/500 = 1.30. Yellow/blue is 583/463 = 1.26 to 583/435 = 1.34. Chartreuse/indigo is 560/435 = 1.29 to 560/408 = 1.37. Magenta/green is 722/543 = 1.33.
Additive complementary-color triples have three color-pairs, whose average wavelength ratio is also 4/3. For three additive complementary colors, ratios are red/blue, 683/463 = 1.48, red/green, 683/543 = 1.26, and green/blue, 543/463 = 1.17. Arithmetic average is (1.5 + 1.25 + 1.2)/3 = 1.32. Geometric average is (1.5 * 1.25 * 1.2)^0.333 = 1.32. For three subtractive complementary colors, ratios are magenta/cyan, 722/500 = 1.45, magenta/yellow, 722/583 = 1.24, and yellow/cyan, 583/500 = 1.17. Average wavelength ratio is 4/3.
Three complementary colors have same relative values: red = 1.5, green = 1.2, and blue = 1, or magenta = 1.5, yellow = 1.2, and cyan = 1.
subtractive complementary colors
Because mixing darkens and blues colors, subtractive complementary color pairs have increasing wavelength ratios. Red/green is 683/543 = 1.26. Orange/blue is 608/463 = 1.31. Yellow/indigo is 583/435 = 1.34. Chartreuse/violet is 560/408 = 1.37.
color wavelength ratios starting at red
Starting with red at 1/1 = 683/683, orange is 8/7 = ~683/608, yellow is 7/6 = ~683/583, green is 5/4 = ~683/543, cyan is 4/3 = ~683/500, blue is 3/2 = ~683/463, violet is 5/3 = ~683/408, and magenta is 7/4 = ~683/380.
color wavelength ratios starting at green
Magenta is 2/3 = ~380/543. Violet is 3/4 = ~408/543. Blue is 5/6 = ~463/543. Cyan is 8/9 = ~500/543. Green is 1/1 = 543/543. Yellow is 17/16 = ~583/543. Orange is 9/8 = ~608/543. Red is 5/4 = ~683/543. Magenta is 4/3 = 720/543.
color wavelength ratios starting at red
Starting with red at 1/1 = 683/683, orange is 8/7 = ~683/608, yellow is 7/6 = ~683/583, green is 5/4 = ~683/543, cyan is 4/3 = ~683/500, blue is 3/2 = ~683/463, violet is 5/3 = ~683/408, and magenta is 7/4 = ~683/380.
color wavelength ratios starting and ending at magenta
On color circles, complementary colors are opposites. Complementary-color pairs have same wavelength ratio, so cyan/red = blue/yellow = magenta/green. Colors separated by same angle have same wavelength ratio, so yellow/red = green/yellow = cyan/green = blue/cyan = magenta/blue = red/magenta. Example color circle has red = 32, yellow = 16, green = 8, cyan = 4, blue = 2, and magenta = 1 and 64. Put into octave as exponentials, red = 2^0.83, yellow = 2^0.67, green = 2^0.5, cyan = 2^0.33, blue = 2^0.17, and magenta = 2^0 and 2^1. Put into octave, magenta = 2/1, red = 9/5, yellow = 8/5, green = 7/5, cyan = 5/4, blue = 9/8, and magenta = 1/1. Complementary colors have ratio 1.412 = ~7/5. Neighboring colors have ratio 1.125 = 9/8. Example wavelengths with these ratios are magenta = 750 nm, red = 668 nm, yellow = 595 nm, green = 531 nm, cyan = 473 nm, blue = 421 nm, and magenta = 375 nm, close to actual color wavelengths.
color harmonic ratios
Color frequency categories are at harmonic ratios: 48 Hz for red, 60 Hz for green, and 72 Hz for blue. 60/48 = 1.25 = 5/4. 72/48 = 1.5 = 3/2. 72/60 = 1.2 = 6/5. See Figure 2. Color-pair wavelength ratios have harmonic relations. Red/magenta = 7/4. Red/violet and magenta/indigo = 5/3. Red/blue = 3/2. Complementary colors red/cyan, yellow/blue, chartreuse/indigo, and magenta/green = 4/3. Red/green and yellow/blue = 5/4. Red/yellow and green/blue = 6/5 or 7/6. Red/orange = 8/7. Green/cyan = 9/8. Yellow/green = 13/12. See Figure 3.
Red, green, and blue add to make white. Magenta, cyan, and yellow add to make black. For red, green, and blue, and for magenta, cyan, and yellow, average of the three color-pair wavelength ratios is 4/3.
Looking at only primary colors red, green, and blue, color-pair wavelength ratios are red/blue 3/2, red/green 6/5, and green/blue 5/4. Red:green:blue relations have 6:5:4 ratios.
Looking at wavelength differences rather than wavelength ratios, magenta, red, orange, yellow, green, cyan, blue, and violet have approximately equal wavelength differences between adjacent colors. See Figure 2. Setting wavelength difference equal to one, color wavelengths form series 8, 7, 6, 5, 4, 3, 2, and 1. See Figure 3.
Assuming colors are like tones, colors can fit into one octave. Primary colors red, green, and blue, and complementary colors cyan, magenta, and yellow, respectively, are equally spaced in octave from 2^0 to 2^1. Magenta, red, yellow, green, cyan, blue, and magenta form series 6, 5, 4, 3, 2, 1, and 0. Magenta = 2^1, red = 2^0.83, yellow = 2^0.67, green = 2^0.5, cyan = 2^0.33, blue = 2^0.17, and magenta = 2^0. Adjacent colors have ratio 2^0.17 = 1.125 = 9/8. All complementary colors have the same ratio, 2^0.5. All complementary-color triples, such as red/green/blue, average 2^0.5. White, gray, and black have average color-pair wavelength ratio 2^0.5. In this arrangement, color-pair ratios are red/magenta ~ 9/5, yellow/magenta ~ 8/5, green/magenta ~ 7/5, cyan/magenta ~ 5/4, and blue/magenta ~ 9/8. See Figure 3. In this arrangement, whites, grays, and blacks are farthest from being octaves and so have dissonance. Other colors have smaller integer ratios and so more consonance. Color categories are at harmonic ratios.
multiple harmonics
One pair has two or three categories, like tone intervals or red/green or red/green/blue. Two pairs make six or seven categories, like octave whole tones or main spectrum colors. Three pairs make 12 categories, like octave half tones or major spectrum colors. Four pairs make 24 categories, like octave quarter tones or major and minor spectrum colors.
summary
Using physical-color wavelengths, wavelength ratios are red/magenta = 7/4, red/violet = magenta/indigo = 5/3, red/blue = 3/2, red/cyan = yellow/blue= chartreuse/indigo = magenta/green = 4/3, red/green = yellow/blue = 5/4, red/yellow = green/blue = 6/5 or 7/6, red/orange = 8/7, green/cyan = 9/8, and yellow/green = 13/12.
Additive complementary-color pairs, such as red/cyan, yellow/blue, chartreuse/indigo, and magenta/green, have same 4/3 wavelength-ratio.
For red, green, and blue additive complementary colors, average of the three wavelength ratios, red/blue, red/green, and green/blue, is 4/3. For magenta, cyan, and yellow subtractive complementary colors, average of the three wavelength ratios, magenta/cyan, magenta/yellow, and yellow/cyan, is 4/3.
These intervals are harmonic musical tones in an octave: C, E, and G in the key of C. Blue and red make a major fifth interval. Blue and green make a minor third interval. Green and red make a major third interval.
Mathematical groups have elements, such as triangles. Operations map group elements to the same or another element. For example, if element is equilateral triangle, rotations around center by 120 degrees result in same element. Finite or infinite tables can show operation results for all elements.
If elements are colors and operation is additive color mixing, adding two colors makes color, by wavelength-space vector addition, following Grassmann's laws {mathematical group and color}. Adding black, white, or gray to color does not change color hue but changes color saturation, so color addition is not a single operation.
Because they cannot be negative but can complement each other, color qualities are vectors {vectors and colors}. Color vectors have three components: hue, saturation, and brightness, or red, green, and blue.
Perhaps, sense qualities are compressed intensity-frequency spectra {information compression and sensations}.
Sense information includes negative information {negative information}, such as not blue.
Perhaps, sense qualities depend on acceleration patterns {acceleration pattern and sensations} and are about flow vibrations, jolts, eddies, vortexes, streamlining, and turbulence.
motions
Translations, vibrations, rotations, reflections, inversions, and transitions can have accelerations. Vibrations, rotations, and transitions have acceleration changes.
accelerations
Forces include tensions, compressions, and torsions. Photon and molecule interactions transfer energy and cause forces, accelerations, and acceleration changes. Materials resist tension, compression, and torsion and reduce initial acceleration to zero acceleration. Accelerations have location, duration, maximum, minimum, and change rate.
jolt types
Acceleration changes (jolts) are vectors, with magnitude and direction, and have different types.
Acceleration can be zero (with no net force), so jolt is zero. Acceleration can be constant positive (due to constant positive force), so jolt is zero. Acceleration can be constant negative (due to constant negative force), so jolt is zero.
Acceleration can increase at constant rate (due to constant positive force change), so jolt is constant positive. Acceleration can decrease at constant rate (due to constant negative force change), so jolt is constant negative.
Acceleration can increase at increasing rate (due to increasing positive force change), so jolt is increasing positive (until resisting force makes it constant positive). Acceleration can decrease at increasing rate (due to increasing negative force change), so jolt is increasing negative (until resisting force makes it constant negative). Acceleration can increase at decreasing rate (due to decreasing positive force change), so jolt is decreasing positive (until it becomes constant). Acceleration can decrease at decreasing rate (due to decreasing negative force change), so jolt is decreasing negative (until it becomes constant).
Acceleration can oscillate between increase and decrease, so jolt oscillates.
collisions
Before inelastic collisions, colliding-object deceleration is zero, and velocity is maximum: kinetic energy = 0.5 * mass * velocity^2. In inelastic collisions, colliding-object deceleration quickly reaches maximum, and velocity starts to decrease: Force = mass * acceleration = k * (S - x) = -k * S, where k is material's resistance factor, x is distance traveled in material, and S is distance at which object stops. After inelastic-collision process ends, colliding-object deceleration and velocity decrease to zero: F = k * (S - x) = 0.
vibrations
At vibration equilibrium point, molecule acceleration is zero, and velocity is maximum. Then, velocity decreases, and deceleration increases. At maximum displacement, velocity is zero, and deceleration is maximum. Then, velocity increases, and acceleration increases, in opposite direction. At equilibrium point, acceleration is zero, and velocity is maximum, in opposite direction. Jolts depend on wave frequency and amplitude.
receptor acceleration patterns
Energy transfer causes receptor-molecule change. Molecule atoms accelerate, change energy to potential energy as they decelerate, and then stop moving. Then, molecule transfers energy to signal molecule, and receptor molecule returns to resting state. Signal molecules go to other cell receptors, making a cell signaling system. Neurotransmitters, neurohormones, and neuroregulators go to receptors on other cells and sustain the code. Receptors, signal molecules, and later molecules have vibrations and so acceleration changes.
String theory has extra spatial dimensions. Universe may have hidden spatial or temporal dimensions. Perhaps, mind is in hidden dimensions, and experience is orthogonal to normal space-time {dimension and sensations}. However, physical activity must affect mind, so mind does not involve extra spatial or temporal dimensions.
Electromagnetism can relate to sense qualities {electromagnetism, sensations}.
electromagnetic induction
Changing electric fields induce magnetism, and changing magnetic fields induce electric force. Perhaps, brain induces mind. For example, brain particles cause mind waves.
fire
Fire is electromagnetic radiation from excited electrons in oxidation reactions. Perhaps, brain has reactions whose secondary effects make mind. Burning is like unconsciousness, and fire is like consciousness.
magnetism
Though net electric charge is zero, electric-charge relativistic motions make observable net electric charge perpendicular to motion, creating magnetism. Perhaps, mind depends on active "charges" whose relative motions and interactions create net effects, but whose static states are not observable.
Physical and mental descriptions use variables. Variables can be measurable and have units. Variables can be ratios with no units. Variables can be not measurable and have no values or units. Perhaps, brain is about measurable variables, but mind involves hidden immeasurable variables {hidden variable and sensations}. Properties that combine other properties can seem ineffable. For example, words can sound the same when used as nouns or verbs, but actually have subtle noun-marker or verb-marker sound features.
Matter and energy properties are discrete. For example, energy has quanta. Matter and energy are both particle and wave. Waves allow probabilistic physical events and transitions without intermediate states. Particle waves are infinite and allow action at distance and non-local effects. Quantum-mechanical mathematical waves simultaneously represent multiple points and energies, and string-theory moving strings simultaneously represent multiple points. Perhaps, sense qualities are brain-activity quantum-mechanical effects {quantum mechanics and sensations}.
mathematical waves
Perhaps, mind and consciousness involve mathematical waves, similar to quantum-mechanical waves. Infinite waves have no definite position and fill space, accounting for sensory field. Waves can have wave packets, accounting for sensations.
complementarity
Quantum-mechanical waves and particles describe event positions and energies (complementarity). Forces are particle exchanges, and energies depend on wave superpositions. Perhaps, brain and mind have complementarity. Brain uses particle motions, and mind uses abstract waves.
electronic transition
Electrons orbiting atomic nuclei move to other orbits with no intermediate stages. Quantum-mechanical waves change frequency with no intermediate frequencies. Perhaps, mind is like quantum-mechanical waves or is intermediate to physical interactions.
virtual particle
Quantum-mechanical particle interactions and wave energy transformations can create particle pairs that exist for less than one quantum time unit. For example, spontaneous energy fluctuations create virtual particle pairs in space vacuum. Interaction cannot create single particles, because one particle cannot conserve momentum. Instruments cannot observe virtual particles, because they recombine rapidly to return vacuum energy to more-probable state. Though they have short existence, virtual particles can interact with real particles. Perhaps, mind is like virtual particles, which can affect brain but have no direct measure.
orbitals
Electron orbitals have one resonating wave, with frequency, amplitude, inertia, and moment. Perhaps, sense qualities are resonating wave packets in three-dimensional orbitals. Orbital amplitude represents intensity. However, orbitals cannot model colors, because colors also have saturation.
spins
Particles have spin, with frequency, amplitude, inertia, and moment. Perhaps, sense qualities are particles with spins. However, spins cannot model colors, because primary-color spins cannot interact or sum to make secondary-color spins.
General relativity shows that masses and energies change space shape, and changed space alters particle motions through space. Perhaps, brain is like masses and energies, and mind is like space {relativity and sensations}. Brain masses affect mind space, and mind space affects brain masses.
Universe has right and left forms, and most physical laws have parity. Perhaps, universe has another right-left-like asymmetry that causes reality to have two sides, physical and mental {right-left symmetry and sensations}. Mind can look behind reality. For example, surfaces have two sides, and back can affect front and vice versa. Mental reality is entirely physical but is complementary to physical reality.
Particle and object collisions, gravitation, and electromagnetism are relatively strong (primary) forces. Perhaps, mental forces and energies are very weak (secondary) forces and energies {subphysical processes}.
Superphysical processes transcend physical forces by extending them {superphysical processes}. Perhaps, mental forces and energies are superphysical.
Perhaps, sense qualities are energies, and their intensities are energy densities {energy and sensations}. Perhaps, perceptual surfaces have types of kinetic and/or potential energy.
Physical forces have one dimension, because they are interactions between particles. Vectors represent forces. Physical energies have no dimensions, because they are integrals of forces over distances. Scalars represent energies. Physical energies can flow, so intensities have one dimension. Vectors represent intensities. Perhaps, sensations have more than one dimension, because they combine properties.
Heat, an extensive quantity, makes temperature, an intensive quantity. Perhaps, brain energy makes mind intensity {heat and temperature and sensations}.
Potential energies are scalars and have type, amount, radial distance, azimuth, and elevation. Sensations are not vectors, because sense qualities do not have direction or flow. Like potential energies, sensations are in fields. Sensations have azimuth, elevation, and radial distance. Perhaps, sensations are like non-physical potential energies {potential energy and sensations}.
Independent things add. Same objects and properties can add. Summing or subtracting two same-type quantities results in values with same unit. Integration involves summation. Summations make extensive quantities.
Interacting objects and properties multiply. Same or different objects and properties can multiply. Multiplying or dividing two quantities results in values with different unit. Differentiation involves division. Divisions make intensive quantities.
Two masses or two charges interact to make gravitational or electric force. Multiplying same units can make intensive quantities: (4 kg) * (6 kg) / (2 meters)^2 = 6 N of force. Multiplying 4 newtons of force and 5 meters of distance makes 20 newton-meters, 20 joules of energy. Multiplying different units can make extensive quantities. Multiplying 4 coulombs and 5 kilograms makes 20 coulomb-kilograms. However, combining charge and mass has no physical meaning, because charge and mass do not interact. Multiplying can make extensive or intensive quantities.
Only continuous quantities can interact. Discrete quantities cannot affect each other. For example, 4 oranges times 5 bananas results in 20 banana-oranges, which do not exist. Multiplying 4 oranges and 5 oranges results in 20 orange-oranges, which do not exist.
New things arise from physical or mathematical interactions. Perhaps, sense qualities arise from physical or mathematical interaction mechanisms {interaction and sensations}. Neurons use no units.
Joining existing things can produce something new {joining and sensations}. Joining alters or destroys existing objects.
Physics is still discovering new physical forces and energies, with unknown properties. Perhaps, mind has new physical forces, energies, and fields {new force or energy}. However, mind does not measurably affect physical world.
Splitting existing things can produce something new {splitting and sensations}. Making something from physical void or vacuum requires splitting. Void can split into opposites: point and anti-point, pole and anti-pole, left spin and right spin, and ON mark and OFF mark. Splitting can destroy existing properties.
Perhaps, colors are like crystals, with different symmetries and harmonics {crystals and sensations}.
Perhaps, sense qualities result from kinetics and dynamics of many abstract particles, which make phases {particles and sensations}.
Solid, liquid, and gas phases depend on material, temperature, and pressure. Within a sense type, sense qualities are like phases {phases and sensations}. Perhaps, red, green, and blue are different phases. Complementary colors mix phases, like at double points. Color mixtures that result in white, gray, and black are at triple points.
Brain is like phosphors, which phosphoresce for seconds after stimulation {phosphorescence and sensations}. Long times allow neuron activities to integrate.
Oscillations can be longitudinal along one dimension, such as chemical-bond-length oscillations. Oscillations can be transverse along two dimensions, such as chemical-bond-angle oscillations. Violin-string points oscillate transversely across resting-string line. Plane waves, such as in vibrating guitar strings, can rotate around travel-direction axis, like helices, in three dimensions. Electromagnetic-wave points have transverse electric-field oscillation and transverse perpendicular magnetic-field oscillation. Electromagnetic waves also travel, so they have three dimensions and can rotate around travel direction. Electrons in electronic orbitals can oscillate in three dimensions.
Waves spread over space. Perhaps, mind is like waves {waves and sensations}. However, waves cannot model colors, because primary-color waves cannot interact or sum to make secondary-color waves.
wave modulation
Television and radio signals have basic frequencies. To carry information about music or scenes, basic-wave amplitude or frequency can vary with signal intensity and frequency. Flow modulation can carry information. Perhaps, mind is modulated brain waves or flows.
frequency transitions
Waves change frequency in one cycle, with no intermediate stages. Mind transitions between mental states with no intermediate states.
People can attend to new or contrasting stimuli without full awareness {attention and first sensation} [Berns et al., 1997] [Debner and Jacoby, 1994] [Hardcastle, 2003] [He et al., 1996] [Lamme, 2003] [McCormick, 1997] [Merikle and Joordens, 1997] [Posner, 1994] [Robertson, 2003] [Tsuchiya and Koch, 2007].
Cortical disease or injury can result in minimal experience {blindsight and first sensation}, such as blindsight, in which people are only aware of object or surface presence, existence, or motion [Azzopardi and Cowey, 1997] [Barbur et al., 1993] [Güzeldere et al., 2000] [Holt, 1999] [Kolb and Braun, 1995] [Sanders et al., 1974].
Sensations label perceptions {labeling and sensations}, to provide meaning for perceptions. For example, the color red is a label for a feature, and "red" and "green" name features. Using a symbol, label, index, reference, or name defines a category, feature, or variable type. Applying a label groups objects, events, relations, or ideas. Indexing helps memory and recall.
Label meaning can depend on relation to body parts. Many means more than number of fingers. Large means larger than body. Right means nearer to right arm than left arm. Up means nearer to head than feet. Complex labels, such as elephant or victory, combine simple labels.
Perhaps, sense qualities arose as marking {marking and first sensation}. Markers provide reference signs, such as indexes, to which other signs can relate. For example, consciousness can mark figure and not ground. Marking has no units, such as length units. However, marking is only information bits and so is not a new thing.
Like music from instruments, brain produces mind {musical instrument analogy and first sensation}.
Analysis finds differences, parts, and functions. Synthesis finds similarities, wholes, and goals. After neuron-assembly information analysis, brain synthesizes intensity and frequency to make first sensation {synthesis and first sensation}.
Sense properties relate to first sensation {sense properties and first sensation}. Sensations require duration, location, intensity, and quality.
intensity
Intensity alone cannot make sensation. Something or nothing, on or off, yes or no, true or false, or 0 or 1 has no type. Thresholds make switches, with no units. Intensity is only information bits and so is not a new thing. Intensity at spatial location has no type. Intensity for duration has no type.
intensity type
Intensity type alone, without intensity, spatial, or temporal information, has no amount. Intensity-type in space, without time or intensity, has no amount. Intensity type at space location for duration has no amount. Intensity type for duration has no amount. Intensity and intensity-type, without temporal or spatial information, has amount and type.
time
Before and after, time flow, or cycles in time, without space, intensity, or intensity type, has no type.
position
Space location alone, without intensity, intensity-type, or temporal information, has no type.
space
Perhaps, sense qualities arose as nearness or farness, right or left, or up or down in space. Space location for duration has no type.
surface
Perhaps, first sensations indicate only surface presence, existence, or motion, with no phenomenal quality, intensity, or pattern, purely mathematical, spatial, and geometric.
Tones can be harsh or smooth, be sharp or flat, and have acute or gradual onset and offset {hearing properties} {tone properties}. Tone pairs can have consonance or dissonance and major or minor intervals.
Physically, sound waves have frequencies with intensities. Frequencies have ratios, so sounds have harmonics, such as octaves, fifths, thirds, fourths, sixths, and sevenths. Physiologically, sounds are independent and unmixed (analytic) and have loudness and tone. Hearing perceptual processes [Kaas and Hackett, 2000] compare adjacent and harmonic frequency intensities to find loudness and tone. Relative sound intensity determines loudness. Loudness ranges from painful to whisper. People can distinguish 100 loudness levels. Sound frequency determines tone. Tones have width, deepness, shrillness, and thickness. High frequencies are narrow, shallow, shrill, and thin. Low frequencies are wide, deep, dull, and thick. People can distinguish 10 octave levels and 12 (or 24) harmonic levels, so people can distinguish 120 tones.
Pain can be high-amplitude pain, acute pain, or dull pain. Pleasure can be high-amplitude pleasure, acute pleasure, dull pleasure, or orgasm {pain properties} {pleasure properties}.
Physically, pains have inelastic distortions. Physiologically, people feel dull or acute pain. Pain perceptual processes [Chapman and Nakamura, 1999] compare nociceptor inputs. Inelastic distortion determines pain, which can be acute or dull. People can distinguish 10 pain levels.
Odors are sweet, putrid, cool, hot, sharp, and flat {smell properties} {odor properties}. Odors can be sweet, like fruit, or putrid, like goat or sweat. Odors can be cool, like menthol, or hot, like heavy perfume. Odors can be sharp and harsh, like vinegar or acid, or flat and smooth, like ether or ester. Aromatic, camphorous, ether, minty, musky, and sweet are similar. Camphor, resin, aromatic, musk, mint, pear, flower, fragrant, pungent, fruit, and sweets are similar. Goaty, nauseating, putrid, and sulphurous are similar. Smoky/burnt and spicy/pungent are similar. Putrid or nauseating, foul or sulfur, vinegar or acrid, smoke, garlic, and goat are similar. Acidic and vinegary are similar. Acidic and fruity are similar. Vegetable smells are similar. Animal smells are similar.
Physically, air-borne chemicals have concentrations, sizes, shapes, and sites and attach to nasal-passage chemical receptors. Physiologically, smells are strong or weak fruity, flowery, sweet, malty, earthy, savory, grassy, acrid, putrid, minty, smoky, pungent, camphorous, musky, urinous, rubbery, tobaccoey, woody, spermous, nutty, fishy, rotten, and medicinal. Smell detects aldehyde smells first, floral smells second, and lingering musky, sweet spicy, and woody smells later. Smells are mild-pungent (flat-sharp) and sweet-putrid. Foul, sulfurous, acidic, acrid, and putrid are pungent and putrid. Pungent, burnt, and spicy are pungent and neutral. Mint, ether, and resin are pungent and sweet. Flowery and fruity are mild and sweet. Musk is mild and neutral. (Mild cannot be putrid.) Smells can be cool, like menthol, or hot, like heavy perfume. Cool and hot mix mild-pungent and sweet-putrid. Smell perceptual processes [Firestein, 2001] [Laurent et al., 2001] compare alcohols (fruity), ethers in concave and trough-shaped sites (ethereal and flowery), esters as chains (sweet), aldehydes (malty), dioxacyclopentanes (earthy, moldy, and potatoey), furanones (savory spice), hexenals and alkene aldehydes (grassy and herby), smallest positively charged carboxylic acids (acrid or vinegary), larger positively charged carboxylic acids as chains (putrid and sweaty and rancid), oxygen-containing-side-group benzene rings in V-shaped sites (minty), polycyclic aromatic hydrocarbons and phenols (burnt and smoky), negatively charged aryls as compact (spicy and pungent), multiple benzene rings in small concave sites (camphorous), multiple-benzene-ring ketones in large concave sites (musky), steroid ketones (urinous), isoprenes (rubber), carotenoids (tobacco), sesquiterpenes (woody), aromatic amines (spermous), alkyl pyrazines (nutty), three-single-bond monoamines (fishy), sulfur compounds (foul and sulfurous and rotten), methyl sulfides (savory), and halogens (pharmaceutical and medicinal). Concentration determines odor intensity, which can range from faint to harsh. People can distinguish 10 intensity levels. Molecule atoms and bonds determine odor shape, size, and site. Sites can be alcohol, ether, ester, aldehyde, ketone, acid, aryl, isoprene, amine, sulfur, and halogen. Shape can be chain, oblong, or ball, with sharp, medium, or smooth shape edges. People can distinguish 1000 odors.
Tastes are salty, sweet, sour, and bitter {taste properties} {flavor properties}. Sour acid and salt are similar. Bitter and salt are similar. Sweet and salt are similar. Sour (acid) and bitter (base) are opposites. Sweet (neutral) and sour (acid) are opposites. Salt and sweet are opposites.
Physically, water-borne chemicals have concentrations, sizes, shapes, sites, acidity, and polarity and attach to tongue chemical receptors. Physiologically, tastes are acid, salt, base, sugar, and savory. Taste has sweetness-saltiness and sourness-saltiness-bitterness. Taste perceptual processes [Kadohisa et al., 2005] [Pritchard and Norgren, 2004] [Rolls and Scott, 2003] compare sugar, acid, base, salt, and umami receptor inputs to find intensity, acidity, and polarity. Acid-salt-base and salt-sweet opponent processes share salt. Concentration determines taste intensity. People can distinguish 10 intensity levels. Molecule atoms and bonds and electric charge determine taste acidity, which can be acidic, neutral, or basic. People can distinguish 3 acidity levels. Molecule atoms and bonds and molecule-electron properties determine taste polarity, which can be polar, half polar, or nonpolar. People can distinguish 3 polarity levels. Polar and acid define sour. Polar and neutral define salt. Polar and base define bitter. Nonpolar and neutral define sweet. Between sour and salt defines umami-glutamate. (Nonpolar cannot be acid or base.)
Temperature can be warm or cool {temperature properties}.
Physically, temperatures have random motions. Physiologically, people feel cool or warm. Temperature perceptual processes compare thermoreceptor inputs. Heat flow determines temperature, which ranges from cold to warm to pain. People can distinguish 10 temperature levels.
Touches can be acute or smooth, steady or vibrating, and light or heavy {touch properties}.
Physically, touches have transverse motions and pressures (compression, tension, and torsion) that displace surface areas. Physiologically, people feel hardness, elasticity, surface texture, motion, smooth surface texture, rough surface texture, tickle, sharp touch, and tingle. Touch perceptual processes [Bolanowski et al., 1998] [Hollins, 2002] [Johnson, 2002] compare free nerve ending (smooth or rough surface texture), hair cell (motion), Meissner corpuscle (vibration), Merkel cell (light compression and vibration), pacinian corpuscle (deep compression and vibration), palisade cell (light compression), and Ruffini endorgan (slip, stretch, and vibration) inputs to find compression-tension and vibration. Pressure compression and tension determine hardness, elasticity, surface texture, motion, smooth surface texture, rough surface texture, tickle, sharp touch, and tingle. People can distinguish 10 compression-tension levels. Stimulus intensity and frequency determines vibration. People can distinguish 10 motion levels.
Colors have brightness, lightness, and temperature {color parameters}. Brightness defines the order black-white, blue/darkest_gray-yellow/lightest_gray, and red/dark_gray-green/light_gray. Color lightness (unsaturability, transparency, sparseness) defines the order black-white, blue-yellow, and red-green. Color temperature (texture, noisiness) defines the order blue-red, cyan-yellow, and green-magenta-black-white-gray.
A coolness-warmth axis and a perpendicular darkness-lightness axis define a color wheel. Blue, green, and red are on the circumference, with equal arcs between them. Coolness-warmth runs from blue -1 through green 0 then red +1, where -1 is cool and +1 is warm. Darkness-lightness runs from blue -1 through red 0 then green +1, where -1 is dark and +1 is light, in the opposite direction around the color circle. Dark and cool make blue (-1,-1). Light and neither warmth nor coolness make green (+1,0). Neither dark nor light and warm make red (0,+1).
Brightness is perpendicular to the color wheel, and the three axes define color space.
Color has brightness, hue, and saturation {color properties}. Color properties come from black-white, red-green, and blue-yellow opponent processes.
hue
Hue depends on electromagnetic-wave frequency [Krauskopf et al., 1982]. Fundamental color categories are white, gray, black, blue, green, yellow, orange, brown, red, pink, and purple [Kay and Regier, 2003]. White, gray, and black mix red, green, and blue. Brown is dark orange. Pink mixes red and white. Purple mixes red and blue. See Figure 1.
Alternatively, colors have six categories: white, black, red, yellow, green, and blue. Blue and red have no green or yellow. All other colors mix main colors. Purple mixes red and blue. Cyan mixes green and blue. Chartreuse mixes yellow and green. Orange mixes red and yellow. Pink mixes red and white. Brown mixes orange and black.
brightness and blackness
Color brightness depends on electromagnetic-wave intensity [Krauskopf et al., 1982]. Darkness is the opposite of brightness and is the same as added blackness. Colors can add black, and white can add black. Black adds to colors linearly and equally. See Figure 2. At all brightness levels, white looks lightest, yellow looks next lightest, green looks next lightest, red looks next lightest, blue looks darker, and black looks darkest.
White surroundings blacken color. Complementary-color surroundings enhance color. Black surroundings whiten color.
saturation and whiteness
Color saturation depends on electromagnetic-wave frequency distribution [Krauskopf et al., 1982]. Colors can add white, and black can add white. White adds to colors linearly and equally. Complete saturation means no added white. Lower saturation means more white. No saturation means all white. Less saturation makes colors look lighter. See Figure 3. Black looks most saturated. At all saturation levels, blue looks next most saturated, red looks somewhat saturated, and green looks less saturated. White looks least saturated.
transparency and opacity
Color transparency depends on source or reflector electromagnetic-wave density. Opaqueness means maximum color density, with no background coming through. Transparency means zero color density, with all background coming through. See Figure 4. With a white background, opacity is the same as saturation, and transparency is the same as no saturation, so colors are the same as in Figure 3. With a black background, opacity is the same as lightness, and transparency is the same as darkness, so colors are the same in Figures 2 and 4. Blue looks most opaque, and green looks least opaque.
color strength
For all color brightnesses, when both colors have equal brightness, black suppresses one color more {color strength}. Red is stronger than blue, because frequency is lower and wavelength is higher. Blue is stronger than green, because frequency is lower and wavelength is higher. Green is stronger than red, because frequency is lower and wavelength is higher. See Figure 6. Less blue needs to balance green and red, so blue is darker than red and green. Less red needs to balance green, so red is darker than green.
For all color brightnesses, when stronger color is 32 bits lower, weaker color can appear. See Figure 6.
Relative color strengths are the same no matter the computer-display color profile, contrast level, or brightness level.
mixtures
Blue is most dark, opaque, saturated, and cool. Red is less dark, opaque, and saturated and most warm. Green is least dark, opaque, and saturated and neither cool nor warm. See Figure 5, which displays the primary colors, their 1:1 mixtures plus CYMK mixtures, and their 2:1 mixtures.
Magenta mixes blue and red. In its group, it is most dark, opaque, saturated, and neither cool nor warm. Cyan mixes blue and green and so is less dark, opaque, and saturated and most cool. Yellow mixes red and green and so is least dark, opaque, and saturated and most warm. Because they add colors, magenta, cyan, and yellow do not directly compare to blue, green, and red.
Violet mixes blue and some red. In its group, it is most dark, opaque, and saturated and slightly cool. Purple mixes red and some blue and so is less dark, opaque, and saturated and is slightly warm. Turquoise mixes blue and some green and so is less dark, opaque, and saturated and is slightly cool. Orange mixes red and some green and so is less dark, opaque, and saturated and is warm. Spring green mixes green and some blue and so is less dark, opaque, and saturated and is neither warm nor cool. Chartreuse mixes green and some red and so is least dark, opaque, and saturated and is neither warm nor cool. Because they add colors differently, these six colors do not directly compare to magenta, cyan, and yellow or to blue, green, and red.
Mixing blue and yellow, green and magenta, or red and cyan makes white, gray, or black, because blue, green, and red then have ratios 1:1:1. White is lightest, because it adds blue, green, and red. Gray is in middle, because it mixes blue, green, and red. Black is darkest, because it subtracts blue, green, and red.
color properties
Physically, light waves have frequencies with intensities. Physiologically, colors are dependent and mixed (synthetic) and have brightness, hue, and saturation. Brightness depends on intensity and ranges from dim to bright. People can distinguish 100 intensity levels. Hue depends on average light frequency and ranges across the color spectrum, from red to violet. People can distinguish 100 hues. Saturation depends on light-frequency distribution and ranges from unsaturated to saturated. People can distinguish 100 saturation levels. Brightness, hue, and saturation define colors. People can distinguish one million colors. Vision perceptual processes also find color temperature and color lightness. Relative light intensities determine brightness. People can distinguish 100 brightness levels. Relative salience and activity determine color temperature, which ranges from cool to warm. People can distinguish 100 color temperatures. Relative transparency determines color lightness, which ranges from dark to light. People can distinguish 100 color lightnesses. Color brightness, temperature, and lightness define colors.
Colors are insubstantial, cannot change state, have no structure, do not belong to objects or events, and are results not processes {color facts}.
number of colors
Colors range continuously from red to scarlet, vermilion, orange, yellow, chartreuse, green, spring green, cyan, turquoise, blue, indigo, violet, magenta, crimson, and back to red. People can distinguish 150 to 200 main colors and seven million different colors.
discrimination
Humans can discriminate colors better from cyan to orange than from cyan through blues, purples, and reds.
people see same spectrum
Different humans see similar color spectra, with same colors and color sequence. Adults, infants, and animals see similar color spectra. Colorblind people have consistent but incomplete spectra.
purity
For each person, under specific viewing conditions, blue, green, and yellow can appear pure, with no other colors, but red does not appear pure.
location
Colors appear on surfaces.
adjacency
Adjacent colors affect each other and enhance contrast.
metamerism
Identical objects can have different colors. Different spectra can have the same color {metamerism}.
hue
Colors have hue. Colors respond differently as hue changes. Reds and blues change more slowly than greens and yellows.
brightness
Colors have brightness (lightness) or absence of black.
opaqueness
Colors have opaqueness. Transparency means no color.
saturation
Colors have saturation or absence of white. Different hues have different saturability and number of saturation levels.
emotion
Psychologically, red is alerting color. Green is neutral color. Blue is calming color.
depth
Blue objects appear to go farther away and expand, and red objects appear to come closer and contract, because reds appear lighter and blues darker.
Color can have shallow or deep depth. Yellow is shallow. Green is medium deep. Blue and red are deep.
lightness
Dark colors are sad because darker, and light colors are glad because lighter. Yellow is the lightest color, comparable to white. Colors darken from yellow toward red. Red is lighter than blue but darker than green. Colors darken from yellow toward green and blue. Green is lighter than blue, which is comparable to black. Therefore, subjective lightness increases from blue to red to green to yellow. See Figure 1. Lightness relates directly to transparency, unsaturability, and sparseness. Blue is dark, opaque, saturable, and dense. Red is lighter, less opaque, less saturable, and less dense. Green is light, more transparent, unsaturable, and sparse. Yellow is lightest, most transparent, most unsaturable, and sparsest.
Blue is similar to dark gray. Red is similar to medium gray. Green is similar to gray. Yellow is similar to very light gray. Magenta is similar to gray. Cyan is similar to light gray. See Figure 1.
temperature
Colors can be relatively warm or cool. Blue is coolest, then green, then yellow, and then red [Hardin, 1988]. White, gray, and black, as color mixtures, have no net temperature. Temperature relates directly to sharpness, emotion level, expansion, size, and motion toward observer. Blue is cool, is sharp and crisp, causes calmness, seems to recede, and appears contracting and smaller than red. Green has neutral temperature, is less sharp and less crisp, has neutral emotion, neither recedes nor approaches, and is neither smaller nor larger. Red is warm, is not sharp and not crisp, causes excitement, seems to approach, and appears expanding and larger than blue. See Figure 2. Red and blue are approximately equally far away from green, so green is average. Magenta has neutral temperature, because it averages red and blue. Cyan is somewhat cool, because it averages green and blue. Yellow is somewhat warm, because it averages green and red. Black, grays, and white have neutral temperature, because mixing red, green, and blue makes average temperature.
Warmness-coolness, excitement-calmness, approach-recession, expansion-contraction, and largeness-smallness relate to attention level, so temperature property relates to salience.
change
Colors change with illumination intensity, illumination spectrum, background surface, adjacent surface, distance, and viewing angle.
constancy
Vision tries to keep surface colors constant, by color constancy processes, as illumination brightness and spectra change.
white
White is relatively higher in brightness than adjacent surfaces. High colored-light intensity makes white.
black
Black is relatively lower in brightness than adjacent surfaces. Black is not absence of visual sense qualities but is a color. Low colored-light intensity makes black.
gray
Gray is relatively the same brightness as adjacent surfaces. Increasing gray intensity makes white. Decreasing gray intensity makes black. Increasing black intensity or decreasing white intensity makes gray.
red
Red light is absence of blue and green. Red pigment is absence of green, its subtractive complementary color. Red is alerting color. Red is warm color, not cool color. Red has average lightness. Red mixes with white to make pink. Spectral red blends with spectral cyan to make white. Pigment red blends with pigment green to make black. Spectral red blends with spectral yellow to make orange. Pigment red blends with pigment yellow to make brown. Spectral red blends with spectral blue or violet to make purples. Pigment red blends with pigment blue or violet to make purples. People do not see red as well at farther distances. People do not see red as well at visual periphery. Red has widest color range. Red can fade in intensity to brown then black.
blue
Blue light is absence of red and green. Blue pigment is absence of red and green. Blue is calming color. Blue is cool color, not warm color. Blue is dark color. Blue mixes with white to make pastel blue. Spectral blue blends with spectral yellow to make white. Pigment blue blends with pigment yellow to make black. Spectral blue blends with spectral green to make cyan. Pigment blue blends with pigment green to make dark blue-green. Spectral blue blends with spectral red to make purples. Pigment blue blends with pigment red to make purples. People see blue well at farther distances. People see blue well at visual periphery. Blue has narrow color range.
green
Green light is absence of red and blue. Green pigment is absence of red. Green is neutral color in alertness. Green is cool color. Green is light color. Green mixes with white to make pastel green. Spectral green blends with spectral magenta to make white. Pigment green blends with pigment magenta to make black. Spectral green blends with spectral orange to make yellow. Pigment green blends with pigment orange to make brown. Spectral green blends with spectral blue to make cyan. Pigment green blends with pigment blue to make dark blue-green. People see green OK at farther distances. People do not see green well at visual periphery. Green has wide color range.
yellow
Yellow light is absence of blue. Yellow pigment is absence of indigo or violet. Yellow is neutral color in alertness. Yellow is warm color. Yellow is lightest color. Yellow mixes with white to make pastel yellow. Spectral yellow blends with spectral blue to make white. Pigment yellow blends with pigment blue to make green. Spectral yellow blends with spectral red to make orange. Pigment yellow blends with pigment red to make brown. Olive is dark yellow-green or less saturated yellow. People see yellow OK at farther distances. People do not see yellow well at visual periphery. Yellow has narrow color range.
orange
Spectral orange can mix red and yellow. Pigment orange can mix red and yellow. Orange is slightly alerting color. Orange is warm color. Orange is light color. Orange mixes with white to make pastel orange. Spectral orange blends with spectral blue-green to make white. Pigment orange blends with pigment blue-green to make black. Spectral orange blends with spectral cyan to make yellow. Pigment orange blends with pigment cyan to make brown. Spectral orange blends with spectral red to make light red-orange. Pigment orange blends with pigment red to make dark red-orange. People do not see orange well at farther distances. People do not see orange well at visual periphery. Orange has narrow color range.
violet
Spectral violet can mix blue and red. Pigment violet has red and so is purple. Violet is calming color. Violet is cool color. Violet is dark color. Violet mixes with white to make pastel violet. Spectral violet blends with spectral yellow-green to make white. Pigment violet blends with pigment yellow-green to make black. Spectral violet blends with spectral red to make purples. Pigment violet blends with pigment red to make purples. People see violet well at farther distances. People see violet well at visual periphery. Violet has narrow color range. Violet can fade in intensity to dark purple then black.
brown
Pigment brown can mix red, yellow, and green. Brown is commonest color but is not spectral color. Brown is like dark orange pigment or dark yellow-orange. Brown color depends on contrast and surface texture. Brown is not alerting or calming. Brown is warm color. Brown is dark color. Brown mixes with white to make pastel brown. Pigment brown blends with other pigments to make dark brown or black. People do not see brown well at farther distances. People do not see brown well at visual periphery. Brown has wide color range.
Simple color space can have orthogonal red, green, and blue coordinates {color space with orthogonal vectors}, with unit vectors at (1,0,0) for red, (0,1,0) for green, and (0,0,1) for blue. Adding red, green, and blue coordinates makes the resultant-vector color.
Brightness is resultant-vector length. For example, bright green can have vector (0,9,0), with length 9. Bright green (0,9,0) and bright red (9,0,0) can add to vector (9,9,0), with length 9 * 2^0.5.
Hue is resultant-vector direction. For example, unit red and unit green can add to yellow (1,1,0).
Saturation is resultant-vector angle to the color-space diagonal. For example, unit red, unit green, and unit blue add to white (1,1,1), which is on the diagonal and so has 0% saturation. Unit red and unit blue add to magenta (1,0,1), which is on the farthest plane, with maximum 45-degree angle to the diagonal, and so has 100% saturation.
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Date Modified: 2022.0225