Binary Descriptions

If a survey of some class of sensation is made more exact by subdivision into two mutually exclusive parts, then we are making a binary description of the experience. All detail and subtlety are reduced to just two possibilities. This simplifies accounting and reporting. The notion that theoretical physics is developed in this binary style was suggested by Anaxagoras about 2500 years ago. We use the following specialized vocabulary to make binary descriptions.

## Whiteness

Any vision, sight or ocular experience that could loosely be described as greyish is called an achromatic visual sensation. These sensations are described using words like grey, black, white, dark, bright, silvery, taupe, leaden, ecru, ashen, beige, pale etc. The reference experience for achromatic sensation is seeing the Sun. So to make a binary description of an achromatic visual sensation compare it to seeing the Sun. Report the result using one of the following algebraic statements. If the two experiences are not comparable, then say that the sensation is not an achromatic visual sensation and express this as $\delta_{w}=0$. If the sensation is like seeing the Sun, then say that it is whitish. Express this as $\delta_{w}=+1$. If the sensation is not like seeing the Sun, then say that it is blackish and that $\delta_{w}=-1$. The number $\delta_{w}$ is called the whiteness.

## Redness

Any sight that could be roughly described as reddish or greenish is called an organic chromatic sensation. We use words like red, green, pink, chartreuse, crimson, turquoise, orange, purple, olive, scarlet, khaki, magenta etc. to identify particular visual sensations within the organic category. reports that, "No color is clearly reddish as well as greenish … redness and greenness … are mutually exclusive."1 Therefore organic visual sensations are capable of binary description. The reference experience for describing organic chromatic sensation is seeing blood.2 So to make a binary description of an organic chromatic sensation, compare it to seeing blood. Report the result using one of the following algebraic statements. If the two experiences are not comparable, then say that the sensation is not an organic chromatic sensation and express this as $\delta_{m}=0$. If the sensation is like seeing blood, then say that it is reddish. Express this as $\delta_{m}=+1$. If the sensation is not like seeing blood, then say that it is greenish and that $\delta_{m}=-1$. The number $\delta_{m}$ is called the redness.

## Yellowness

Any sight that could be described as yellowish or bluish is called an inorganic chromatic visual sensation. We use words like yellow, blue, gold, cyan, indigo, brown, orange, violet, turquoise, chartreuse, azure, ocher, cerulean, sepia etc. to identify particular visual sensations within the inorganic category. reports that, "no color is both yellowish and bluish … yellowness and blueness are mutually exclusive."3 Therefore inorganic visual sensations are susceptible of binary description. The reference experience for inorganic chromatic sensation is seeing gold. So to make a binary description of an inorganic chromatic sensation, compare it to seeing gold. Report the result using one of the following algebraic statements. If the two experiences are not comparable, then say that the sensation is not an inorganic chromatic sensation and express this as $\delta_{e}=0$. If the sensation is like seeing gold, then say that it is yellowish. Express this as $\delta_{e}=+1$. If the sensation is not like seeing gold, then say that it is bluish and that $\delta_{e}=-1$. The number $\delta_{e}$ is called the yellowness.

## Coldness

Any hazardous perceptions of heat or cold are called dangerous thermal sensations. We use words like icy, boiling, freezing, scorching, frosty and blistering to describe these sensations. They are not like touching a living person, temperatures are significantly higher or lower. The reference experience for these sensations is touching ice. So to make a binary description of a dangerous thermal sensation, compare it to touching ice. Report the result using one of the following algebraic statements. If the two experiences are not comparable, then say that the sensation is not dangerous and express this by writing $\delta_{T}=0$. If the sensation is like touching ice, then say that it is freezing. Express this as $\delta_{T}=+1$. If the sensation is not like touching ice, then say that it is burning and that $\delta_{T}=-1$. The number $\delta_{T}$ is called the coldness.

## Warmness

Any mild perception of heat that happens in routine human activity is called a safe thermal sensation. Safe thermal sensations are described using words like warm, cool, balmy, chilly and lukewarm. They are similar to the temperature of a living person. The reference experience for a safe thermal sensation is touching steam. So to make a binary description of a safe thermal sensation, compare it to touching steam. Report the result using one of the following algebraic statements. If the two experiences are not comparable, then say that the sensation is not a safe thermal sensation and express this as $\delta_{\tau}=0$. If the sensation is like touching steam, then say that it is warm. Express this as $\delta_{\tau}=+1$. If the sensation is not like touching steam, then say that it is cool and that $\delta_{\tau}=-1$. The number $\delta_{\tau}$ is called the warmness.

## Oddness

Any corporeal perception associated with a sense of pressure, hearing or touch is called a somatic sensation. Somatic sensations are described using words like hard, soft, loud, quiet, slap, tickle, push, pull, scream, whisper, port, starboard, bass, treble and so on. The reference experience for describing somatic sensation is hearing a heartbeat. So to make a binary description of a somatic sensation, compare it to hearing a human heartbeat. Report the result using one of the following algebraic statements. If the two experiences are not comparable, then express this by writing $\delta^{*} =0$. If the sensation is like hearing a heartbeat, then say that it is on the left. Express this as $\delta^{*} =+1$. If the sensation is not like hearing a heartbeat, then say that it is on the right and that $\delta^{*} =-1$. The number $\delta^{*}$ is called the oddness.

## Sourness

Any flavor or gustatory perception that could be roughly described as acidic or caustic is called a sour taste sensation. We use words like soapy, tart, corrosive, sharp, astringent, tangy, acerbic, rancid, vitriolic, biting, vinegary etc. to identify these flavors. To make a binary description of a sour sensation compare it to tasting a lemon. Report the result using one of the following algebraic statements. If the two experiences are not comparable, then say that the sensation is not a sour sensation and express this as $\delta_{\sf{H}}=0$. If the sensation is like tasting a lemon, then say that it is tart. Write this as $\delta_{\sf{H}}=+1$. If the sensation is not like tasting a lemon, then say that it is soapy and that $\delta_{\sf{H}}=-1$. The number $\delta_{\sf{H}}$ is called the sourness.

## Saltiness

Any flavor or gustatory perception that could be loosely described as something like drinking water is called a moist sensation. We use words like briny, fresh, pickled, pure, fishy, drinkable, alkaline, clean, saline, etc. to describe specific tastes in this category. The reference experience for describing moist sensations is tasting the ocean. So to make a binary description of a moist taste sensation, compare it with a sip of seawater. Report the result using one of the following algebraic statements. If a sensation cannot be compared with drinking water, then say it is not a moist sensation and write $\delta_{\sf{I}}=0$. If a sensation is like tasting the ocean, then call it a brackish taste and express this as $\delta_{\sf{I}}=+1$. If a sensation is not like tasting like the ocean, then say it is potable and report $\delta_{\sf{I}}=-1$. The number $\delta_{\sf{I}}$ is called the saltiness. And the word salty is often used as a catchall for moist sensations.

## Sweetness

Any flavour or gustatory perception that could be vaguely described as something like tasting honey is called a sweet sensation. We use words like yummy, sugary, umami, caramelly, savory, candied, spicy, brothy, glazed, meaty, syrupy etc. to describe these flavours. We can make binary descriptions of sweet sensations by comparing them with other sensations, and historically the great pioneers of chemistry by direct contact with their discoveries. But now testing supersedes tasting, so consider an experiment: Dissolve many similar test particles in water and pass a beam of polarized light through the solution. Check to see if the axis of polarization varies. If the angle does not change, then say that the particle is not sweet and write $\delta_{\sf{S}}=0$. If the axis is rotated clockwise, then the particle is a dextrorotary isomer like most naturally occurring sugars. So say that the particle is sugary, and express this mathematically as $\delta_{\sf{S}}=+1$. If the axis is rotated counterclockwise, then the particle is a levorotary isomer like most naturally occurring amino acids. Then call the sensation savory and write $\delta_{\sf{S}}=-1$. The number $\delta_{\sf{S}}$ is called the sweetness. It may, for example, be perceived directly in the flavour difference between spearmint leaves and caraway seeds.
 Next step: Anaxagorean sensations.
 Summary
 Noun Definition Binary Descriptors $\sf{\text{A mutually exclusive pair of characteristics.}}$ 2-1
 Adjective Definition Whiteness $\delta_{w} \equiv \begin{cases} +1 &\sf{\text{if a visual sensation is whitish}} \\ \; \; 0 &\sf{\text{if a sensation is not greyish }} \\ -1 &\sf{\text{if a visual sensation is blackish }} \end{cases}$ 2-2
 Adjective Definition Redness $\delta_{m} \equiv \begin{cases} +1 &\sf{\text{if a visual sensation is reddish }} \\ \; \; 0 &\sf{\text{if a sensation is not reddish or greenish }} \\ -1 &\sf{\text{if a visual sensation is greenish }} \end{cases}$ 2-3
 Adjective Definition Yellowness $\delta_{e} \equiv \begin{cases} +1 &\sf{\text{if a visual sensation is yellowish }} \\ \; \; 0 &\sf{\text{if a sensation is not yellowish or bluish }} \\ -1 &\sf{\text{if a visual sensation is bluish }} \end{cases}$ 2-4
 Adjective Definition Coldness $\delta_{T} \equiv \begin{cases} +1 &\sf{\text{if a thermal sensation is freezing }} \\ \; \; 0 &\sf{\text{if a sensation is not thermally dangerous }} \\ -1 &\sf{\text{if a thermal sensation is burning }} \end{cases}$ 2-5
 Adjective Definition Warmness $\delta_{\tau} \equiv \begin{cases} +1 &\sf{\text{if a thermal sensation is warm }} \\ \; \; 0 &\sf{\text{if a sensation is not thermally safe }} \\ -1 &\sf{\text{if a thermal sensation is cool }} \end{cases}$ 2-6
 Adjective Definition Oddness $\delta^{*} \equiv \begin{cases} +1 &\sf{\text{if a somatic sensation is on the left side }} \\ \; \; 0 &\sf{\text{if a sensation is not somatic }} \\ -1 &\sf{\text{if a somatic sensation is on the right side }} \end{cases}$ 2-7
 Adjective Definition Sourness $\delta_{\sf{H}} \equiv \begin{cases} +1 &\sf{\text{if a sour taste sensation is tart }} \\ \; \; 0 &\sf{\text{if a sensation is not sour }} \\ -1 &\sf{\text{if a sour taste sensation is soapy }} \end{cases}$ 2-8
 Adjective Definition Saltiness $\delta_{\sf{I}} \equiv \begin{cases} +1 &\sf{\text{if a moist taste sensation is brackish }} \\ \; \; 0 &\sf{\text{if a sensation is not moist }} \\ -1 &\sf{\text{if a moist taste sensation is potable }} \end{cases}$ 2-9
 Adjective Definition Sweetness $\delta_{\sf{S}} \equiv \begin{cases} +1 &\sf{\text{if a sweet taste sensation is sugary }} \\ \; \; 0 &\sf{\text{if a sensation is not sweet }} \\ -1 &\sf{\text{if a sweet taste sensation is savory }} \end{cases}$ 2-10