26 Chapter 2 What made it possible for Berlin and Kay to find these regularities was their discovery of focal colors.If one simply asks speakers around the world to pick out the portions of the spectrum that their basic color terms refer to,there seem to be no significant regularities.The boundaries be- tween the color ranges differ from language to language.The regularities appear only when one asks for the best example of a basic color term given a standardized chart of 320 small color chips.Virtually the same best ex- amples are chosen for the basic color terms by speakers in language after language.For example,in languages that have a basic term for colors in the blue range,the best example is the same focal blue for all speakers no matter what language they speak.Suppose a language has a basic color term that covers the range of both blue and green;let us call that color grue.The best example of grue,they claim,will not be tur- quoise,which is in the middle of the blue-to-green spectrum.Instead the best example of grue will be either focal blue or focal green.The focal colors therefore allow for comparison of terms across languages. The existence of focal colors shows that color categories are not uni- form.Some members of the category RED are better examples of the cate- gory than others.Focal red is the best example.Color categories thus have central members.There is no general principle,however,for pre- dicting the boundaries from the central members.They seem to vary, somewhat arbitrarily,from language to language. Kay and McDaniel The Berlin-Kay color research raised questions that were left un- answered.What determines the collection of universal focal colors? Why should the basic color terms pick out just those colors?Kay and Mc- Daniel (1978)provided an answer to these questions that depended jointly on research on the neurophysiology of color vision by Devalois and his associates and on a slightly revised version of Zadeh's fuzzy set theory. DeValois and his associates (DeValois,Abramov,and Jacobs 1966; De Valois and Jacobs 1968)had investigated the neurophysiology of color vision in the macaque,a monkey with a visual system similar to man's. Their research concentrated on the neural pathways between the eye and the brain.They found six types of cell.Four of these,called opponent re- sponse cells,determine hue,while the other two determine brightness. The opponent response cells are grouped into two pairs,one having to do with the perception of blue and yellow,the other having to do with the perception of red and green.Each opponent response cell has a spontane- ous rate of firing-a base response rate that it maintains without any ex-
26 Chapter 2 What made it possible for Berlin and Kay to find these regularities was their discovery of focal colors. If one simply asks speakers around the world to pick out the portions of the spectrum that their basic color terms refer to, there seem to be no significant regularities. The boundaries between the color ranges differ from language to language. The regularities appear only when one asks for the best example of a basic color term given a standardized chart of 320 small color chips. Virtually the same best examples are chosen for the basic color terms by speakers in language after language. For example, in languages that have a basic term for colors in the blue range, the best example is the same focal blue for aU speakers no matter what language they speak. Suppose a language has a basic color term that covers the range of both blue and green; let us call that color grue. The best example of grue, they claim, will not be turquoise, which is in the middle of the blue-to-green spectrum. Instead the best example of grue will be either focal blue or focal green. The focal colors therefore aUow for comparison of terms across languages. The existence of focal colors shows that color categories are not uniform. Some members of the category RED are better examples of the category than others. Focal red is the best example. Color categories thus have central members. There is no general principle, however, for predicting the boundaries from the central members. They seem to vary, somewhat arbitrarily, from language to language. Kay and McDaniel The Berlin-Kay color research raised questions that were'left unanswered. What determines the collection of universal focal colors? Why should the basic color terms pick out just those colors? Kay and McDaniel (1978) provided an answer to these questions that depended jointly on research on the neurophysiology of color vision by DeValois and his associates and on a slightly revised version of Zadeh's fuzzy set theory. DeValois and his associates (DeValois, Abramov, and Jacobs 1966; DeValois and Jacobs 1968) had investigated the neurophysiology of color vision in the macaque, a monkey with a visual system similar to man's. Their research concentrated on the neural pathways between the eye and the brain. They found six types of cell. Four of these, called opponent response cells, determine hue, while the other two determine brightness. The opponent response cells are grouped into two pairs, one having to do with the perception of blue and yellow, the other having to do with the perception of red and green. Each opponent response cell has a spontaneous rate of firing-a base response rate that it maintains without any ex-
Kay and McDaniel 27 ternal stimulation.There are two types of blue-yellow cells.The +B-Y cells fire above their base rate in response to a blue stimulus,and below their base rate in response to a yellow stimulus.The Y-Bcells do the re- verse:they fire above their base rate in response to yellow and below their base rate in response to blue.Similarly,there are two types of red-green cells:+G-R cells fire above their base rate in response to green and be- low in response to red,while +R-Gcells fire above in response tored and below in response to green.The two types of blue-yellow cells jointly de- termine a blue-yellow response,while the two kinds of red-green cells jointly determine a red-green response. Focal blue is perceived when the blue-yellow cells show a blue response and when the red-green cells are firing at the neutral base rate.Purple is a combination of blue and red;it is perceived when the blue-yellow cells show a blue response and the red-green cells show a red response.Tur- quoise is perceived when the blue-yellow cells show a blue response and the red-green cells show a green response.Pure primary colors-blue, yellow,red,and green-are perceived when either the blue-yellow or red- green cells are firing at their neutral base rates.Nonprimary colors corre- spond to cases where no opponent cells are firing at neutral base rates. The remaining two kinds of cells are light-sensitive and darkness- sensitive.Pure black,white,and gray are perceived when the blue-yellow and red-green cells are all firing at their neutral base rates and making no color contribution.Pure black occurs when the darkness-sensitive cells are firing at their maximum rate and the light-sensitive cells are firing at their minimum rates.Pure white is the reverse. Given these results from neurophysiological studies,Kay and McDan- iel apply a version of fuzzy set theory to make sense of the Kay-Berlin re- sults.For example,they define degree of membership in the category blue as the proportion of blue response on the part of the blue-yellow cells. Pure blue(degree of membership 1)occurs when the red-green response is neutral.Blues in the direction of purple or green or white have an inter- mediate degree of membership in the blue category.Corresponding definitions are given for other primary colors.The accompanying dia- 1.0 RED BLUE GREEN YELLOW RED .5 R B R 0 400 450 500 550 600 650 700 Wavelength NM
550 600 650 Wavelength NM 450 500 O.........-'---'--L-.L-L.-.....L>o:<.L-l--L.loL.l-..-L-.L-'-....L..-L-.L:>L.L.......I..-..L.......l-L.-.....I..-..L.......l---.L..--'---'=-..... 400 Kay and McDaniel 27 ternal stimulation. There are two types of blue-yellow cells. The +B - Y cells fire above their base rate in response to a blue stimulus, and below their base rate in response to a yellow stimulus. The + Y - Bcells do the reverse: they fire above their base rate in response to yellow and below their base rate in response to blue. Similarly, there are two types of red-green cells: + G - R cells fire above their base rate in response to green and below in response to red, while + R - Gcellsfire aboveinresponsetored and below in response to green. The two types of blue-yellow cells jointly determine a blue-yellow response, while the two kinds of red-green cells jointly determine a red-green response. Focal blue is perceived when the blue-yellow cells show a blue response and when the red-green cells are firing at the neutral base rate. Purple is a combination of blue and red; it is perceived when the blue-yellow cells show a blue response and the red-green cells show a red response. Turquoise is perceived when the blue-yellow cells show a blue response and the red-green cells show a green response. Pure primary colors-blue, yellow, red, and green-are perceived when either the blue-yellow or redgreen cells are firing at their neutral base rates. Nonprimary colors correspond to cases where no opponent cells are firing at neutral base rates. The remaining two kinds of cells are light-sensitive and darknesssensitive. Pure black, white, and gray are perceived when the blue-yellow and red-green cells are all firing at their neutral base rates and making no color contribution. Pure black occurs when the darkness-sensitive cells are firing at their maximum rate and the light-sensitive cells are firing at their minimum rates. Pure white is the reverse. Given these results from neurophysiological studies, Kay and McDaniel apply a version of fuzzy set Theory to make sense of the Kay-Berlin results. For example, they define degree of membership in the category blue as the proportion of blue response on the part of the blue-yellow cells. Pure blue (degree of membership = 1) occurs when the red-green response is neutral. Blues in the direction of purple or green or white have an intermediate degree of membership in the blue category. Corresponding definitions are given for other primary colors. The accompanying diao~ I 0 f;V 'Nv f;V
28 Chapter 2 grams give curves that correlate degree of membership in color categories with wavelengths in nanometers for hues and percentage of refectance for black and white. The neurophysiological account only characterizes the primary colors: black,white,red,yellow,blue,and green.What allows us to"see"other colors as being members of color categories?What about orange,brown, 1.0 WHITE BLACK 6 0 20 40 60 80 100 Percent of Reflectance purple,etc.?Some cognitive mechanism in addition to the neurophysiol- ogy is needed to account for those.Kay and McDaniel suggested that such a mechanism would make use of something akin to fuzzy set theory. The postulation of a cognitive mechanism that has some of the effects of fuzzy set theory enables Kay and McDaniel to do two things that the neurophysiological account alone could not do.First,it enabies them to characterize focal nonprimary colors (orange,purple,pink,brown,gray, etc.in the following intuitive way: ORANGE RED and YELLOW PURPLE BLUE and RED PINK RED and WHITE BROWN BLACK and YELLOW GRAY BLACK and WHITE Thus,ORANGE is characterized in terms of the fuzzy set intersection of the RED and YELLow curves.(Actually,for technical reasons the definition is twice the fuzzy-set intersection value.See Kay and McDaniel 1978,pp. 634-35,for details.)Correspondingly,PURPLE is defined in terms of the fuzzy set intersection of BLUE and RED,and GRAY in terms of the fuzzy set in- tersection for BLACK and WHITE.PINK and BROWN require somewhat differ- ent functions based on fuzzy set intersections. The second advantage of fuzzy set theory is that it permits an intuitive account of basic color categories that include more than one focal color. Dani,for example,has only two basic color terms:'mili contains black and all the cool colors,the greens and blues;mola contains white and all the warm colors,the reds,oranges,yellows,pinks,and red-purples.Some
28 Chapter 2 grams give curves that correlate degree of membership in color categories with wavelengths in nanometers for hues and percentage of reflectance for black and white. The neurophysiological account only characterizes the primary colors: black, white, red, yellow, blue, and green. What allows us to "see" other colors as being members of color categories? What about orange, brown, 1.0 .......9- o.c <U 5 <U <U • '-.0 ifE a~ BLACK 20 WHITE 40 60 Percent of Reflectance 80 100 purple, etc.? Some cognitive mechanism in addition to the neurophysiology is needed to account for those. Kay and McDaniel suggested that such a mechanism would make use of something akin to fuzzy set theory. The postulation of a cognitive mechanism that has some of the effects of fuzzy set theory enables Kay and McDaniel to do two things that the neurophysiological account alone could not do. First, it enables them to characterize focal nonprimary colors (orange, purple, pink, brown, gray, etc.) in the following intuitive way: ORANGE = RED and YELLOW PURPLE = BLUE and RED PINK = RED and WHITE BROWN = BLACK and YELLOW GRAY = BLACK and WHITE Thus, ORANGE is characterized in terms of the fuzzy set intersection of the RED and YELLOW curves. (Actually, for technical reasons the definition is twice the fuzzy-set intersection value. See Kay and McDaniel 1978, pp. 634-35, for details.) Correspondingly, PURPLE is defined in terms of the fuzzy set intersection of BLUE and RED, and GRAY in terms ofthe fuzzy set intersection for BLACK and WHITE. PINK and BROWN require somewhat different functions based on fuzzy set intersections. The second advantage of fuzzy set theory is that it permits an intuitive account of basic color categories that include more than one focal color. Dani, for example, has only two basic color terms:mili contains black and all the cool colors, the greens and blues; mala contains white and all the warm colors, the reds, oranges, yellows, pinks, and red-purples. Some
Kay and McDaniel 29 languages have basic color categories containing both blues and greens, while others have basic color categories containing both reds and yellows. Such cases can be accounted for intuitively by using fuzzy set union DARK-COOL BLACK Or GREEN Or BLUE LIGHT-WARM WHITE Or RED Or YELLOW COOL GREEN Or BLUE WARM RED Or YELLOW Thus,Kay and McDaniel make the claim that basic color categories are a product of both neurophysiology and cognitively real operations that can be partially modelled by fuzzy set intersection and union. At present,this is the only plausible account we have of why the facts of basic color categories should be as they are.The Kay-McDaniel theory has important consequences for human categorization in general.It claims that colors are not objectively "out there in the world"indepen- dent of any beings.Color concepts are embodied in that focal colors are partly determined by human biology.Color categorization makes use of human biology,but color categories are more than merely a consequence of the nature of the world plus human biology.Color categories result from the world plus human biology plus a cognitive mechanism that has some of the characteristics of fuzzy set theory plus a culture-specific choice of which basic color categories there are. The Kay-McDaniel theory seems to work well for characterizing the focal colors corresponding to basic color categories.But it does not work as well at the boundaries between colors.According to the Kay- McDaniel account,the boundaries,as well as the focal colors,should be uniform across languages.But this is simply not the case.The most de- tailed work on the detailed mapping of color categories,especially in non- focal areas,has been done by MacLaury(in preparation).Among the test cases for the Kay-McDaniel theory are cases where a language does not have a separate color category for nonprimary focal colors,like purple and orange,colors that,in the Kay-McDaniel account,are"computed" on the basis of fuzzy set theory plus the response curves for the primary colors.The Kay-McDaniel theory predicts that colors like purple and or- ange should be treated uniformly across languages and that they should always be on the boundaries between basic color categories in languages that do not have separate categories for them. But MacLaury has found cases where purple is entirely within the cool color range (a single color with focal points at blue and green)and other cases where purple is on the boundary between cool and red.He has also found cases where brown is subsumed by yellow and other cases where it is subsumed by black.That is,what we call"brown"falls within the range
Kay and McDaniel 29 languages have basic color categories containing both blues and greens, while others have basic color categories containing both reds and yellows. Such cases can be accounted for intuitively by using fuzzy set union. DARK-COOL = BLACK or GREEN or BLUE LIGHT-WARM = WHITE or RED or YELLOW COOL = GREEN or BLUE WARM = RED or YELLOW Thus, Kay and McDaniel make the claim that basic color categories are a product of both neurophysiology and cognitively real operations that can be partially modelled by fuzzy set intersection and union. At present, this is the only plausible account we have of why the facts of basic color categories should be as they are. The Kay-McDaniel theory has important consequences for human categorization in general. It claims that colors are not objectively "out there in the world" independent of any beings. Color concepts are embodied in that focal colors are partly determined by human biology. Color categorization makes use of human biology, but color categories are more than merely a consequence of the nature of the world plus human biology. Color categories result from the world plus human biology plus a cognitive mechanism that has some of the characteristics of fuzzy set theory plus a culture-specific choice of which basic color categories there are. The Kay-McDaniel theory seems to work well for characterizing the focal colors corresponding to basic color categories. But it does not work as well at the boundar:.=s between colors. According to the KayMcDaniel account, the boundaries, as well as the focal colors, should be uniform across languages. But this is simply not the case. The most detailed work on the detailed mapping of color categories, especially in nonfocal areas, has been done by MacLaury (in preparation). Among the test cases for the Kay-McDaniel theory are cases where a language does not have a separate color category for nonprimary focal colors, like purple and orange, colors that, in the Kay-McDaniel account, are "computed" on the basis of fuzzy set theory plus the response curves for the primary colors. The Kay-McDaniel theory predicts that colors like purple and orange should be treated uniformly across languages and that they should always be on the boundaries between basic color categories in languages that do not have separate categories for them. But Mad.aury has found cases where purple is entirely within the cool color range (a single color with focal points at blue and green) and other cases where purple is on the boundary between cool and red. He has also found cases where brown is subsumed by yellow and other cases where it is subsumed by black. That is, what we call "brown" falls within the range
30 Chapter 2 of a category with a center at pure yellow in some languages,and it falls within the range of a category with a center at pure black in other lan- guages. In Kay-McDaniel terms,this means that the fuzzy-set-theoretical func- tions that compute conjunctions and disjunctions for color categories are not exactly the same for all people;rather they vary in their boundary conditions from culture to culture.They are thus at least partly conven- tional,and not completely a matter of universal neurophysiology and cognition.What this requires is a revision of the Kay-McDaniel theory to permit conceptual systems for color to vary at the boundaries,by having the exact nature of the disjunction function be somewhat different in dif- ferent systems.Such differences may not only be at the boundaries but at the focal peaks.Kay and McDaniel's theory implied that each binary dis- junctive color category(e.g.,cooL BLUE or GREEN)should have two focal peaks (e.g.,both focal blue and focal green).MacLaury has found cases where there is a cool category covering blue and green,but where there is a skewing effect such that the center of the category is at pure green alone or pure blue alone.Thus,in Kay-McDaniel terms,conceptual systems seem to have disjunction functions that take the blue and green response curves as input and yield an output curve with only one focal center.This would require a cognitive mechanism with more than just something akin to the operation of union in fuzzy set theory. Color categories,thus,are generative categories in the same sense in which kinship categories characterized by Lounsbury are.They have generators plus something else.The generators are the neurophysiologi- cally determined distribution functions,which have peaks where the pri- mary colors are pure:black,white,red,yellow,blue,and green.These generators are universal;they are part of human neurophysiology.The 'something else"needed to generate a system of basic color categories consists of a complex cognitive mechamism incorporating some of the characteristics of fuzzy set theory union and intersection.This cognitive mechanism has a small number of parameters that may take on different values in different cultures. It is important to bear in mind that it is not just the names for colors that vary.The color names do not just attach to the neurophysiologically determined distribution functions directly.Cognitive mechanisms of the sort described above must be postulated in addition.There are general characteristics of the cognitive mechanisms,for example,the use of something like fuzzy set theory union and intersection.But,as MacLaury shows,color cognition is by no means all the same across cultures.Nor is it by any means arbitrarily different across cultures.The possible color ranges depend upon limited parameters within the cognitive mechanism
30 Chapter 2 of a category with a center at pure yellow in some languages, and it falls within the range of a category with a center at pure black in other languages. In Kay-McDaniel terms, this means that the fuzzy-set-theoretical functions that compute conjunctions and disjunctions for color categories are not exactly the same for all people; rather they vary in their boundary conditions from culture to culture. They are thus at least partly conventional, and not completely a matter of universal neurophysiology and cognition. What this requires is a revision of the Kay-McDaniel theory to permit conceptual systems for color to vary at the boundaries, by having the exact nature of the disjunction function be somewhat different in different systems. Such differences may not only be at the boundaries but at the focal peaks. Kay and McDaniel's theory implied that each binary disjunctive color category (e.g., COOL == BLUEor GREEN) should have two focal peaks (e.g., both focal blue and focal green). MacLaury has found cases where there is a cool category covering blue and green, but where there is a skewing effect such that the center of the category is at pure green alone or pure blue alone. Thus, in Kay-McDaniel terms, conceptual systems seem to have disjunction functions that take the blue and green response curves as input and yield an output curve with only one focal center. This would require a cognitive mechanism with more than just something akin to the operation of union in fuzzy set theory. Color categories, thus, are generative categories in the same sense in which kinship categories characterized by Lounsbury are. They have generators plus something else. The generators are the neurophysiologically determined distribution functions, which have peaks where the primary colors are pure: black, white, red, yellow, blue, and green. These generators are universal; they are part of human neurophysiology. The "something else" needed to generate a system of basic color categories consists of a complex cognitive mechamism incorporating some of the characteristics of fuzzy set theory union and intersection. This cognitive mechanism has a small number of parameters that may take on different values in different cultures. It is important to bear in mind that it is not just the names for colors that vary. The color names do not just attach to the neurophysiologically determined distribution functions directly. Cognitive mechanisms of the sort described above must be postulated in addition. There are general characteristics of the cognitive mechanisms, for example, the use of something like fuzzy set theory union and intersection. But, as MacLaury shows, color cognition is by no means all the same across cultures. Nor is it by any means arbitrarily different across cultures. The possible color ranges depend upon limited parameters within the cognitive mechanism