Colour Words, Bayes and Language Complexity Mike Dowman 27 May, 2005

About me

Colour Term Typology There are clear typological patterns in how languages name colour.  neurophysiology of vision system  or cultural explanation? Constraints on learnable languages or an evolutionary process?

Basic Colour Terms Most studies look at a subset of all colour terms: Terms must be psychologically salient Known by all speakers Meanings are not predictable from the meanings of their parts Don’t name a subset of colours named by another term

Number of Basic Terms English has red, orange, yellow, green, blue, purple, pink, brown, grey, black and white. crimson, blonde, taupe are not basic. All languages have 2 to 11 basic terms Except Russian and Hungarian Some people dispute concept of basic colour term

Prototypes Colour terms have good and marginal examples  prototype categories People disagree about the boundaries of colour word denotations But agree on the best examples – the prototypes Berlin and Kay (1969) found that this was true both within and across languages.

Berlin and Kay (1969) Small set of possible colour term systems 98 Languages in study Only Cantonese, Vietnamese, Western Apache, Hopi, Samal and Papago didn’t fit the hierachy Berlin and Kay’s Implicational Hierarchy. purple pink orange grey white black red green yellow blue brown

World Colour Survey 110 minor languages (Kay, Berlin, Merrifield, 1991; Kay et al 1997; Kay and Maffi, 1999) All surveyed using Munsell arrays Black, white, red, yellow, green and blue seem to be fundamental colours They are more predictable than derived terms (orange, purple, pink, brown and grey)

Evolutionary Trajectories white + red + yellow + black-green-blue white + red + yellow + green + black-blue white-red-yellow + black-green-blue white + red-yellow + black-green-blue white + red + yellow + black + green-blue white + red-yellow + black + green-blue white + red + yellow + black + green + blue white + red + yellow-green-blue + black white + red + yellow-green + blue + black

Derived Terms Brown and purple terms often occur together with green-blue composites Orange and pink terms don’t usually occur unless green and blue are separate But sometimes orange occurs without purple Grey is unpredictable No attested turquoise or lime basic terms

Exceptions and Problems 83% of languages on main line of trajectory 25 languages were in transition between stages 6 languages didn’t fit trajectories at all  Kuku-Yalanji (Australia) has no consistent term for green  Waorani (Ecuador) has a yellow-white term that does not include red  Gunu (Cameroon) contains a black-green-blue composite and a separate blue term

Criticism of Kay Much more variability than Kay suggests – both within and across languages Criteria for distinguishing basic colour terms don’t work Colour is often conflated with other properties: texture, variegation, etc. Colour words can only be understood in relation to the rest of the language Colour words have religious and cultural significance  Saunders (1992), MacLaury (1997), Levinson (2001), MacKeigan (2005)

Neurophysiology and Unique Hues Red and green, yellow and blue are opposite colours De Valois and Jacobs (1968):  There are cells in the retina that respond maximally to either one of the unique hues, black or white.

Psycholinguistics: Rosch/Heider Free choice of colour chips:  People prefer to pick unique hues  True across cultures and languages Better memory for colour chips:  Can pick out chip better in array after 30s  Dani can learn names for unique hues more easily than for other colours But these last two results are disputed

Kay and McDaniel (1978) Universal colour categories Red, yellow, green, blue, black and white:  Derived from cell’s neural responses Purple, pink, brown and grey  Derived via fuzzy intersections Composite categories  Derived via fuzzy unions

Tony Belpaeme (2002) Ten artificial people Colour categories represented with adaptive networks CIE-LAB colour space used (red-green, yellow-blue, light-dark) Sometimes multi-generational, sometimes single generation

Guessing game Speaker tries to find a word that names a topic colour but not a context one If this fails he modifies his colour categories Otherwise word and topic + context shown to the hearer If hearer can distinguish topic from context, word-category association strengthened. Otherwise hearer is shown the correct topic, and adapts his colour category

Emergent Languages Coherent colour categories emerged that were shared by all the agents Colour space divided into a number of regions – each named by a different colour word But some variation between speakers And no explanation of Typology

Belpaeme and Bleys (2005) Colour terms represented using points in the colour space Colours chosen from natural scenes, or at random  Few highly saturated colours Emergent colour categories tend to be clustered at certain points in the colour space Similarity with WCS was greatest when both natural colours were used and communication was simulated

The Speaker makes up a new word to label the colour. Start The hearer hears the word, and remembers the corresponding colour. This example will be used to determine the word to choose, when it is the hearer’s turn to be the speaker. Yes (P=0.001) A speaker is chosen. A hearer is chosen. A colour is chosen. Decide whether speaker will be creative. No (P=0.999) The speaker says the word which they think is most likely to be a correct label for the colour based on all the examples that they have observed so far. My Model

Colour Space red - 7 orange purple blue - 30 green - 26 yellow - 19

Possible Hypotheses high probability hypothesis medium probability hypothesis low probability hypothesis

Equations Bayes’ Rule Probability of an accurate example at colour c within h if hypothesis h is correct Probability of an erroneous example at colour c R c is probability of remember an example at colour c R h is sum of R c for all c in hypothesis h R t is sum of R c for whole of the colour space

Probability of the data Problem – we don’t know which examples are accurate p is the probability for each example that it is accurate e is an example E is the set of all examples Probability for examples outside of hypothesis (must be inaccurate) Probability for examples inside of hypothesis (may be accurate or inaccurate)

Hypothesis Averaging We really want to know the probability that each colour can be denoted by the colour term  So, sum probabilities for all hypotheses that include the colour in their denotation  Doing this for all colours produces fuzzy sets Substituting into Bayes’ rule:

Urdu

Evolutionary Simulations Average lifespan (number of colour examples remembered) set at: 18, 20, 22, 24, 25, 27, 30, 35, 40, 50, 60, 70, 80, 90, 100, 110 or simulation runs in each condition Languages spoken at end analysed Only people over half average lifespan included Only terms for which at least 4 examples had been remembered were considered

Analyzing the Results Speakers didn’t have identical languages  Criteria needed to classify language spoken in each simulation For each person, terms classified as red, yellow, green, blue, purple, orange, lime, turquoise or a composite (e.g. blue-green) Terms must be known by most adults Classification favoured by the most people chosen

Typological Results Percentage of Color Terms of each type in the Simulations and the World Color Survey

Derived Terms 80 purple terms 20 orange terms 0 turquoise terms 4 lime terms

Divergence from Trajectories 1 Blue-Red term 1 Red-Yellow-Green term 3 Green-Blue-Red terms Most emergent systems fitted trajectories: 340 languages fitted trajectories 9 contained unattested color terms 35 had no consistent name for a unique hue 37 had an extra term

Does Increased Salience of Unique Hues Matter?

Unique Hues Create More Regular Colour Term Systems 644 purple terms 374 orange terms 118 lime terms 16 turquoise terms Only 87 of 415 emergent systems fits trajectories

Adding Random Noise

Noise has Little Effect Derived terms: 60.6% purple 26.8% orange 9.9% lime 0.3% turquoise

How Reliable is WCS Data? Would a model that more closely replicated the WCS data be a better model? Field linguists tend to suggest that colours are much more messy than Kay et al suggest WCS is only a sample – not a gold standard Is data massaged to fit theories?

Number of Colour Terms Emerging

Coherence and Complexity What makes languages coherent? Shared communicative goals? A shared conceptual space? Feedback and negotiation? Consideration of others’ knowledge? What makes languages complex? More words aid communication? Many meanings leads to many words?

Taking Colours out of the Model Speaker says a new word to the hearer twice Start Yes (P=0.0001) A speaker is chosen. A hearer is chosen. Decide whether speaker will be creative No (P=0.9999) Speaker says a word he has heard at least twice to the hearer

Emergent Languages Average shared vocabulary always over 97%

Conclusions Level of creativity no noticeable effect (except when very high) Coherent languages emerge even with large number of people (1000)  Coherent languages emerge without feedback  And without consideration of other peoples’ language knowledge Languages are complex because we talk a lot  Not because complex languages help us to communicate

Coming Soon…  Syntax  Learnability  Minimum Description Length (MDL)  Minimum Message Length (MML)  Friday 3 rd June (same time, same place)