Fig 1.
A representation of how misalignment of interests could lead to linguistic change.
(a): A fully informative language. The speaker uses a different word for each object, allowing the listener to perfectly translate each word back into the object it came from, and to act optimally in response—that is, to choose an action value equal to the object value. (b): An ambiguous language, using the same polysemic word for objects 1/2 and 1. The polysemy confuses the listener, who cannot translate it accurately, and therefore cannot identify the object when it is 1/2 or 1. (c): For the states and actions shown here, there is one configuration of the speaker’s preferred action per state, that is aligned with the listener’s preferred action per state (game I), as well as eleven possible scenarios where
for at least one state; that is, the speaker would prefer an action greater than the listener would prefer. The degree of misalignment for the whole game, Γ, can be graded as the sum of misalignments per state, times the frequency of that state. Here we additionally multiply Γ by 12, simply so the net misalignment is always a whole number. These games are shown in larger scale in Fig B in S1 File.
Fig 2.
Misalignment of interests leads to loss of lexical breadth in a language.
Here we show the average frequency of one-word and two-word languages in the asymmetric game(s) with k = 100 and μ = 0.001. A one-word language has two columns of Pij summing to 0 (two words never used), while a two-word language has one column of Pij summing to 0. Increasing misalignment leads to invasion by two-word languages and then by one-word languages. Roman numerals denote mean values, whereas ribbons denote one standard deviation above/below the mean. Nearly identical results hold for the symmetric case, see Fig E in S1 File. The overlapping game symbols for Γ = 1 are II,III, and for Γ = 2 are IV,VI.
Fig 3.
Meanings often change over time due to misaligned interests.
(a): Changes in the speakers’ perception of their lexica. In each generation, we keep track of whether or not the most probable word used for a state among the population changes (swaps). Tallying the number of swaps gives one measure of change in lexical meaning over time. Note that while a word can be most probable for more than one state, we require a swap lead to changing in the overall strategic ranking of available words in the eyes of the population of speakers (b): The average number of word-swaps per generation in all twelve games, with k = 100 and μ = 0.001. The blue line denotes a linear best-fit. (c): Changes in the listeners’ perception of their lexica. Similar to (a), we tally the number of changes in the most probable action for the listeners in response to a word. However, unlike in (a), here we measure simply the steps (in Hamming distance) between the previous and current generation. (d): The average number of action swaps per generation in all twelve games, with k = 100 and μ = 0.001. The blue line denotes a linear best-fit. All panels here are for the asymmetric game, but the symmetric game has nearly identical results, see Fig H in S1 File. The overlapping game symbols for Γ = 1 are II,III, and for Γ = 2 are IV,V,VI.
Fig 4.
Original meaning of words is lost with increasing misalignment.
(left): A natural measure for long-term language change is with what probability speakers use word x for state 0, y for 1/2, and z for 1 at the end of the game, since this is the fully-informative language which constitutes the initial condition for all players. This can be written as a “percentage change” in the form 1 − (Sijδji)/3, where is the population-averaged speaking matrix and
is the population-averaged listening matrix (and Einstein summation conventions have been implemented). (Right): A similar metric for the listeners.
is understood to be the 3 × 5 matrix with
and all other entries equal to zero. Both panels shown are for the asymmetric game, however the symmetric game shows nearly identical results, see Fig I in S1 File. Note that the upper bounds of 2/3 (left) and 4/5 (right) reflect two different situations—in the limit of high μ, each word becomes equiprobable for each state (probability 1/3 for speakers, so Tr(S) = 1, and 1/5 for listeners, so
); in the limit of high Γ, one-word languages come to dominate (Fig 2), so one diagonal element of S is always equal to 1 and the rest to 0.
Fig 5.
Mutation rate (innovation) leads to preservation of old intensifiers, as well as “verbose” individuals (those who use all possible words).
Here we show averaged results over 100 realizations in the asymmetric version of Game V with k = 10 and μ = 0.005 (a,b) versus μ = 0.1 (c,d) In this rendition, a new word becomes available via de-lexicalization every 500 generations, beginning from our normal three words in the first generation. (a): The average number of speakers using n ≠ 2 words exists at an extremely small mutation-selection balance in comparison to two-word speakers. (b): The mean fitness of verbose individuals is always dominated by that of two-word speakers. (c): At higher mutation rates, verbose speakers are found in a higher proportion roughly matching the ratio of the two mutation rates. (d): However, their mean fitness is much higher than in (b), and the most verbose speakers in any period are equally fit, and always dominate less verbose n ≠ 2 speakers.
Fig 6.
The life cycle of intensifiers, with empirical examples.
(a): Most hyperbolic language originates as factual, indicative language that is then re-purposed (“de-lexicalization”, shown in green) as a figurative device. Once a word has “used up” its hyperbolic value, it decreases in usage and is supplanted either by a new bleached word or, frequently, by an older hyperbolic term whose loss of value has been forgotten by the current generation (a process called “recycling”, shown in blue). When words fall below a certain threshold of use without being recycled, they are lost from the language (red). (b): The rise and fall of swithe, the original English intensifer, from its de-lexicalization from the adjective swith meaning “strong” through its peak in early Middle English until its loss from the language. Data drawn from a large corpus of poetry and prose [54]. (c): The “revival” of intensifying well. Teal bars show the average usage of well as an intensifier among competing intensifiers from the 10th to the 17th century in the same corpus as (b). The red point represents the television show The Inbetweeners, where its social context of use may represent a much longer vernacular use not reflected in the literary record [55]. (d): Recycling in a particular speech community. The frequency of usage of the four main intensifiers in Toronto when grouped by age of speakers shows that different intensifiers dominate in different sub-communities, with terms unused by an older group (such as really) being recycled into the dominant intensifier by a younger generation [51]. (e): A novel example of de-lexicalization. We collected instances of football players “giving X% effort” from eight major British periodicals, where X is a number greater than 100. The numbers 110, 120, 130, and 140 are introduced in sequence and increase in frequency thereafter, though all continue to be used once they have been introduced. (f): A sub-corpus of (e) focusing on a single coach (Antonio Conte). We show that the population-level trends are often driven by verbose, innovative individuals, who also preserve older intensifiers at low frequencies in the lexicon.