DIFFERENTIAL NUMERICAL QUANTIFICATION OF SAME VAGUE QUANTIFIERS Sneha Agarwal Y9588 SE 367: Introduction to Cognitive Science Mentor: Dr. Amitabha Mukerjee Abstract Often, the answers to many psychological and social studies surveys are in the terms of “many a times” and “not often”. Every time the responses cannot be in numbers. Conversion to numerical values can be important for computation purposes. Here, the study is on the non-numerical quantifiers in Hindi language, like, , ई and . This paper tries to account for the factors that make the mapping of language quantifiers to non-language ones, non-linear. Experiments have been done to show how the other objects present in the picture about and also, how the spacing of objects in space affects our decisions about the main object being asked about. Finally, this paper comes up with an interesting study on how the answers changed from people with highly-developed analytical powers to the ones with normal analytical abilities. Introduction In various behavioral studies, answers are not often in terms of numbers. Finally, we do need computers to interpret such results for us. But, various factors involved make it impossible to do so. Including proper variations due of such factors should highly improve the mapping of vague quantifiers to numerical scale. The basic theme of this paper is based on the paper by Coventry et al, 2005 [2] . The aim of this project is to carry out experiments on the lines of Coventry, using Hindi language quantifiers rather than English and to verify their hypothesis. An additional variation of percentage of screen covered and the group of people being questioned has been added here. Experiments 1. Experiment I It is to show that people go wrong on estimation when the numbers go higher. Results As expected, people guessed the number „5‟ right. They were close even when the flowers were „8‟ but different greater when the number escalated to „13‟. The participants reported that the numbers were easier to guess when the flowers were grouped together, which is also indicated by better estimation of grouped flowers than mixed flowers. Here itself, the effect of number of green flowers can be seen as the approximation bars went down even when the number of yellow flowers in the pictures was constant. This result is comparable to the results obtained in Coventry et al, 2005 [2] . Here, too, the estimate de-linearizes as the number increases with still lower estimates for mixed scenes. 2. Experiment II To study the effect of number of green flowers, number of yellow flowers and their relative positioning on the deciding the most appropriate sentence for that picture Results Greater the number of yellow flowers, higher the quantifier chosen. Increase in the number of green flowers decreased the ratings for higher quantifiers. Relating to Coventry et al, 2005 [1] , The objects used here were striped (focus object) and plain fishes (other object). They used 5 quantifiers, namely, „a few‟, „few‟, „several‟, „many‟ and „lots‟. Sentence to be rated on a scale of 1-7, on the basis of their appropriateness for the scene are - There are [QUANTIFIER] striped fish. The ratings for higher quantifiers go up and of lower quantifiers go down as the number of striped fishes increase. More the number of plain fishes, higher are the ratings for lower quantifiers and vice versa. Apart from the repetition in the trend of decreasing ratings, mixed scenes showed little higher ratings than mixed yellow flowers. In Coventry et al, 2005 [2] , higher ratings are there for lower quantifiers in the mixed scene as the number of striped fishes increase. Lower are the ratings for higher quantifiers when the number of focus objects increases. 3. Experiment III PART I This was to study the effect of the ratio of the screen occupied by the flowers. Results This variation did not show any variations in answers, except at one or two places. Already trained minds of the undergraduates was thought to be the reason behind this. So, people aged between 20-40 years of age and educated up-to only class 12 were chosen instead. PART II Results Now, the effect of screen filling could be easily seen. For completely filled screens, higher quantifiers were chosen as compared to the choice for corresponding picture in which the screen was only partially filled. Discussion The second experiment demonstrates the effect of other flowers present in the picture on the ratings for the main flowers even though the green flowers are mentioned nowhere in the questions. Secondly, it shows that when grouped, flowers appear to be larger in number, backed by the results of experiment 1. These context effects show that the mapping between numerical quantifiers and numbers cannot be linear. The reason also being that as the number increased, the correctness of the estimation of the number of yellow flowers went down, as demonstrated in the first experiment. Even here the results were affected by the surrounding factors, independent of the number of yellow flowers. The results are comparable to that obtained by Coventry, et al. In the last experiment, where there were filled and not-filled scenes, the experiment failed with the undergraduate students. A possible argument is that they identified that there was no difference other than variation in size and hence, the corresponding pictures were essentially the same. These people did have developed analytical skills and to some extent are familiar with such tricks. Therefore, it was decided to change the group of people being questioned. This time it was people who had received formal education maximum up-to only class 12, ensuring to some level that their analytical brain were not as trained. Finally, the results did show drastic differences for size variations. So, this brings in a new factor of variation – the group of people to whom the questions are asked. REFERENCES 1. 
Coventry KR, Cangelosi A, Newstead S, Bacon A, Rajapakse R (2005) Grounding natural language quantifiers in visual attention. In: 27th annual meeting of the cognitive science society, Stresa, July 2005 2. Coventry KR, Lynott L, Cangelosi A,Knight L, Joyce D, Richardson DC. Spatial language, visual attention, and perceptual simulation. Brain and Language 2010
