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Semantic Numerosity

This is my honors Bachelor's thesis from the University of Illinois Urbana-Champaign which covers Semantic Numerosity.

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Semantic Numerosity

  1. 1. Semantic Numerosity Jeet Samarth Raut Submitted in fulfillment of the requirements for the honors degree of Cognitive Psychology at University of Illinois Urbana-Champaign 2011
  2. 2. The brain is an amazing organ. It weighs a mere three pounds and astonishingly contains as many as 100 billion brain cells(Magill's Medical Guide Revised Edition. Salem Press, 1998: 221.) It is the most complex organ in the human, and controls major functions of the body, such as: moving, reasoning, processing the five types of sensory information, thinking, and speaking to name a few. Since ancient times, humans have sought out to find what makes everything in the brain work and try to explain the functions of the different areas of the brain. In the 1950’s there was a shift in interest and researchers started trying to find models to describe the manner in which the brain works. These models combined psychology, linguistics, philosophy, computer science, artificial intelligence, and neuroscience, and the study of these models assimilated into a new field, known as cognitive science. 60 years later, the field of cognitive science is as busy as ever. New discoveries illicit more research as researchers delve into the intricacies of the mind. A great example of this is the field of linguistics. Linguistics is used to examine grammar, but this grammar is one which is unfamiliar to most people. Grammar is the set of rules used to generate a language. When you think of grammar, what you probably think of is what a student would learn in a elementary school English class. Perscriptive grammar is how some educators believe people should talk and write, and insignificant to cognitive science. Examples of perscriptive grammar include not starting a sentence with a preposition(“Also I am thirsty.”) and using the word “whom”. What we seek out to learn is the “natural” or descriptive grammar, which is the way to describe how people actually talk and write. Descriptive grammar used in everyday language because the entire concept of linguistics is based on communicating, and what we study is the
  3. 3. behavior of communication.(Carrol, 26) Linguistics is divided into several sub-categories of study. These include the ways in which we physically produce speech(phonetics), the manner in which we analyze an individual word’s structure(morphology), the structure of sentences (syntax), the meaning of words and sentences(semantics), and the how the linguistics is used to communicate (pragmatics) . Psycholinguistics is a interdisciplinary study combining linguistics and psychology. It is divided into 3 main categories, language acquisition, language comprehension, and language production. This paper will primarily focus on a specific question about language production, though there is much overlap from the other two categories. If you are reading this, you are presumably an English speaker, and as an English speaker, when you attempt to pluralize words, you make sure that there is more than one of whatever you are pluralizing so that there is agreement and the statement makes sense. For example consider the following four statements: 1.That dog barked. 2.Those dogs barked. 3.*That dogs bark. 4.*Those dog. (In linguistics, an * will precede grammatically incorrect sentences.) “That” can only be used to refer to a singular object and “those” can only be used to refer to plural objects, and this property of word agreement is known as grammatical number. (Bock and Miller, 48) Pluralization is dependent on the grammatical number, and every category of linguistics is involved with the pluralization. How would you pluralize a word that you are unfamiliar with? Jean Berko asked children that exact question in a 1958 paper entitled The Child's Learning of English Morphology. She took group of pre-school students ranging in age from five to seven, and had them participate in a sentence
  4. 4. completion test, an example of which is listed below. This is a wug Now there is another one. There are two of them. There are two _________. Just like you or I would complete the sentence, the overwhelming majority(91%) of the pre-schoolers answered with “wugs”, by adding “-s” to the unknown word. The same test was given with other made up words such as “gulch” and “heaf”, and though the pre-schoolers weren’t quite as accurate( 36% came up with “gulches” and 86% came up with “heaves”) some still knew how to pluralize the unknown words. The aforementioned noun endings “-s”, “-es” and “-ves” are known as morphemes and are the smallest unit of meaning, and they add a pluralized meaning to nouns.(Berko, 159) The grammatical number is used extensively in understanding and producing these morphemes, and therefore the morphemes are an essential part of pluralization. As you may have noticed by now, all the plural morphemes had a feature in common, they all contain the letter “s”. The grammatical number is also important on the way we physically produce the sounds to pluralize words. The “s” sound is known as an alveolar fricative. The “alveolar” specifies that the sound is made at the alveolar ridge, the bumpy area right behind your upper set of teeth. The
  5. 5. “fricative” means that the person creates a narrow passage of air, and the friction of the air and the narrow passage makes the sound. There are two different types of alveolar fricatives, the voiced alveolar fricative, and the unvoiced alveolar fricative. An example of a voiced alveolar fricative is the word “dogs” which is pronounced more like the word “dogz”. If a sound is voiced, it means that the vocal chords continue to vibrate if you hold the sound. If you say the word “dogs” and continue to hold the “s” at the end, and then you place your hand on your neck, you will feel your vocal chords vibrating. This is contrasted with a unvoiced alveolar fricative, an example of which is the “s” at the end of the word “cats”. If you place your hand on your throat while saying cats, you will feel no vibrations. Since grammatical number effects the way we pluralize words, it also then effects the movements that we make in our mouths to produce plural morphemes. Robert Manell, The Articulation of Fricatives, 2001 http://clas.mq.edu.au/ phonetics/phonetics/ consonants/fricatives.html Figure 4
  6. 6. I’m sure by now the concept of the grammatical number might seem very simple to you, as long as you have more than one object in a set its pluralized right? While this is true for the model of the grammatical number, it conflicts with another process known as enumeration. Let’s say that you are given two separate unique sets of items. You are not allowed to explicitly count the number of objects in each of these sets, but you wish to compare the number of items in each set. We can then deem this specific characteristic of number which differentiates between the two sets as the numerosity When figuring at the numerosity of an object, we can search with relative numerosity( seeing if one set has a greater number or a fewer number of items in comparison to another set), or we can search with the absolute numerosity (where we examine the specific number of objects given as an integer value)(Kaufman, Lord, Reese, and Volkman, 498). Forms of numerosity include estimation and subitization, but before we define those terms, lets examine counting. Counting is the process that everyone is accustomed to. It is a serial process which allows a person to determine the numerosity of a set, In order to specify the numerosity of any group we have to successively pair each object in the group with a numeral from the numeral-series, beginning of course with the first number in the series. This operation we call counting.(Kaufman, Lord, Reese, and Volkman 500). Counting is usually done by increments of one, but it is also not uncommon to count in groups of two, three or four. Estimation is the first major form of enummeration. It is an educated guess as to how many of an object is contained within a set. The more objects there are in a set that a person is estimating, the less accurate the estimation will be, and the less confidence the person estimating will have. If a subject is asked to state the numerosity of a set containing greater than four objects, it is considered estimation. Subitization is the second major form of enummeration that we’ll discuss. It’s
  7. 7. etymology stems from the latin verb subitare which means “to arrive suddenly”. It is believed to be a parallel process dependent on the total number of objects in a set being less or equal to three(though there is a dispute whether it incorporates four). First proposed by Kaufman, Lord, Reese, and Volkman in the 1949 paper The Discrimination of Visual Number, subitization deals with the rapid, confident, and accurate assessment of enummeration on a set of objects containing three or less objects. Counting, estimation, and subitization are used in conjunction with each other in order to figure out the conceptual number. The conceptual number is what it sounds like, it is the idea of an number, but is not dependent on language. To most people, having two different mechanisms of numerosity may seem strange, but both are necessary in order to pluralize speech. As an English speaker, it becomes obvious that you would pluralize a word as long as there is more than one of an object in a set, but in doing so, you you are ignoring information about numerosity that the brain is giving you. It is hypothesized that English speakers ignore the process of subitization, because they only need to know that there is more than one of an object, but there needs to be more research done before we can come to a conclusion. This gap in the knowledge is what we intend to fill. There is further evidence of conceptual number usage that can be observed throughout the developmental stages of childhood. Famed psychologist Jean Piaget believed that a child’s mind was a blank slate, and that children learned enummeration through sersory-motor interactions with objects around them. Piaget cited a child’s likelihood to think that two sets of similar numbered objects could be thought to have differing numerosities when one of the sets was spaced further apart than the other. For example, if you had a set of four marbles, each spread three inches apart from each other, compared to a set of four marbles each spread four inches away from each other, the child would say that the set that contained the marbles that were each four inches apart would have a higher numerosity. It is important to note that these children were at
  8. 8. least five years old because they all implicitly had knowledge of the grammatical number. (Dehaene, 42) Piaget ideas were proven incorrect by Mehler and Bever in their 1967 paper Cognitive Capacity of Very Young Children. They hypothesized that part of the reason that children fell prey to picking longer or bigger sets was that the children could not understand exactly what the experimenters were asking them to do. They also thought that another major problem was that there was no motivation for the children to try to know the numerosity of sets. Mehler and Bever then set up an experiment where the told children aged from two to four to decide which set of clay pellets had more members. The results were the same as Piaget’s experiments. They then replaced the clay pellets with similar looking M&M’s and told to the children to pick one of the rows and eat as many pieces of candy from that row as they wanted. The rows consisted of a spread out row of four M&M’s and a close row of six M&M’s. What they discovered was that the children would consistently take the shorter rows which contained more M&M’s. Mehler and Bever then concluded that motivation was necessary and that Piaget’s test could not correctly measure a child’s numeric aptitude. What was also amazing was the fact that the subjects for the study included children who were as young as two years old, but still managed to pick the shorter rows which contained more M&M’s. This study shows that children who have not mastered speech have a knowledge of the conceptual number, which strongly suggests that conceptual number and grammatical number are two independent mechanisms. Conceptual number can also be seen in the youngest of children. In 1983, Sue Eleen Antell and Daniel Keating set up an experiment where they had 21 to 144 hour old babies look at a card with two dots on it. The subsequent cards either had less area between the two dots, or had three dots occupy the space. The experiment measured the amount of time that the babies would look at the cards. This measure is significant becaue babies tend to spend a longer time looking at objects they don’t expect to be
  9. 9. there. What they found is that even though the length of the row of dots was similar, the babies could still differentiate the numerosity of the dots. This study is extremely important because it shows that infants have knowledge of the conceptual number before they they even acquire and produce language! If you examine the years of publication of the journal articles cited in this paper, you way notice that the some are quite old, but none of the papers discuss both grammatical number and conceptual number. This is notable because while grammatical number and conceptual number may be two separate mechanisms, they could influence each other. This leaves room for many new and exciting discoveries in the field. The only published paper regarding both grammatical number and conceptual number is entitled Computation of Semantic Number from Morphological Information by Iris Berent, Steven Pinker, Joeseph Tzelgov, Uri Bibi, Liat Goldfarb in 2005. They discovered that people gather the grammatical number from words the same way that people gather the conceptual number from visual cues, and that while they are separate, they are both essential for speech. It is important to note that the aforementioned study was in Hebrew and no comparable study has ever been conducted in English. We cannot assume that the results of the study would be applicable to English because Hebrew pluralizes in a different way than English does. In the 1930’s, linguist Benjamin Whorf and his mentor Edward Sapir proposed a new theory in linguistics, linguistic relativity. Linguistic relativity states that language dictates the way in which we perceive the world. This is why we must conduct language experiments in English to understand the grammatical number and conceptual number in English speakers. Since each language is different, we cannot look at the results of experiments conducted in other languages( for example, Hebrew in the previous experiment) and assume that they apply to English in the same manner. There are however similarities between all the languages in the world and Whorf and Sapir Whorf had been studying various Native American tribes and a famous example of linguistic
  10. 10. relativity is the language of Eskimos. Whorf stated that since Eskimos had a couple of hundred words for the English word “snow”, that the Eskimos could perceive differentiations in snow that English speakers could not. This was later proven false when it turned out that the Eskimos simply had compound words for strings of English words( for example, “heavy, wet, snow” would be a compound word different from “heavy snow”). Another example is with color terms. Paul Kay and Brent Berlin published a book in 1969 entitled Basic Color Terms: Their Universality and Evolution. The book outlined their theory that there is a sequential order of color term acquisition Each row signifies one color. The arrows indicate the progression of language if you have another color term in a language. For example, the 2nd box has 3 colors because the color white/red/yellow differentiates into white and red/yellow A Typological and Evolutionary Scheme Covering Most World Color Survey Languages (Source: Kay and Maffi 1999, Figure 3.) This graph shows how languages differentiate color. In the first box, we see that all languages have at least two colors groups, and if a language were to have three color terms, the first stand-alone color is white. Not all languages have all the colors however. The Berinmo tribe is located in Papua New Guinea who only have five color terms, but we know that they do not see in just five colors, they just do not differentiate names for colors like English speakers do. In Russian, there a completely separate term for light blue (sinij) then there is for a dark blue (goluboj). The same can be said about number terms in regards to plurality. For example the Togan tribe has “duals” which can be contrasted with singular and plurals that are found in English. Duals are nouns that have different endings than the same word in its singular form. We don’t have any in
  11. 11. English, but imagine that the word “dogen” appeared in English and its definition was “2 dogs” This would be different than it’s singular form “dog” and it’s plural of 3 or more, “dogs”. We know that the speakers of Tongan subitize in order to create duals but we know that their perception of two objects is the same as ours, even though we don’t have duals. If the theory of linguistic relativity is true, it is essential that we conduct research attempting to figure out if the grammatical number and the conceptual number share the same mental resources in English speakers At this point, you might be wondering what the point of studying plurality is and why we spend government money researching it. It is estimated that we use grammatical number and conceptual number once every five seconds or once every 16 words in active speech! This cognitive system is used thousands of times daily, yet we do not understand this commonly used process. By researching this topic, we are hoping to understand this particular cognitive model, and hopefully it will help us to understand other models of the brain, which is the goal of cognitive science.
  12. 12. Works Cited Antel, Sue Ellen; Keating, Daniel P. (1983) Perception of Numerical Invariance in Neonates Child Development, 54, 695-701 Berent, I; Pinker, S; Tzelgov, J; Bibi, U; & Goldfarb, (2005) Computation of Semantic Number from Morphological Information Journal of Learning and Memory, 53, 342-358 Berko, J. (1958) The Child's Learning of English Morphology. Word, 14, 150-177. Berlin, Brent & Kay, Paul (1969) Basic Color Terms: Their Universality and Evolution University of California press, Berkeley Bock, J. K., & Miller, C. A. (1991). Broken Agreement. Cognitive Psychology, 23, 45-93. Carroll, D. W. (2008). Psychology of Language. (5th ed.). Superior: University of Wisconsin. Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The Discrimination of Visual Number. American Journal of Psychology, 62, 498-525. Mehler, Jacques & Bever, Thomas (1967)Cognitive Capacity of Very Young Children Science 158, 141 - 142 Magill's Medical Guide Revised Edition. Salem Press, 1998: 221 Pinker, S. (1994). The Language Instinct: How the Mind Creates Language. New York,
  13. 13. : William Morrow and Company, Inc.

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This is my honors Bachelor's thesis from the University of Illinois Urbana-Champaign which covers Semantic Numerosity.

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