Character (mathematics)

About: Character (mathematics) is a research topic. Over the lifetime, 46723 publications have been published within this topic receiving 411412 citations.

Orientation of letters and errors in their recognition

Abstract: Subjects named alphabetic characters that had been rotated, reflected, or inverted. Inversions induce more errors than mirror reflections and reflections induce more than rotations. In a significant number of mistakes a transformed character was assumed to be normally oriented, but in most a transformed character was confused with the mirror image of the original. The data suggest the existence of an “orientation set” in which the identiflcation of ambiguous characters depends largely on their anticipated orientation. The individuality of the data for the different orientations suggests that different transformations are compensated for in part by different mechanisms.

Mechanisms of Belief-Desire Reasoning Inhibition and Bias

Abstract: Biases in reasoning can provide insight into underlying processing mechanisms. We demonstrate a new bias in children's belief-desire reasoning. Children between 4 and 8 years of age were told a story in which a character was mistaken about which of three boxes contained some object. The character wanted to go to one of the boxes, but only if it did not contain the object. In this scenario, the character would be expected to avoid the box where she falsely believed the object to be, but might go to either of the remaining boxes. Though the character was equally likely to go to either box, children were biased to predict that the character would go to the box that contained the object. In a control task, the character had the same desire but did not have a false belief; in this case, children showed no bias, choosing the two correct answers equally often. The observed pattern of bias was predicted by a developmental model of belief-desire reasoning. Competent belief-desire reasoning depends on a process of ...

Peirce on the Index and Indexical Reference

Abstract: Although the index is one of the best known features of Peirce's theory of signs there is little appreciation of Peirce's theory of the index amongst contemporary philosophers of language. The prevailing view is that the interesting early history of indexicals begins with Hans Reichenbach and his account of token-reflexivity (Reichenbach, 1947).1 Reichenbach maintains that an indexical like T means something like "the utter of this token". Although this seems intuitive enough, Reichenbach's account is undermined by its failure to capture the content of what we take ourselves to be saying in using indexicals. For instance, when John says, UI am thirsty", we take the content of John's utterance to be that John is thirsty. The token-reflexive theory suggests that the content of John's utterance is that the utter er of the token CV is thirsty. These two things are different. As for more current theories, David Kaplan's work (1969, 1978, 1979, 1989a and 1989b) provides the clearest account of indexical reference. Kaplan's account draws a famous distinction between character and content. Character is akin to a rule or simple linguistic meaning such that the character of T is "the utterer, or agent of the context". Content on the other hand is the meaning that arises from applying that rule, or character, to a particular context. So, in a context where John says, "I am thirsty", applying the character of T to that context will yield John as content. But, applying the character of 'I' to a context where I am the utterer or agent will yield me as content. In such cases, the character remains the same, but the content differs. Where, though, does Peirce's theory of the index fit into any of this? In short, there is no appreciation of Peirce's theory in Kaplan's work, although Kaplan does show some awareness of Peirce. For instance, when explaining his use of the word "index" for words like "I", "here", "now" etc. Kaplan says:

Complex character generator

Abstract: A character compaction and generation method and apparatus which is particularly adapted to the generation of complex characters such as Kanji characters. A dot matrix defining a given character is compacted into a sparse matrix, with the original character being reconstructed for printing or display from the compacted character defined in the sparse matrix. Each character in the complex character set is compacted and stored in memory one time only, with decompaction being performed each time a given character is to be generated. A set of symbols are defined to represent different patterns which occur frequently in the entire complex character set. Different combinations of the symbols define a given character. The information stored for each sparse matrix representing a given character is comprised of each symbol in the sparse matrix, its position, and its size parameter if the symbol represents a family of patterns which differ only in size. Three groups of different patterns are defined which occur frequently in the complex character set, namely, a first group which has a fixed size for each pattern, a second group which has one size parameter which must be specified for each pattern, and a third group which has a plurality of size parameters which must be specified for each pattern.