## 1 9/4/05 Mathematics and Narrative

### BibTeX

@MISC{Turner_19/4/05,

author = {Mark Turner},

title = {1 9/4/05 Mathematics and Narrative},

year = {}

}

### OpenURL

### Abstract

For over two millennia, it has seemed irresistible to imagine that the essence of all reality lies in numbers, and that a transcendent system of mathematics, if we could only know it synoptically, cosmically, would provide the answers to our questions. The Pythagorean insight that the capacious and sensory world of music is an avatar of ratios of numbers, and that, as a result, melody and harmony carry mathematical patterns, must have seemed like a revelation. The idea that mathematics lies somehow behind everything has motivated inquiry since the Ancient Greeks. If music—from Pythagoras to fractals—can be mathematics, and the heavens and their motions can be mathematics, perhaps human biology and even the soul are mathematical systems, to be tuned like stringed instruments to their perfect order. This impulse to seek the essence of reality in mathematics is compelling. As an undergraduate student, I hoped to find within mathematics some technical instruments sufficient to describe the human central nervous system and the brain. The impulse to do so was not mystical or merely reductionistic. The human brain has on the order of 10 to

### Citations

485 |
Constructions: A Construction Grammar Approach to Argument Structure
- Goldberg
- 1995
(Show Context)
Citation Context ...e domain of language. One of our most basic small spatial stories is Caused Motion: an agent performs an action that causes an object to move in a direction, as in "He threw the ball over the fence" (=-=Goldberg 1995-=-). This is associated in English with the Caused-Motion construction, whose basic form is NounPhrase-VerbPhrase-NounPhrasePrepositionalPhrase. But we can make sense of many things that are not caused ... |

252 | Neural Darwinism: The theory of neuronal group selection - Edelman - 1987 |

169 | Morphology of the folktale - Propp - 1968 |

128 | From Etymology to Pragmatics: Metaphorical and Cultural Aspects of Semantic Structure - Sweetser - 1990 |

117 | The Remembered Present: A Biological Theory of Consciousness - Edelman - 1987 |

113 | Conceptual integration networks - Fauconnier, Turner - 1998 |

72 |
Mappings in Thought and Language
- Fauconnier
- 1997
(Show Context)
Citation Context ...ilities for mathematical thought. Blending and the Human Mind What is blending? (Technical introductions to the nature and mechanisms of blending can be found in Fauconnier and Turner, 2002 and 1998; =-=Fauconnier 1997-=-; Turner 2001 and 2005. See also Goguen 1999.)s5 9/4/05 Let us begin with an example. A man is participating in a wedding. He is consciously enacting a familiar mental story, with roles, participants,... |

64 |
An introduction to algebraic semiotics, with applications to user interface design
- Goguen
- 1999
(Show Context)
Citation Context ...he Human Mind What is blending? (Technical introductions to the nature and mechanisms of blending can be found in Fauconnier and Turner, 2002 and 1998; Fauconnier 1997; Turner 2001 and 2005. See also =-=Goguen 1999-=-.)s5 9/4/05 Let us begin with an example. A man is participating in a wedding. He is consciously enacting a familiar mental story, with roles, participants, a plot, and a goal. But while he is fulfill... |

46 |
Mathematics: The Loss of Certainty
- Kline
- 1980
(Show Context)
Citation Context ...nto a directed line, complex numbers could be mapped onto points in a twodimensional plane. He provided geometric constructions for the counterparts of the real or complex roots of ax 2 + bx + c = 0 (=-=Kline 1980-=-, page 272). In effect, Wallis provided a consistent model for the mysterious numbers, giving some substance to their formal manipulation. Although Wallis's mapping showed the formal consistency of a ... |

5 | The Literary Mind: The Origins of Language and Thought - Turner - 1996 |

2 |
Cognitive Dimensions of Social Science: The Way We Think About Politics
- Turner
- 2001
(Show Context)
Citation Context ...matical thought. Blending and the Human Mind What is blending? (Technical introductions to the nature and mechanisms of blending can be found in Fauconnier and Turner, 2002 and 1998; Fauconnier 1997; =-=Turner 2001-=- and 2005. See also Goguen 1999.)s5 9/4/05 Let us begin with an example. A man is participating in a wedding. He is consciously enacting a familiar mental story, with roles, participants, a plot, and ... |

1 | The Phantom Tollbooth. NY: Random - Juster - 1961 |

1 | Linear Design." Narrative Design: A Writer's Guide to Structure - Bell - 1997 |