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Geometry and Meaningby: Dominic Widdows
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Notes for this articleRight on!
"Once a field finds its math, they begin to feed on each other and coevolve. Old scientific puzzles get satisfactory explanations, new puzzles inspire further developments in math, and the math points to new questions in the science---to what else might be true and worth investigating. That is how physics, for example, has become so thoroughly mathematical.
Can this happen with anything as rich, varied, and complex as human thought and language? My guess is that it will once the appropriate math has been found, and the key is that it be appropriate."
From the foreword by Pentti Kanerva http://infomap.stanford.edu/book/chapters/foreword.html
The perfect agenda, just do it...
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Abstract<div>From Pythagoras's harmonic sequence to Einstein's theory of relativity, geometric models of position, proximity, ratio, and the underlying properties of physical space have provided us with powerful ideas and accurate scientific tools. Currently, similar geometric models are being applied to another type of space--the conceptual space of information and meaning, where the contributions of Pythagoras and Einstein are a part of the landscape itself. The rich geometry of conceptual space can be glimpsed, for instance, in internet documents: while the documents themselves define a structure of visual layouts and point-to-point links, search engines create an additional structure by matching keywords to nearby documents in a spatial arrangement of content. What the <i>Geometry of Meaning</i> provides is a much-needed exploration of computational techniques to represent meaning and of the conceptual spaces on which these representations are founded.<br><br></div>
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