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Dimensional Analysis

Dimensional Analysis

The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...

Dimensional Analysis

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Related Experiment Video

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

The dimensionality of discourse.

Isidoros Doxas¹, Simon Dennis, William L Oliver

¹Center for Integrated Plasma Studies, University of Colorado, Boulder, CO 80309, USA.

Proceedings of the National Academy of Sciences of the United States of America

|March 3, 2010

Summary

This summary is machine-generated.

Paragraph structure across languages and genres reveals a consistent two-scale topology. This finding suggests universal constraints on how authors craft prose, impacting text dimensionality.

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Area of Science:

Computational linguistics
Text analysis
Literary studies

Background:

Understanding the underlying structure of written text is crucial for fields like natural language processing and literary analysis.
Previous research has explored various linguistic features, but a consistent topological analysis across diverse corpora is lacking.

Purpose of the Study:

To investigate the topological structure of paragraph spaces in text corpora of varying genres, audiences, and languages.
To determine if a consistent dimensionality pattern exists across different textual contexts.

Main Methods:

Analysis of five text corpora from different genres and languages.
Application of topological analysis to paragraph spaces.
Control simulations using randomly permuted word instances.

Main Results:

All five corpora exhibited a consistent two-scale structure in paragraph spaces.
The dimension at short distances was consistently lower than at long distances.
The short-distance dimension was approximately eight, and random permutations did not show this low-dimensional structure.

Conclusions:

The observed two-scale topological structure in paragraph spaces appears to be a universal feature of written prose.
This topology imposes significant constraints on authorial choices in text construction.
Findings suggest potential universal principles governing prose composition.