The gravity of meaning: Physics as a                                  metaphor to model semantic changes                  ...
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The gravity of meaning: Physics as a metaphor to model semantic changes

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Based on a computed toy example, we offer evidence that by plugging in
similarity of word meaning as a force plus a small modification of
Newton's 2nd law, one can acquire specific "mass" values for index
terms in a Saltonesque dynamic library environment. The model can
describe two types of change which affect the semantic composition of
document collections: the expansion of a corpus due to its update, and
fluctuations of the gravitational potential energy field generated by
normative language use as an attractor juxtaposed with actual language
use yielding time-dependent term frequencies. By the evolving semantic
potential of a vocabulary and concatenating the respective term
"mass" values, one can model sentences or longer strings of
symbols as vector-valued functions. Since the line integral of such
functions is used to express the work of a particle in a gravitational
field, the work equivalent of strings can be calculated.

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The gravity of meaning: Physics as a metaphor to model semantic changes

  1. 1. The gravity of meaning: Physics as a metaphor to model semantic changes Sándor Darányi and Peter Wittek Sandor.Daranyi@hb.se, peterwittek@acm.orgK EY POINTS T HE METAPHOR • Index terms and term mass; This representation has the following advantages: • Newton’s 2nd law and deterministic me- • It utilizes physics as a metaphor to model the dynamics of chanics; language change; • Velocity and acceleration of language • It demonstrates the connection between sentence structure change; and work carried out in a field based on classical (Newto- nian) mechanics, i.e. is feasible to quantify the work con- • Work in a gravitational field. tent in documents; • It models such a field as the gravitational potential energyF UTURE W ORK terms possess in the presence of language norms, with sim-The current model yields variable term mass ilarity as a force between pairs of them as the gradient ofover observation periods, which departs from the above potential;its roots in classical mechanics. Although ul- • It naturally bridges the gap between language analysis andtimately language may show different ‘symp- language generation.toms of behaviour’ as physics does, we areworking on an alternative to yield constantterm mass values, leading to scalability tests Based on a computed toy example, we offer evidence that by plugging in similarity of word mean-and evaluation of the new model. ing as a force plus a small modification of Newton’s 2nd law, one can acquire specific ‘mass’ val- ues for index terms in a Saltonesque dynamic library environment [2]. The model can describeSecondly, we want to visualize the evolving se- two types of change which affect the semantic composition of document collections [1]: the ex-mantic potential fields of document collections pansion of a corpus due to its update, and fluctuations of the gravitational potential energy fieldto understand the nature and importance of generated by normative language use as an attractor juxtaposed with actual language use yieldingsuch fields for sentence construction as an en- time-dependent term frequencies [3]. By the evolving semantic potential of a vocabulary and con-ergetic process. catenating the respective term ‘mass’ values, one can model sentences or longer strings of symbols as vector-valued functions. Since the line integral of such functions is used to express the work of a particle in a gravitational field, the work equivalent of strings can be calculated.R ESULTSEvolution of an indexing vocabulary over time Calculation of term mass over t0 -t2 t = 0 Doping Football Performance Skiing Training Doping Football Performance Skiing Training d1 5 2 0 0 0 v1 9 9 0 25 36 d2 4 0 0 3 1 v2 49 49 4 16 0 d3 0 0 4 0 5 a 40 40 4 -9 -36 d4 6 0 2 0 0 F 1.56 1.28 1.24 1.35 1.37 d5 0 3 0 0 4 m 0.039 0.032 0.31 0.15 0.038 t=1 d1 5 2 0 0 0 d2 4 0 0 3 1 d3 0 0 4 0 5 d4 6 0 2 0 0 d5 0 3 0 0 4 d6 2 3 0 1 1 d7 1 0 0 4 5 t=2 d1 5 2 0 0 0 d2 4 0 0 3 1 d3 0 0 4 0 5 d4 6 0 2 0 0 d5 0 3 0 0 4 d6 2 3 0 1 1 d7 1 0 0 4 5 d8 5 6 1 1 0 d9 2 1 1 3 0R EFERENCES M ORE INFORMATION[1] A. Baker. Computational approaches to the study of language change. Language and Linguistics Compass, 2(3):289–307, 2008. Related papers and more infor-[2] G. Salton. Dynamic information and library processing. 1975. mation are available at[3] H. White. Cross-textual cohesion and coherence. In Proceedings of the Workshop on Discourse Architectures: http://www.squalar.org/ The Design and Analysis of Computer-Mediated Conversation, Minneapolis, MN, USA, April 2002.

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