Is Word Order Asymmetry Mathematically Expressible?
The computational procedure for human natural language (CHL) shows an asymmetry in unmarked orders for S, O, and V. Following Lyle Jenkins, it is speculated that the asymmetry is expressible as a group-theoretical factor (included in Chomsky’s third factor): “[W]ord order types would be the (asymmet...
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| Format: | Article |
| Language: | English |
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PsychOpen GOLD/ Leibniz Institute for Psychology
2013-11-01
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| Series: | Biolinguistics |
| Subjects: | |
| Online Access: | https://doi.org/10.5964/bioling.8967 |
| _version_ | 1797338110977114112 |
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| author | Koji Arikawa |
| author_facet | Koji Arikawa |
| author_sort | Koji Arikawa |
| collection | DOAJ |
| description | The computational procedure for human natural language (CHL) shows an asymmetry in unmarked orders for S, O, and V. Following Lyle Jenkins, it is speculated that the asymmetry is expressible as a group-theoretical factor (included in Chomsky’s third factor): “[W]ord order types would be the (asymmetric) stable solutions of the symmetric still-to-be-discovered ‘equations’ governing word order distribution”. A possible “symmetric equation” is a linear transformation f(x) = y, where function f is a set of merge operations (transformations) expressed as a set of symmetric transformations of an equilateral triangle, x is the universal base vP input expressed as the identity triangle, and y is a mapped output tree expressed as an output triangle that preserves symmetry. Although the symmetric group S3 of order 3! = 6 is too simple, this very simplicity is the reason that in the present work cost differences are considered among the six symmetric operations of S3. This article attempts to pose a set of feasible questions for future research. |
| first_indexed | 2024-03-08T09:26:21Z |
| format | Article |
| id | doaj.art-c69389ca8c25483d92bc886f23bf7ff6 |
| institution | Directory Open Access Journal |
| issn | 1450-3417 |
| language | English |
| last_indexed | 2024-03-08T09:26:21Z |
| publishDate | 2013-11-01 |
| publisher | PsychOpen GOLD/ Leibniz Institute for Psychology |
| record_format | Article |
| series | Biolinguistics |
| spelling | doaj.art-c69389ca8c25483d92bc886f23bf7ff62024-01-31T09:59:34ZengPsychOpen GOLD/ Leibniz Institute for PsychologyBiolinguistics1450-34172013-11-01727630010.5964/bioling.89678967Is Word Order Asymmetry Mathematically Expressible?Koji Arikawa0St. Andrew's University, Osaka, JapanThe computational procedure for human natural language (CHL) shows an asymmetry in unmarked orders for S, O, and V. Following Lyle Jenkins, it is speculated that the asymmetry is expressible as a group-theoretical factor (included in Chomsky’s third factor): “[W]ord order types would be the (asymmetric) stable solutions of the symmetric still-to-be-discovered ‘equations’ governing word order distribution”. A possible “symmetric equation” is a linear transformation f(x) = y, where function f is a set of merge operations (transformations) expressed as a set of symmetric transformations of an equilateral triangle, x is the universal base vP input expressed as the identity triangle, and y is a mapped output tree expressed as an output triangle that preserves symmetry. Although the symmetric group S3 of order 3! = 6 is too simple, this very simplicity is the reason that in the present work cost differences are considered among the six symmetric operations of S3. This article attempts to pose a set of feasible questions for future research.https://doi.org/10.5964/bioling.8967costeconomyequilibriumgalois groupgeometrysymmetrythird factortransformationunmarked word order |
| spellingShingle | Koji Arikawa Is Word Order Asymmetry Mathematically Expressible? Biolinguistics cost economy equilibrium galois group geometry symmetry third factor transformation unmarked word order |
| title | Is Word Order Asymmetry Mathematically Expressible? |
| title_full | Is Word Order Asymmetry Mathematically Expressible? |
| title_fullStr | Is Word Order Asymmetry Mathematically Expressible? |
| title_full_unstemmed | Is Word Order Asymmetry Mathematically Expressible? |
| title_short | Is Word Order Asymmetry Mathematically Expressible? |
| title_sort | is word order asymmetry mathematically expressible |
| topic | cost economy equilibrium galois group geometry symmetry third factor transformation unmarked word order |
| url | https://doi.org/10.5964/bioling.8967 |
| work_keys_str_mv | AT kojiarikawa iswordorderasymmetrymathematicallyexpressible |