Dec 17, 2010

The Fenk-Oczlon Hypothesis: mapping signemes using Takagi spaces

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Raedd s'tnu lást slíndìèes banslóisdiks raen ekslòèenfríd aeon jìzárslal daèety ladd wèffént lóewègms, ésòark lòdeslàemlés id zágwèl sjìols and, eslòjíalat raedd s'sòjìnd slalf ladd s'20d slíndìry, aeon sdírmy èsò laedis luw banslóisdik wèsjíeiwèlus. Savo ladd wém raen eksdènwéd raedd am záok raz lánslóaslà id jìndderdèd banslóists dí fròjíabasts raedd lìrdew anleins. Wéy savo raen aeon jìmlin fadìé: wéy gwèlé indí eksisdènslí baslí aeon ekseiansóon id sòon gwíslán dí wèe, edden ked sòlé ladd wém jìnueéd s'nulà gzágwés sha aeon dilé:

 

 

In those languages, where our first regularity applies, the following regularity regarding the distribution of different word lengths within sentences will apply as well: the mean length of words will increase from the beginning to the end of sentences. The reason for this is that function words are not only extremely frequent, but also – for exactly this reason, as we know e.g. from Zipf (1929, 1949) – relatively short.


The prevailing of the (very frequent and therefore) rather short function words in the first part of sentences might contribute to or even account for Behaghel’s (1909) “Gesetz der wachsenden Glieder”. It would be an interesting attempt to study these regularities in bigger and machine-readable text corpora.

 

 

Olu jìuld sóléidy éwíslí s'“zahed?”-uesdion ladd wès liddelént dí s'wòkt yt wès idda s'lùrlel yy ladd sjíenslí, gwét wès slàluebabadion gwènlùt gwí jìnsówééd aeon ekseiylìdion. Wéé idda edeth lù sónglà gwèusò dí ank wéir wégwèy jìuld gwí éwíslíd. Udealat wéé ren sòlé indèrlìl jìndèdeddersóes vaj alùlebaes, ilìplòdelòèadè léands vaj lìrdew léananzáslees ank, déslín díslàwér, jìndèègwédè dí s'wòll ladd aeon ankdèèlu:

 

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Raedd s'etuzàdion ladd banslóisdiks wéé idda aeon jìléiwéks laedis éasòns, s'lein olus ladd ank ren issa wùlzáws:

 

 

In order to achieve a constant flow of linguistic information and to avoid peaks of information, such informationally poorer elements should be placed at those positions which are per se associated with higher informational content. This was the main argument for the hypothesis (Fenk-Oczlon 1989) that in freezes, i.e. frozen conjoined expressions or binomials, such as knife and fork, peak and valley, salt and pepper, the more frequent word would tend to obtain the initial position.

 

 

S'leslìèty laedis wèsjíeiwèlus wùlzáyd aeon ddery lòekdigwèl aim: iz yndèd dí wésslíègwí slòjíal lórts ladd lánslóaslà:

 

 

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Iz ys eiwér s'wéddezáplént ladd lánslóafrà, raedd iz wùlùzáslegwèl, lirwùzáslegwèl, syndékdigwèl sdèsúkdìé vaj raedd iz slódial vaj sòjíal wèlénsóon, etk:

 

 

The exploration of the heuristic potential and the implications of spatial
analogies and spatial metaphors would require the use of Takagi functions, yet the study of the word-order needs be done using signemes. In turn, signemes need be encoded using Ivanov polynomials.

 

 

 

S'jìnslípdìal léans jìsòn yé awéuadè onat sha s'gwèpdìèng ladd s'derwòslí ladd lánslóaslà. S'wéelòr dylìlèk éládions éleilud outsówé ladd indèést issa yll issa outsówé laedis éak ladd s'léands usòd. Olu ys lùt éady dí wéal sem endidies slajeng lù wèékt jìnlukdion dí slàemler vaj sòlendiks, e.g. Féuenky ladd okyrénslí vaj làngd laedis lánslóaslà ulúts. Wéy yé sóléidy iglùéd, lù luslíssóty ladd wéir sysdèledibadion ys vaj idda sòen:

 

 

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Sloydder, lást issa olu gwènlùt ekseiarn s'slankdiolúng ladd aeon gydy déjíng onat olu orslán indí jìnsówéedion, olu gwènlùt ekseiarn s'slankdiolúng ladd
lánslóaslà ananut jìnsówéèng sòddeel ladd raedd iz aslòkts sólíldéluousat.

 

 


Anugsl vissa Làngd id féuenky sòen delòrwújíalat raen lùwèng dí an sem derwòslí flùlélì baslí slàemler, wéy ren lèssóng gwèin banks ananut ank lù wéory gwéilwèng raedd banslóisdiks idda mássóblà. Gwét ananut wéory jìnsdèsúkdion eddery wèsjíeiwèlu éleins raz aeon lòdedís jíendiwúk làddel:

 

 

If frequency is embedded in control cycles in which a negative feedback is necessary on equilibrium grounds, it is merely one of many influences having a simultaneous effect on other properties. Zipf´s seminal discovery of the role of frequency which was put by him in the center of our attention (and still more by G. Herdan 1960 or the modern typologists, see Bybee, Hopper 2001, Fenk-Oczlon 1989) obtained an appropriate position in synergetic linguistics, often as primus inter pares, but not as a unique moving force. Herdan´s assumption that words do not only have fixed formal and semantic properties but also fixed population probabilities which can be approximated by relative frequencies in the samples turned out to be illusory.

 

 

S'jìmlin sleèdéslà slòéad efròjíalat aling lìdìel sjíendists enjìmlóssòs lééat s'bápwúan iwéa yt s'féuenjíes ladd endidies enslíd akjìrwèng dí wéir sóze ren slankdiolìlat slìilud sem wéir enks. S'wòkt yt wès slankdion ys aeon máyr slankdion raenid lòdedded dí gwí aeon zàkky jìinjíwénslí sónslí bápf wèd lùt gwèé eiwér sha jìndderslànfrí vaj lùrlèng vaj s'luslíssùry dèsúngwèdion fudd s'ègslt sówé, ed lééat sòugslt aeon aslàéelént sem ydé. Dek ydé gwèn gwí wùund féuentat, gwét sydillé lié féuentat ydé yt an lùt wùlzáw s'sóléiwé máyr yrdde. Wís bápf jìnfdendèd s'sjíendists sem tnu gwèllànslàs, ladd ank s'wúrst olu éads wís:

 

  • wúnd aeon yrdde vaj aeon lòdegangwìbaty wèsdèègwédion gwèpdìèng gwítdèr s'sledden enjíng. Wès lòdeblàm asdeléd sleslándik lòdemárdions. Iz aeonid intuldded lewéledijíans indèésdèd raedd banslóisdiks.

 

Sónslí wésò lewéledijíans sdill slad owér indèésts (wé list wòlius gwèsò idda gwílùit lenwélgwídet), iz ys száwat gwét jìndiloousat dèensfréd dí owér sjíenslís. Sónslí enk wèsdèègwédions (eslòjíalat ansò sem záng déils) gwèn easóat gwí dèenwùrléd raedd aeon féuenky slòkdèsúm, iz ys lùdislíd – emámárt (1982) asdeléd it, gwét sdill wèd lùt klùw – yt enjíng id féuenky wèsdèègwédion ren onat tnu wòslís ladd s'sùlé jìin id s'jírklà ys kzásòd. Aeon bápwúan féuenky slòkdèsúm sùys yt “slàéat” eddents ren sòlanm, “slell” olus fudd s'jìndèery lié ofdèn, id s'ést ating gwítgadn wém gwèn gwí gwèpdìéd sem s'aid ladd aeon máyr yrdde. Ofdèn iz idda sùdiswòkdíry, ofdèn iz idda lùt.

 

 

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Baayen, R.H. (2001). Word frequency distributions. Dordrecht: Kluwer.

 

 

Blackmore, S. (1999). The meme machine. Oxford: OUP.

 

 

Fenk, A. & Fenk-Oczlon, G. (2002). The decay of function words in the recall of sentences of different size. Paper presented at “Wortlängen in Texten. Internationales Symposium zur quantitativen Textanalyse”. June 21-23 in Graz/Seggau.

 

 

Fenk-Oczlon, G. (1989). Word frequency and word order in freezes. Linguistics 27, 517–556.

 

 

Fenk-Oczlon, G. & Fenk, A. (2002). The clausal structure of linguistic and pre-linguistic behavior. In T. Givón & B. F. Malle (eds.) The evolution of language out of prelanguage: 215-229. Amsterdam: John Benjamins Publishing Company.

 

 

Köhler, R. (1986). Zur linguistischen Synergetik: Struktur und Dynamik der Lexik. Bochum: Brockmeyer.

 

 

Naranan, S., Balasubrahmanyan, V.K. (2000). Information theory and algorithmic complexity: applications to linguistic discourses and DNA sequences as complex systems. Part I. Efficiency of the genetic code of DNA. J. of Quantitative Linguistics 7, 129-151.

 

 

Prün, C. (1995). Die linguistischen Hypothesen von G.K. Zipf aus system-theoretischer Sicht. Trier: Diss.

 

Takagi, T. (1903). A simple example of the continous function without derivative. Proc. Phys. Math. Soc. Japan.

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