Language /An elementary 5-dimensional model applied in different sciences
- some reflections - 

What is syntax - or "grammar"?

It could be repeated here:

- It works as the binding force between parts of a sentence as "the whole".
As a binding force it represents a higher d-degree than the separate "words" in our model.

- It is a testimony of the multidimensional network in the brain connecting sense in sentences.

- It is the translation to linear order of motor articulation from this multidimensional sense.

This transformation is no easy task. In peoples' oral speech there may be many breaks, deviations, new starts of a sentence etc. To transform thought-nets to linear, written sentences may be one of the obstacles for many to express themselves literary.

Syntax concerns many levels as in a level chain, both the primary word class categories, in itself a whole dimension chain as proposed here, and the secondary and tertiary... ("fractional") developments within these word classes.
   As embracing many levels it gets a character of depth.

Such structures could be resembled with main roots and side roots of plants as "word-bushes" or word-trees with ramifications in mould of memory... - or the same above the ground: syntax then as a "high" level. What is got from the sky is of course equally necessary for the development of plants!

As a geometric illustration of complex structures we could perhaps use the pentagon: the 5-sided regular figure, which if all corners get connected with each other give new pentagons in the middle etc. (See figures at end of this file.)
   From all these aspects Syntax appears as a high-dimensional level as it was supposed to be, representing d-degree 4 in the big level chain.

However, syntax varies very much between different languages - also between closely related ones, and it changes over time, sometimes over few decades.
   We expect a deeper level of speech production to be more universal, showing more similarities, being closer to the unity of mankind. It obviously isn't. (At least in any simple sense.)

The opposites could perhaps be united if we look at the two gradients of the big level chain in analysing speech: D-degree 4 of syntax will correspond to d-degree 1 of phonemes, and d-degree 4 in the gradient from phonemes will correspond to d-degree 1 of syntax.

Sentences developed along a z-axis in the figure?

Phonemes and rows of phonemes are referred to "lexicon" and the most differentiating level between languages.
   Orders of phonemes are more closely coupled to semantic sense, much closer than word order and syntax: in Swedish: sak-ask-ska means "thing" - "box" - "shall". A "wrong" linear order of words in the syntax of a certain language may still be passably understood.

Sense as centre in one gradient develops to order of phonemes, here illustrated by the circles, which also may represent differentiations among languages. Phonemes as centres in the other gradient develop to semantic sense in opposite direction.
   Hence, syntax as a deep binding force among word categories (in the middle step) represents simultaneously very developed linear rows of phonemes. Syntax as more superficial, developed to linear structure, represents a deep, high-dimensional level of phonemes.

The gradients could be identified with the two opposite dimension chains of Structure and Motions (motions also geometrical characterized) in the dimension model applied here. Motions from phonemes (individual sounds). Structure from the whole sense:

A related aspect is that outer poles of d-degree 4 in our model are 0 and 00 of d-degree 5 (the "whole"). They define Direction. These poles meet in d-degree 0/00 of Motions (with poles out of d-degree 1 called "motions to and from each other").
   This could imply a direct jump to speech from 0/00 (equivalent 5'), viewed in synthesizing direction?
   Compare that the cranial motor nerve to the tongue departs from "mdulla oblongata", a very deep level in the brain (in many aspects representing d-degree 4 in analysis of levels of the brain; coming files.)
   In the two gradients the debranched degrees in the dimension chain of structure outwards will represent the phoneme sequences of motions in inward direction: 0-1-2-3-4-5.
   We have one (1) d-degree of motion in d-degree 4. (Proposed identified as L-waves on the physical level. Cf. the opposite directions in individual phonemes as implosive / explosive phases in Saussure's analysis.)
   This motion, proposed as linear in d-degree 4, may be interpreted as the start of sound rows in the opposite gradient from phonemes.
   Hence, sequences of phonemes in speech and development of the syntax in the other gradient and direction, could be expected as more or less simultaneous, parallel processes.
   There is of course nothing universal in which phonemes or word order of grouped ones that are picked from the stockpile. Yet, these views are perhaps part of the reasons why we could look at syntax as of high d-degree.

Syntactic elements as lexical pieces:

It has been suggested in an earlier file that the way a certain language expresses such things as genitive, plural, passive form, past tense etc. are stored in the brain as lexical pieces, this then making up a secondary level above the stores of nouns, verbs, adjectives...
   Note that the "lexical" gradient from phonemes and morphemes stretches along the whole gradient of levels to the developed sense, to the opposite gradient from Sense.
   It's an assumption here that children immediately apprehend whole situations and their immanent "grammar" - in the semantic interpretation of this word.
   Compare also some children's ability to talk backwards (CEL) - revealing a sense for an immanent or underlying duality in directions.

Thus, what may be universal in "grammar" would be that which is common in human minds: the geometrical sense in such categories as genitive, plural, passive form, past tense etc. - together with the conceptions corresponding to the more elementary word classes. Fundamental geometries expressing Direction - Mass, forms - Space, Locations - Time, Distances-Singular/plural and other such properties.
    (Different aspect from secondary and third levels of differentiations may be more or less developed by different groups.)

Hence, a genitive - or a plural - or a locative may be identified as universal pieces of grammar, corresponding to geometries which are interpretable in terms of the dimension model as proposed here. While the different ways to express genitives etc. in a language seems mainly "lexical" - having a deep history of developments behind it.

Chomsky has (earlier) seen syntax as a property of a certain language, independent of sense, as pure grammar. We can judge the construction of a sentence as grammatically wrong even it doesn't make sense.
   That's right to a certain degree. However, it obviously depends on our possibility to recognize what is meant to be nouns, verbs, adjectives etc. It's relying on the level of what we call primary word class differentiations. A simple row of not interpretable morphemes or "words" cannot be judged as ungrammatical.
   It's necessary to recognize geometries as such as having semantic sense.

The structure of our brains shows the same organization as the main "categories of aspects" in the radial ARAS system upwards towards cortex and a corresponding system downwards the body, in the "circular" cortex with transversal connections, in columns of nerve sells in cortex for special sensory/motoric areas etc. (About the brain in coming "Biology" files.)

One universal feature seems to be the need of a verb for a relating "full" sentence. "It is beautiful." Why "is"? Compare cries - first unbarred sounds. The need of a verb could be compared with the need of vowels among consonants for a single word.
   It has also a parallel in the pathways of signals in the brain through nerve fibres versus nerve cells as enclosed units.
   In Arabic much of the grammatical differentiations - belonging to Syntax - are said to be expressed in the vowels, while the substance of sense lies in the consonants (LB). Vowel changes in word stems of IE have the similar function.
   This aspect: vowels - verbs - syntax looks like an example of how d-degree 4 could be expressed in different steps of the big level chain, along the main axis of the two gradients. (About differentiation of phonemes here.)

Features of the dimension model: what could be universal:

a) That which is said above: the concepts behind "word categories" as fundamental aspects on the world.

b) The truism that verbs are connected with adverbs, nouns with their properties - per definition: in interpretations here:
   d-degree 4 with 1,
   d-degree 3 with 2.

(They may also be regarded as two different "levels": polarization 5 → 4 + 1 the deeper step.)
   It corresponds partly with division of sentences in noun phrases and verb phrases, the NP-VP-division. (One part of it the transformation from anti-parallel direction in d-degree 4 to a perpendicular relation in d-degree 3:

Two first things in the model allow obviously for differentiated syntax and word order:
   - Verbs may be apprehended as said above in d-degree 4 of Direction, or polarized into active, passive as poles of d-degree 3, or as radial connections subject - object in d-degree step 3-2 or as motions in d-degree 0/00 - or even as just linear in d-degree 1.
   - Nouns may be apprehended as 0-poles, first centres, or as encircled enclosed units in d-degree 3 (pole 3a) - or perhaps as "nounified" properties...

To these ambiguities come the 3 main directions in the chain: outwards - inwards - or vertical as in the loop model.

Linear order:

The "correct" linear, 1-dimensional order of a sentence should be the last factor established in Syntax, seen from the gradient of Sense.
   For instance: Starting with an adverbial: is the right order of noun and verb then V→-N or N → V in a certain language?
   A phrase like "Fortunately he didn't take that job" starts with an adverbial. The same phrase in Swedish grammar would be "Fortunately took he not that job".
   The division of sentences in noun and verb phrases (NP-VP) may tell us about underlying connections between parts of sentences but not about linear word order. A strong wish of an object may give the object first place.

Start of a sentence - what is needed?
- It needs some kind of purpose or aim, in this sense direction semantically.
- It needs verbs as it needs vowels, as written above.
- It demands surely too a "topic" as a kind of centre but not necessary as first word.
   Chomsky talks about the sovereign position of the Subject in a sentence, maybe pronouns developed to subjects, with nouns as centres. We could translate it here to the need of a 0-pole (with reference to Big Bang!). A 0-pole from which follows direction outwards. (It's implied also in the very act of speaking, opening the mouth for an utterance.) Some may however regard the direction outwards as the most essential happening.
- The start is obviously also depending on the speech situation, context, references - speech as answers, as re-actions.

Word order SVO... and attributes (LL):
Linguists have tried to group languages according to dominant use of word order for Subject - Verb - Object in main phrases. The order varies much within the same language family.
VSO: e. g. Celtic, Arabic, Maori)
SOV: e. g. Persian, Turkish, Japanese)
SVO: e. g. most IE languages, Finnish-ugr., Chinese)
Hence alternatives:

It seems to agree approximately with what could follow as possibilities from our dimension chain of word classes above - and may also depend on the ambiguities mentioned above in interpretations of verbs and nouns in the model here.
   Something of a trend has been found in the position of attributes (A) in these 3 word orders (LL): In VSO: A after, in SOV: A before, in SVO: A before or after. It just seems as a natural trend to place attributes close to the noun classes S and O, if possible away from the verbs. (?)

Such a dominating order (among V, S, O) may perhaps be regarded as the typical one in a certain language for construction of a "telling" phrase, a statement. Then through "transformational rules" (NC) give all other possible phrases in that language? This approach however concerns obviously a certain language, not universal features.
Are there any "universals" in the very principle for these transformations? As a stepwise rearrangement?

Order of steps in the proposed dimension chain for word classes has of course no simple connection with word order in typical sentences, if such are recognized.
   Yet, a stepwise development should in some sense be implicated in our model, as polarization steps. The place of debranched degrees however, according to the loop model, makes it ambiguous: e.g. where to position adverbials and where attributes, - in the first steps 5 → 4 → 3 or "the other way around'.
   Together with the mentioned other ambiguities in dimensional interpretation of verbs and (Pro)-nouns in the chain, it multiplies the differentiating possibilities.

Polarizations as a main property in our dimension model imply that a higher d-degree get polarized into complementary "outer" poles or "partial structures" of next lower d-degree of structure:

Counting with these pole relations also, together with the connections 4-1 and 3-2 of the loop model - and the view on central chain steps as 4 = 3 + 1, →3 = 2 + 1, → 2 = 1 + 1..., gives a lot of possible connecting steps between the word categories: as for instance from 0 via 4 and 1 to 2a, via 2 to 3a and back to 4b, and via 4b to 4 to 00 etc.
   Poles in the d-degrees may decide such things as relations active-passive, hence subject and semantically this as object, a step to real objects from transitive verb, poles as 3a-3b deciding both relation nouns /verbs as radii and as outer poles of d-degree 2 for instance inner/outer properties of nouns, positions or opposite forms of nouns as things... etc.
   We may ask if word order is a testimony of how embryonic whole situations as unity structures on a "field level" once were polarized into words - historically and / or in development of the sentences as process in the brain.

Protein folding:

Do there exist similarities with the folding of proteins?
Scientists occupied with the genetic code, use a linguistic terminology in their research. It's natural, since this code has the function of a language. (About the genetic code on this site here.).

The synthesis of proteins at the ribosomes is linear, an additive development. The folding to secondary and globular structures follows afterwards. (About protein synthesis here.)
   We could regard developed "linear" sentences as in fact more or lees intrinsically "inflected" through the "3"-dimensional space... with our aspects here on geometries of different dimension degrees. An inflection of whole sentences, corresponding to the one on the word level in inflecting languages.
   From the aspect of the phoneme gradient this order would be true: first linear, then "folding". From the semantic point of view, in that gradient, such a folded sentence comes first.
   Hence, we could ask - as researchers do - how the future folding of proteins is embedded in the RNA-code for the separate proteins.

We had as written before that syntax, regarded as d-degree 4 in the level chain, had its complement in d-degree 1, the linear dimension, in he gradient from phonemes.

A suggestion is to imagine that a virtual reading of e. g. 4 bases in the mRNA chain could correspond to an internal code for folding and in this sense be embedded. In similarity with reading poles 4a or 4b in d-degree 3 in our model.
   There are 5 bases (nucleotides): 1 (T) inwards DNA, 4 outwards in mRNA, U-G-C-A. They become 3 in codons in decoding at ribosomes, or 2 where 3rd base is indifferent, and become 1 in nucleotides when acting as coenzymes (in -MP, -DP, -TP-form). Could there exist an implicit "4-base phase" of "reading" preceding the 3-base reading?
   Compare how enzymatic cuttings of DNA sometimes are illustrated, giving sticky ends, which may be 4, in every case not coinciding with divisions in 3. Compare also tRNA-ends A-C-C- where the 4th base after last C seems to have an important role for recognition of the tRNA. And, at the ribosomes, the importance some findings attribute to which bases precede the codon for a special amino acid.

As there are "jumping genes" and recurrent pieces of genes and proteins as "words" or "motives" appearing in different proteins, multi-wordy parts of linguistic whole phrases should be expected to turn up in different contexts, selected, repeated and established as "for instance", "it is"; a multitude of ready-made expressions to use in forming whole sentences as a third, forth or fifth...level for specialized jumps between poles in the dimension chain.
About storage in the brain:
It's proposed above that forms of grammatical relations as genitives, plural, past time etc. are lexically stored, not only separate words.
   A similarity is assumed with how our eyes analyze elementary geometrical forms, which then are combined to more complex structures in the associative area of visual cortex:
(This could explain confusions by persons with lesions in linguistic centra of the brain. The mix of snow and salve, for instance, or man with poncho with spruce fir , with two examples collected from a detective story.)

Together with experiences it leads to a conclusion that e.g. this is a window. There are two essential differences. Speech includes the symbolic reference to a word for it, the word window. And speech or language engages all senses, including the inner kinetic ones. It's a question to think with the whole body as Einstein said and as children surely do.
   Could the stores for pieces of language resemble Lego pieces - with knobs for connections to other possible Lego pieces in different angles? Could we imagine word class groups as cells with their more or less specialized receptors?

The fact that nerve fibres connecting nerve cells in the brain develop during early childhood (as they continue to do on demand) is of course one part of the answer to why children so easily apprehend the grammatical structure of a heard language.
End note:
The pentagon figure:

Syntax illustrated by such a pentagon, a 5-corner figure, with a risk to mislead the imagination:

a. Combining sides in a figure showing the polarizations of 5 in 4/1 and 3/2 gives a pentagon - or pentose ring in biochemistry, figure a.

(A digression: Adding the polarization 5 → 0/00 gives 9 positions as atoms in a purine base. e. g. Adenine. With the broken lines a hexagon. However, the 6- and 5-rings in a purine base only shares 1 side. The way to get only a hexagon is of course to regard 5' in the figure polarized into 0 <— 00-poles, giving a 6th side...)

Fig a.

b. The pentagon:
Connecting all corners in a pentagon creates a new inner pentagon, drawing all diagonals in this gives a third "deeper" pentagon etc. It could perhaps illustrate the principle of levels in the grammatical, geometrical differentiations within word classes, even if some diagonals seem inadequate.

(A hexagon with all corners connected gives an inner hexagon, the same principle.)

Number of connections
if all corners were connected with one another:
1 level: 5 x 4 / 2 = 10
2 levels: 52 x 24/2 = 300
3 levels: 53 x 124/2 = 7750

(Cf. circa 5 types of consonants and average value of numbers of phonemes in a language about the magnitude of 25 etc.)


To Language families

© Åsa Wohlin
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Texts are mostly extractions from a booklet series, made publicly available in year 2000








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