Language /An elementary 5-dimensional model applied in different sciences
 Geometry at bottom
Verbs - Nouns - Adjectives - Adverbs
 

Geometry at bottom:

1. The basic character of main word classes as verbs, nouns and adjectives is here traced back to the features of dimension degrees (d-degrees) 4 - 3 - 2 in the dimension model, at bottom geometrical:

- Verbs as originally with the character of vectors, d-degree 4,
- Nouns signifying closed units, "mass units" in d-degree 3,
- Adjectives separating nouns, possible to identify as originally indicating the surface of nouns, d-degree 2.
- "How"-adverbs from adjectives. About adjectives and adverbs, see below.

This view on the different word types is of the same kind as the philosopher Kant called "categories of aspects" on the world and saw as given in human brains.

2. Also linguists talk in terms of geometry.
Closer similarities seem to exist with Roman Jakobson's analyzis of the 8 cases in Russian according to a description by Beard (LB) (RJ, p. 60), in concepts as "direction", "extent" (size) or "volume" and "border, periphery". How Jakobson's 4th concept "ascription" (Russian "nadelitenost") shall be interpreted, is a bit unclear in this reference, = "attributed" (?). Note that the descriptions here concern a sub-category of nouns.
   Beard himself talks about "earlier word stems with mostly geometrical meaning which have been reduced to a parasitic existence".

3. It would be reasonable to believe that the analysis of both a situation which gives the Meaning and heard language from outside had similarities with how the eye and the visual centre in cerebrum analyzes visual impressions from outside into basic geometrical forms, for instance in direction (vectors), distance to centres (amplitudes), angles, straight/bent etc.

There are also sensory nerve cells that only get activated by changes, i. e.. are of a derivative kind.

4. This geometrical analysis 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 a spruce fir, with two examples collected from a detective story.

5. Compare too that Chinese is said to separates noun classes of spatial versus flat objects, of spread out versus long and narrow objects.


6. Debranching of d-degrees:
Our dimension model implies that lost degrees of structure in directions outwards may meet the "other way around": from step 5 → 4 one d-degree, from step 4 → 3 second d-degree:

The "Loop model":

The opposite directions will meet in the middle of step 3 → ← 2:



With a perpendicular view on this figure, we may rewrite it as in three polarizations of d-degree 5:

   5" → 3<—> 2
   5' → 4 <—> 1
   5 →  0 <—> 00

We get a figure like this, which also may give a basis (or reason for) the main division of sentences in VP, verb phrases, and NP, noun phrases, of the Chomsky school:

(In his figure we have what here is called the "haploid" version of a dimension chain with a term from biology, where start 5 and end 0/00 are replaced by pole 0, the centre and 00, the anticentre.)

D-degree 5 is in the model regarded as the ultimate, underlying binding force in lower d-degrees - and lower d-degrees are defined as polarizing forces in relation to higher ones.

With the aspect of debranched degrees, we may imagine how components semantically included in the whole "Meaning" or Sense, may become separate expressions for outer relations between parts of the sentence.

It gives a basis for the debranching or separation of what is called "form words" or particles as suffixes - or prefixes, infixes and prepositions, case signs etc. That's quanta as "carriers" of the binding force in Syntax, expressed in physical terms.

An evolution has been going on it's said towards "more and more of free form words" and "movability of the form elements", characteristic not only for Indo-European languages but also for Semitic languages and in Chinese.
   In terms of our model it implies a trend towards lower d-degrees and superposed levels where more and more d-degree steps as relations get quantified and "substantivized" to separate units.


Verbs - Nouns

Bow - bow - bowed: verb - noun - adjective

1. The verbs as vectors represent primarily radial structures, the relations of the subject to its surroundings, to other units; the nouns or the substantival primarily circular, demarcated units.

2. This main polarity may be founded in the nervous system, in the opposition between frequency modulated signals outward from the cells and the amplitude modulated signals inwards the cells. Cf. frequency related time in waves, connected with processes - verbs. And amplitude, a spatial quantity, related distance as height, connected with volumes - nouns. (Incoming signals have a circular spread in the cell membranes.

3. Hence, we may see the verbal character as primarily expressing directions and forces (vectors, d-degree 4 or 4→3) and the nouns as demarcated, located, "substantiated" units in d-degree 3 or step 3→2. The difference corresponds to the concepts of Forces in d-degree 4 versus Mass in d-degree 3 in the first identification of physical qualities in a dimension chain.
   D-degree step 4 → 3 implies a step towards "circular structure", a way towards differentiation and demarcation: the nouns get precipitated.

(The essential question how pole 4a, inward direction in our model, transforms to a circular pole in d-degree 3 is also related to the question why bodies rotate, both in micro- and macrocosm. It's perhaps illustrated in a car engine and depending on the centre displacement of the inward direction, expressed in very generalized terms. This both astronomically, mechanically and in certain centre displaced personalities.)

4. Original word stems were mostly verbs in Indo-European and Semitic languages, which then developed into nouns (LB).
   Grow - grass - green for instance derive from the same root with the basic meaning something like "shoot up".
   In Ural-Altaic languages mood and tense forms as first differentiation of verbs were in reality nominative stems derived from verbs (BC), hence followed the same direction outwards as the development verbs → nouns.

5. In Etruscan the same morphemes or phoneme combinations developed to verbs and to nouns according to the linguists (AP) - and presumably the same applies to many other languages.
   Compare "eat" in Thai language = eat rice (kinkhhao), a word which has to be disintegrated into parts if other nouns - or verbs - objects should be referred to. * (See a note below.)

6. We have also that a verb can stand alone in a sentence as an imperative: "Run!". A noun not. In this sense verbs get closely related to first primary types of sentences, and this in turn to moods as a first differentiation of verbs. On the psychological level connected with "aim", "will" as inner direction.

7. The main relation verbs - nouns may be interpreted in three different ways in a dimensions chain of word categories:

- In d-degree 4 the verbs with open structures represent vectors outwards/inwards in relation to nouns in d-degree 3 or step 3-2.

- In d-degree step 3 - 2, which in simple geometrical terms implies a polarization into radial versus circular in our model, the verbs appear as radii, the radial "pole" versus nouns as the circular, enclosing one. As radii the verbs become relations between e. g. subjects and objects.

- In a d-degree step, as 4 → 3, one d-degree is debranched in the structure and translated to external Motion, that is d-degree 0/00. (A main feature of our model, if not meeting as d-degree 1 "the other way around" inwards.)

Remember that outer poles of d-degree 4 are 0 and 00, (centre - anticentre), defining the quality Direction, which meet in last d-degree 0/00 of motions.
Hence, in a 3rd aspect verbs may represent linear "pathways" (of d-degree 1) or these polarized into expressions for Motions as such. (4→3+1, 1→0/00)

8. This 3rd aspect on verbs as words for motions may be regarded as a consequence when the noun (as subject or object) is singled out and named, is "substantiated". Its complement becomes a word for motions, course of events, processes.

9. Verbs as vectors, verbs as radii, verbs as motions: Irrespective of which of the interpretations of the relation verbal - substantival that in a certain context seems most valid, they are all three complementary in the sense of the model but in different ways:
   - as higher d-degree versus lower (also a 0-00-relation),
   - as complementary poles of the same d-degree 3, or
   - as structure versus motions.
(The dimension chain for Motions become opposite directed versus the one of Structure in the basic form of the dimension model.)

10. As the field level in physics is regarded an underlying binding forces between substantiated mass particles in lower d-degree, so (transitive) verbs act as "binding forces between subjects and objects.
   We may simultaneously regard the consequence of the two gradients of the big linguistic level chain : In the gradient where phonemes represent first centre, the morpheme level will represent d-degree 4 and hence may polarize into both the opposite poles of d-degree 3, nouns and verbs as radii as pointed out above.

11. Vectors within an imagined circle give 3 aspects:
- directions outwards - inwards
- pointing out different points ("centra", things" on the circle, in the surroundings,
the reference aspect,
- the property of being radii, connecting subject — object (as centre — anticentre).

The first vector aspect could decide or be connected with type of sentence - or order of words (~ directions) in the sentence but also secondarily certain differentiations within verbs as active/passive forms, 1st or 2nd person as subject etc.
   The pointing out of something in the surroundings (on the circumference) as centre c2 implies for instance demonstrative pronouns or articles - which in a simple geometrical way then may appear as suffixes as terminal points for the radii - a "suffix" with function of pronouns.
   At the transition of verbs to the character of radii, the relation itself between subject and object, the vector property may have been debranched to prepositions, primary words for directions and adverbial qualifiers.


12. Vowels — verbs:
Verbs as open structures, as vectors from a centre, may in this respect be compared with vowels within phonetics, with one centre, one inner (vibrating) catch or "gate", and the nouns with consonants which also or only are defined by a second outer gate or demarcation.

13. Arabic triplets of consonants are said to represent the semantically demarcated sense, not "nouns" but the "substance" of the meaning, while the vowels are responsible for variations as in tense or persons, what can be assigned to the syntax (LB).
   It reminds of how vowels can be implicitly understood in consonants as in Hebrew and other writing.

14. Why do we want a verb for a "full" sentence? "It is beautiful". Why is? / - Of the same reason that we need vowels between consonants to get a word stem?
- Because there is pathways in our brains between stores of pronouns or nouns?
- Verbs for transitions among stores of other parts of sentences? Auxiliary verbs as "is", "becomes", "would be"...
The least "whole" sentence would be a pronoun (or noun) and a verb: He ran. (D-degree 0 → 4 in our model.)

15. There is also the elementary conceptual opposition and complementarity continuous — quantified:


Saussure wrote about points of syllable divisions: parts of words with character of implosions and explosions respectively:
- implosions (~ inward direction), comparable with the way from vowel to plosive: the air stream of the vowel gets barred,
- explosions: the way from plosives to vowels, barred air stream gets released. c → ac, (~ outward direction).

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A note:
It's possible to imagine complex word categories made up of one transitive predicate with included object as first "words". Compare the mentioned "eat" in Thai language = eat rice (kinkhhao). In a hypothetical morpheme aka = hunt buffalo the first two phonemes could have developed to a verb ak-, for Swedish jaga (= hunt), the two latter -ka to the word for Swedish ko (= cow).
   Departing from morphemes with potentially both substantival and verbal sense, one could imagine two series, 1) one series with verbs including objects, 2) one series with nouns including predicates. The two series could function as two crossing coordinate axes or "scales", which leads to the "discovery" that all points on one scale principally could be combined with all points on the other. Something that leads to the ramification of morphemes to verbs and nouns respectively, more "alienated" linguistic categories.


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Adjectives — Adverbs

Adjectives are here suggested as at bottom, originally and sensorially of 2-dimensional character, as surfaces of nouns. (D-degree 2 or step 2 —1 in second part of a dimension chain. —> 2 <—> 1.)


Properties of nouns and some determinations of verbs are of course more or less included in the meaning of words for nouns and verbs. They may be released from these and become added as separate parts of sentences and own word categories - when nouns and verbs become more generalized.
   Mountain, hill, alp are different nouns which in the words include different secondary properties of height (c. amplitude) as adjectives. Walk, run indicates different kinds of a person's motions in relation to velocity (cf. frequency), corresponding also to adverbs of manner.

As debranched d-degrees from higher steps according to the loop version of a dimension chain, the adverbs and adjectives get connected "the other way around" with the verbs and nouns respectively.


Adjectives:

Adjectives may be regarded as polarizations of nouns. (Compare that lower degrees in our model is defined as polarizing forces in relation to higher ones.)
   Secondary "polarizations" of nouns such as in gender and "classes" of the type living/dead things have also a roughly adjectival character.

Quality, kind, character - such that adjectives and many adverbs represent - must be assumed as at least equally primary categories as verbs and nouns from a semantic aspect. In the beginning there was dark and light - in mythologies but probably also for newborn babies. Compare morphemes or phoneme combinations with virtual double sense of nouns and verbs.
   (Morphemes, in the gradient from phonemes representing d-degree step 4 - 3 in our interpretation, in the other gradient from the whole Meaning d-degree step 2-1, that's corresponding steps in the loop model.)
   During the translation to sentences however, they seem derived from verbs and nouns, in any case in Indo-European languages according to SEO.

A linguist as Robert Beard (RB) distinguishes 5 main types of adjectives expressing qualities: three out of verbs, 2 out of nouns. (In his description those derived from verbs could be translated to "which does", "which can be" or with participles, and those from nouns to "which have" (a property?), "which resemble".)
   Note that adjectives as attributes cannot be followed by pronouns in our languages at least, which supports the view that pronouns don't originate from nouns but originate from a more high-dimensional step.


The aspect of adjectives as the "surface" of nouns, should be compared with the aspect in physics where an atom may be analyzed in terms of pure shells also the nucleus) as well as in other d-degrees. In the same way a noun may be dissolved in its qualities and a "3-dimensional body" be analyzed as aggregation of surfaces.
   Atoms as "substantival" units become in a deeper analysis "sewed up" of qualities:
   Cf. that colours (and dark-light) originate from jumps between orbits in electronic shells of atoms. Perhaps such adjectives are primary ones? As electromagnetic waves emitted by atoms bear witness to their structure, the adjectives indicate the character of the nouns.

Adjectives in relation to nouns could also be interpreted in analogy with the dual property of elementary particles as electromagnetic waves and particles: the substantival particle structure disintegrated, broken up.
(Cf. aspects in files about physics. The wavy property becomes one expression for the increasing degrees of motions in lower degrees of structure.)

As distinctions through comparisons by the sensory nervous system adjectives may be regarded as a derivative which describes changes in a "3-dimensional" curve; the speaker as observer of relations. Cf. that there are nerve cells that only get activated by changes, i. g. are of the derivative type.

The polar character of elementary adjectives and a lot of adverbs is obvious, the division in complementary "poles" if expressed in terms of the dimension model: - in words as dark — light, in words for valuation as good — bad, sick — healthy, or in opposites as fast — slow, first — last, late — early etc., (As we have "complementary" colours.)

Compare the physical concept "Charge", polarized +/-, (and quarks "up" and "down") proposed as a physical quality in d-degree 2 in relation to Mass when analyzed as of d-degree 3 in this model.

In the dimension model the complementary "poles" (or partial structures) of d-degree 2 have been proposed as inside / outside or convex / concave as first elementary geometrical definitions. In one language the forms of adjectives are said to differentiate between inner and outer properties.    (There are also languages where lexical derivations of nouns differentiate between the flesh, the inner content in animals and their surface, their skin (RB).

The polar type of elementary adjectives separating nouns could be said to draw up a linear derivative, comparable with Distance in d-degree 1. Outer poles in -degree 1 (=2a and 2b) include charge and could also be viewed as secondary derivations from d-degree 4 of Direction.


Comparisons:
Comparisons are a characteristic feature for adjectives and "How-adverbs" derived from them. As waves have maxima and minima in amplitudes, so have adjectives and such adverbs: they can be compared - a distinguishing quality for these word categories.

This feature could be interpreted as a consequence of the transition from vector character in d-degree 4 to scalars in lower degrees: quantitative comparisons become possible between qualities.
   Comparisons may in some languages be replaced by repetitions (or a word like very in English), equivalent with plural forms - on the way to the 00-pole, which in the model also represent multiplicity.
   Comparisons may sometimes also be applied to nouns (from step 3-2) in some languages as a further development of nouns towards the adjectival through suffixes, in greater - smaller (diminutives): in Hungarian szamar = donkey, szamarbb = a bigger donkey (example from RB).

Relative clauses:
Adjectives have been regarded as a category of words out of implicitly understood relative clauses (RB). (Compare his translations above: "which does, which have".) Why this interpretation of adjectives? As pointed to above there are lot of adjectives that seem as elementary as word category as verbs and nouns.
   The view could eventually be explained by the loop version of our model. D-degree 2 as result of the debranched degrees in step 5 → 4 → 3 will in that sense refer backwards to higher degrees of both verbs and nouns, parts of a possible relative clause.

Here its suggested that real relative clauses should be regarded as developments through the middle step 3← ↑ → 2 (or 3 → ↓ ← 2) towards a new or embedded level in the sentence. Compare about Adverbs blow.


(Cf. also figure of a pentagon in file Syntax.)


Adverbs:

1. Adverbs answering the questions How - Where - When may be referred to d-degree steps →1 → 0/00 in a dimensional interpretation:

- How-adverbs for manner of activities may be regarded as derivations from adjectives in d-degree 2. Note that outer poles of d-degree 1 are 2b/2a: 2b— 1 — 2a
   In Swedish a simple addition of suffix -t transforms an adjective to n how-adverb, in English typically -ly.

- Where-adverbs as in "run away" are semantically connected with Distance, the linear dimension of d-degree 1.
   Many Latin adverbs are said to be case forms of nouns which have "happened to drift apart", (BC). Case form as locative? Distance as one of the components in Position, connected with Space from d-degree 3. (Cf. first figure in this file.)

- When-adverbs are of course expressions for Time, a physical quantity that in our model is identified as result of Motions in d-degree 0/00.
   Many expressions for Time are, as linguists have pointed out, originally expressions for space, such as afterwards, long (time) etc.

Perhaps these When- and Where- adverbs, coupled to the physical quantities Time and Distance should be regarded as the most original ones?

In short, these How-, Where-, When-adverbs describe the unidirection way in the dimension chain 2 → 1 → 0/00: (nouns) → adjectives → adverbs.


2. Vector type of adverbs, another category:
These adverbs should be regarded from the aspect of the loop model, where we had the direct polarization of 5 → d-degrees 4 → 1:
   The adverbs for directions as forward — backward, here — away, stand up — sit down... should be identified with the debranched vector character of d-degree 4 of verbs when verbs are generalized. Cf. come - go: verbs already with direction included. D-degree 4 defined as Direction, polarized outwards - inwards.
   Cf. in Swedish var? (= where, ~ for area, place), vart? (= corresponding adverb = in which direction).

3. Adverbial parts of clauses:
In our dimension model the d-degree "0/00" for motions as such is also identified as 5' (5 dimensions all translated to motions). This makes it a possible start for a new dimension chain.
   This aspect may elucidate why adverbial expressions for time and space and other kinds easily develop to multy-word elliptic clauses or whole subordinate clauses.

In our model d-degree 1 may get polarized, then in the poles 1b and 1a = "motions from each other", and "motions to each other", implying a reappearance of direction, d-degree 4, (Vdiv/Vconv). The poles become also connected with the opposition continuous - quantified. (Cf. Phonemes.) "Motions from each other", divergent, draws up distance, "motions to each other", convergent, defines a new centre.

The word category adverbs has sometimes been called a "sink" for all words not possible to refer to any other class of words. Compare this with the fact that that d-degree 1 is represented in each step in a dimension chain.

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Additions:
The principle of complementarity is central in our model: each d-degree polarized into partial structures as "outer poles" of next lower degree. What would be the corresponding first complementary poles in higher d--degrees?
   - For types of sentences: perhaps statements - questions,
   - From d-degree 4 defined as outward/inward direction: possibly active / passive verb forms,
   - From d-degree 3 defined as radial/circular: first the opposition verbs as radii versus nouns, secondarily perhaps the opposition Subject / Object (or generally oblique cases).

Secondary developments:
According to our views on "level chains": If the categories of words are regarded as a primary dimension chain, then each step in this chain may develop to whole ("fractal") secondary chains and steps in these to tertiary ones...
   The dimensional features may weaken and become stepwise less easily recognizable, yet account for all differentiations within categories of words - or elementary "concepts" that human being have felt needed in their different languages.

*

To Differentiations of Verbs

© Åsa Wohlin
Free to distribute if the source is mentioned.
Texts are mostly extractions from a booklet series, made publicly available in year 2000

 

 

 

 

 

 


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