The number of grammatical differentiations of verbs (potentially or in Indo-European languages?) seems to be of the magnitude 5 - 6. Perhaps these different aspects on verbs could be connected with d-degrees or steps in our model, in a secondary dimension chain of verbs? Here a suggestion, where the situation for speech could be regarded as one determining factor in moods:

There is a connection between moods and tenses as between steps 5 - 4 and 1-0/00 in the loop model of a dimension chain:
   Suffixes for moods became auxiliary verbs in the development from Latin in Indo-European languages, auxiliaries also for determination of tenses.

We can also find a semantic connection between steps 4 - 3 and 1 - 2: between intransitive - transitive character and the aspect of duration:
Intransitive verbs have the character of a state (or condition), something continuous as "duration", transitive verbs with more character of bordered, delimited actions.

Active - passive verb forms is a secondary polarization of transitive verbs, of unidirection outwards (pole 4b) towards an object versus inwards the subject (pole 4a).
   In passive verbs this displacement to a change in direction inwards the subject is expressed by simply addition of the suffix -s in Swedish, derived from a reflexive pronoun.
   Here we have a connection to next differentiation with inclinations after 1st, 2nd, 3rd person etc., as the polarization of d-degree 4 in 4b/4a gives d-degree 3 in the dimension chain: start of substantiations towards the category of nouns, deciding the inclination after person.

In certain Uralic languages the verbs have double suffixes, marking both the subject and the object (BC,u) of transitive verbs.

(In a language as Swedish oppositions concerning moods and intransitive - transitive verbs as in tense inclinations are stronger marked through vocal changes in word stems than in active - passive forms and person suffixes. Possibly while these differentiations represent a deeper level in the loop version of our dimension chain?)

Moods: — step 5 - 4:

Moods are described as "a form category that indicates the speaker's apprehension of what is said". Linguists talk about 5 to 4 moods, in Greek 5, in Latin (or languages from Latin?) 4. With differentiations in moods we get a third level in the "fractal" developments within the dimension chain.

- Indicative (something stated, related)
- Imperative (exhorting, urging)
- Infinitive
- Subjunctive (something thought, possible, conditional)
- Optative (Greek: what is wished)

An Uralic language as Yurak (Nenets) is said to have 10 moods (BC,u). Uralic and some other languages have also negation verb forms; Turkish has a "mood negatives".
   The question form should reasonably be possible to apprehend as a mood too when the imperative is a mood and it seems really to exist as a mood in certain languages (same source BC,u). It's said that negation particles and question particles originally have been identical in Indo-European and Semitic languages (LB). Hence it sounds right to connect moods with the whole situation for speech and the relation speaker — addressee.
   With the indicative taken as the basic form of a full sentence, as developed straight "outwards" in the sense of attitude, it seems possible to interpret the other moods as representing geometries of different degrees in the direction inwards as from 00-pole and "a-poles" in the model:

In geometrical terms:
- 4a: straight inward direction, towards 2nd person, imperative.
- 3a: circular geometry: the infinitive with character of noun.
- 2a: convex form, open curve: the subjunctive, the eventually possible.
- 1a: defined as "motions towards each other" in the model: the optative,
see annotations below.
- 00: the opposite direction in the whole chain, the indicative turned in direction to negation or question mood.

The imperative is the purest example of the direct relation speaker - addressee, as centre - anticentre poles, the elementary direction, d-degree 4, in the situation of speech.
   They include he most single-worded type of sentences as "Run!", one single verb (verbs in d-degree 4).
   The speaker is centre-displaced as to the surface of the addressee, which implies that the sentence in a real semantic meaning lacks a subject. The direction of imperatives is essentially inwards.


(The imperative could also be said to represent "law" and rules, as syntax is proposed as from d-degree 4 in the big level chain of linguistic analysis.

In languages like Swedish the verb gets often reduced to the pure verb stem, without any suffixes.

The infinitive represents linguistically the "infinite" (the 00-pole). It has a recognized subjectival character of d-degree 3 and can function both as subject and object, as an objective complement.
   Uralic languages have instead of infinitives case forms of verbal nouns (BC,u).

The subjunctive, the only imagined, possible or conditional, may perhaps be expressed as if- sentences. The speaker's psychological attitude is a kind of detour, or "the other way around" in relation to statements about facts, as it were connected with the loop model of the chain.
   In relation to indicatives as "substantiated" actual facts, the subjunctive implies a dissolution, an opening, something unsubstantiated of more wavy character. Hence here suggested as in from step 2 ← 1.

The optative as "wished" could be interpreted as a catching motion and has in relation to the subject the inward direction. It could illustrate the definition of d-degree pole 1a as "motions towards each other" in our model, psychologically:

(It's said that an expression as the Swedish "Leve konungen" (English "cheer the king…!") is the rest of present tense subjunctive in optative use. Hence a wish as a positive possibility, connected with the subjunctive.)

It sounds probable that auxiliary verbs have developed from these later moods within Indo-European languages, those moods that represent the only potential, imagined or wished - in this sense the internal of the subject? Subjunctive verb forms are in Swedish for instance alternatively expressed through auxiliary verbs for passed time, in this sense in the inward direction of time:
("Om det vore så = Om det hade varit så…" = If it were so... If it had been so...)

Tenses, auxiliary verbs, — step 1 ← 0/00:

1. Tenses are tools for the time aspect relative the present in the situation of speech. They become parts in the angle steps of time displacements through levels.

2. The subject as a centre, geometrically first as origin (the 0-pole) becomes toward higher levels a growing circle, The auxiliary verbs for past time could be regarded as internal radii within the subject. (A verb as "be" is a basic form as a radius without directions.)

3. With the subject centre displaced to its surface, its circumference, as in possessive position, the radius gets the direction inwards the past: the auxiliary verb marks the time displacement inwards.
   The possessive as the case for "ownership" (normally for nouns) is an expression for this position of the subject at its own surface, enclosing its belongings or possessions. In Lappish also verb stems may be in the genitive and in Uralic languages more generally the genitive is also used to indicate points of time and time periods.
   According to one opinion possessive suffixes in Uralic and Turkish languages have originally been combined with expressions for completed actions. (BC,u). With the geometrical view above this seem natural.

In an Indo-European languages as Swedish (also in English) the auxiliary verb for past time is ha (have)- hade..., a verb for ownership too (Swedish "innehav"). An enclosing word. In opposition to this the auxiliary verb for the future is skall (= shall), a word which originates from skuld, (meaning debt), the opposition to ownership in economic terms (!).

These auxiliary, "possessive" verbs imply also terminated activities. Demarcations as shells are creations of inward direction.

Perfectives of auxiliary verbs for the future as shall - should become connected with e.g. subjunctive moods above. They get an anticipating character, as from a still larger incorporating circle (In real outward direction towards the future there are strictly speaking no such angle steps defined. "He will have finished this work tomorrow": in such a phrase the speaker has already positioned himself at a point in the future.)

The relation between auxiliary verbs and main verbs should be possible to interpret as a relation between different coordinate axes, including a displacement in tense. (A language as Swedish has 5 tenses, 3 for the past, 1 for the present and 1 for the future.)
   The changes between progressive and terminated activities as between continuum and quantum jumps could be compared to the steps in a ladder: horizontal resting-planes varying with level steps.

Time displacements inwards "inflect" verbs in languages as Indo-European through a change backwards in the word stem of the vowel. The "strong verbs".
   This "mutation" goes often to a more inner vocal. Both seem to express the past as a "genealogical tree" inwards.
   The vowel changes in word stems when the verb is substantivized is of the same kind. Swedish examples: springa (run) - sprang (ran) - språng (a jump); - ligga (lie) - låg (lay) - läge (location); stjäla (steal) - stal (stole) - stulit (stolen) - stöld (a theft).
   These vowel changes for past time and nouns for the activity are both characterized in direction and enclosures respectively by inward direction. So does direction inwards, ~ past time, transform to "circular" structure, ~ nouns, in the dimension model.

Duration, — step 2← 1:

The differentiation between progressive and terminated activities has the general character of continuous versus quantified (00 versus 0 in our model - or perhaps d-degree steps versus d-degrees). One argument here for interpreting this differentiation as an expression in d-degree step 2 — 1 is that it concerns borders for actions, "perfective", borders similar to enclosing surfaces (d-degree 2). (Inside ~ finished, enclosed; outside ~ open, not terminated.) Cf. the poles 2a / 2b of d-degree 1.

In Uralic languages there seems to be 3 polarizations as for duration aspects:
(BC,u):

a) The first polarity is easily identifiable with the poles 0 and 00, quantified - continuous. They could be compared with poles 1a and 1b in our model: "motions to each other", defining a centre, quantifying, and "motions from each other", defining distances, a durative type.

b) The second polarity could possibly be interpreted as d-degree 1 ("rapidly", a quantified linear series?) - with its outer poles 2b/2a.

c) The third polarity should then be these poles 2b and 2a, for start of a durative activity and the closing down of it. That implies borders (in this sense 2-dimensional, for the activity.

Intransitive / transitive verbs, — step 4 → 3:

Intransitive activity concerns the subject itself, as a person is a whole in itself when sleeping. That means it's double-directed outwards/inwards as d-degree 4 unpolarized.
   As said above it implies a state, related to the concept "condition", therewith also including a connection with the concept duration as in the loop model.

Transitive verbs are unidirected as activated working forces with explicit directions.
We get the polarization into active - passive forms:

- The active form binding the subject with an object as 00-pole and anticenter on the circumference.
- The passive making the subject an object in itself.

Hence the relation Intransitive → Transitive corresponds to a step 4 → 3.

Outer poles of d-degree 3 are 4a and 4b, in our model assumed as perpendicular to one another, the inward direction transformed to a circular geometry.

How such a geometry eventually appears in passive verb forms of languages may be left as an open question. Semantically the passive could be said to make the subject to an encircled object.

The opposition intransitive - transitive is in a language as Swedish often expressed through vowel change in word stems: sova (sleep) - söva (get to sleep), ligga (lie) - lägga (lay), in similarity with tense changes in strong verbs.

Conjugations after person, singular - plural, — step 3-2:

This differentiation concerns persons, that is nouns, here d-degree 3 as class of words.

Verb suffixes get the character of "pro-nouns". They may be regarded as a result of the displacement from the "I-You"-situation of speech to the describing sentence and principally 3rd person, where also the I and the You may get character of references.

While most of the verb suffixes for persons seem to originate from the word class pronouns, it's doubted now that those for 1st and 2nd person really do so in Indo-European languages. (BC,s). Here the original situation of speech with Speaker - Addressee as 0 - and 00-poles, before the "tangential" coordinate axes of relating sentences develop, could be responsible for that doubt.

In Uralic languages it seems that 3rd person not was expressed as verb suffixes but in a substantival construction, a noun derived from a verb, something which further supports the interpretation of this differentiation with d-degree 3 and the step 4→ 3 as verbs to nouns.

It's curious but significant that the suffixes for person originate from possessive pronouns, not the nominative ones.
   Also this fact seems pointing to the centre displacement in the situation of speech, and pronouns as referring backwards to something mentioned, geometrically similar to the person at its circumference as an "owner" of his content.

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To Differentiations of Nouns