Systematics is a discipline based on the numbers one to twelve, in which each of those numbers defines a different kind of system with a known systemic attribute. It was developed by J. G. Bennett out of Gurdjieff's presentation of the laws of three (attribute: Dynamism) and of seven (attribute: Transformation), deepening the idea into what appears to be a new number science for which the primary point of reference is

Systematics is a new way of seeing. A Whole system is being understood as divided into parts called terms. Terms are distinct whilst operating "on the same level". The limited number of terms are sufficient to describe an aspect of a given System for the purpose of understanding it, and interacting with it. First proposed by J. G. Bennett, Systematics is conservatively delineated at Bennett constrained himself to systems having one to twelve terms which, taken together, can describe many facets of system behaviour and these first twelve types of systematics relate most easily to common situations whilst being small enough to suit human minds.

I have found within Systematics diagrams a strange relationship to the notion of conservation (e.g. Kirchoff's laws, which apply to dynamic systems in general) when astronomical time periods are seen as relationships (connectives) between astronomical terms. This may mean that astronomical periods involving sun moon and planets, when seen from earth (i.e. synodically), form parts of a whole (viz.holistic) system, exactly as Bennett posited for multi-term systems. Astronomic time may be an opportunity to learn about the systematics of whole systems, whilst learning more about the time system surrounding the Earth. It is an interesting fact: that whole systems cannot be seen without a special effort. Generally conceived as purely qualitative, Systematics here appears quantitative with regard to astronomical time. 

Tetrad of the 19 year Metonic Period

In February 2009 I found an excellent example involving the nineteen year Metonic Period.


You may want to study what is meant by a 4-fold tetradic system in systematics.

The four terms can be expressed as:

 1 TetradOf Metonic TERMS

Figure 1 The four terms of the Metonic system 
with which the text will find conservation of quantative time periods 
in between, as the lines shown.


It is also good to view the YouTube slide presentation (11 minutes) which prefixes what is to follow:

2 TetradOf Metonic NUMBERS  3 TetradOf Metonic NUMBERS 13368 
 Figure 2 Quantifying relationships between terms around the "outside"  Figure 3 Seeing the upper triangle as 254 divided by19 = 13.368 orbits per solar year
 4 TetradOf Metonic NUMBERS 27321  5 TetradOf Metonic NUMBERS Year
 Figure 4 Seeing the lower triangle 
as 10,000 divided by 366 
equal to 27.32166 days of the lunar orbit
 Figure 5 The emergence of the Solar Year 
as composite horizontal connective of 365.242 days, the sum of the values in the upper and lower triangles

My notes of the time were:

  1. We notice four effective terms which combine to give 254/19 x 10,000 / 366 = 365.242
  2. These support the goal of achieving the 19 year recurrence of the same configuration of sun, moon and starts.
  3. The instrumentality used to achieve this is the moon's orbit
  4. The ground of this tetrad is the rotation of the earth relative to the sun
  5. Direction then appears as the (vague term) solar logos of the solar day and year

The ambiguity of the solar logos can be resolved by increasing the number of terms so the solar logos becomes the solar day and the solar year. A five fold systematics is called the Pentad.


You may want to study the pentad at

"An entity has meaning in its own right. This gives it an unique character and an inner and outer range of significance. Nothing less is sufficient for an independent structure. The inner range of significance includes the potentialities of the entity and partly stems from the nature or kind of entity and partly from its history. Any real thing is potentially more than it ever actually is. This is true of situations as well as of entities such as a man."


It is this "inner range of significance" (between higher and lower nature) which is opened up between the solar day and the solar year. The "entity in its own right" is the lunar orbit and the outer range is between the unit of earth rotation (Chronon) and the 19 year Metonic.


The two triangular cycles of figure 3 and 4 above have split so as to form 13.368 orbits per solar year and 27.321 solar days per orbit. The outer range on the right gives the numerocity required to achieve such a state of affairs by dividing by 19 and 254 and multiplying by 366 and 10,000. The rotation of the earth divides up the earth orbital period by 365.242 days. Those solar days then give 6939 days in a metonic period of nineteen years.

In some way the moon becomes the measure which "eats" the rotational energy of the earth through tidal interaction. Longer term cyclicities like the metonic (such as the synodic preiodicities of the outer planets in particular) provide an environment of what I call emergent cohesion in which many resonant intervals between synodic time periods appear to be governed by pure numerical litims such as 19 years. Whilst we see anniversaies called synods and might arrange them within a calendar, the realities of what we call discrete mathematics cause pure numbers to function as "attractors" .

In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system.[1] System values that get close enough to the attractor values remain close even if slightly disturbed.

In the pentad, the topmost term is the "god" which feeds on the "thing in itself", because the pentad is a good presentation of Gurdjieff's cosmic principle Trogoautoegocrat - the law of reciprocal maintenance. The relatively small integer number nineteen is to be found in 13.369 orbits being 13 plus 7/19th of an orbit. This guarantees that after 19 repetitions there must be a whole number of orbits. The "attraction" of low number repeat cycles is their stability and simplicity which tends towards conservation of energy, in this case the gravitational energy within dynamic systems. The elements within a dynamic system might naturally find such synodic anniversaries but one could not rule out that in organising the world of time, 

“This system, which maintains everything arisen and existing, was actualized by our ENDLESS CREATOR in order that what is called the ‘exchange of substances’ or the ‘Reciprocal-feeding’ of everything that exists, might proceed in the Universe and thereby that the merciless ‘Heropass’ [time] might not have its maleficent effect on the Sun Absolute.

Gurdjieff, G.I. Beelzebub's Tales. 7.136-7

The  Moon presents itself as a highly variable cycle of behaviours yet it largely exhausts its main cycles under a recurring nineteen fold regime. The creation of diversity reminds us of the extreme diversity found on the earth of living beings that live "under the moon", the sub-lunary world of geocentric astronomy. One can see that the geocentric view is not essentially "wrong" but is an equally valid perspective that happens to carry simplifying numerical messages lost to a world of heliocentric physics.