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Relations between beings, organization

1. Bases

How do beings relate to each other, and what manages the relations. To make it simple, one could say that all that was at first enforced by laws of matter (attraction), and, as far as the digital universe develops for itself, they end to be enforced by "soft" laws.

Inside a biological body, the main coordinations are supported by enzyme circulation and by nervous (digital) system or, more exactly, systems, since the human body, for instance, has several ones, including specific (sub) systems for cardiac control, for instance. The control functions are then distributed between the central system (brain), various local systems, and finally the cell control systems.

In a computerized system, links are ensured electronically through wires, optically (mainly fibre optics) or wireless. The main control is concentrated in a central unit, hosting an "operating system", but
- with important unit controls for various devices such as disks and more or less integrated "peripherals"
- sometimes with a radically non-central type of control, a "connexionist" view of things, mainly with "neural networks" (at present, the only practical way of implementing these networks is to program them on classical computers, but that is not a real breach into the theoretical principle of non centrality).

At the most global level, it is tempting to imagine something as a "general operating system" managing the totality of communications. The web, Google, the rather permanent remote control of computers seems to go this way. Orwell's threats, or a new kind of Brave New World ? See below what we say of digital relativity.

There are two main elementary structures : hierarchy and loop. They are minimal in the sense that a minimum of relations are necessary to build them : n relations for n elements in loops, n-> 1 in hierarchies. They also correspond partly to order and equivalence relations in set theory.

The loops bear complexity, reflexivity, recursivity. Hierarchy bears little "complexity" because, at least in principle, on can always deal only with the higher levels.

We could find examples in sociology or market, useful. not difficult to be transcribed. We can also find models in the web and computer networks, the anthills and beehive.

If we describe the structures induced by communication, we can use a representation with graphs. A simple " A and B are related implies no direction not periodicity. The relation is transitive, symmetric and reflexive (it is useful to say that A is in relation with itself). Then, such relations define an equivalence relation, and a partition in subsets of beings communicating with each other.

The relations may be oriented (emitter/receiver, for instance), and valued, according to the number of bits exchanged, by cycles, or sets of cycles, or the distance between beings.

A being is totally controlled by another one if it communicates with it exclusively. Could be more precise.


Between high-livel beings, relation may be “communication” at a series of levels.

We could describe a set of features for a relation : symmetrical/asymmetrical, strong/weak...

2. Hierarchy and nesting

Note : that is not specifically digital !

There a first basic (trivial) hierarchy induced by the (law of) non intersection of beings other than content/container. Then we have bits at the low extreme, and the global universe a the highest, with systems of parts, subsystems, groups, etc. in between.

The creation of a hierarchy is done to delegate functions and then to alleviate the high level being. Then the domination relation is transitive, and the tree grows.

The simplest solution puts all elements along one line, each being dominating another one and being dominated by another one (but for the extremes of course). Here, the number of hierarchical levels is equal to the number of elements. This solution is rarely optimal. And the domination risks to be uncertain beyond several levels of differences.

Another very simple solution is to have one dominant element, and all the others below (and here also, generally ordered).

If S receives a strong flow of unpredictable I (but somehow "interesting", i.e. not totally white blank) it may consider that this flow on its I is sufficient to make its own Land accept a sort of dependence. Some S" could say that S is henceforth predictable as S' mirror, (if S does not add something). That could be risk for S, it its survival depends on its unpredictability.

The number of levels as well as the hierarchical span are not arbitrary, it the structures have to be viable. Thresholds limit the number of subordinates to one authority, of neutrons in a nuclear core. Mass default according to atomic weight may even be taken as the search of an optimum by Nature.

Narrow spans (from 7 to 12) fit for hot relations and rich interrelations between human beings. Pleiades and cenacles. Stars and polyhedra. Beyond seven, the notion of plurality is nearly lost.

But the survival of these structures calls for a supporting space, and matter. Continuous space is a limit, as the liquid or the perfect gas. Concrete space bears always some grain, of measurable size. You can count the number of grains in a paper sheet or an mud bloc. In this case, a very large hierarchical span will generally be looked for in order to get flush forms, white sheets, liquid marks and stable results in votations. A lot of technological processes aim to the creation of this gap. Sometimes destroying pre-existing structures.

beings also use nesting and layering, somehow analogue to hierarchies in matter, but more supple. If a same region, physical in DU, is called by two beings to create different beings, there goes no without problem if it is at the same moment. As long as one stay virtual, it is no more problematic that several millions of maps for the same place on Earth.

Functional nesting

Let the input I be a sequence of beings   in, with same O, we say that the operation will split as following :
first for i from 1 to n,

The state at time n : En = fn (in)    (the may exist several)  and on  = g(in)

,then the functions e = f(e)

then the functions o = f(e).

It may be important to chose a right order or operations (lexicographic order, for instance.
Then a typology of functions (assignment, operations... functions properly said

3. Loops

A catalogue of circularities:
- iteration loop (programming)
- feedback loop (cybernetics)
- C++ "this"
- paradox
- conscience
- auto-reference, the self, the mirror stage
- mirror; not a loop in itself; more generally, effects of O on I (at the following cycle).

Self loops. Cycles (see time).

Beyond some level of cognitive systems, a being can identify the modifications of its perceptions as a consequence of its own actions. Hence the mirror testn, and building of the Ego

Yet the basic cybernetic loop.

Special case: people talking about themselves.

More efficien on written texts than in speech.



4. Dependance, causality

Of course, independence.

5. Communication

low/high level

6. Operations

The operator/operand distinction or merging.


Blend (pictures)
Text and image operations
Material operations: move on the raster, cuts.
Behaviour operations.

7. The Maelstrom scheme

This pattern lets combine a raise or fall, with a circle, with features : minimal diameter, curve equation (notably, curvature radius in the ransition phase between the comparatively flat periphery and the steep parts of the center.

We can considere the diabolo as static or dynamic, as a flow int which everything tends to be sucked.

How to locate oneself in the diabolo :

keep confortable on periphery, or play the hero arount the mouth of the pit

8. Varia to be developped and edited

sociology, market would be useful. not difficult to transcribe
models taken on web, computer networks, anthill, beehive

If S receives a strong flow of unpredictable I (but somehow "interesting", ie not totally white blank) it may considera that this flow on its I is sufficient to make its own L,and accept a sort of dependnce
some S" cold say that S is henceforth predictable as S' mirror, (if S does not add something)

that could be risk for S, it its survival depends on its unpredictgability

9. Systems algebra


Communication matrix between systems


"En gestion et en ingénierie, l'on peut s'attendre à ce que les interconnexions et les interactions entre les composants d'un système soient plus importantes que les composants eux-mêmes pris isolément". Forrester, cité par Forte. 1966

"Cristal... arborescence très plate. Dans l'usage ordinaire, nous avons tendance à réserver le mot arborescence aux systèmes divisés en un nombre petit ou modéré de sous-systèmes."HA Simon 1/110. 1969

"Face à un processus complexe, sur lequel on dot réaliser une fonction de commande complexe, une approche de commande à plusieurs niveaux peut être réaliser suivant deux voies simultanément:

- la fonction de commande globale peut être diviseé en fonctions de commandes plus simples formatn une hiérarchie, ce qui conduit à une décomposition verticale en sous-systèmes de commande;

- le processus peut être décomposé en sous-processus plus simples commandés par des critères locaux, les actions de commande locales étant coordonnées par les niveaux supérieurs de la hiérarchie. " (Source ?  Mélèse ? )

"Une unité de commande s'intéresse à des aspects d'autant plus généraux du système global qu'elle appartient à un niveau élevé de la hiéarchie des unités de commande. Elle est liée à des dynamiques d'autant plus faibles, et ses périodes d'intervention sont d'autant plus longues que ce niveau est plus élevé. "HA Titli, 1/21 1975

"Quel que soit le niveau du problème, il existe toujours un niveau supérieur qui délivre les objectifs." Mélèse 1972

"Un ensemble de systèmes comporte toujours une organisation hiérarchisée:

-un système supérieur assure la coordination et dispose du plan de référence général;

- si les systèmes subordonns disposent d'un domaine d'autonomie de décision particulier, l'ensemble complexe peut ne constituer un système que sous certains aspects " Martzloff


1.. DU and its parts

About addresses
Ideally, with DU taken as of only one dimension, the address could consist only with the number of the first bit (possibly first and last bits). That would be absolute addressing.

In practice, DU is parted in various subspaces and we use “relative” addresses, with a hierarchy or addresses inside, for instance the directories and subdirectories in a disk or a web site.

Thesis : The smaller is the subspace, the shorter can be the address.
We have had an example with the phone numbers. At the beginning of the XXth century, a Company could just mention “telephone” on its correspondence sheet: human operators could find it directly from its name. Then, for convenience as well as automation needs, numbers have been used. For instance, in a small town : 67 (if you called from another town, you would add “69 at Lasseube (France). Then the number has been enlarged progressively to
00 335 47 32 18 67

Thesis : Within the same (sub)space, relative addresses are longer than absolute ones. There is a sort of gap (here, "excess" of code) in order to access to an individual, and to describe it. For a population, the minimum is the logarithm of the population. For the French social NIR (security social code), 1 38 08 75 115 323, that is 1013, of 6.107 inhabitants.

At the other extreme from the bits, we can consider a global digital universe, DU taken globally. That is perhaps unrealistic, and more sensible to consider that there is a plurality of digital worlds, separated/connected by analog/physical regions...

It could be useful to distinguish in it:
- a general memory, or general bit raster (DU itself)
- action and management rules and operators (Global operating system, GOS)
- ways of ensuring communication between beings...

For life, there is no such raster, and it uses the laws of matter to effect these functions. See architectures.

More generally, see structures in chapter 7

Globally, DU is necessarily auto referent. Parts of DU refer to other parts. And some parts refer to themselves. (a map of addresses contains necessarily the address of the map ?). In a first analysis, probably, auto referent parts should be put aside.

GOS functions are, or may be :
- general clocking ; that is not necessary ; processes could go asynchronous, or synchronize without any global intervention (communication protocols)
- laws operations (and "enforcement"), security ; that could be mainly local ; at the global level, ownership of territory is ensured by the underlying matter ; the more digital the world, the more "soft" is the assignment of locations inside DU as well a in underlying matter ;
- noise generation ; normally, it will not be properly assigned to a DU processor ; but why not;
- communication between processors ; here also, roles may parted between matter and more or less general processors
- controlling the operations of non autonomous beings ; that, de facto, is more the task of local beings ;
- insure the reproduction of DU upon itself at each global cycle, if we retain this kind of model ; this point is near to metaphysical.

GOS may be seen as the DU's God. It this case, it must front the paradoxes of the creator, of the rational God of natural theology, and every self-referent being.

We shall now use frequently the term "material" to mean the location and disposition of a being in DU, opposed to ifs "formal" features. When referring to the material universe of common sense, we shall call it "physical".


The number of dimensions (mathematically speaking) has not here the radical implications which mark the physical universe. DU is at first sight rather indifferent to dimensions. As well one dimension in all, as one dimension per bit. . Genome is one dimensional for its basic structures. 2D is of frequent use for chip design and for representations, because our vision is so structured. More exactly, it is frequently 2+, or 21/2, with the use of layers (chips, raftered images) or of compacted perspective for maps, for instance.

The dimensions are important when being have relations, then must be defined :
- independence of subparts
- difference in metrics.
Unless otherwise stated, DU may be thought of as a one dimension bit string.

The space is indefinite, potentially infinite. Infinite may be called for by a loop without stop condition, but of course we never get there by a finite number of cycles.

There is no proper zero, anyway



Causes, causality


Cause matérielle, cause formelle.

Parmi les causalités, on distingue formellement depuis Aristote (informellement depuis bien plus longtemps, voire Gn. 1) la matière et la forme. Cela correspond à des parties différentes des Ngrammes. 

Noter que l'idée de matière n'est pas si immédiate que cela. Mais elle émerge assez naturellement du travail du potier, voire de l'agriculeur.

A la matière sont attachées des propriétés de permanence (poids, mouvement) et de capacité à recevoir des formes (ductilité des métaux précieux chez Saint Thomas).
A la forme sont attribués les propriétés de relations  (ça, c’est pas très bon).
Le corps et l'âme.


1.9. Varia

Clever and selfish ... These words are anthropomorphic. But, as with Dawkins it may be an efficient scheme, a useful “theoretical fiction”.

Possibly a double way of bits into matter :

- a small surface into a raster (e.g. pixels, voxels)

- a partition of a space into two parts.

Bits and infinity : through recursion.


Organization of systems

Modélisation des systèmes. Et systémique
Le composant