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Aggregation

Two systems A and B may be in one of the following situations:

  1. A=B, the systems are one and the same.
  2. AÎB, A belongs to B. We may also say that A is in the scope of B, or A is a subsystem of B. BÎA is the opposite. The coupling of A to B is said to be “loose”, as in B owns A.
  3. AÌB, A is contained by B, or B includes A. The coupling of A is said to be “hard” as in fused to, organic part of, intrinsic part of B. This does not imply that AÎB. AÉB is the opposite of AÌB.

A

AA

P1

AB

CA

C

F2

CCA

CC

F1

CBA

CB

A scenario in which AÌB (A is part of B), but AÏB (A doesn’t belong to B) is described in the following section on Femurs. The notion of disowned containment is what differentiates a black box from a white one, and the foundation of any form of usefulness no matter what the problem domain would be.

Femurs

Two systems A and B interact by means of sharing substance. In the following figure we illustrate two adjacent systems A and B linked together around a certain subsystem F of system B. Subsystem F is substantially part of system B (FÌB), but also functionally part of system A (FÎA). System A may have subsystems such as P1 that are part of A's substance. B also may have components such as P2, which are part of its substance. F is not part of A's substance (FËA). An object cannot be part of the substance of two distinct non-overlapping systems, and this is the Principle of Object Coherence.

A

P1

F

P2

B

A scenario such as the one above, whereby a subsystem F of a system B is blended into another system A is called a Femur. A femur of a system B is a piece of B's substance placed into another system A. The placement is done without overlapping in tune with the Principle of Object Coherence.

The links between the femur F and its owner B are said to be Hard, whereas the links between the femur F and the receptacle system A are said to be Loose.

Connectors

Largely speaking, a Connector is a system that supplies at least one of its sub-systems as Femur to one other system. System B in the previous section was such a Connector. The following figure illustrates a quaternary connector C supplying subsystems Fa, Fb, Fd and Fe to systems A, B, D, and E. The resemblance of system C to the silhouette of a four-legged beast may be accidental, but just as well serves as an example of what a connector is: a human being, me unfortunately, knee deep into trouble D and E, and with problems A and B on my hands. I own feet Fd and Fe, as well as hands Fa and Fb, but trouble D and E together with problems A and B are not intrinsically mine. A, B, D, and E are loosely coupled with C. A and B would have better been my gloves, and D and E my shoes, but in this example they aren’t.

A

D

B

E

Fa

P2

C

Fb

Fd

Fe

Might want to note for future reference that:

1.      subsystems (hands) Fa and Fb in the illustration above are of a different type to that of subsystems (feet) Fd and Fe. In other words the femurs of a connector may be of different (specialized) types, the only commonality needs to be their ability to interact with other systems as subsystems of those. Note also,

2.      as the useful property of a connector, that systems A, B, D and E may interact with each other through their connector. And,

3.      The femur of a connector isn’t just any shared subsystem, but only one that is intrinsic part of the connector’s substance, and therefore hard coupled/fused to it.

Hierarchical connectors

Systems are recursive concepts as they are made of other systems.

In the following picture A is a system made of subsystems AA and AB.

C is a system that owns subsystems CA and CB which is a connector. CB has sub system F1 a femur into system A.

 

CC is a sub-connector of connector CB. CC has a femur F2 into subsystem AB of system A. The endpoint of connector CC is AB.

 

The relationships are as follows:

  1. AAÎA, ABÎA, CBÎC, CBÎC, CCÎC
  2. F1ÌCB, F2ÌCC
  3. AAÌA, P1ÌAB, CAÌC, CBAÌCB, CCAÌCC, although as far as this section is concerned this last point is irrelevant.

We note here that the whole of system C is a Connector in that it exports a subsystem made of F1 and F2 for use in system A. This is not an elementary femur though, because F1 and F2 may not both be intrinsic parts of C. We call such a structure C a virtual connector, or a structured connector, or a logical connector.

The onion core

The choice of decomposing a system into subsystem is a subjective matter that may depend on the observer’s point of view or on the purpose driving us to do the classification. The figure above may as well look as follows, with CB and CC subsystems of A rather than C. No matter how the scope is organized though, the hard links within CB and CC remain the same. Solid structure containment is not subject of interpretation and are concrete.

CA

C

A

AA

P1

AB

F2

CCA

CC

F1

CBA

CB

A choice such as the one described above, where we can’t determine whether CB and CC belongs to A or to C, introduces an element of uncertainty in our model, and we need to eliminate it. We therefore introduce the following rule: Systems are compared based on their proximity to the Core’s center, only at the same depth level.

With this rule, if CBA is closer to O (the center of the system) than F1, then subsystem CB is to be considered as belonging to C. If F1 is closer to O (along path A), then CB is to be considered as a subsystem of A. If F1 and CBA are at the same depth level with respect to O, then the indecision remains. To eliminate it we introduce another rule applicable only to connectors:

 

A connector’s endpoint femurs are at the same depth level with one another, and all deeper than the connector itself. We will see that to “be” a connector a system needs to have a Node aspect that differs from its femurs. The connector guarantees that the level of its nodal aspect is higher than that of each femur.

 

Hit Counter Created on 05/27/2009 06:34:12 AM, modified on 05/27/2009 06:34:12 AM

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