top
prior

2.CN AND TRUE MAPPING.
----------------------

2.1.INTRODUCTION.
-----------------
Before entering the details of the True Mapping Algorithm (TMA), let us 
state that it is no purely theoretical concept, but has been tested in 
practice, in a particularily difficult context. Indeed, Trace, our 
Year-2000-Bug Processor has been based upon our Shell CN (Cognitive 
Network) which uses exclusively the TMA. This application proves 
the applicability of the TMA, as well as the exceptional versatility, 
flexibility and adaptability of information 
systems based upon it.  

We insist on this solid ground, because the description and implications 
ot the TMA sound at the first glance as complete madness. Indeed, it 
calls in question the well founding of the entire existing Informatics 
(excluding purely mathematical Computing), which is based upon a false 
IMA (Inverted Mapping Algorithm). As the reader probably does not 
believe his eyes, I repeat: 

ALL EXISTING IS' ARE BASED UPON A FALSE MAPPING ALGORITHM IMA.

This accouns for their lack of flexibility, maintainability and conver-
tibility.

Let us first shortly discuss the established IMA, its falsity and its
drawbacks. This will lead to the TMA, emerging as the natural, obvious
consequence and remedy. Prior to the discussion, let us revise some
terms related to structures.

Ownership, parent, child: 
Superstructure owns substructure. They may be called respectively parent
and child.

Structural scope:
A child may be referenced only within parent's scope. Given parent p and
child c, only c of p, written c[p] is a valid reference; c standing 
alone is meaningless.

Generality:
Parent is more general than child. Child is more specific than parent.

2.2.IMA (Inverted Mapping Algorithm).
-------------------------------------
According to IMA an Entity consists of Attributes and maps to a Record 
or a Table. Attributes map to Fields (of a record) or Columns (of a 
Table).

Saying that Entity e consists of Attributes a(n) is a loose way of 
saying that: 

S1: a(n) is substructure of e.

Consequently: 
S2: e is parent of a(n), 
S3: e is more general than a(n), 
S4: only a(n)[e] may be defined and a(n) standing alone is meaningless.
S5: Attributes of different Entities exist in different scopes and, con-
    sequently, are never identical. When they have equal value it is a coin-
    cidence, not an identity. 

Let us examine statements S1-5 in the light of a simple example.
Let a(n) have "colour" as type and "blue" as instance. Let 3 Entities
having among others the Attribute "blue" be:
e1: the sky,
e2: the Gainsborough's painting "Blue Boy",
e3: the french flag.
Let us ignore the colour nuances and admitt that any nuance of blue
is "blue".

Then: 
S4: "blue" standing alone is meaningless. 
    FALSE. "blue" as such is a perfectly meaningful idea.
S5: "blue" of e1 has nothing to do with "blue" of e2 and of e3. 
    FALSE. "blue" is "blue" wherever it occurs.
S3: "blue" is less general than e1, e2 and e3.
    FALSE. The scope of "blue" obviously encompasses all three Entities
    and, for that matter, all imaginable "blue" Entities. "Blue" is more
    general than any Entity which is "blue" (and other attributes).
S2: e1 or e2 or e3 is parent of "blue".
    FALSE. "blue" is parent of all blue (and other attributes) Entities.

Finally, and generally:

S1: a(n) is substructure of e.
    FALSE. e is substructure of a(n). 
           It holds for n=1,nm; nm>1; For nm=1 e=a(1).

Statements S1-5 are, indeed, so obviously, so clearly, so fundamentally 
false, that it is hard to imagine how they could become the foundation
of the most advanced and sophisticated technology, of Informatics.
It looks like a collective hypnosis and obsession.

Having said that, we are first to admit that practical use of the IMA
had a perfect pragmatical justification: that of performance. Indeed,
the TMA's was, till recently, prohibitively slow and still stays too 
slow for very large systems.

However, honestly admitted performance based compromise is something
else than professing a false algorithm to be Gods Word and to impose it
dogmatically via all Design, Mapping and Architecture Gurus. We shall 
see this honest compromise in the conclusion. It consists in using the 
TMA wherever possible and in drawing consciously a clear inversion line
through the DB, under which IMA is used in a way minimising its draw-
backs.

2.3.TMA (True Mapping Algorithm).
---------------------------------
After the above discussion of the IMA, the description of the TMA 
follows nearly automatically. 

Sa: a single attribute A is identical with the Entity E[A]. E[A] has
    the most general scope of level "1" or "root".
Sb: a multi-attribute Entity E[A,B,C,..] is the intersection of root
    Entities E[A] and E[B] and E[C] and ...
Sc: ONLY Attributes (or root Entities) are stored in the DB and each 
    ONLY ONCE.
Sd: Higher level Entities are not stored. They are Explosion Functions
    which are EXECUTED upon requests. In other terms THERE ARE NO 
    RECORDS or stored fixed structures AT ALL. All virtual structures
    encompassed by the DB are available via Explosion / Implosion
    Functions. They are not application functions, but inherent parts
    of the TMA Shell (eg. our CN). They support fuzzy logic, so that 
    CN is an AI shell, but we do not discuss it at the moment.

Let us illustrate the TMA with a simple example showing a small collec-
tion of books. 

As we said, only root Entities are stored. They are:

type        instance

book_id     book_01
            book_02
            book_03
            book_04
            book_05
author_id   author_01
            author_02     
            author_03     
            author_04     
name        mann
            zweig
first_name  thomas
            heinrich
            stefan
            arnold
language    english
            french
            german
title       der_lehrer_unrat
            die_schachnovelle
            le_debat
            verwirrung_der_gefuehle
            zauberberg
            the_magic_mountain
            la_montagne_magique

Explosion of all book_id's:
---------------------------

..1.book_01............................................................
...2.der_lehrer_unrat..................................................
....3.german...........................................................
...2.author_02.........................................................
....3.heinrich.........................................................
....3.mann.............................................................

..1.book_02............................................................
...2.die_schachnovelle.................................................
....3.german...........................................................
...2.author_03.........................................................
....3.stefan...........................................................
....3.zweig............................................................

..1.book_03............................................................
...2.le_debat..........................................................
....3.french...........................................................
...2.author_04.........................................................
....3.arnold...........................................................
....3.zweig............................................................

..1.book_04............................................................
...2.verwirrung_der_gefuelle...........................................
....3.german...........................................................
...2.author_03.........................................................
....3.stefan...........................................................
....3.zweig............................................................

..1.book_05............................................................
...2.zauberberg........................................................
....3.german...........................................................
...2.la_montagne_magique...............................................
....3.french...........................................................
...2.the_magic_mountain................................................
....3.english..........................................................
...2.author_01.........................................................
....3.thomas...........................................................
....3.mann.............................................................

Full Navigation (Implosion / Explosion) of the name "mann".
-----------------------------------------------------------

..1.mann...............................................................
...2.author_01.........................................................
....3.thomas...........................................................
....3.book_05..........................................................
.....4.zauberberg......................................................
......5.german.........................................................
.....4.la_montagne_magique.............................................
......5.french.........................................................
.....4.the_magic_mountain..............................................
......5.english........................................................
...2.author_02.........................................................
....3.heinrich.........................................................
....3.book_01..........................................................
.....4.der_lehrer_unrat................................................
......5.german.........................................................

Full Navigation of the language "french".
-----------------------------------------

..1.french.............................................................
...2.le_debat..........................................................
....3.book_03..........................................................
.....4.author_04.......................................................
......5.arnold.........................................................
......5.zweig..........................................................
...2.la_montagne_magique...............................................
....3.book_05..........................................................
.....4.author_01.......................................................
......5.thomas.........................................................
......5.mann...........................................................

Full Navigation of the title "zauberberg".
------------------------------------------

..1.zauberberg.........................................................
...2.book_05...........................................................
....3.zauberberg.......................................................
.....4.german..........................................................
....3.la_montagne_magique..............................................
.....4.french..........................................................
....3.the_magic_mountain...............................................
.....4.english.........................................................
....3.author_01........................................................
.....4.thomas..........................................................
.....4.mann............................................................

2.4.RESUME.
-----------
CN is the first processor based upon the TMA. The totality of existing 
Informatics is based upon a non-true IMA (Inverted Mapping Algorithm). 
IMA is responible for the rigidity of existing systems and for the 
enormous difficulty to maintain, to modify and to convert them. TMA, on
the contrary provides entire flexibility and convertibility as build in
features of the algorithm.