trumod.htm.htm
Philippe Nicolaļ-Dashwood
philippe.nicolai@wanadoo.fr
Wed, 21 Mar 2001 16:57:02 +0100
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2.CN AND TRUE MAPPING.
----------------------
2.1.INTRODUCTION.
-----------------
Before entering the details of the True Mapping Algorithm (TMA), let us=20
state that it is no purely theoretical concept, but has been tested in=20
practice, in a particularily difficult context. Indeed, Trace, our=20
Year-2000-Bug Processor Trace is based
upon our Shell CN (Cognitive Network) which uses exclusively the=20
TMA. This application proves the applicability of the TMA, as well as=20
the exceptional versatility, flexibility and adaptability of information =
systems based upon it. =20
We insist on this solid ground, because the description and implications =
ot the TMA sound at the first glance as complete madness. Indeed, it=20
calls in question the well founding of the entire existing Informatics=20
(excluding purely mathematical Computing), which is based upon a false=20
IMA (Inverted Mapping Algorithm). As the reader probably does not=20
believe his eyes, I repeat:=20
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:=20
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=20
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=20
or a Table. Attributes map to Fields (of a record) or Columns (of a=20
Table).
Saying that Entity e consists of Attributes a(n) is a loose way of=20
saying that:=20
S1: a(n) is substructure of e.
Consequently:=20
S2: e is parent of a(n),=20
S3: e is more general than a(n),=20
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.=20
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:=20
S4: "blue" standing alone is meaningless.=20
FALSE. "blue" as such is a perfectly meaningful idea.
S5: "blue" of e1 has nothing to do with "blue" of e2 and of e3.=20
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).=20
It holds for n=3D1,nm; nm>1; For nm=3D1 e=3Da(1).
Statements S1-5 are, indeed, so obviously, so clearly, so fundamentally=20
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=20
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=20
see this honest compromise in the conclusion. It consists in using the=20
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=20
follows nearly automatically.=20
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=20
ONLY ONCE.
Sd: Higher level Entities are not stored. They are Explosion Functions
which are EXECUTED upon requests. In other terms THERE ARE NO=20
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=20
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.=20
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 =20
author_03 =20
author_04 =20
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=20
Informatics is based upon a non-true IMA (Inverted Mapping Algorithm).=20
IMA is responible for the rigidity of existing systems and for the=20
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.
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<A href=3D"55.htm">top</A>
<!-- Mon compteur de votes WebOrama -->=20
<A target=3D_top =
href=3D"http://vote.weborama.fr/fcgi-bin/vote.fcgi?3374">Votez pour ce =
site au WebOrama</A>=20
<!-- fin de mon code-->=20
<P>
2.CN AND TRUE MAPPING.
----------------------
<P>
2.1.INTRODUCTION.
-----------------
Before entering the details of the True Mapping Algorithm (TMA), let us=20
state that it is no purely theoretical concept, but has been tested in=20
practice, in a particularily difficult context. Indeed, Trace, our=20
Year-2000-Bug Processor <A href=3D"trace.htm">Trace</A> is based
upon our Shell CN (Cognitive Network) which uses exclusively the=20
TMA. This application proves the applicability of the TMA, as well as=20
the exceptional versatility, flexibility and adaptability of information =
systems based upon it. =20
<P>
We insist on this solid ground, because the description and implications =
ot the TMA sound at the first glance as complete madness. Indeed, it=20
calls in question the well founding of the entire existing Informatics=20
(excluding purely mathematical Computing), which is based upon a false=20
IMA (Inverted Mapping Algorithm). As the reader probably does not=20
believe his eyes, I repeat:=20
<P>
ALL EXISTING IS' ARE BASED UPON A FALSE MAPPING ALGORITHM IMA.
<P>
This accouns for their lack of flexibility, maintainability and conver-
tibility.
<P>
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.
<P>
Ownership, parent, child:=20
Superstructure owns substructure. They may be called respectively parent
and child.
<P>
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=20
alone is meaningless.
<P>
Generality:
Parent is more general than child. Child is more specific than parent.
<P>
2.2.IMA (Inverted Mapping Algorithm).
-------------------------------------
According to IMA an Entity consists of Attributes and maps to a Record=20
or a Table. Attributes map to Fields (of a record) or Columns (of a=20
Table).
<P>
Saying that Entity e consists of Attributes a(n) is a loose way of=20
saying that:=20
<P>
S1: a(n) is substructure of e.
<P>
Consequently:=20
S2: e is parent of a(n),=20
S3: e is more general than a(n),=20
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.=20
<P>
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".
<P>
Then:=20
S4: "blue" standing alone is meaningless.=20
FALSE. "blue" as such is a perfectly meaningful idea.
S5: "blue" of e1 has nothing to do with "blue" of e2 and of e3.=20
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.
<P>
Finally, and generally:
S1: a(n) is substructure of e.
FALSE. e is substructure of a(n).=20
It holds for n=3D1,nm; nm>1; For nm=3D1 e=3Da(1).
<P>
Statements S1-5 are, indeed, so obviously, so clearly, so fundamentally=20
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.
<P>
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=20
slow for very large systems.
<P>
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=20
see this honest compromise in the conclusion. It consists in using the=20
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.
<P>
2.3.TMA (True Mapping Algorithm).
---------------------------------
After the above discussion of the IMA, the description of the TMA=20
follows nearly automatically.=20
<P>
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=20
ONLY ONCE.
Sd: Higher level Entities are not stored. They are Explosion Functions
which are EXECUTED upon requests. In other terms THERE ARE NO=20
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=20
CN is an AI shell, but we do not discuss it at the moment.
<P>
Let us illustrate the TMA with a simple example showing a small collec-
tion of books.=20
<P>
As we said, only root Entities are stored. They are:
<P>
type instance
<P>
book_id book_01
book_02
book_03
book_04
book_05
author_id author_01
author_02 =20
author_03 =20
author_04 =20
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
<P>
Explosion of all book_id's:
---------------------------
<P>
..1.book_01............................................................
...2.der_lehrer_unrat..................................................
....3.german...........................................................
...2.author_02.........................................................
....3.heinrich.........................................................
....3.mann.............................................................
<P>
..1.book_02............................................................
...2.die_schachnovelle.................................................
....3.german...........................................................
...2.author_03.........................................................
....3.stefan...........................................................
....3.zweig............................................................
<P>
..1.book_03............................................................
...2.le_debat..........................................................
....3.french...........................................................
...2.author_04.........................................................
....3.arnold...........................................................
....3.zweig............................................................
<P>
..1.book_04............................................................
...2.verwirrung_der_gefuelle...........................................
....3.german...........................................................
...2.author_03.........................................................
....3.stefan...........................................................
....3.zweig............................................................
<P>
..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.............................................................
<P>
Full Navigation (Implosion / Explosion) of the name "mann".
-----------------------------------------------------------
<P>
..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.........................................................
<P>
Full Navigation of the language "french".
-----------------------------------------
<P>
..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...........................................................
<P>
Full Navigation of the title "zauberberg".
------------------------------------------
<P>
..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............................................................
<P>
2.4.RESUME.
-----------
CN is the first processor based upon the TMA. The totality of existing=20
Informatics is based upon a non-true IMA (Inverted Mapping Algorithm).=20
IMA is responible for the rigidity of existing systems and for the=20
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.
</FONT>
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