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System - Sub System 'Algebra'
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| Operations as
Systems |
Unit |
Transformation |
Operations as Sub Systems |
Unit |
Transformation |
System (+,-,*,/)
Sub System
Sub System (+, -,*, /) Sub System
System (+, -,*, /) System |
x
x
x |
X or Constant
(unique)
X
X or A
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System (+, -,*, /) Sub System
Sub System (+, -,*, /) Sub
System
System (+, -,*, /) System
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C
C
C |
A
A or B or X
A or B or X |
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'System-Sub System Algebra, Transformation Categories of expressions
of Systems - Sub Systems, The following
categories are derived from Constant unit unknown expressions I developed
in 1984 and their various derivations. At the time I developed
these expressions, I just thought they were a neat way to characterize
Quantitative and Qualitative values. But they have proven useful in
characterizing these System - Sub System expression combinations.
Examples of Systems and/or Sub Systems are:
Apple Tree System, Apple B, Apple Tree
Branch A; Apple A System and Orange B System, Apple System
and Apple Seed Sub System, Human Body System and Human Body Organs
Sub System(s), Universe System and Planetary Sub Systems; Apple System,
Orange System, Apple Seed Sub System; Atomic-Molecular Systems and their
Sub Systems...A operational sub system could be operations within above
mentioned systems. A operational system would be external to mentioned
systems
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Operations in this breakdown
are considered Systems.
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Operations are Sub Systems in this breakdown and
by default within the System A
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| System A (
/ ,*) System B; Transformation X unit x |
System A ( /,* )
System B; Transformation A unit constant ? |
| System A
( / ,*) Sub System B ; Normal Transformational
or Factorial |
System A ( / ,*)
Sub System B ; Transformational A unit constant |
| System A ( / ,*)
System A ; Transformation X unit constant |
System A ( / ,*) System A ; Transformation A unit constant
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| Sub System B ( / ,*)
Sub System B ; Transformation X unit x. |
Sub System B ( / ,*) Sub System B ;
Transformation X unit constant |
| Sub System A ( / ,*)
Sub System B ; Transformation X unit x. |
Sub System A ( / ,*) Sub System B ;
Transformation X unit constant |
| System A -
System B; Non Transformational, Non Intelligent. or X unit x. |
System A - System
B; Transformation A unit constant |
| System A +
System B; Non Transformational, Non Intelligent |
System A + System
B; Transformation C unit x. |
| System A -
Sub System B ; Transformation X unit x |
System A - Sub
System B ; Transformation A unit constant |
| System A
+ Sub System B ; Transformation C unit x |
System A +
Sub System B ; Transformation A unit constant |
| System A - System
A = Transformation XA unit x |
System A - System A = Transformation
A unit constant. |
System A + System A = Transformation
XA unit x
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System A + System A = Transformation A unit constant |
| Sub System B - Sub
System B ; Transformation X unit x. |
Sub System B - Sub System B ; Transformation
A unit constant |
| Sub System B + Sub System
B ; Transformation X unit constant |
Sub System B + Sub System B ; Transformation A
unit constant |
| Sub System B -
Sub System A ; Transformation X unit x |
Sub System B - Sub System A ; Transformation
A unit x; |
| Sub System B + Sub System
A ; Transformation X unit x |
Sub System B + Sub System A ; Transformation A
unit x |
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..........or something like the above
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Expression of Sub System and Non Sub System give highest degree of order?
Expression of System and Non System gives least degree
of order? Explaining Bible expression the Least is the Greatest and Greatest
is the least. Analysis of Nature of Expressions of Items and/or Events and their
Non Items and/or Events would be useful. ie When/where do these expressions
occur and subsequent implications.....Note: The observation that systems
appear to produce but always quit after a time.. Life Systems, and all other
systems. Is there a Reason for this?.....The expression of a Sub System and
some System Ax might be a Transformation combination giving a Transformation
category that would produce result of highest degree of order and should be
included in the above Transformation category table.
01-01-2012 Explanation mathematically and existentially of paradox stated
by Jesus in Bible, "The Least is the Greatest, and the Greatest is the Least":
This paradox is explained within the System, Sub System Paradigm. Where the
expression of a System Z and its' many Sub Systems (A,B,C,D) the given "Greatest"
or Z(A,B,C,D) = + - / * ; ; AND the expression of a
Sub System (D) as: D(x) = + - / * ; D(1) = + - / * ;
or D(1,0) = + - / * ; or D(N) = + - / * ; or D(1+0)
= + - / * ; or even f(D) = + - / * ; the supposed "Least Greatest",
is expressed as a function of the same basic operations modeled as systems.
These expressions show that functional expression Z(A,B,C,D) where, Z,A,B,C,D
are all partial system constructs give a much more limited System functionality
as each object is a unique partial system construct expressed by another unique
partial system construct z , gives an increasingly limited system wide functionality.
On the other hand some low hierarchal sub system D expressed as a function of
the same functional source of basic operations modeled as systems would give
a system wide functionality. This is attributable to the lack of constraints
offered through its' expressions as opposed to with Z(A,B,C,D) =
+ - / * .
This is applicable to many existential phenomena experienced in our contemporary
world.
Government and experiences within this construct. Communication within
Mass Media and Mass Media editorial constructs. Big corporations having
trouble competing.
01-31-2011 It is said that God Created the Universe.
Maybe better said God is Creation. And also consider
the Science of Psychology and the System , Sub System Paradigm, where "God
is Love". Some would then argue , God is Evil. I argue that
this argument is dependent on the functional context of the argument.
God is Evil , has a different result when expressed as a sub system ,
than when expressed as a component of the Principal System. See the series
of expressions below
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Sub System God/Evil = >
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Sub System God/Love = >
| Multiple Metaphors, Contexts and
Meanings for the four General System Behavioral Components: |
| Every(x) |
Any(x) |
Some(x) |
Non(x) |
| functional context, |
traditional working matrix
for Mathematics |
purpose, reason, actual
function |
non functional component, or non stated
functionality |
| Every(+)Every(-)Every(*)Every(/) |
Any(+)Any(-)Any(*)Any(/) |
Some(+)Some(-)Some(*)Some(/) |
Non(+)Non(-)Non(*)Non(/) |
| functional context of Principal
System |
complete set items/events
of Universe |
functional intersection
of:
functional context of Principal System, complete set of Universe,
all knowledge |
all knowledge |
| Fruit(x) |
Apple + Non Apple + Orange
+ Non Orange + Grape + Non Grape |
f(x) |
Non Apple + Non Orange
+ Non Grape |
| Life or Body system environment |
Life or Body system functional
capacity |
DNA |
non stated functionality
, stupidity constant, mutations |
| Molecules,
Scientist, etc. |
Atoms |
Quantum Theory |
non causal/effect |
Constant unit unknown
(Symbol as example) |
A-Z |
Intersection
of other components - giving definition domain. Visualizing components
in Venn Diagram. |
A-Z (+, - ,*, / ) |
| Qualitative |
Unique Object(s) |
Intersection of other components
functionality |
f(0) = + / - * |
f(1) = + - / *
1 variable - 1 Any ; + - / * ; basic operations expressed as systems. |
f(1 + 0) = + - / *
1 variable - 1 Any. 0 variable - 0 Any . + - / * ; basic
operations expressed as systems. 1 + 0 , the functionality of
any object and it's non functionality. |
f(1, 0) = + - / *;
Intersection of other components functionality. Visualized in a Venn
Diagram.
1 variable - 1 Any. 0 variable - 0 Any ; + - / *; basic operations
expressed as systems. |
f(0) = + - / *
0 variable - 0 Any ;+ - / * ; basic operations expressed
as systems. |
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All Objects as Systems and Operations as Systems
All Objects in this portion are Sub Systems expressed as Systems of
a Principal System. Operations are intended to be independent Systems
as generally in Mathematics , but could be considered as a sub system
to some principal system.
- Where A = Bacteria and B = Person;
- A(x) * B(x) => C(x) or f(Illness)
- A(x) / B(x) => B(x, A(x))
- A(x) + B(x) => System C of Unconditional Logic
- B(x) - A(x) => C(x) or f(Wellness)
- Management for Job A + - / Job B
- Job A(x) *Job B(x) => C(x) or f(conflict)
- Job A(x) / Job B(x) => Job B(x, Job A(x))
- Job A(x) + Job B(x) => System C of Unconditional
Logic
- Job B(x) - Job A(x) => C(x) or f(System One)
- Functions of Operations as Systems
- f(+,/) = 1 unit x
- f(+, * ) = 1unit x, 1 unit y, 0 unit x
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Zim Math Grammar Interpretations
A is a Principal System; B, C are Sub Systems.
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Verbs - Principal System Events A + / - *
Sub System Word Item B / Word Event Definition B
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Plural - Principal System Events A +
/ - * Sub System Word Item B / Word Events Definition B
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Knouns - Principal System Items A +
/ - * Sub System Word Item B / Word Events Definition B
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Definitions or Qual Constructs -
f (1B,0B) = + / - *
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Declaratives - Item B /* Event B * Item B /*
Event B ; Item B/*Event B * Item A /* Event
A
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Adjectives - Principal System Events A
+ / - * (Sub System Word Item B + / - * Sub System
Word Item C)
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Sentence Structures - Principal System Events A
+ / - * (Sub System Word Item B + Sub System
Word Item C)
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Phrase Structures - (Sub System Word Item
B + Sub System Word Item C) Event 1
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'Exhaustive' List of Non-Functional Expressions
Non Functional Expressions could be said to consist of Partial System
constructs or System Wide Expressions or both. The nature of the
expressed Non-Functional construct could be said to be: Numeric,
Qualitative, an Unknown Construct or some combination of all these
possibilities. Here is a small sampling of these possibilities:
- Zero unit A unit 1
- Zero unit 1 unit A
- A unit Zero unit 1
- A unit 1 unit Zero
- 1 unit A unit Zero
- 1 unit Zero unit A
- Zero unit A-Z unit 1-N
- Zero unit 1-N unit A-Z
- A-Z unit Zero unit 1-N
- A-Z unit 1-N unit Zero
- 1-N unit A-Z unit Zero
- 1-N unit Zero unit A-Z
The operations below denote either a complete system construct or partial
system construct.
- + Zero
- - Zero
- / Zero
- * Zero
- + - / * Zero
- A - Z + Zero
- A - Z - Zero
- A - Z / Zero
- A - Z * Zero
- A - Z + - / * Zero
- 1 - N + Zero
- 1 - N - Zero
- 1 - N / Zero
- 1 - N * Zero
- 1 - N + - / * Zero
- ___ + Zero
- ___ - Zero
- ___ / Zero
- ___ * Zero
- ___ + - / * Zero
- ___ , ___ ... ___ + - / * Zero
More Non-Functional Expressions below:
- 1 minus 1
- N minus N
- System 1 - System 1
- System 1 + System 1
- Zero = ____
- Zero = ____ unit Zero
- Zero = ____ unit 1
- Zero = ____ unit A
- Zero = ____ unit N
- Zero = +
- Zero = -
- Zero = /
- Zero = *
- Zero = function of any combination or partial system expression, of
the basic operations, + - / *
- Zero = A + - / * B + - / * . . . + - / * Z; or any
partial expression thereof.
- f(Zero) = A + - / * B + - / * . . . + - / * Z; or
any partial expression thereof for any " f " = ____ .
- Zero as a complete Numeric System
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Complete Survey of Expressions of God
An expression of God or an expression of an object with the full
functional capacity offered by God could be said to consist of any
function (A-Z) or Numeric construct(s) or Unknown Construct(s)
or some combination thereof of numeric
objects 1 and/or 0 expressed with basic operations modeled as
complete systems. Here are some of
the possible initial expression construct(s)
- A-Z(1,0) = + - / *
- N(1,0) = + - / *
- 1-N(1,0) = + - / *
- ___ (1,0) = + - / *
- ___ , ___ ... ___(1,0) = + - / *
- A-Z(1+0) = + - / *
- N(1+0) = + - / *
- 1-N(1+0) = + - / *
- ___ (1+0) = + - / *
- ___ , ___ ... ___(1+0) = + - / *
- A-Z(1) = + - / *
- N(1) = + - / *
- 1-N(1) = + - / *
- ___ (1) = + - / *
- ___ , ___ ... ___(1) = + - / *
- A-Z(0) = + - / *
- N(0) = + - / *
- 1-N(0) = + - / *
- ___ (0) = + - / *
- ___ , ___ ... ___(0) = + - / *
- A-Z( __ ) = + - / *
- N( __ ) = + - / *
- 1-N( __ ) = + - / *
- ___ ( __ ) = + - / *
- ___ , ___ ... ___ ( __ ) = + - / *
- A-Z( G_d ) = + - / *
- N( G_d ) = + - / *
- 1-N( G_d ) = + - / *
- ___ ( G_d ) = + - / *
- ___ , ___ ... ___ ( G_d ) = + - / *
( "G_D" , could be considered a new form of
Math Construct. It is neither a qualitative, numeric, or an unknown
construct, putting this into its own category of symbolic-Math
construct. I had experimented with other forms of such constructs in
1985, with math expressions of so called Chinese symbols (I know no Chinese)
.)
Author/Owner - Zim Olson
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