3. Detailed description of the universe (equations)

Status
Not open for further replies.
S

StanyBecker

Registered Member
\texttt{0. Developing theories:}
\newline
\newline
Problem:
\newline
When we develop a theory based on observations and measurements, we can never be sure that this theory will always hold.
\newline
For instance, some observations and measurements can be unexplainable, leading to another theory.
\newline
An example if this is quantummechanics.
\newline
\newline
Another thing that can happen: some observations and measurements are put to discussion at some later stage, undermining the current theory.
\newline
\newline
\newline
Solution proposal:
\newline
We start from some logical proposition to be helt valid, called the '{\Large founding proposition}'.
From there, we develop logically the theory.
That way, we can never run into problems because observations and measurements are unexplainable. (As you know, observations can be deceiving ...)
\newline
If some observations and measurements are unexplainable, this means there is a flaw (a bad or badly worked out proposition).
\newline
It shouldn’t be to hard to find and correct that flaw.
\newline
\newline
It is also possible that observations and measurements are put to discussion at some later stage.
\newline
This however can never overthrow the already developed theory.
\newline
That theory was developed on sound logical base and not on the observations and measurements in question (or any other).
\newline
At most, it can put some propositions to discussion, but never the way the theory was developed! (developed logically on propositions)
\newline
Some propositions may have been suggested on not valid enough grounds, so they should be reconsidered and have the theory redeveloped from there.
\newline
\newline
\newline
This can be seen as a new paradigm (a new point of view): don’t use observations and measurements as a base, but logical theories.
\newline
It doesn’t add any new knowledge, it just changes the way we look at it.
\newline
\newline
You could compare this with the way the position of planets was predicted: at first, only circles were used.
\newline
However, that couldn’t explain the movements of the planets.
\newline
So they tried circles on circles (so-called epicircles).
\newline
But that was still unsuccesfull, so they started to add more epicircles (like circles on circles on circles and so on).
\newline
\newline
The someone said: also allow ellipses, and suddenly the movement-description became simple …
\newline
\newline
In this, “also allow ellipses” can be seen as a new paradigm.
\newline
\newline
In this comparison, “use only circles” plays the role of “observations and measurements” and “also allow ellipses” that of “start from some 'founding proposition'”.
\newline
\newline
\newline
As a ‘proof of concept”, I included a few examples of this method:
\newline
As a first (very general) `founding proposition’, I used “every theory is described using codes”. (“1. Build theories”)
\newline
Then, from this `founding proposition’ , a mathematical system is proposed. (“2. General description of the universe”)
\newline
In a thirth step, this mathematical system is worked out into a system of equations.
\newline
This system is then discussed. (“3. Detailed description of the universe (equations)”)
\newline
Using other `founding proposition’s, other theories were set up. (“4. Process-management” and “5. Data-management”)
\newline
This to show the generality of the use of `founding proposition’s.
\newline
\newline
Of course, every theory is worth looking at in its own right.
\newline
Certainly the theories about the universe should be looked at for their contents.
\newline
\newline
\newline
So to conclude:
\newline
When starting from a 'founding proposition', you should build one general enough to hold everything you intent tos include in your theory.
\newline
From there, you should develop up the desired theory using only logic.
\newline
Observations and measurements can then be used to either confirm the theory or to detect a flaw in the construction ...
\newline
 
\texttt{1. Build theories:}
\newline
\newline
Problem:
\newline
How can we build sound theories that will always hold?
\newline
As stated in '0. Developing theories', we should use some 'founding proposition' to soundly build theories.
\newline
So, as a starting point, we should find a 'founding proposition' that is basic enough to include everything we want to include.
\newline
\newline
Solution proposal:
\newline
As a 'founding proposition' that is basic enough to include everything we want to include, I suggest we take as 'founding proposition' for “Build theories” the following: “{\Large every theory is described using codes}”.
\newline
In this, “theory” nor “codes” is described any further …
\newline
All we can say is that “theory” is what we describe and that we use “codes” to do so.
\newline
\newline
This means that everything described with codes is included.
 
\texttt{2. General description of the universe:}
\newline
\newline
Problem:
\newline
Using “{\Large every theory is described using codes}” as 'founding proposition' (see '1. Build theories'), we should be able to describe the universe.
\newline
How can we do that starting from “every theory is described using codes”?
\newline
\newline
Solution proposal:
\newline
It has been proven that every code can be represented by a real number (an element of $\mathbb{R}$).
\newline
So, if we replace every code by its representation in $\mathbb{R}$, we can use real numbers instead of codes.
\newline
\newline
The 'founding proposition' “every theory is described using codes” can be interpreted as “every theory is an ordered list of codes”.
\newline
Using the representations in $\mathbb{R}$ of those codes, we get “every theory is an ordered list of real numbers”.
\newline
\newline
Now, we only consider descriptions with a finite number of codes.
\newline
However, because we don’t know that limit, we allow a countable number of codes ('$\#$$\mathbb{N}$' codes).
\newline
So, we can say every description has a representation (in real numbers) that belongs to $\mathbb{R}^{\#\mathbb{N}}$ this means every description can be represented by a vector in '$\mathbb{R}$, $\mathbb{R}^{\#\mathbb{N}}$, +'.
\newline
\newline
As you know, '$\mathbb{R}$, $\mathbb{R}^{\#\mathbb{N}}$, +' is a vector space.
\newline
This means that every description can be seen as a vector in the vector space '$\mathbb{R}$, $\mathbb{R}^{\#\mathbb{N}}$'.
\newline
\newline
\newline
Here, we limit the descriptions to the one describing the universe.
\newline
\newline
That description (as any other) can be seen as a vector in the vector space '$\mathbb{R}$, $\mathbb{R}^{\#\mathbb{N}}$'.
\newline
\newline
Now, we will impose a few constraints typical for the description of the universe:
\newline
\newline
1. We only consider 'objective' descriptions, independent of the 'coordinate-system'.
\newline
This constraint implies the use of tensor-notation for the functions describing the components of the description.
\newline
\newline
2. We treat every point and by extension every area as equal.
\newline
This means that a description valid in one area is valid in all areas.
\newline
So, we see that we only have to consider descriptions built by one set of functions describing the components of the description.
\newline
In other words: What we don't want is that there are more functions in different areas that need to be "glued together" on some border to get continuity.
\newline
An example:
\newline
% f: x<0 => bs(x)=sin(x), x<=0 => bs(x)=2*sin(x)
f: x$<$0 $\Rightarrow$ bs(x)=sin(x), x$\geq$0 $\Rightarrow$ bs(x)=2*sin(x)
\newline
The functie f is continuous for x=0 because sin(0)=0 and 2*sin(0)=0.
\newline
The first derivative (cos(x) resp. 2*cos(x)) however isn't for x=0: cos(0)=1, 2*cos(0)=2.
\newline
That kind of solutions is excluded.
\newline
\newline
Only functions ‘f’ belonging to '$C^\mathbb{R}_\infty$' (continuous and infinitely derivable in $\mathbb{R}$.) are allowed.
\newline
\newline
Now, saying that a function is element of '$C^\mathbb{R}_\infty$' and saying it can be written as a polynomial is logically the same:
\newline
Every function element of $C^\mathbb{R}_\infty$' can be developed in a polynomial, for instance its Taylor-series. (A Taylor-series leads to a polynomial based on derivatives.)
\newline
On the other hand, it is clear that every polynomial is an element of $C^\mathbb{R}_\infty$'.
\newline
\newline
So, we can conclude:
\newline
The functions describing the components of the description of the universe must use tensor-notation.
\newline
Only polynomials are allowed as functions describing the components of that description.
\newline
\newline
\newline
\newline
Equations:
\newline
We already know that the functions describing the components of a description are polynomials using tensor-notation.
\newline
Now we still need to find those functions.
\newline
To do that, we need equations using tensor-notation.
\newline
\newline
The composition of those equations depends on the problem being solved.
\newline
Once these equations are set up, the problem is solved.
\newline
The solution is now said to be in 'equation-form'.
\newline
\newline
The problem with the 'equation-form' is that it is unusable in practice.
\newline
So we have to transform the 'equation-form' into one that \emph{is} usable in practice.
\newline
This action is often called: solving the equations.
\newline
In doing so, we carefully take precautions not to leave out or introduce solutions in any of the transformations.
\newline
All this is purely mathematical, no problem interpretation whatsoever is done here.
\newline
\newline
\newline
Let's concentrate on the transformations converting the 'equation-form' into one that is usable in practice.
\newline
\newline
We already know that every solution is a real function (codes).
\newline
However, this doesn't mean we have to limit ourselves to real numbers in the transformations converting the 'equation-form' into a 'practically usable form', also called 'a solution'.
\newline
\newline
This also means that we can have 'solutions' that have parts with other things than real numbers.
\newline
We have to exclude those solutions.
\newline
\newline
So, we need to solve the equations (transforming them into a 'practically usable form').
\newline
To do that, we need "the biggest field" that includes the field '$\mathbb{R}$, +, *'.
\newline
\newline
This field turns out to be '$\mathbb{H}$,+,*', the so-called quaternions.
\newline
\indent
(see url "https://en.wikipedia.org/wiki/Quaternion")
\newline
The quaternions are an extension of the complex numbers in the sense that quaternions have three imaginary components ('i', 'j' and 'k'), the complex numbers only have one ('i').
\newline
This means every equation in $\mathbb{H}$ consists out four equation in $\mathbb{R}$: one real equation, and one in 'i', 'j' and 'k' respectively.
\newline
Now, since we have only real number (representation of codes), the equations for 'i', 'j' and 'k' are in reality identities.
\newline
This gives rise to three dimensions in every solution (the identities for the imaginary components).
\newline
This could be the reason we live in three dimensions.
\newline
\newline
Suppose, we have solved the equations and excluded the solutions with imaginary parts.
\newline
Now, there can still be solutions that do not give a real number in some points, but go to infinity.
\newline
Because we use polynomials as solution, there are no singularities.
\newline
It is however still possible that divergence occurs from a certain point.
\newline
We also need to exclude those solutions, or said in other words: only solutions with convergence-radius '$\infty$' are acceptable.
\newline
\newline
Conclusion:
\newline
After solving the equations in $\mathbb{H}$ (quaternions), we first need to exclude all solutions with imaginary parts.
\newline
(Only real solutions are acceptable because of the link with codes.)
\newline
Then, we also need to exclude all solutions with finite convergence-radius (meaning they go to infinity from some point).
\newline
\newline
So, we found that an objective scientific description of any system uses equations in tensorial notation and that these equations should be solved using H, the quaternions.
\newline
After obtaining the solutions, only those without imaginary parts and with convergence-radius '$\infty$' are acceptable.
\newline
 
\texttt{3. Detailed description of the universe (equations):}
\newline
\newline
In '2. General description of the universe', we already deducted from the foundation “every theory is described using codes” a useable conclusion:
\newline
“{\Large After solving the equations in $\mathbb{H}$ (quaternions), we first need to exclude all solutions with imaginary parts.}
\newline
{\Large (Only real solutions are acceptable because of the link with codes.)}
\newline
{\Large Then, we also need to exclude all solutions with finite convergence-radius (meaning they go to infinity from some point).}”
\newline
\newline
\newline
Now, we continue with the description of the universe:
\newline
\newline
Deduction on mathematical (geometrical) grounds:
\newline
We use the “Einstein summation convention”.
\newline
\newline
Tensorcalculus en geometry:
\newline
$R_{i j}$ = $R_{i t j}^t$ $\Rightarrow$ $R_{m n}$ (Ricci Tensor)
\newline
(see 'https{:}//en.wikipedia.org/wiki/\texttt{Ricci\_curvature}')
\newline
\newline
R = $R_{t s}$ * $g^{t s}$ $\Rightarrow$ R
\newline
\newline
% $R_{j k l}^i$ = $\partial_k$ * $\Gamma_{j l}^i$ - $\partial_l$ * $\Gamma_{j k}^i$ + $\Gamma_{j l}^t$ * $\Gamma_{t k}^i$ - $\Gamma_{j k}^t$ * $\Gamma_{t l}^i} $\Rightarrow$ $R_{k i j}^l$ (Riemann Tensor)
$R_{j k l}^i$ = $\partial_k$ * $\Gamma_{j l}^i$ -
$\partial_l$ * $\Gamma_{j k}^i$ +
$\Gamma_{j l}^t$ * $\Gamma_{t k}^i$ -
$\Gamma_{j k}^t$ * $\Gamma_{t l}^i$
$\Rightarrow$
$R_{k i j}^l$ (Riemann Tensor)
\newline
(see 'https://en.wikipedia.org/wiki/\texttt{Riemann\_curvature\_tensor}')
\newline
\newline
$\Gamma_{b c}^a$ = $g^{a t}$ * ( $\partial_c$ $g_{b t}$ + $\partial_b$ $g_{c t}$ - $\partial_t$ $g_{b c}$ ) / 2 $\Rightarrow$ $\Gamma_{b c}^a$
\newline
\indent
$\Rightarrow$
\newline
$\Gamma_{b c}^a$ = $g^{a t}$ * $\partial_c$ $g_{b t}$ / 2 + $g^{a t}$ * $\partial_b$ $g_{c t}$ / 2- $g^{a t}$ * $\partial_t$ $g_{b c}$ / 2 $\Rightarrow$ $\Gamma_{b c}^a$
\newline
(Christoffel symbols)
\newline
\indent
(see "https://en.wikipedia.org/wiki/\texttt{Christoffel\_symbols}")
\newline
\newline
Inverse matrix:
\newline
$g_{i t}$*$g^{t j}$= $\delta_i^j$ $\Rightarrow$ $g^{n m}$
\newline
\newline
All tensors are function of the coordinats '$x^i$'.
\newline
\newline
\newline
There still has to be found an equation for '$g_{i j}$'.
\newline
This has to be done on mathematical grounds (for as far as possible).
\newline
\newline
{\Large Constraint}: we take it that all movement goes along geodesics.
\newline
This implies following equations:
\newline
$v^t$*$\partial_t$ $v^j$ + $\Gamma_{t s}^j$ * $v^t$ * $v^s$ = 0 $\Rightarrow$ $v^n$ {movement along geodesics}
\newline
$g_{t s}$ * $v^t$ * $v^s$ =1 { speed as unity-vector }
\newline
leading to
\newline
$w^t$ *$\partial_t$ $w^j$ + $\Gamma_{t s}^j$ * $w^t$ * $w^s$ = 0 $\Rightarrow$ $w^n$
\newline
w * w = $g_{t s}$ * $w^t$ * $w^s$ $\Rightarrow$ w {square norm}
\newline
w * $v^n$ = $w^n$ $\Rightarrow$ $v^n$
\newline
\newline
\newline
Let us define a so-called “impuls-vector” '$p^i$' the following way:
\newline
$\mu$ * $\mu$ = $g_{t s}$ * $p^t$ * $p^s$ $\Rightarrow$ $\mu$ {mass}
\newline
\newline
$p_i$ = $g_{i t}$ * $p^t$ $\Rightarrow$ $p_i$
\newline
\newline
$p^n$ = $\mu$ * $v^n$ $\Rightarrow$ $p^n$ {impuls-speed connection}
\newline
\newline
{\Large Constraint}: we take it that we can fully describe reality (the universe) using the impuls as defined above.
\newline
\newline
Now, because movement goes along geodesics and that kind of movement preserves the metric, we can also say that the movement goes along so-called “killing vectors”.
\newline
\indent
(see url "https://en.wikipedia.org/wiki/\texttt{Killing\_vector\_field}",
\newline
\indent
so “K” denotes a “Killing Field” if '$\nabla_m$ $K_n$ + $\nabla_n$ $K_m$ = 0' with “$\nabla$” the covariant derivative)
\newline
\newline
{\Large Constraint}: we take it that the impuls “p” describes movement.
\newline
When the impuls “p” describes movement and movement goes along geodesics, we can say that “p” must be a “Killing Field”.
\newline
\newline
This means '$p_n$' must obey
\newline
'$\nabla_m$ $K_n$ + $\nabla_n$ $K_m$ = 0': $\nabla_m$ $p_n$ + $\nabla_n$ $p_m$ = 0
\newline
\newline
Filling out the definition of covariant derivative “$\nabla$” then gives:
\newline
\indent
($\nabla_j$ $v_i$ = $\partial_j$ $v_i$ + $\Gamma_{k j}^i$ * $v_k$,
\newline
\indent
see url "https://en.wikipedia.org/wiki/\texttt{Covariant\_derivative}\#\texttt{Covector\_fields}")
\newline
( $\partial_m$ $p^n$ + $\Gamma_{k m}^n$ * $p^k$ ) + ( $\partial_n$ $p^m$ + $\Gamma_{k n}^m$ * $p^k$ ) = 0
\newline
or
\newline
$\partial_m$ $p^n$ + $\Gamma_{k m}^n$ * $p^k$ + $\partial_n$ $p^m$ + $\Gamma_{k n}^m$ * $p^k$ = 0
\newline
and
\newline
$p_i$ = $g_{i j}$ * $p^j$
\newline
\indent
$\Rightarrow$
\newline
$\partial_m$ $p^n$ + $\Gamma_{k m}^n$ * $p^k$ + $\partial_n$ $p^m$ + $\Gamma_{k n}^m$ * $p^k$ = 0
\newline
$p_i$ = $g_{i j}$ * $p^j$
\newline
\newline
This forms the equation for a “killing vector”.
\newline
It is a two-indexes equation in which '$g_{i j}$' (via '$\Gamma_{k i}^l$') appears.
\newline
So, we can use this equation to determine '$g_{i j}$'.
\newline
This means we have:
\newline
$\partial_m$ $p^n$ + $\Gamma_{k m}^n$ * $p^k$ + $\partial_n$ $p^m$ + $\Gamma_{k n}^m$ * $p^k$ = 0 $\Rightarrow$ $g_{i j}$
\newline
$p_i$ = $g_{i j}$ * $p^j$ $\Rightarrow$ $p_i$
\newline
\newline
\newline
{\Large So, to resume}:
\newline
Tensorcalculus and geometry
\newline
$R_{i j}$ = $R_{i t j}^t$ $\Rightarrow$ $R_{m n}$ (Ricci Tensor)
\newline
R = $R_{t s}$ * $g^{t s}$ $\Rightarrow$ R
\newline
$R_{j k l}^i$ = $\partial_k$ $\Gamma_{j l}^i$ - $\partial_l$ $\Gamma_{j }^i$ + $\Gamma_{j l}^t$ * $\Gamma_{t k}^i$ - $\Gamma_{j k}^t$ * $\Gamma_{t l}^i$
$\Rightarrow$ $R_{k i j}^l$
\newline
\newline
$\Gamma_{b c}^a$ = $g^{a t}$ * $\partial_c$ $g_{b t}$ / 2 + $g^{a t}$ * $\partial_b$ $g_{c t}$ / 2- $g^{a t}$ * $\partial_t$ $g_{b c}$ / 2 $\Rightarrow$ $\Gamma_{b c}^a$
\newline
\newline
\newline
Inverse matrix
\newline
$g_{i t}$ * $g^{t j}$= $\delta_i^j$ $\Rightarrow$ $g^{n m}$
\newline
\newline
\newline
movement along geodesics
\newline
$w^t$ *$\partial_t$ $w_j$ + $\Gamma_{t s}^j$ * $w^t$ * $w^s$ = 0 $\Rightarrow$ $w^n$
\newline
w * w = $g_{t s}$ * $w^t$ * $w^s$ $\Rightarrow$ w
\newline
w * $v^n$= $w^n$ $\Rightarrow$ $v^n$
\newline
\newline
\newline
definition impuls vector
\newline
$\mu$ * $\mu$ = $g_{t s}$ * $p^t$ * $p^s$ $\Rightarrow$ $\mu$
\newline
$p_i$ = $g_{i t}$ * $p^t$ $\Rightarrow$ $p_i$
\newline
$p^n$ = $\mu$ * $v^n$ $\Rightarrow$ $p^n$
\newline
\newline
\newline
killing vector
\newline
$\partial_m$ $p^n$ + $\Gamma_{k m}^n$ * $p^k$ + $\partial_n$ $p^m$ + $\Gamma_{k n}^m$ * $p^k$ = 0 $\Rightarrow$ $g_{i j}$
\newline
$p_i$ = $g_{i j}$ * $p^j$ $\Rightarrow$ $p_i$
\newline
\newline
\newline
\newline
This all renders the following system of equations describing reality (the universe):
\newline
\{
\newline
$R_{i j}$ = $R_{i t j}^t$ $\Rightarrow$ $R_{m n}$
\newline
R = $R_{t s}$ * $g^{t s}$ $\Rightarrow$ R
\newline
$R_{j k l}^i$ = $\partial_k$ $\Gamma_{j l}^i$ - $\partial_l$ $\Gamma_{j k}^i$ + $\Gamma_{j l}^t$ * $\Gamma_{t k}^i$ - $\Gamma_{j k}^t$ * $\Gamma_{t l}^i$ $\Rightarrow$ $R_{k i j}^l$
\newline
$\Gamma_{b c}^a$ = $g^{a t}$ * $\partial_c$ $g_{b t}$ / 2 + $g^{a t}$ * $\partial_b$ $g_{c t}$ / 2- $g^{a t}$ * $\partial_t$ $g_{b c}$ / 2 $\Rightarrow$ $\Gamma_{b c}^a$
\newline
$g_{i t}$ * $g^{t j}$ = $\delta_i^j$ $\Rightarrow$ $g^{n m}$
\newline
$w^t$ *$\partial_t$ $w_j$ + $\Gamma_{t s}^j$ * $w^t$ * $w^s$ = 0 $\Rightarrow$ $w^n$
\newline
w * w = $g_{t s}$ * $w^t$ * $w^s$ $\Rightarrow$ w
\newline
w * $v^n$ = $w^n$ $\Rightarrow$ $v^n$
\newline
$\mu$ * $\mu$ = $g_{t s}$ * $p^t$ * $p^s$ $\Rightarrow$ $\mu$
\newline
$p_i$ = $g_{i t}$ * $p^t$ $\Rightarrow$ $p_i$
\newline
$p^n$ = $\mu$ * $v^n$ $\Rightarrow$ $p^n$
\newline
$\partial_m$ $p^n$ + $\Gamma_{k m}^n$ * $p^k$ + $\partial_n$ $p^m$ + $\Gamma_{k n}^m$ * $p^k$ = 0 $\Rightarrow$ $g_{i j}$
\newline
$p_i$ = $g_{i j}$ * $p^j$ $\Rightarrow$ $p_i$
\newline
\}
\newline
In the solutions, our attention goes out to '$\mu$' and '$v^n$' (the position and speed of matter) and to '$g_{i j}$' (the determination of distance).
\newline
\newline
\newline
As already pointed out, we don’t have to restrict ourselves to '$\mathbb{H}$' when solving these equations, but we have to use '$\mathbb{H}$' to do so.
\newline
As also shown, every equation becomes one equation (real component) and three identities (imaginary components).
\newline
Now, four dimensions (on real and three imaginary ones) with one {\Large constraint} (equation) leaves three free dimensions.
\newline
In my opinion, that’s the reason we experience three dimensions.
\newline
\newline
\newline
When have found all the solutions, we need to exclude the solutions that hold imaginary parts, as well as those with a finite convergence-radius (meaning they go to infinite beyond some point).
\newline
\newline
\newline
When we look to the equations above, we notice that most of them (all of them but one) can be brought back to an equation with partial derivatives, of which the “0”-function is a solution.
\newline
The “0”-function means: NO universe.
\newline
BUT, there is also one equation that isn’t like the others: the equation governing the inverse matrix.
\newline
This equation does NOT allow a “0”-solution.
\newline
So, because the equation governing the inverse matrix, its solution must have values different fom zero (cannot be the “0”-matrix), inducing all the other functions to also be non-zero.
\newline
\newline
{\Large Or said in a one-liner:}
\newline
{\Large The universe exists because the “0”-matrix doesn’t have an inverse.}
\newline
 
\texttt{4. Process management:}
\newline
\newline
Problem:
\newline
How can we specify uniformly an informatics-routine and simplify the building of it?
\newline
\newline
Some reseach based on articles of Martin Ward led to the insight that every informatics-routine can be specified by a (logical) proposition.
\newline
(source: via url “http://www.gkc.org.uk/martin/papers/index.html”)
\newline
As stated in '0. Developing theories', we should use some 'founding proposition' to soundly build theories.
\newline
So, the “founding propositions” we use here is “{\Large all informatics-routines can be resumed in a (logical) proposition}”.
\newline
This proposition is called the “routine-proposition”.
\newline
This “routine-proposition” is to be helt valid by the informatics-routine being specified.
\newline
\newline
As we see, a “routine-proposition” seems to be an ideal candidate to specify an informatics-routine.
\newline
It is simple and uniform and it contains all the information stored in the routine, but nothing more.
\newline
\newline
As a “proof of concept”, I tried to develop an implementation based on the founding propositions above.
\newline
In this, I succeeded!
\newline
The result is an application called “ReqLan” (requirement language).
\newline
\newline
A high-level “routine-proposition” still needs to be refined using (logically derived) low(er)-level (sub)“routine-proposition”s.
\newline
This goes on until we have reached a certain (well-specified) level of propostions.
\newline
Then we have got a '“routine-proposition” and its derivation'.
\newline
From there, “ReqLan” can take over the generation.
\newline
\newline
\newline
You could also use other versions of “ReqLan” to produce other kinds of text (rather then having to edit them yourself).
\newline
Examples are management-texts or user-manuals.
\newline
\newline
Maintenance on these informatics-routine can also be done on the level of the '“routine-proposition” and its derivation'.
\newline
If an adjustment has to be made, you should look up the involved propositions and adjust them.
\newline
Then you can regenerate the code using “ReqLan” on the adjusted '“routine-proposition” and its derivation'.
\newline
\newline
Using a “routine-proposition” (with or without its derivation), it is easy to communicate what an informatics-routine extacly does
and what it doesn’t do.
\newline
This could be important when specifying informatics-routines in a general and uniform way.
\newline
So, indeed, a “routine-proposition” seems to be an ideal candidate to specify an informatics-routine in a general and uniform way.
\newline
\newline
\newline
Another matter is how to get this “routine-proposition”!
\newline
\newline
Because of the enormous variety in the input (the problems to be solved), it is almost impossible to give a general method.
\newline
\newline
The closest I can get is proposing to develop a set of (hopefully) reusable templates that can be filled out.
\newline
From those filled out templates, the '“routine-proposition” and its derivation' should then be generated.
\newline
From there, “ReqLan” can take over further generation.
\newline
\newline
Anotyher way of course is to use the classical means, but to work towards a “routine-proposition” (and its derivation).
\newline
\newline
\newline
So, in my opinion the use of “routine-proposition” could be helpfull in developing, maintaining and specifying informatics-routines
in a general and uniform way.
\newline
\newline
\newline
As an example, you could give the development of a "salary-system", a system that pays the correct (gross) salary every month to each
employee.
\newline
\newline
\indent
This is a possible way to do so:
\newline
We suppose we have information with the monthly salary per managent-level and per seniority.
\newline
We load that information. (a number of assignment-propositions)
\newline
Besides that, we know when each employee was hired and in what level.
\newline
Now, every first of the month, the "salary-system" is started with as “routine-proposition”: "every employee received the correct (gross)
salary for the previous month." (a proposition)
\newline
Initially, it is installed that NO employee received his or her correct (gross) salary.
\newline
So, we refine "every employee received the correct (gross) salary for the previous month." to "for every employee: this employee received
his or her correct (gross) salary for the previous month."
\newline
Now, we need to refine "this employee received his or her correct (gross) salary for the previous month." (a proposition)
\newline
We do this by loading the information (managent-level and seniority) for that employee. (a few assignment-propositions)
\newline
Then, for that employee, we get the correct (gross) salary from the information loaded about the monthly salary per managent-level and per
seniority. (again using assignment-propositions)
\newline
\newline
\newline
{\Large Conclusion:}
\newline
The development and maintenance of an informatics-routine can be done in a general and uniform way by stating what it is supposed to do.
\newline
This by using a so-called “routine-proposition”, a proposition that is to be helt valid by the informatics-routine to be built.
\newline
From this “routine-proposition”, the routine (amongst other things) can be generated.
\newline
 
\texttt{5. Data management:}
\newline
\newline
\newline
\newline
Problem:
\newline
How can we store and manage data in a uniform and flexible way?
\newline
Since every initialisation or update is done via an assignment, it seems to make sense to store assignments.
\newline
As stated in '0. Developing theories', we should use some 'founding proposition' to soundly build theories.
\newline
As 'founding propositions', we take here “{\Large all data-management is done via assignments}”.
\newline
Then, we store assignments of the form 'object'.'property'='value', rather than fields of columns (properties) in a table (object).
\newline
\newline
When storing that kind of assignments instead of columns (properties) in a table (object), we don’t need to know about relationships between tables (objects), because there is no use of tables when storing 'object'.'property'='value'-like assignments.
\newline
\newline
This means that we don’t have to create a so-called datamodel that we need to normalize, implement or adjust first.
\newline
We can start immediately inserting data (assignments).
\newline
\newline
Also, if there is need for new properties, you can just add them as assigments without going through the trouble of having to adjust a datamodel, due to those new properties.
\newline
\newline
This makes the data-processing more transparant.
\newline
\newline
It also means you can manage all kinds of heterogenuous data in one application!
\newline
\newline
This facilitates things like combining heterogenuous data, e.g. combine data from firms with data from cars to see how many company-cars there are, who owns them and who uses them.
\newline
\newline
Another example is the insertion of the number of train-users between two stations.
\newline
This can be recorded when the train conductor controlls the train-users.
\newline
\newline
To store the data in a data-base, you need to go through a long, time-consuming and difficult process.
\newline
After that, you still need to develop the extraction of the data you want in the data-base environment (not the easiest one).
\newline
\newline
To store the data in “AssSet”, you only need to store the fact that a train-users is controlled.
\newline
All the extraction of the data you want can now be developed in a real developers environment (which is a lot easier).
\newline
\newline
There are many more of those examples around (the sky is the limit).
\newline
\newline
\newline
Of course, there still is a datamodel for the storing of assignments, but it is hidden from the user (the data-consultant), as it should be.
\newline
The users (the data-consultants) have operators at their disposal for managing data.
\newline
\newline
Internally, the data is not stored in tables with columns, but in binary trees.
\newline
This increases flexibility.
\newline
\newline
As a “proof of concept”, I tried to develop an implementation based on the founding propositions above.
\newline
In this, I succeeded!
\newline
The result is an application called “AssSet” (Assignment Set).
\newline
\newline
\newline
The method described here (storing assignments) can also provide help in the use and storing of so-called metadata (data about data).
\newline
You can do this by inserting the desired specification in an assignment with a (possible new) property.
\newline
A way to specify a property is to use a specification of the value determining routine of that property and store it as a new property.
\newline
This is an objective specification from which all other use-defined specifications should be derivable.
\newline
So, this specification seems to be a good candidate for a uniform and complete specification.
\newline
\newline
A way to specify routines is discussed in the article about “Process management”.
\newline
\newline
\newline
A few suggestions of where “AssSet” could prove to be an asset (mainly because “AssSet” has no need for a data-model).
\newline
There are of course many more examples than the few suggestions made here, or as they say in “Open Data”: The sky is the limit.
\newline
\newline
‘Add data-properties’:
\newline
When we use a data-base as data-source and we need to add a data-property, we face a lot of prior problems .
\newline
First of all, we need to install a place in the data-base to hold the data.
\newline
This is usually done via an adjustment of the data-model and possibly a renormalisation.
\newline
This already can be a hard and time-consuming task.
\newline
Then we need to implement this adjustment on the data-model in the data-base and reload the (adjusted) database.
\newline
Again, this can be a hard task to accomplish.
\newline
\newline
Only then, we can think about adding data for the new data-property.
\newline
\newline
When using “AssSet” as data-source, this is a lot easier.
\newline
All you have to do is to store the apprpopriate asignments, using uniform and easy operators.
\newline
“AssSet” will guarantee (behind the screens) an effective storage.
\newline
\newline
(Also see the examples about the company-cars and the train-users)
\newline
\newline
\newline
‘Big Data’
\newline
Because you can put everything assignable in ‘AssSet’, it this the ideal environment for ‘Big Data’ and its analysis (using other available Java-tools).
\newline
This is because you don’t have to worry about data-models or other things.
\newline
You can just add assignment of (very) heterogeneous nature in the same application!
\newline
\newline
(Like the examples about the company-cars and the train-users)
\newline
 
Please try formatting your posts to remove all the code (e.g. "\newline")

This is a discussion forum. You should post a topic for discussion. You can link to your paper, or attach it to your discussion post.

I have closed your thread and moved it out of our Physics subforum, since it is very difficult to read in its current form. Please start a new thread and try again. Use a single thread, not many separate threads.
 
Status
Not open for further replies.
Back
Top