text:
\section{Introduction to the problem}

The standard QCD evolution equation
\begin{equation}
\label{eq:Evolequ}
\begin{split}
  \partial_t D_k(t,x)
&= \sum_j {\EuScript{P}}_{kj}(t,\cdot)\otimes D_j(t,\cdot)(x),
\\
f(\cdot){\otimes} g(\cdot)(x)
   &\equiv \int_0^1 dx_1 dx_2 \delta(x-x_1 x_2)f(x_1)g(x_2)
    \equiv \int_x^1  \frac{dx_2}{x_2} f
                      \Bigl(\frac{x}{x_2}\Bigr)g(x_2),
\end{split}
\end{equation}
describes response of the parton distribution function (PDF) $D_k(t,x)$
to a change of the large energy scale $Q=\exp(t)$.
Variable $x$ is identified as a fraction of the hadron momentum carried by parton
of the type $k$ (quark, gluon).
Evolution kernel ${\EuScript{P}}$ is calculable within perturbative QCD.

The above evolution equation (\ref{eq:Evolequ})
is an important ingredient in many QCD perturbative calculations.
It can be solved using variety of the numerical methods, including Monte Carlo method.
The knowledge of $D_{k}(t_0,x)$ at certain initial $t_0$, is required
for solving evolution equation at other $t>t_0$.
The initial PDF is fitted to experimental data.

The principal aim of this work is to derive the following%
 analytical solution of the
above QCD evolution equations
\begin{equation}
\label{eq:Evolsolu}
\begin{split}
D_k(t,x) =&
     \int\limits_0^1 dz'\; dx_0\;
     G_{kk}^B(t, t_{0},z')\;
     D_k(t_0,x_0)\delta(x-z' x_0)
  +\sum_{n=1}^\infty \;
      \int\limits_0^1 dx_0\;
\\&~~~~~~\times
   \sum_{{k_{n-1},\dots,k_{1},k_{0}}}
   \Bigg[ \prod_{j=1}^n \int\limits_{t_0}^t dt_j\;
     \Theta(t_j-t_{j-1}) \Bigg]\;
   \int\limits_0^1 dz'_{n+1}\;
   \Bigg[ \prod_{i=1}^{n}
     \int\limits_0^1 dz'_i\;dz_i\;
     \Bigg]\;
\\&~~~~~~\times
   G_{kk}^B(t,t_n,z'_{n+1})\;
   \Bigg[ \prod_{i=1}^n
     \EuScript{P}_{k_ik_{i-1}}^A (t_i,z_i)\;
     G_{k_{i-1}k_{i-1}}^B(t_i,t_{i-1},z'_i) \Bigg]\;
\\&~~~~~~\times
      D_{k_0}(t_0,x_0)
      \delta\bigg(x- x_0 \prod_{i=1}^n z_i \prod_{i=1}^{n+1} z'_i
     \bigg),
   \;\;\; k_n=k,
\end{split}
\end{equation}
where we have isolated flavour conserving (bremsstrahlung) part of the kernel%
\footnote{Since $\EuScript{P}^A_{kk}=0$, only flavour changing indices
$k_i\neq k_{i-1}$ enter in the flavour sum in eq.~(\ref{eq:Evolsolu}).}
$\EuScript{P}^B_{kj}\equiv\delta_{kj}\EuScript{P}_{kk}$ from
the total kernel, $\EuScript{P}_{kj}=\EuScript{P}^A_{kj}+\EuScript{P}^B_{kj}$,
and $G_{kk}^B(t_1,t_0,z)$ is the solution of the following simplified evolution
equation, similar to eq.~(\ref{eq:Evolequ}),
\begin{equation}
\label{eq:EvolGA}
 \partial_t G_{kk}^B(t,t_0,z) =
    {\EuScript{P}}^B_{kk}(t,\cdot)\otimes G_{kk}^B(t,t_0,\cdot)(z),
\end{equation}
see Section \ref{sec:real-thing} for the details.
The boundary condition is $G_{kk}^B(t_0,t_0,z)=\delta(1-z)$.
See also fig.~\ref{fig:hierarchy} for graphical representation.

\begin{figure}[!ht]
  \centering
  \epsfig{file=hierarchy.eps,width=140mm}
  \caption{\sf
	Kinematics in the 2-level
	emission tree of eq.~(\ref{eq:Evolsolu}).
    }
  \label{fig:hierarchy}
\end{figure}

It is important to provide formal proof of eq.~(\ref{eq:Evolsolu}),
because it is a critical ingredient in several new Monte Carlo algorithms
of the non-Markovian type%
\footnote{It can serve as basis of a novel type of the Markovian MC as well.}
described in refs.~\cite{Golec-Biernat:2006xw} and~\cite{Jadach:2003bu},
and possibly in other future works.

Let us now explain in details
notation used in eqs.~(\ref{eq:Evolequ}-\ref{eq:EvolGA}).
In function $D_k(t,x)$
variable $1\geq x \geq 0$ is the fraction
of the hadron momentum carried by the parton
of the type $k=G,q_i,\bar{q}_i$, i.e. gluon, quark or antiquark,
at the high energy scale $Q$, conveniently translated into
the ``evolution time'' variable $t=\ln Q$.
In QCD the PDF represents the wave function
of the hadron close to the light-cone.
See ref.~\cite{Collins:2003fm} for an expert discussion on the precise
meaning of PDF in QCD, in a wide context of the so-called
{\em factorization theorems}~\cite{Collins:1984kg,Collins:1981uk,Bodwin:1984hc}
in the gauge Quantum Field Theories.

In this work we shall restrict ourselves to the most
common QCD evolution equations of the DGLAP type~\cite{DGLAP},
with the kernel splitting functions%
\footnote{The DGLAP kernels in the $\overline{MS}$ scheme were
   calculated in QCD at the two levels beyond the
   leading-logarithmic (LL) approximation.}
incorporating the QCD coupling constant
(for the sake of the simplicity of notation)
\begin{equation}
  {\EuScript{P}}_{kj}(t,z) = \frac{\alpha(t)}{\pi} P_{kj}(t,z).
\end{equation}
The QCD kernel functions are singular,
with singularities of the type $(\ln(1-z)^n/(1-z))_+$.
We shall typically regularize them with the help of an explicit
small infrared (IR) cutoff parameter%
\footnote{The infinitesimal parameter $\varepsilon$ can be $t$-dependent,
  without any loss of generality in the following treatment.}
$\varepsilon$ as follows:
\begin{equation}
\label{Peu}
{\EuScript{P}_{kj}(t,z)}=-\EuScript{P}^{\delta}_{kk}(t,\varepsilon) \delta_{kj}\delta(1-z)
                 +\EuScript{P}^{\Theta}_{kj}(t,z),
\;\;
       \EuScript{P}^{\Theta}_{kj}(t,z)=\EuScript{P}_{kj}(t,z)\Theta(1-z-\varepsilon).
\end{equation}
The important Sudakov formfactor $\Phi_{k}(t,t_0)$
is directly related to the virtual part of the kernels:
\begin{equation}
    {\Phi_{k}(t,t_0)} = \int\limits_{t_0}^t  dt'\;
       \EuScript{P}^\delta_{kk}(t',\varepsilon).
\end{equation}
Finally the (bremsstrahlung-type) auxiliary distribution
\begin{equation}
\begin{split}
\label{eq:GAbrems}
G_{kk}^B &(t,t_0,z) = \delta(1-z)
\\ &
  +\sum_{n=1}^\infty \;
      \bigg[ \prod_{i=1}^n \int\limits_{t_0}^t dt_i\;
      \Theta(t_i-t_{i-1})  \int\limits_0^1 dz_i\bigg]
      e^{-\Phi_k(t,t_n)}
      \bigg[\prod_{i=1}^n
           \EuScript{P}_{kk}^\Theta (t_i,z_i)
            e^{-\Phi_{k}(t_i,t_{i-1})} \bigg]
      \delta\big(x- \prod_{i=1}^n z_i \big)
\end{split}
\end{equation}
is an iterative%
\footnote{We shall explain in the next Section why we call it ``iterative''.}
solution of the flavour-diagonal evolution equation of eq.~(\ref{eq:EvolGA}).
See also fig.~\ref{fig:bremstree} for graphical representation of the
above gluonstrahlung segment of the evolution.

\begin{figure}[!ht]
  \centering
  {\epsfig{file=bremstree.eps,width=140mm}}
  \caption{\sf
	Kinematics in the
	pure brems\-strahlung emission tree of eq.~(\ref{eq:GAbrems}).
    }
  \label{fig:bremstree}
\end{figure}

\section{The solutions}
If our only aim was to prove the correctness of eq.~(\ref{eq:Evolsolu})
as a solution of eq.~(\ref{eq:Evolequ}),
then the simplest approach would be just to substitute it into this equation
and check with a little bit of algebra that indeed it is the solution.
Our aims are however more general:
(i) to derive eq.~(\ref{eq:Evolsolu}) in a more systematic way,
(ii) to understand better its relation to the other widely known
and used iterative solutions of eq.~(\ref{eq:Evolequ}),
(iii) to prove that its {\em exclusive} content,
in terms of the fully differential distribution
in all variables $t_i$ and $z_i$, $i=1,2,...,n$, for each $n$,
is exactly the same as in other iterative solutions, commonly used in the
MC approaches.

Having all the above in mind, let us proceed methodically,
first with deriving solution of the evolution of eq.~(\ref{eq:Evolequ}),
in terms of a time-ordered exponential, widely used in the literature.
Next, we shall present first example of the derivation of eq.~(\ref{eq:Evolsolu})
by means of reorganizing the evolution equation and solving it once again.
Then, we shall present second example of the derivation,
in which the above time-ordered exponential
is algebraically reorganized (transformed) into eq.~(\ref{eq:Evolsolu}).
Finally the third derivation of eq.~(\ref{eq:Evolsolu}) based on straightforward
reorganization of the multiple sums and integrals will be included in the Appendix.

\subsection{Time-ordered exponential}

The solution of eq.~(\ref{eq:Evolequ})
can be established quickly and rigorously,
for instance by means iteration, as a time-ordered exponential
of the kernel operator $\EuScript{P}$ in the vector (linear) space indexed
by one continuous variable $x$ and one discrete $k$.
More precisely,
eq.~(\ref{eq:Evolequ}) in a more compact matrix notation reads
\begin{equation}
  \partial_t {\bf D}(t) = {\bf P}(t) \; {\bf D}(t)
\end{equation}
and its solution in the same compact matrix notation is given by
\begin{equation}
\label{eq:solumatr}
  {\bf D}(t) = \exp\left( \int_{t_0}^t {\bf P}(t') dt' \right)_T \; {\bf D}(t_0)
       = {\bf G}_{P}(t,t_0) D(t_0),
\end{equation}
where we employ the following well known {\em time-ordered exponential}
evolution operator%
\footnote{Here and in the following we define
$\prod_{i=1}^n A_i \equiv A_n A_{n-1}\dots A_2A_1$.}
\begin{equation}
\label{eq:torder}
{\bf G}_{H}(t,t_0)=
{\bf G}(H;t,t_0)=
\exp\left( \int_{t_0}^t {\bf H}(t') dt' \right)_T
 = {\bf I} +\sum_{n=1}^\infty
      \prod_{i=1}^n  \int_{t_0}^t dt_i \theta_{t_i>t_{i-1}} {\bf H}(t_i),
\end{equation}
for $t\geq t_0$.
It is familiar to all readers
from the textbooks of the Quantum Mechanics%
\footnote{However, we do not require ${\bf H}$ to
     be hermitian and ${\bf G}$ to be unitary.}.
We define function $\theta_{x>y}$
to be equal 1 when $x>y$ and equal 0 otherwise.

The compact solution of equation (\ref{eq:solumatr}),
can be translated into more traditional integro-tensorial notation,
with explicit sums and integrals:
\begin{equation}
  \label{eq:IterPeu}
  \begin{split}
 D_k(t,x)
 &= \left\{
   \left[ \exp\left( \int_{t_0}^t dt'\; {\bf P}(t',\cdot)\otimes
   \right)\right]_T\; {\bf D}(t_0,\cdot)
   \right\}_k
\\&
= D_k(t_0,x)
  +\sum_{n=1}^\infty \;
   \sum_{k_{n-1}...k_{1}k_{0}}
   \int_0^1 dx_0\;
\\&~~~~~~~~~~~~~~~~~\times
   \bigg[ \prod_{j=1}^n \int\limits_{t_0}^t dt_j\;
          \theta_{t_j>t_{j-1}}
          \int\limits_0^1 dz_j\;
          \EuScript{P}_{k_jk_{j-1}}(z_i)
   \bigg]\;
     D_{k_0}(t_0,x_0)\; \delta_{x= x_0\prod_{i=1}^n z_i},
  \end{split}
\end{equation}
where $\delta_{x=y}\equiv \delta(x-y)$.
We realize, that the above formula, although rigorous and very elegant,
is useless for any practical evaluations,
because it contains polynomials of the negative and singular terms
comming from products of $-\EuScript{P}^\delta \delta(1-z)$ factors.
In principle these inconvenient terms can be resummed
(exponentiated) with the help of the direct but tedious algebra
on the multiple flavour indices and $z$-integrals%
\footnote{Similarly as the method used in the Appendix to re-sum
another part of the kernel.}.
In the following section we shall do it using more elegant methods.

Having defined the time ordered exponential evolution operator ${\bf G}_{H}$,
let us quote its basic features and extend its definition for the latter use.
The well known rule%
\footnote{Chapman-Kolmogorov-Smoluchowski-Einstein relation,
see ref.~\cite{kampen,walecka}.}
\begin{equation}
\label{eq:Urule}
   {\bf G}_{H}(t,t_x){\bf G}_{H}(t_x,t)= {\bf G}_{H}(t,t_0),
   \quad t\geq t_x \geq t_0
\end{equation}
helps to manipulate products  of the time-ordered exponents.
We may also define the inverse operator for the
``backward evolution'' ($t<t_0$) as follows
\begin{equation}
\label{eq:BackEvol}
  {\bf G}_H(t_0,t) \equiv {\bf G}^{-1}_{H}(t,t_0),\quad t<t_0,
\end{equation}
where the inverse operator is constructed using%
\footnote{
  The algebraic proof that
  ${\bf G}^{-1}_{H}(t,t_0){\bf G}_{H}(t,t_0)={\bf I}$,
  using eq.~(\ref{eq:torder}), we leave to the reader.
  The matrix elements of ${\bf G}^{-1}$
  can be non-positive and highly singular.}
${\bf G}^{-1}_{H}(t,t_0)\equiv {\bf G}_{(-H)}(t,t_0)$.
With help of the above definition
validity of eq.~(\ref{eq:Urule}) can be extended to any $t_x$.

\subsection{Derivation by reorganizing evolution equation}

In the following we show how to resume singular $\EuScript{P}^\delta$ terms
by going back to the evolution equation,
reorganizing  it and solving it once again.
We are going to show this standard trick in a detail,
because, subsequently, we shall generalize it to the case
of an arbitrary part of the kernel (instead of the $\EuScript{P}^\delta$ part).
It is essentially a warm-up example.

\subsection{Resuming virtual part of the kernel -- warm-up example}
Inserting explicitly regularized kernel, our evolution equation
takes the following form
\begin{equation}
  \label{eq:EvolD}
  \partial_t D_k(t,x)=
  - \EuScript{P}^{\delta}_{kk}(t)\; D_k(t,x)
  +\sum_j \EuScript{P}^{\Theta}_{kj}(t,\cdot)\otimes D_j(t,\cdot)(x).
\end{equation}
It can be transformed into%
\footnote{This integro-differential form is exposed in the
 QCD textbooks, see ref.~\cite{stirling-book},
 and is also used in the numerical
 evaluation (evolution) of PDFs using non-Monte-Carlo
 methods, for instance ref~\cite{qcdnum16}.}
\begin{equation}
  \label{eq:EvolTilde}
    \partial_t \Big(  e^{\Phi_k(t,t_0)} D_k(t,x) \Big)
    = \sum_j
      e^{\Phi_k(t,t_0)}  \EuScript{P}^\Theta_{kj}(t,\cdot) e^{-\Phi_j(t,t_0)}
      \otimes e^{\Phi_j(t,t_0)}  D_j(t,\cdot)(x).
\end{equation}
Changing slightly notation the above is transformed into
\begin{equation}
\begin{split}
  &\partial_t \tilde{D}_k(t,x)
    = \sum_j \tilde\EuScript{P}^\Theta_{kj}(t,\cdot) \otimes \tilde{D}_j(t,\cdot)(x),
\\&
   \tilde{D}_k(t,x) \equiv \exp(\Phi_k(t,t_0)) D_k(t,x),
\\&
  \tilde\EuScript{P}^\Theta_{kj}(t,z) \equiv
  \exp(\Phi_k(t,t_0))  \EuScript{P}^\Theta_{kj}(t,z) \exp(-\Phi_j(t,t_0))
\end{split}
\end{equation}
or in an equivalent compact matrix formulation it reads
\begin{equation}
\begin{split}
   \partial_t \tilde{D}(t)= \tilde{\bf P}^{\Theta}(t) \; \tilde{D}(t).
\end{split}
\end{equation}
The time ordered solution
\begin{equation}
\label{eq:soluP}
\begin{split}
\tilde{D}(t)&= \exp\left( \int_{t_0}^t \tilde{\bf P}^{\Theta}(t') dt'\right)_T\;
               \tilde{D}(t_0)
             = {\bf G}_{\tilde{\bf P}^\Theta}(t,t_0)\; \tilde{D}(t_0)
\end{split}
\end{equation}
of the evolution equation is widely known and exploited routinely in
many practical evaluations of solutions of the QCD evolution.
It is usually written in the traditional integro-tensorial
representation similarly as eq.~(\ref{eq:IterPeu}),
in terms of of the initial $D(t_0)$ and the product of $\EuScript{P}^\Theta$,
taking the following familiar shape:
\begin{equation}
\label{eq:SolIter}
\begin{split}
 &D_k(t,x) = e^{-\Phi_k(t,t_0)} D_k(t_0,x)
  +\sum_{n=1}^\infty \;
   \sum_{k_0,\dots,k_{n-1}}
      \bigg[ \prod_{i=1}^n \int\limits_{t_0}^t dt_i\;
      \Theta(t_i-t_{i-1})  \int\limits_0^1 dz_i\bigg]
\\&~~~~~~~\times
      e^{-\Phi_k(t,t_n)}
      \int\limits_0^1 dx_0\;
      \bigg[\prod_{i=1}^n
           \EuScript{P}_{k_ik_{i-1}}^\Theta (t_i,z_i)
            e^{-\Phi_{k_{i-1}}(t_i,t_{i-1})} \bigg]
     D_{k_0}(t_0,x_0) \delta\big(x- x_0\prod_{i=1}^n z_i \big).
  \end{split}
\end{equation}
Trivial identity
\begin{equation}
\label{eq:trivial}
e^{-\Phi_i(t_i,t_0)} e^{\Phi_i(t_{i-1},t_0)}= e^{-\Phi_i(t_i,t_{i-1})}
\end{equation}
was also employed.
The above solution of the evolution equation
is used as a basic formula in the Monte Carlo evaluation of the PDFs
using Markovian MC algorithms,
see for example ref.~\cite{Jadach:2003bu}.
We shall refer to this solution as non-hierarchic iterative solution of the
evolution equation.

Let us remind the reader, that
in the above warm-up exercise we have resummed the relatively simple component
$\EuScript{P}^B_{jk}(t,z)=-\delta_{jk}\EuScript{P}^\delta_{kk}(t)\delta(1-z)$
of the evolution kernel,
which was completely diagonal, both in $k$ and in $z$.
In this special case ${\bf G}^{-1}_{\EuScript{P}^B}$
is trivially calculable, contrary to more general case of non-diagonal
$\EuScript{P}^B$ discussed in the following.

Let us now come back to our principal aim,
proving eq.~(\ref{eq:Evolsolu}), where less trivial component of the
kernel will be isolated/resummed.

\subsection{Resumming gluonstrahlung -- the real thing}
\label{sec:real-thing}

In order to prove eq.~(\ref{eq:Evolsolu}),
we need to resum (exponentiate) the following part of the kernel
\begin{equation}
  \EuScript{P}_{jk}^B(t,z) = \delta_{jk} \EuScript{P}_{kk}(t,z)
                   =  -\delta_{jk}\EuScript{P}^\delta_{kk}(t)\delta(1-z)
                      +\delta_{jk}\EuScript{P}^\Theta_{kk}(t,z),
\end{equation}
which is diagonal in the flavour indices, but not in $z$.
This part of the kernel is always IR divergent and generates
multiple gluon emission process, that is {\em gluonstrahlung}.
The remaining {\em flavour-changing}
part of the full kernel is defined as $\EuScript{P}^A=\EuScript{P}-\EuScript{P}^B$.
The original full evolution equation and its solution read
\begin{equation}
 \partial {\bf D}(t)= \Big({\bf P}^A(t) + {\bf P}^B(t)\Big)\;  {\bf D}(t),\quad
 D(t) = \exp\left( \int_{t_0}^t \Big({\bf P}^A(t')+{\bf P}^B(t')\Big) dt'
           \right)_T \; {\bf D}(t_0).
\end{equation}
At this point, the $G_A$-function of eq.~(\ref{eq:GAbrems})
can be identified with the following operator
\begin{equation}
\label{eq:GA}
 {\bf G}_B(t,t_0) \equiv {\bf G}_{P^B}(t,t_0)
  = \exp\left(\int_{t_0}^t {\bf P}^B(t')dt' \right)_T,\quad
\end{equation}
where
\begin{equation}
\label{eq:GA2}
 \partial_t {\bf G}_B(t,t_0) = {\bf P}^B(t)\; {\bf G}_B(t,t_0),
\end{equation}
see also eq.~(\ref{eq:EvolGA}).

In order to derive eq.~(\ref{eq:Evolsolu}) we proceed
analogously as in the derivation of eq.~(\ref{eq:SolIter});
we shall introduce ${\bf G}_A(t,t_0)$ in the evolution equation,
similarly as we have introduced $\exp\big(\Phi_k(t,t_0)\big)$.
The main complication will be in the non-commutative
nature of ${\bf G}_A(t,t_0)$.
Let us introduce in the evolution an equation auxiliary PDF
\begin{equation}
  \tilde{\bf D}(t) = {\bf G}^{-1}_B(t,t_0)\; {\bf D}(t),\quad
   {\bf D}(t)={\bf G}_B(t,t_0)\;\tilde{\bf D}(t),
\end{equation}
getting after the differentiation
\begin{equation}
  {\bf G}_A(t,t_0)\; \partial \tilde{D}(t)
 +\Big(\partial{\bf G}_A(t,t_0)\Big) \tilde{D}(t)
= \Big({\bf P}^A(t) + {\bf P}^B(t)\Big)\; {\bf G}_A(t,t_0)\;\tilde{D}(t).
\end{equation}
After inserting eq.~(\ref{eq:GA2}) we obtain
\begin{equation}
  {\bf G}_B(t,t_0)\; \partial \tilde{\bf D}(t)
 +{\bf P}^B(t)\; {\bf G}_B(t,t_0) \tilde{\bf D}(t)
= \Big({\bf P}^A(t) + {\bf P}^B(t)\Big)\; {\bf G}_A(t,t_0)\;\tilde{\bf D}(t).
\end{equation}
The term proportional to ${\bf P}^A$ gets eliminated
\begin{equation}
  {\bf G}_B(t,t_0)\; \partial \tilde{\bf D}(t)
= {\bf P}^A(t)\; {\bf G}_B(t,t_0)\;\tilde{\bf D}(t).
\end{equation}
and we return to the usual evolution equation
\begin{equation}
\partial \tilde{\bf D}(t)
  = \tilde{\bf P}^A(t)\;\tilde{\bf D}(t),\qquad
\tilde{\bf P}^A(t)
\equiv {\bf G}^{-1}_B(t,t_0)\; {\bf P}^A(t)\;{\bf G}_B(t,t_0)\;
\end{equation}
with the usual solution
\begin{equation}
 {\bf D}(t) = {\bf G}_B(t,t_0)\;
  \exp\left( \int_{t_0}^t \tilde{\bf P}^A(t') dt' \right)_T \;
  {\bf D}(t_0).
\end{equation}

The last step on the way to eq.~(\ref{eq:Evolsolu})
is elimination of the operator ${\bf G}^{-1}_B(t,t_0)$ being
part of $\tilde{\bf P}$.
The reason for that is that ${\bf G}^{-1}$ is not well suited for
any numerical evaluation, especially of the MC type, due to alternating sign
in the exponential expansion, hence it is better to eliminate it
from the final result.
It is done with the help of the following identity
\begin{equation}
\begin{split}
&{\bf G}_B(t,t_0)\; \exp\left( \int_{t_0}^t \tilde{\bf P}^A(t') dt' \right)_T=
\\&~~~~~~~~~~~~~
={\bf G}_B(t,t_0)+
 \sum_{n=1}^\infty
 \left[
 \prod_{i=1}^n \int_{t_0}^{t}dt_i\; \theta_{t_i>t_{i-1}}
    {\bf G}_B(t_{i+1},t_{i})
    {\bf P}^A(t_{i})
 \right]
 {\bf G}_B(t_{1},t_{0}),
\end{split}
\end{equation}
where $t_{n+1}\equiv t$.
This identity is derived rather easily by inspecting each $n$-th term in the
expansion of the time ordered exponent and applying
the following relation%
\footnote{See eqs.~(\ref{eq:Urule}-\ref{eq:BackEvol})
       and the accompanying discussion.}
(analogous to eq.~(\ref{eq:trivial}))
\begin{equation}
{\bf G}_B(t_{i+1},t_0)\; {\bf G}^{-1}_B(t_i,t_0)
={\bf G}_B(t_{i+1},t_{i})\; {\bf G}_B(t_i,t_0)\; {\bf G}^{-1}_B(t_i,t_0)
= {\bf G}_B(t_{i+1},t_{i})
\end{equation}
for each pair ${\bf G}_B {\bf G}^{-1}_B$ sandwiched between
adjacent  ${\bf P}^A$'s.
The final solution reads
\begin{equation}
\label{eq:solumatr2}
\begin{split}
&{\bf D}(t)=
{\bf G}_B(t,t_0)\; {\bf D}(t_0)+
\\&~~~~~~~~~~~~~
+\sum_{n=1}^\infty
 \left[
 \prod_{i=1}^n \int_{t_0}^{t}dt_i\; \theta_{t_i>t_{i-1}}
    {\bf G}_B(t_{i+1},t_{i})
    {\bf P}^A(t_{i})
 \right]
 {\bf G}_B(t_{1},t_{0})\; {\bf D}(t_0).
\end{split}
\end{equation}
When translated into the integro-tensorial notation, the above formula
turns out to be identical with our target eq.~(\ref{eq:Evolsolu}).
In this way we have completed its derivation.

It is now obvious why
eq.~(\ref{eq:Evolsolu}) we call a {\em hierarchic} solution of the
evolution equation.
It is because its components ${\bf G}_A$ are solutions of
another simpler evolution equation (gluonstrahlung) of its own.
Higher level evolution embeds lower level simpler evolution as
a building block.

\subsection{Derivation by reorganizing time-ordered exponential}
A disadvantage of the derivation presented above is that
it exploits the inverse evolution operator ${\bf G}^{-1}$,
which is in a general case difficult to define properly, while it drops out from
the final result of eqs.~(\ref{eq:Evolsolu})
or (\ref{eq:solumatr2}) anyway.
The natural question is therefore whether we could derive
eq.~(\ref{eq:Evolsolu}) without introducing
the operator ${\bf G}^{-1}$ in the intermediate stages of the proof.

Furthermore, going back to the modified evolution equation
and solving it once again obscures the relation%
\footnote{Such a relation is relevant for parton shower applications.}
between variables $(k_i,z_i)$
in the non-hierarchic solution of eq.~(\ref{eq:SolIter}) on one hand
and the hierarchic one of eq.~(\ref{eq:Evolsolu}) on the other hand.
In the following we shall, therefore,
present an alternative example of the derivation of eq.~(\ref{eq:solumatr})
without explicit use of the inverse evolution operator ${\bf G}^{-1}$.
In such a case, the relation between variables $(k_i,z_i)$
in eq.~(\ref{eq:SolIter}) and eq.~(\ref{eq:Evolsolu})
can be traced back (recovered) more easily.

The following derivation will be strongly reminiscent to a derivation
of identity $F(x,y)=\exp(x+y)=\exp(x)\exp(y)$
by means of the Taylor expansion%
\footnote{Note that such a derivation is almost equivalent
to a direct multiplication of the infinite sums for $\exp(x)$ and $\exp(y)$,
but more transparent algebraically.}
with respect $y$ i.e.
$F(x,y)= \sum_{n=0}^\infty (x^n/n!) \partial^n_x F(x,y)\big|_{x=0}$.

Let us introduce slightly modified evolution operator
\begin{equation}
{\bf G}'_{\bf H}(t,t_0)=
{\bf G}'({\bf H};t,t_0)= {\bf G}({\bf H};t,t_0)\;\theta_{t\geq t_0},
\end{equation}
where ${\bf G}$ was already defined as the time-ordered exponential
in eq.~(\ref{eq:torder}).
The additional $\theta$-factor ensuring $t\geq t_0$ is
will make the following algebra more compact.
We define ${\bf H}={\bf H}_\lambda={\bf B}+\lambda {\bf A}$
(we shall set $\lambda=1$ at the very end of calculation).
The whole derivation relies on the following identity%
\footnote{Quite similar identity holds for an arbitrary
   $\lambda$-dependence in ${\bf H}(\lambda)$.}
\begin{equation}
\label{eq:Urule3}
  \partial_\lambda {\bf G}'_{\bf H}(t,t_0)
 =  \int_{t_0}^{t} dt_1\;
    {\bf G}'_{\bf H}(t,t_1)\; {\bf A}(t_1)\;
    {\bf G}'_{\bf H}(t_1,t_0),
\end{equation}
which can be derived using definition
of eq.~(\ref{eq:torder}),
and reorganizing all integrations over $t_i$'s.
The second derivative follows trivially:
\begin{equation}
\begin{split}
  \partial^2_\lambda {\bf G}'_{\bf H}(t,t_0)
&=  \int_{t_0}^{t} dt_1\; dt_2\;
    {\bf G}'_{\bf H}(t,t_2)\;   {\bf A}(t_2)\;
    {\bf G}'_{\bf H}(t_2,t_1)\; {\bf A}(t_1)\;
    {\bf G}'_{\bf H}(t_1,t_0)\\
&+  \int_{t_0}^{t} dt_1\; dt_2\;
    {\bf G}'_{\bf H}(t,t_1)\;   {\bf A}(t_2)\;
    {\bf G}'_{\bf H}(t_1,t_2)\; {\bf A}(t_1)\;
    {\bf G}'_{\bf H}(t_2,t_0)\\
&=2!\int_{t_0}^{t} dt_2\; dt_1\;
    {\bf G}'_{\bf H}(t,t_2)\;   {\bf A}(t_2)\;
    {\bf G}'_{\bf H}(t_2,t_1)\; {\bf A}(t_1)\;
    {\bf G}'_{\bf H}(t_1,t_0),
\end{split}
\end{equation}
and the $n-$th derivative is%
\footnote{Strictly speaking we should use mathematical induction
   over $n$ to verify this.}
\begin{equation}
  \partial_\lambda^n {\bf G}'_{{\bf H}_\lambda}(t,t_0)
 =  n!\;\prod_{i=1}^n \Bigg(
    \int_{t_0}^{t} dt_i\;
    {\bf G}'_{{\bf H}_\lambda}(t_{i+1},t_{i})\; {\bf A}(t_{i})\;
    \Bigg)
    {\bf G}'_{{\bf H}_\lambda}(t_1,t_0),
\end{equation}
where $t_n\equiv t$.
Now, let us use Taylor expansion
\begin{equation}
{\bf G}'_{{\bf H}_\lambda}(t,t_0)
={\bf G}'_{{\bf H}_{\lambda=0}}(t,t_0)
+\sum_0^\infty \frac{\lambda^n}{n!} \;
 \partial_\lambda^n {\bf G}'_{{\bf H}_\lambda}(t,t_0)\Big|_{\lambda=0}.
\end{equation}
Noticing that
${\bf G}'_{{\bf H}_\lambda}(t_{i+1},t_{i})\big|_{\lambda=0}
={\bf G}'_{\bf B}(t_{i+1},t_{i})$,
we obtain
\begin{equation}
   {\bf G}'_{{\bf H}_\lambda}(t,t_0)
 =  {\bf G}'_{\bf B}(t,t_0)
   +\sum_{n=1}^\infty
    \lambda^n\;\prod_{i=1}^n \Bigg(
    \int_{t_0}^{t} dt_i\;
    {\bf G}'_{\bf B}(t_{i+1},t_{i})\; {\bf A}(t_{i})
    \Bigg)
    {\bf G}'_{\bf B}(t_1,t_0),
\end{equation}
We may set $\lambda=1$ at this point.

Identifying ${\bf A}={\bf P}^A$,
${\bf G}'_{\bf H}={\bf G}'_{P^A+P^B}$ and
${\bf G}'_{\bf B}={\bf G}'_{P^B}$
we obtain more familiar identity%
\footnote{As previously we define
  ${\bf G}'_X(t_i,t_j)={\bf G}_X(t_i,t_j)\theta_{t_i>t_j}$. }
\begin{equation}
   {\bf G}'_{P^A+P^B}(t,t_0)
 =  \Bigg\{ {\bf I}
   +\sum_{n=1}^\infty
    \prod_{i=1}^n \bigg(
    \int_{t_0}^{t} dt_i\;
    {\bf G}'_{B}(t_{i+1},t_{i})\; {\bf P}^A(t_{i})
    \bigg)\Bigg\}
    {\bf G}'_{B}(t_1,t_0),
\end{equation}
which leads immediately to eqs.~(\ref{eq:solumatr}) and (\ref{eq:Evolsolu}).
In this way we have completed the {\em second} proof of eq.~(\ref{eq:Evolsolu}) --
this time without any reference to backward evolution operator ${\bf G}^{-1}$.

\subsection{Straightforward derivation}
In addition to two elegant proofs of eq.~(\ref{eq:Evolsolu})
presented in the previous Sections,
we include in Appendix third proof,
which relies on a rather straightforward method
-- it starts from eq.~(\ref{eq:solumatr2}) and through
tedious reorganization of the sums over flavour indices
(change of the summation order) and relabeling of
the variables transforms it into eq.~(\ref{eq:Evolsolu}).
The advantage of this third proof is that relation between
integration and summation variables in both formulas is exposed
in a manifest way.
This might be useful in the construction of the exclusive MC model
of the parton shower type.

\section{Discussion}
We are fully aware, of course,
that all three derivations of eq.~(\ref{eq:Evolsolu}),
shown in this work represent a well established
mathematical formalism, very similar to that in use in the Quantum Mechanics,
theory of Markovian processes and renormalization group in
the Quantum Field Theory.
We did not add much to the development of the corresponding area of mathematics.
Rather, our main aim was to customize
this known formalism to the specific needs of solving
the QCD evolution (also numerically),
such that solution of eq.~(\ref{eq:Evolsolu})
and the other similar ones are obtained in an effortless and rigorous way.
Having all this in mind, let us
comment on certain selected aspects
of the presented formalism,
on their possible refinements, extensions and applications.
We shall concentrate mainly on two points:
\begin{itemize}
\item Extension to beyond-DGLAP evolutions in QCD, like CCFM and others.
\item Possible application in the Markovian MCs and the related question
      of the momentum sum rules and normalization of PDFs.
\end{itemize}

\subsection{Extensions beyond DGLAP evolution}
In our definitions of the evolution of PDFs
eqs.~(\ref{eq:Evolequ}-\ref{eq:Evolsolu}) and the rest of the paper
we have restricted ourself to DGLAP type~\cite{DGLAP} evolution,
leading-logarithmic (LL) version or its next-to-LL extensions.
This restriction is however inessential and the validity of our
derivations can be extended to a more general evolution equation
\begin{equation}
\label{eq:genevoleq}
  \partial_t D_k(t,x)
 = \sum_j \int_x^1 du\; \EuScript{K}_{kj}(t,x,u) D_j(t,u),
\end{equation}
in which the dependency of the generalized
kernel $\EuScript{K}(t,x,u)$ is more general than only through the ratio $z=x/u$.
The above more general evolution equation is used for instance
in the CCFM-type models%
\footnote{It is also closer to the spirit of of the
          parton shower MC and unintegrated PDFs.}
of PDF \cite{CCFM}.
The DGLAP case of eq.~(\ref{eq:Evolsolu}) is obviously covered
by eq.~(\ref{eq:genevoleq}), with the following identification
\begin{equation}
  \EuScript{K}_{kj}(t,x,u) = \frac{1}{x}{\EuScript{P}}_{kj}\left(t,\frac{x}{u}\right)
  = \frac{\alpha(t)}{\pi} \frac{1}{x} P_{kj}\left(t,\frac{x}{u}\right).
\end{equation}
The compact matrix notation used in the time-ordered exponentials
can easily accommodate multiplications of the kernels $\EuScript{K}(t,x,u)$
such that all relevant algebra in the previous sections remains unchanged.
Let us only indicate how the product of two kernels gets redefined
\begin{equation}
   \big( {\bf P}(t_2){\bf P}(t_1)\big)_{kj}(x,u)=
   \sum_{j'} \int_x^1 du'\; \EuScript{K}_{kj'}(t_2,x,u') \EuScript{K}_{j'j}(t_1,u',u).
\end{equation}
The reader can easily verify that the rest of the compact matrix algebra
in our derivations remains unchanged.

\subsection{Sum rules and Markovianization}
As already mentioned, results of this work were instrumental
in the modelling QCD evolution using {\em non-Markovian} type
Monte Carlo techniques in
refs.~\cite{Jadach:2005bf} and \cite{Jadach:2005rd}.
The corresponding MC programs simulate
DGLAP and CCFM class evolutions.

However, the solution eq.~(\ref{eq:Evolsolu}) may be also used
to construct an interesting example of the Markovian MC in which
single step in the Markovian chain is a Markovian process of its own.
Without going into fine details, let us indicate how this can be done.
To this end we have to invoke momentum sum rule
\begin{equation}
  \sum_k \int_0^1 dx\; xD_k(t,x) =0
\end{equation}
and reorganize slightly eq.~(\ref{eq:Evolsolu}).
Staying for simplicity with the DGLAP case (LL and beyond)
the above sum rule determines virtual part of the kernel
\begin{equation}
  \EuScript{P}^{\delta}_{jj}(t,\varepsilon)=
  \sum_k \int_0^1 dz\; z\EuScript{P}^\Theta_{kj}(t,z).
\end{equation}
The above is used to set up properly Markovian MC and in particular
to split Sudakov formfactor $\Phi_k(t)$ into bremsstrahlung part and the rest
(flavour changing part)
\begin{equation}
\begin{split}
& {\Phi_{k}(t,t_0)} ={\Phi^{A}_{k}(t,t_0)}+{\Phi^{B}_{k}(t,t_0)},
\\&
   {\Phi^{B}_{k}(t,t_0)} =
  \int_{t_0}^t  dt'\; \int_0^1 dz\; z\EuScript{P}^\Theta_{kk}(t',z).
\\&
   {\Phi^{A}_{k}(t,t_0)} =
  \int_{t_0}^t  dt'\;
 \sum_{j,\; j\neq k} \int_0^1 dz\; z\EuScript{P}^\Theta_{jk}(t',z).
\end{split}
\end{equation}

By means of pulling out $\Phi^{A}_{k}(t)$ and multiplying both sides of
eq.~(\ref{eq:Evolsolu}) by $x$, we obtain the following
formula suitable for a Markovian MC
\begin{equation}
\label{eq:Evolsolu2}
\begin{split}
xD_k(t,x) =&
     \int\limits_0^1 dz'\; dx_0\;
     {\cal U}_{kk}^B(t, t_{0},z')\;
     x_0D_k(t_0,x_0)\delta(x-z' x_0)
  +\sum_{n=1}^\infty \;
      \int\limits_0^1 dx_0\;
\\&\times
   \sum_{{k_{n-1},\dots,k_{1},k_{0}}}
   \Bigg[ \prod_{j=1}^n \int\limits_{t_0}^t dt_j\;
     \Theta(t_j-t_{j-1}) \Bigg]\;
   \int\limits_0^1 dz'_{n+1}\;
   \Bigg[ \prod_{i=1}^{n}
     \int\limits_0^1 dz'_i\;dz_i\;
     \Bigg]\;
\\&\times
   {\cal U}_{kk}^B(t,t_n,z'_{n+1})\;
   \Bigg[ \prod_{i=1}^n
     e^{-\Phi^{A}_{k_{i-1}}(t_i,t_{i-1})}
     z_i\EuScript{P}_{k_i,k_{i-1}}^{A} (t_i,z_i)\;
     {\cal U}_{k_{i-1}k_{i-1}}^B(t_i,t_{i-1},z'_i) \Bigg]\;
\\&\times
      x_0 D_{k_0}(t_0,x_0)
      \delta\bigg(x- x_0 \prod_{i=1}^n z_i \prod_{i=1}^{n+1} z'_i
     \bigg),
   \;\;\; k_n=k,
\end{split}
\end{equation}
where
\begin{equation}
{\cal U}_{kk}^B(t_1,t_0,z)
\equiv e^{\Phi^{A}_{k}(t_1,t_0)}
       z G_{kk}^B(t_1,t_0,z)
\end{equation}
obeys evolution equation of eq.~(\ref{eq:GAbrems}),
with the substitution
$\Phi_{k}(t_i,t_{i-1})\to  \Phi^{B}_{k}(t_i,t_{i-1})$
and with both side multiplied by $z$.
The evolution operator ${\cal U}$ obeys nice "unitarity" rule
\begin{equation}
  \int dz\; {\cal U}_{kk}^B(t,t_0,z) =1
\end{equation}
for any $t$, $t\geq t_0$, in addition to the usual boundary condition
${\cal U}_{kk}^A(t_0,t_0,z)=\delta(1-z)$.

Eq.~(\ref{eq:Evolsolu2}) can be now used to define
hierarchic (nested) Markovian Monte Carlo algorithm.
The normalized probability distribution of the forward
Markovian step in the flavour-changing
upper level Markovian process reads:
\begin{equation}
\begin{split}
&\omega(t_i,x_i,k_i|t_{i-1},x_{i-1},k_{i-1})
 =\omega(t_i,z_i z'_i x_{i-1},k_i|t_{i-1},x_{i-1},k_{i-1})
\\&~~~~~~~~~~~~~~~~~~
 =(1-\delta_{k_ik_{i-1}})
      e^{-\Phi^{A}_{k_{i-1}}(t_i,t_{i-1})}\;
      z_i \EuScript{P}_{k_ik_{i-1}}^A (z_i)\;
      z'_i {\cal U}^B_{k_{i-1}k_{i-1}}(t_i,z'_i | t_{i-1}),
\\&
\int_{t_{i-1}}^{\infty} dt_i \; \sum_{k_i}
\int_0^1 d z_i \int_0^1 dz'_i\;\;
   \omega(t_i, z_i z'_i x_{i-1},k_i|t_{i-1},x_{i-1},k_{i-1})
\equiv 1.
\end{split}
\end{equation}
For the lower level bremsstrahlung process one may use standard
Markovian MC technique of ref.~\cite{Golec-Biernat:2006xw}.

Let us discuss selected details of the above scenario.
Here, all $k_i$ and $t_i$, $i=1,2,...n$ can be generated before
generation of any $z$-variables in a separate Markovian algorithm
with the stopping rule being the usual condition $t_{n+1} \geq t$.
(See ref.~\cite{Golec-Biernat:2006xw} for more details on the
the Markovian class MC algorithms.)
Variables $z_i$ of the flavour-changing kernels can also be generated
at this early stage.

The interesting question is: how and when do we generate
$z'_i$ according to gluonstrahlung operator
${\cal U}^B_{k_{i-1}k_{i-1}}(t_i,z'_i | t_{i-1})$?
If we have known an analytical (even approximate)
representation of this function,
or its precise value from the look-up tables,
then we could readily generate them before entering into
MC simulation of the bremsstrahlung subprocess.
That would lead us to the use of the constrained MC of
refs.\cite{Jadach:2005bf,Jadach:2005rd,zinnowitz04} for the bremsstrahlung segments.
Alternatively, $z'_i$ may come out from a separate
Markovian MC module simulating gluonstrahlung sub-process
starting at $t_{i-1}$ and stopping at $t_i$,
with the normalized probability distribution of single Markovian
step defined in ref.~\cite{Golec-Biernat:2006xw}.
In this latter case we would have simulated in the MC
a hierarchic system of Markovian processes,
with the master flavour-changing Markovian process and many Markovian subprocesses,
each of them implementing pure brems\-strahlung, flavour conserving, emissions.

The above hierarchic Markovian MC scheme, although quite interesting,
seems to have no immediate practical importance.
However, it may find applications in some future works.

\section{Summary}
The basic aim of this paper is to provide solid technical foundation
to other works in the area of the Monte Carlo simulation of the evolution
of PDFs and parton shower in QCD.
Our basic result is the solution of the evolution equation
of eq.~(\ref{eq:Evolsolu}), which was proved algebraically using three method.
Its primary application is construction of the constrained
MC algorithms of ref.~\cite{Jadach:2005bf}.
In addition, we also describe hypothetical application of such a solution
in the Markovian MC algorithm.
Although we are aware of many interesting relation of the discussed problems
and solutions to other areas in physics,
we did not attempt to elaborate on that too much, in order to keep
the paper compact and transparent.
Let us mention also, that our solution can be used many times
leading to a nested structure with several levels of the hierarchy.

\vspace{10mm}
\noindent
{\bf\large Acknowledgments}

\noindent
We would like to thank W. P\l aczek  for  useful discussions
and reading the manuscript.
We thank for warm hospitality of the CERN PH/TH division were part
of this work was done.

\newpage

redpajama_set_name: RedPajamaArXiv


The beauty of wild places could be their undoing as they attract us to them—leaving them touched by human hands and eventually less than wild. We are consuming wilderness at an alarming rate, using it and changing it as we do so.
Though we sometimes act otherwise, the mountains don't exist for our amusement. They owe us nothing and they require nothing from us. Hudson Stuck wrote that he and the other members of the first party to climb Mount McKinley felt they had been granted "a privileged communion with the high places of the earth." As mountaineers traveling in the wilderness, our minimum charge for this privilege is to leave the hills as we found them, with no sign of our passing. We must study the places we visit and become sensitive to their vulnerability, then camp and climb in ways that minimize our impact.
The privileges we enjoy in the mountains bring responsibilities. Therefore, the facts of mountaineering life today include permit systems that limit access to the backcountry, road and trail closures, environmental restoration projects, legislative alerts, and the clash of competing interest groups. While we tread softly in the mountains, it's also time to speak loudly back in town for support of wilderness preservation and sensitive use of our wild lands. As mountaineers, we need to be activists as well as climbers if we want our children to be able to enjoy what we take for granted.


Is the above title true? Is television indeed, the greatest invention ever?
Well, probably many people have many different ideas about that question. But one thing is for sure: television has had an enormous impact upon the world! And it has found its way into more and more homes around the world, in ever-increasing numbers.
Truly in many households, it has become the centerpiece of life! And it makes a wonderful babysitter for the young, and a faithful friend to the old and to the infirm and to the confined.
But television has not remained constant. Television has devolved from a somewhat quasi-moral beginning, and has gradually devolved down, down, down, into deeper and deeper decadence and immorality. Since its first appearance in the mid 20th Century, it has morphed from a "Leave It To Beaver" mentality to a…well…let it suffice to say: it's less than it once was, to put it mildly.
But be not deceived, O Pilgrim of the Cross! Just because there are still some seemingly nice shows on TV, don't be fooled by such "innocence". Television has about it an insidious evil, which is as subtle as that old double-tongued old Serpent in the Garden who deceived our first parents. And its chief target is the unsuspecting Christian family!
And this article will lightly explore some of these subtle deceptions, which are spoiling God's vineyard: deceptions so insidious, that most Christians are not even aware of!
Never before in the history of mankind, has there been an image that could speak! Through the ages, people around the world have created their idols: Idols of wood! Idols of stone! Idols of silver or gold! Idols that couldn't walk, talk, or do anything good…or anything evil!
Notice that Scripture says these idols "speak not", and also " for they cannot do evil, neither also is it in them to do good".
So then, if we shouldn't be afraid of mere lifeless images, then what about an image that CAN talk…and CAN do evil?
Well, the obvious inference here is, yes, those kinds of images we should be very afraid of!
Almost 2,000 years ago, the Apostle John, was given the Revelation, in which God prophesied that Satan would, in the last days, create an image which would be given life!
This image WOULD be able to speak… "And he had power to give life unto the image of the beast, that the image of the beast should both speak…".
So this passage foretells of a day in which Satan will create a TALKING IMAGE. And this talking image will have the power to cause Christians to be killed!
So, 2,000 years later, we have arrived at a day in which this particular Bible prophecy is now possible!
Never before in history was such a thing devised! Never before was such a subtle and sinister image imagined as a reality! But we now have an image that can speak to almost the entire world! We now have an image that can teach…almost the entire world! We have an image that can talk 24 hours a day, 7 days a week, 365 days a year…right in the very midst of our own living room! It is the centerpiece of the American home, and fast becoming the centerpiece of homes around the world! A talking image! Incredible!
IMAGINE! The Bible prophesied about this, 2,000 years ago! You would think that knowing this, the people would be very alarmed. But we're not! We all too often have a ho-hum, laissez-faire attitude toward this most revered (and yet malignant) member of our family! Yes, you could say that television is the "Soma" for the great masses of humanity!
Just as that drug, Soma, kept the masses self-satisfied in that infamous novel, so too, television keeps us and our children in a semi-hypnotic-like state! It is even the designated babysitter in many homes!
What people must keep in mind, is that God created this world to be a wonderful garden in which Humanity could enjoy the beauty of nature, and rich and joyful communion with their Creator.
But of course, this paradise was lost, when mankind decided to rebel against God's government of unselfish love.
And so God, for His own eternal purpose, allowed, "that old serpent, called the Devil, and Satan", to tempt Mankind into sin and rebellion. At that point, Mankind had traded God away for a new Master…"the god of this world", the Devil. Now at that moment the Earth and all its inhabitants had been taken captive by this master deceiver.
But in spite of Man's rebellion, God had left open the door of mercy. Mankind still had the ability to return back to God.
But Lucifer, in his jealous hatred, was not content to allow Mankind such an easy access back to God. And so Lucifer went to work to create his new kingdom, turning it into a place which fallen Mankind could not and would not find their way back into God's sheepfold. And through his own "Workers of Iniquity", Lucifer worked tirelessly to create his kingdom, the mighty Babylon. The kingdom of sin and selfishness.
And it is Satan's purpose to invent new ways to keep the human race from turning back to God. And of course, television (and Internet, radio, etc.) is one of his crowning achievements in his warfare against Heaven!
"And he (the False Prophet) had power to give life unto the image of the beast, that the image of the beast should both speak, and cause that as many as would not worship the image of the beast should be killed." Revelation 13:15.
And so television, even by its very own name, seems to fulfill this 2,000 year old prophecy! The Prince of the Power of the Air (waves?) appears to have achieved his ultimate weapon against God and against God's people! (see Ephesians 2:2).
And so often, God's people plop our children right down in front of this electronic Pied-Piper, perhaps every day. And our children are being more and more conformed to this serpent-like talking-image every single day, right under our noses! And the Bible foretold that this would happen!
Is this not amazing!? Of course, you would expect the people of the world to do these things. But we who claim to love God and follow the Bible should be deathly afraid of this talking-image-maker, known as television!
Now the Bible never says the name, "television". And we need to be careful, not to add anything to God's Word (see Revelation 22:18). And we need to keep an open mind, that there may be much more to this "image that speaks", than just television. But the basic concept in this article of, "how Satan is now compelling the world to conform to his image", seems to be the concept that God wants us to understand concerning the image of the Beast.
So read this article, and see if the case presented in this article is not a compelling argument in favor of the concept that television is, at the very least, a partial fulfillment of Revelation 13:15. You make up your own mind. But even if there were to come in the future, a further understanding of this prophecy, the principles herein are nevertheless biblically sound, concerning the Beast and his image.
Certainly, even if you were to take television completely out of this discussion, the principles laid out in this article seem to be biblically sound, and speak dramatically to this very day in which we are now living! But you read, and you decide for your own self.
Lucifer knows that in order to have himself worshipped, doesn't require the world to believe that he even exists! It only requires for people to love his attributes. The Bible points out, that a mere name has no power. It's the qualities of character that determine just who our God is.
Listen… "They answered and said unto Him, Abraham is our father. Jesus saith unto them, If ye were Abraham's children, ye would do the works of Abraham…Ye are of your father the Devil, and the lusts of your father ye will do." John 8:39, 44.
These were God's professed people, whom Jesus called the children of the Devil! Because even though they invoked the name of God, they possessed the selfish attributes of the Devil!
IS TO LOVE THE gOD OF THIS WORLD!
And so Satan works undercover, so as to make the world believe that he doesn't exist.
And thus, having erased himself out of existence, he then creates a world, filled with idols…which are tokens of his attributes. By so-doing, he accomplishes his grand scheme…to gain the homage he desires, by causing Earth's inhabitants to love this present sinful and selfish world that Lucifer has designed; a world with all its desires of the flesh, desires of the eyes, and all its proud attainments (see 1st John 2:16).
Listen… "And they (the people of the world) worshipped the dragon which gave power unto the beast: and they worshipped the beast, saying, Who is like unto the beast? who is able to make war with him?" Revelation 13:4.
And so, this passage is fulfilled, simply by the people of the world, loving this world-system, with all its selfish wares and ways.
WHOSE CHARACTER DO WE LOVE?
So we don't need to bow down to a statue of a pagan idol, in order to pay homage to Lucifer. Simply by pursuing the things of this, the Devil's selfish world; by conforming ourselves to the customs, vanities and behaviors of this unbelieving world, are we not worshiping the author of this present evil World-System…Lucifer, who Scripture refers to as, "the prince of this world" John 14:30?
BEFORE GOING INTO THE SPECIFIC SUBJECT OF TELEVISION, IT MIGHT BE WELL TO SPEND A FEW MINUTES DISCUSSING THE WORKINGS OF SATAN, AND HOW THE PEOPLE OF THIS WORLD RELATE TO HIM. SO THIS NEXT LITTLE SECTION WILL BE DEVOTED TO JUST THAT.
There are many who mistakenly believe that the Antichrist Beast is going to be one single person: perhaps a business-man or religious leader. And because they are so locked into this idea, they tend to ride rough-shod over this passage from Revelation Chapter 17, which explains what this Beast actually is.
So this Antichrist Beast, which, by the way, is in the image of the Dragon of Revelation 12, is a composite of various kingdoms and various kings. And if we're going to let the Bible be its own interpreter, then we cannot conclude that this Beast is one single human. This Beast is, in actuality, this present world-system, headed up by that serpent of old, the Devil, and Satan, as he has controlled various kings and kingdoms over the past millenniums of time.
This above old picture is one of many which came out of the Great Reformation, and shows that the Christians of that day believed that the apostate church, riding this multi-faceted beast, was a picture of the Mystery Harlot and the Antichrist Beast of Revelation!
And this is what the Mark of the Beast is actually all about, when you really think about it. This present World-System, and all its loyal citizens comprise Satan's Antichrist Beast.
Listen to Scripture… "Little children, it is the last time: and as ye have heard that antichrist shall come, even now ARE THERE MANY ANTICHRISTS; whereby we know that it is the last time." 1st John 2:18.
From this verse it becomes evident that an Antichrist is not some hideous monster. It is not some diabolical Dr. Evil (as this picture portrays.) No, there are many Antichrists. And they are merely the people of this fallen world ruled over by, "the god of this world"… Satan!
Just listen… "and this is that [spirit] of antichrist…They are of the world: therefore speak they of the world, and the world heareth them." 1st John 4:3, 5.
OK, so antichrists are of the world, speak of the world, and the world listens to them.
Well, just listen to this… "Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience:" Ephesians 2:2.
So by this statement, we see that the spirit of Satan, the "Prince of the Power of the Air" now works in the children of disobedience, i.e., the people of the world! And so any person whose everyday behavior, is as the people of the world, well, this is a clear indication that the, "prince of the power of the air" is the spirit now working in him or her. When we partake of a worldly spirit, we may just be partaking of the spirit of Anti-Christ.
And just one last proof, that there are no neutral fence-sitters in this world. Listen to Jesus… "He that is not with Me is against Me; and he that gathereth not with Me scattereth abroad." Matthew 12:30.
Either we are firmly ensconced in Christ's sheepfold, or we are in Satan's camp. There's no middle ground, as far as the people of this world are concerned. And of course, there are many in the Church who, as Jesus said… "This people draw nigh unto Me with their mouth, and honor Me with their lips; but their heart is far from Me." Matthew 15:8.
WHO IS CHIEF OF SINNERS!
God knows our hearts, each and every one! He sees the wickedness within. And as Jeremiah put it… "The heart is deceitful above all things, and desperately wicked: who can know it? I the LORD search the heart, I try the reins, even to give every man according to his ways, and according to the fruit of his doings." Jeremiah 17:9, 10.
Now Jeremiah 17:9, 10 is speaking in general terms. He's not speaking of one heart. Nor is He speaking of some hearts. God here is speaking of every heart. Paul knew this. He freely admits…"For I know that in me (that is, in my flesh,) dwelleth no good thing" Romans 7:18.
This above passage is one of the most remarkable revelations in Scripture. It reveals that Satan, is a spiritual power which indwells each and every person who is not indwelt by the Spirit of Holiness.
But it also reveals that the, "prince of the power of the air" is working within all those who have not made the Bible their guidebook for all matters of life.
The point is, that though we humans give credit to ourselves for our accomplishments, in reality, this world is actually being micro-managed by the, "god of this world", who works invisibly behind the scenes! So if we really want to point the accusing finger at the real bad guys in this world, then let's give credit where credit is due. The Devil is now at work in the children of disobedience, orchestrating a world of selfish pleasures. If we look at the many inventions which entertain and allure us, we really need to understand that it is, "the prince of this world" who has most likely inspired men to invent and produce these things.
WE HAVE MET THE ENEMY…AND IT IS US!!!
The fact is, there are many Antichrists. An Antichrist is merely anyone who denies Jesus either in word or in lifestyle.
Listen… "He is antichrist, that denieth the Father and the Son." 1st John 2:22. As it states here, an Antichrist is anyone who denies the Father and the Son.
So Christians are safe then. Right? Because we acknowledge both the Father and the Son. Right?
Let's not imagine such nonsense for a minute! No, just because we profess to know the Father and Son, does not mean that we truly, truly, confess the Father and His Son. Let's not think that we Christians are safe from such a condemnation!
Just listen… "They profess that they know God; but in works they deny Him, being abominable, and disobedient, and unto every good work reprobate." Titus 1:16.
God is speaking here of His professed people! (And this is the New Testament being quoted!) And it says here that I can profess to believe in Jesus, while at the same time my ungodly behavior denies Jesus. So God sees right through our façade. God is not impressed with mere words. Our life, and our thoughts, and our deeds are our true witness, as to just who is our true father…God or Satan.
person will emerge as the Antichrist Beast? Well, for one thing, most theologians and Bible teachers hammer that idea, day and night, about a singular person being Antichrist.
But to be balanced here, there is one Bible passage which speaks of the "man of sin" (see 2 Thessalonians 2:3). And this is what gives impetus to the idea that one single human individual will emerge on the world stage.
Listen… "Let no man deceive you by any means: for that day shall not come (the Day of the Lord), except there come a falling away first, and that MAN OF SIN be revealed, the son of perdition; Who opposes and exalts himself above all that is called God, or that is worshipped; so that he as God sits in the temple of God, showing himself that he is God." 2nd Thess. 2:3, 4. And while this passage appears to be speaking of a literal human, it is not necessarily referring to a human.
Listen… "How art thou fallen from heaven, O Lucifer, son of the morning!….They that see thee shall narrowly look upon thee, and consider thee, saying, IS THIS THE MAN that made the earth to tremble, that did shake kingdoms;" Isaiah 14:16.
So the Bible itself refers to Lucifer (Satan) as a man in this passage. Satan is the ultimate, "man of sin", one could possible say.
Now, having said all this, it is possible that Satan may use various key people in the world at times, to do his own evil bidding. But the main focus should be on Lucifer, and not on humans.
Listen… "Put on the whole armour of God, that ye may be able to stand against the wiles of the devil. For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places." Ephesians 6:11, 12.
So in this passage, God is placing the complete onus on Satan, as the true enemy of Christians, thus removing the focus from off of mere men. Mere men are being used by Satan, it is true! But they are only puppets in his hand. Oh yes, humans may persecute Christians, and even torture and kill them. But it is Satan, behind the scenes, who is "pulling the strings", so to speak.
He is the, "spirit that now works in the children of disobedience:" Ephesians 2:2. Anyone who is not fully consecrated to God can be used as Satan's instrument of destruction, whether he be bond or free: Christian or Gentile.
But in these last days, Satan has developed the means of exerting mind-control over the masses: Christian and secular alike. Satan knows that he is in danger of losing control over humanity, in these last days! And so, in effort to marshal his vast armies, he has developed the means of "brain-washing" and exerting mind-control, via the high-tech devices now being used by more and more of the world's population.
Oh yes, these devices have a definite benign purpose for communication. But this article will attempt to show how seemingly good things are being used also as tools of Satan to control the minds of the people and nations around the world.
And television, not only tells such lies 24/7/365 , but also dresses up those lies, making them look and sound very appealing, mingling them with truth and beauty.
But what does this have to do with "Me" making an image to the Beast? After all, I've never even carved one single statue in my lifetime!
But wait! If my character becomes conformed to the qualities which our modern-media society compels us to conform to…then I become an image…and image to the beast…and ultimately, into an image of Satan, though to a lesser degree! In a very real sense, I have carved an idol in my heart!
So now it begins to be seen that this image is much more than just television. That is why this article is titled, Television AND the Image that Speaks". Because the image of the Beast is a much deeper and broader concept than mere technical devices. It really has to do with just who is sitting upon the throne of my heart. What or who a person worships, is really about whoever a man, or woman, or child gives homage to; and the modern media is all about character. Satan's character!
Any time I behave in an un-Christ-like manner, I am denying God. I then, am behaving in the spirit of an Antichrist.
When the Disciples wanted Jesus to call fire down from Heaven on the Samaritans, Jesus plainly told them… "But He turned, and rebuked them, and said, 'Ye know not what manner of spirit ye are of.'" Luke 9:55.
So Jesus here is plainly indicating that the Disciples were not under the power of the Holy Spirit at that moment in time.
When Peter rebuked Jesus, He answered Peter in this way… "But He turned, and said unto Peter, Get thee behind Me, Satan: thou art an offence unto Me: for thou savourest not the things that be of God, but those that be of men." Matthew 16:23.
Peter was doing the work of Satan, and Jesus addressed Peter as Satan. Or perhaps Jesus was speaking to the spirit within Peter, who was Satan.
When Peter denied Jesus, he was then, in essence, in "the same camp" with those unbelievers whom Peter was warming himself with (see John 18:18). He should not have been mingling with those Antichrists, who were surrounding him!
Listen to Habakkuk… "Therefore the law is slacked, and judgment doth never go forth: for the wicked doth compass about the righteous; therefore wrong judgment proceedeth." Habakkuk 1:4.
This verse is from Habakkuk and is the essence of what the Book of Habakkuk is all about: that God's people are surrounded by unbelievers, causing wrong judgment to come forth from God's camp.
The Book of Habakkuk is about fleeing from the overwhelming influence of Chaldeans (Antichrists). Chaldeans merely represented the people of the world who would eventually surround God's people to the point that God's people were commanded to flee.
Listen… "Therefore the law is slacked, and judgment doth never go forth: for the wicked doth compass about the righteous; therefore wrong judgment proceeds….And the LORD answered me, and said, Write the vision, and make it plain upon tables, that he may run that readeth it. For the vision is yet for an appointed time, but at the end it shall speak, and not lie: though it tarry, wait for it; because it will surely come, it will not tarry." Habakkuk 1:4 & 2:2, 3.
Yes, God has allowed the people of the world to surround His people. God has allowed His people to be corrupted by worldly associations, just as He allowed the Jews the same. But at the end, God will call His people out from among them. And this is what the Book of Habakkuk is all about.
Listen again… "And the LORD…said, Write the vision, and make it plain upon tables, that he may run that readeth it. For the vision is yet for an appointed time, but at the end it shall speak, and not lie:" Incredible! If ever there were ominous and foreboding words from God, these are it!
This is perhaps one of the most important concepts in Scripture… "Wherefore I also said, I will not drive them out from before you; but they shall be as thorns in your sides, and their gods shall be a snare unto you." Judges 2:3.
It is the essence of many of the Old Testament stories. All those OT stories about the children of Israel rooting out the enemies were merely metaphorical pictures of what Christians must do in our own heart and mind. We must purify our hearts! We need to root out all those sinful traits which have long ruled over our minds. Those sinful traits which are common among the unbelievers of the world, but have no place in the hearts and minds of God's people!
Notice this verse says, "EVERY MAN that has this hope in Him (Jesus), purifies himself…". The purification of the heart as Christ is pure, is not an option, but, a must! Everyone who names the name of Christ must depart from iniquity!
So here we see the difference between a true child of God, and a, "false brethren". The false brethren love this world and have no desire to be fully purified into Christ's image. Oh yes, they are very happy to put Jesus on a pedestal and to venerate Him. But never to become like Him within!
If you or I have the attributes of this World-System guiding our lives, then, in essence, we have the Mark of the Beast. On the other hand, if we have the virtues and attributes of Jesus guiding our lives, we then have God's seal in our foreheads ("in our forehead" actually means, in our heart and mind—see Deuteronomy Ch. 6:6-8). To put it concisely, it's all about, "just who is ruling my heart?".
Just listen… "For the weapons of our warfare are not carnal, but mighty through God to the pulling down of strong holds; Casting down imaginations, and every high thing that exalteth itself against the knowledge of God, and bringing into captivity every thought to the obedience of Christ; And having in a readiness to revenge all disobedience, when your obedience is fulfilled." 2nd Corinthians 10:4-6.
This passage is commanding Christians that our hearts and minds must be totally purified, and filled with godly thoughts. Now Paul put this passage in military terms. And he did this for a very good reason. This is the battle we must fight! This is the hill we must take! And this is the war we must win! To overcome self is the great work before us!
Just as this above verse shows, Paul sometimes framed Bible exhortations in a military-type language. The Christian life is one of spiritual rest. But it is also one of warfare. Spiritual warfare! This is one of the great paradoxes of the Gospel. Paul tells the Corinthian Church that it is the final achievement of every Christian to gain complete control over his or her heart and mind.
Isn't this an amazing passage? These verses are very seldom spotlighted today, to say the least! As a matter of fact, most Christian circles don't even believe this commandment is possible! But the fact is, the closer we come to Jesus, the more we realize that this is indeed possible!
Listen to Paul's confession… "I can do all things through Christ which strengtheneth me." Philippians 4;13. If a Christian is willing to stay in the battle and fight that "Good Fight", he or she will eventually overcome in every area of life!
But Paul said it in military terms… "For the weapons of our warfare are not carnal, but mighty through God to the pulling down of strong holds; Casting down imaginations, and every high thing that exalteth itself against the knowledge of God, and bringing into captivity every thought to the obedience of Christ;" 2nd Corinthians 10:4, 5.
And the reason Paul put it in military terms, is because he knew this would be every bit as much a battle as was the overtaking of the Promised Land by the children of Israel! Oh no, we are not to use slaughter weapons as does the world, to win our war. But we are to root out the enemy…out of our heart. This is the Christian warfare! This is what overcoming is all about for the Christian!
If God is ruling, then my heart will be filled with God's attributes. And God wants no compromise. God does not accept a divided heart… "Ye cannot serve God and Mammon." Matthew 6:25.
If Lucifer is ruling, then my heart will be filled with the attributes of the world. Listen to what God has to say about Antichrists… "They (antichrists) are of the world: therefore speak they of the world, and the world heareth them." 1st John 4:5.
Television has become the centerpiece of our society, our homes and our lives. It is a remarkable invention! It is a powerful tool! It can change minds. It can marshal armies. It can shift the paradigm of societies. It can win elections. It can ruthlessly mock its enemies, even to the point of suicide, if necessary! It can frighten us! It can pacify us. It can tell us what to wear, how to talk, what to do, what to think, what to love, and even who to hate!
Television can be our best friend (and our worst enemy!) It is always willing to be our comforter. With just the click of a button, this "Electronic Prince of the Power of the Airwaves" will ride to our rescue: to rescue us from our loneliness…from our discouragement…from our boredom; when nobody else wants to be with us, it never turns us away. It is the perfect "friend"! It lives to entertain us! It loves to make us smile! Make us laugh! To satisfy us with gossip! Make us cry! To sooth us with beautiful music! To tell us stories: just about any type of story we desire!
Television is the proverbial "Needy Clown", yearning to be adored, and willing to do or say anything to get such adoration! It is often seductive, smart, stupid, sexual, original, even intellectual, at times. It can be beautiful! Charming! Witty! Wise! Humanitarian! Revengeful! Loving! Hateful! Right! Wrong! Greedy! Generous! Good! Evil! It is the "be-all, end-all" of our wants and needs!
It is the Ultimate Pied Piper of Hamlin! It is as wily and subtle as that serpent in the garden, as it utters its vague innuendos against the Bible and against those who love the Bible. It can make good appear as evil, and make evil appear as good. And it will lead us down that proverbial "primrose pathway". And it will take us and our children down, down, down…to the place we would not want to go, if we really understood the situation…as God sees it. And if it can rule the world, it can certainly rule my heart!
In other words, my dear darling soul, television is exactly like Lucifer (Satan), and exactly like his World of Sin; with just the same attributes of, "the prince of this world"! And as the, "the god of this world", this Pied Piper of Sheol has the magical powers to do all these things!
Yes, television is the ultimate "Charming Gigolo". And he's right there in the midst of our living room, seducing us and our children! And ultimately, this gigolo from Hell will rob us of everything we might possess, that has any eternal value, only to leave us desolate & very bankrupt on that Great & Fearful Day of God Almighty!
This is the argument which is generally presented by those who wish to defend television.
The purpose of this article is to convince, that TV is not neutral. It will be shown that TV is like a, "stacked deck of cards". It is "stacked in favor of the house"…Satan's house! But you have to understand exactly where it is that Satan wants to take you.
Most people have a wrong view of what Satan is all about. They believe that if there is a Devil, that he's only found in Satanic Cults, or with Black Magic. Few really understand that Satan is the god of this world. He can be a very moralistic spirit, if that suits his purpose.
Listen to Scripture… "Satan himself is transformed into an ANGEL OF LIGHT. Therefore it is no great thing if his ministers also be transformed as the ministers of righteousness; whose end shall be according to their works." 2nd Corinthians 11:14, 15.
Satan actually doesn't mind having a moral world. He just doesn't want people to turn to the Jesus of the Bible. And so he creates religions (and other gospels) that have a form of godliness, but with, "another Jesus" (2nd Corinthians 11:4).
Oh yes, Satan creates a lot of trouble in the world. But as one person put it, "Satan doesn't care whether you go to Hell as a prostitute, or as a school teacher!" Just as long as you don't begin exercising "saving faith" in Christ. And he certainly doesn't want people devoting themselves to searching the Scriptures to get to know God (see John 17:3). And Satan really, really hates to see people becoming changed into the image of Jesus (see 2 Corinthians 3:18)! Hence, the invention of television: Satan's Masterpiece of Mind-Control!
6. To excite and titillate our senses so much, that Bible study seems boring. ("…having their conscience seared with a hot iron;" 1st Timothy 4:2). When we rely on television to entertain us, it often becomes more and more difficult to open our Bibles and just read or study.
7. To blunt the conscience by exposing us to sinful behavior, over and over each day. ("Be not deceived: evil communications corrupt good manners. 1st Corinthians 15:33″) When we behold sin, over and over again on TV, sin begins to lose its fearfulness and horror.
But Satan is a very subtle being… "Now the serpent was more subtle than any beast of the field which the LORD God had made." Genesis 3:1.
Satan doesn't wish to "blow his cover". Everything he does has to be accomplished so imperceptibly, that nobody is alarmed. It's like that old "Frog in the Fry Pan" proverb. You can cook a live frog in the hot water of the fry pan if you gradually turn up the heat. But on the other hand, if you put him all of a sudden into hot water, he'll just hop right out.
Froglegs Swikee_Kodok_Oh_with_Rice – Wikipedia – share-alike lic.
And like that proverbial frog-in-the-fry-pan, so too, Satan is leading the world down a gradual slope. Obviously, Satan loves wickedness. And wherever he can, he'll drag people deep into sin. But his goal is not necessarily to make us into a world full of immoral decrepit perverts! Oh no! He's quite often content to just kill us…spiritually kill us; to make us into a "moralistic people, yet without a true connection to the God of Scripture". And he causes there to be enough really horrible people to make us think "we're not so bad".
And so the mission of television is to steal away our burning, dedicated love for the God of Abraham, Isaac, and Jacob! And to keep us so busy, busy, that we neglect that moment by moment relationship with our Lord and Savior!
And the goal of television is to set up an idol in our heart; an idol with the very same attributes which this world has, and which "the god of this world" possesses…Lucifer… "And take heed to yourselves, lest at any time your hearts be overcharged with surfeiting, and drunkenness, and cares of this life, and so that day come upon you unawares." Luke 21:34.
Just look at this unwatchful Christian in this above drawing. He's filled up his life with so much Mammon, he's not aware that his Judgment Day is here!
"And take heed to yourselves, lest at any time your hearts be overcharged with surfeiting, and drunkenness, and cares of this life, and so that day come upon you unawares." Luke 21:34.
Here is a stern warning for we who are standing on the threshold of the Day o f the Lord, to beware of becoming too entangled with the affairs of this world, lest that Day come upon us by surprise.
Listen to this amazing verse… "the god of this world hath blinded the minds of them which believe not, lest the light of the glorious gospel of Christ, who is the image of God, should shine unto them." 2nd Corinthians 4:4.
Notice this verse speaks of the image of Christ. The image of Christ is the image that God wishes for us to behold! And we should be totally immersing ourselves in God's Word, instead of allowing ourselves to become side-tracked by such entertainments as television.
Below is an expose of the subtle ways in which Satan gains control of the mind, through the medium of television. These are subtle ways in which Satan corrupts Christian character, which many Christians do not consider when choosing a program to watch.
Well what's wrong with watching a little nightly news? A number of things.
1. NEWS DEADENS THE CONSCIENCE. Listen to Scripture… "Who among us shall dwell with the Devouring Fire? who among us shall dwell with Everlasting Burnings? He that walks righteously…that stops his ears from hearing of blood, and shuts his eyes from seeing evil" Isaiah 33:14, 15.
Notice it says here that only those who stop their ears from the hearing of blood, and the seeing of evil, will dwell with the Devouring Fire (God). Sounds a lot like the nightly news, doesn't it?
To sit and watch evil and to hear blood (violence) on a daily basis, will most certainly have an effect on the Soul. This above verse tells us just who will stand in the Day of Judgment: those who shut their eyes from seeing evil, and their ears from hearing violence. As children of God, we don't want to dwell on crime and violence… "Finally, brethren, whatsoever things are true…honest…just…pure…lovely…of good report..virtue…praise, think on these things!" Philippians 4:8. Does television fulfill this Bible verse? Of course not!
2. NEWS IS HABIT-FORMING. This fallible pen can personally testify that TV news is habit-forming. It can be a real time-thief! Paul warns Believers... "See then that ye walk circumspectly, not as fools, but as wise, Redeeming the time, because the days are evil." Ephesians 5:15, 16. Christians should be hiding God's Word in our hearts, during our leisure hours. Obviously this cannot be accomplished when we are preoccupied with TV…or Internet…or radio.
3. THE SPIRIT OF GOSSIP. Have you ever noticed that when you are with friends, and they begin to share some new gossip, how your ears perk up? Maybe even your heart beats a little faster? We sinful humans have within us, a morbid desire to hear gossip. TV or radio news can be, quite often, a form of gossip, and only strengthens that desire within us.
4. "EVIL COMMUNICATIONS CORRUPTS GOOD MANNERS"… Many of us Christians think that we can just watch news and not be affected by TV or radio news. But in this we deceive ourselves!
Listen to 1st Corinthians 15:33… "Be not deceived: evil communications corrupt good manners." We who are running the Christian race quite often are deceived into thinking that we can dabble a little bit in the world.
But in order to gain a Christ-like character, even a, "little foolishness will destroy much wisdom"(Ecclesiastes 10:1). Oh yes, we can't help but mingle with unbelievers in the workplace, etc.. But to voluntarily expose ourselves to the ungodly chatter of unbelievers for the sake of enjoyment…is not a wise course at all for a Christian!
But does this mean we must lock ourselves up in our houses and never go out? No, it just means that we should take heed to what we do and who we expose ourselves to.
5. PHILOSOPHY AND VAIN DECEIT… Have you noticed how Christians today mingle the purity of the Gospel with politics and conspiracy theories of various types? It is so important for us to not mingle our belief with the various ideologies of the world. Colossians is largely based on this idea, and warns against mingling worldly philosophies into the purity of Christ (see Colossians 2:8). 1st Timothy also warns… "…keep thyself pure." 1st Timothy 5:23.
6. OVER-STIMULATION… Isn't it true that the exciting amusements of the world tend to make our Bible studies rather boring?
Well, news can accomplish such an over-stimulation of our senses. It's much easier and more pleasurable to just sit back and watch gossip and conspiracies and wars and controversies on the news, than it is to sit down with Bible and concordance, isn't it?
7. BAD WITNESS TO OTHERS… And just think about the example I am setting for others! My kids…my grandkids… fellow Christians, neighbors, etc.. Even if they aren't with me, they can guess what Mom and Dad, or Grandma and Grandpa are doing! My neighbors will see that certain glow from my window. And they know that glow is not an angel visitation (But actually it is…angels from HELL!) It's the glow from my TV! And the next day, I certainly WON'T have Heaven's glow on my face which tells the world I've, "been with Jesus" Acts 4:13.
But also, setting in front of our TV, is setting a bad example for others to follow. And we just don't realize what a powerful influence for good or evil, that our example is (see Mark 9:42).
An entire article could be written on Satan's sophistry in the making of movies. But one short comment will be given to show how Satan continues his stealth warfare against Christ and His Followers.
Quite often in the movies, Christians are portrayed as weak and defenseless, like a flock of nervous little birds. On the other hand, the hero of the story is often portrayed as strong, and handsome, and brash, and fearless, usually saving the Christians from the bad guys. Of course, this kind of astigmatism against Christians is right out of Satan's playbook!
But another lesson learned from such a movie situation is that Christians shouldn't depend on the Lord, but should be more like the hero of the movie, relying on his own bravery and strength to solve his dilemma.
Along these same lines, Satan sets up a standard of conduct for his kingdom (this world). And in so-doing he has used the television and movie industry to promote the idea that men are less-than-men if they display tenderness and compassion toward others. And so, Christ, who is the very embodiment of tenderness and pity does not measure up to Satan's standards for men. This also is right out of Satan's playbook, in how this Master-Deceiver makes men fearful of appearing less than "manly", if they display any softness and tenderness.
We are extremely fortunate to have a tender, understanding, and compassionate God, Jehovah, who runs this universe! On the other hand, we can see how things would be run, if Lucifer was the god of this universe. All we have to do is just look at this present world around us, and we can see the results of what a lack of compassion can accomplish.
Any person who has a tender conscience needs only look around at all the woe and misery in this pathetic world, and realize that humanity isn't doing so well in our attempt at running this world our way. And television and movies, have only amplified this idea that being hard-hearted is somehow manly, and a good thing. And as a result, Christian men who watch this stuff, become very fearful of being totally Christ-like. Satan has caused men to be deathly afraid of being seen as exercising Christ-like tenderness.
1. THE SPIRIT OF JESTING. Please observe Scripture… "And walk in love, as Christ…But fornication, and all uncleanness, or covetousness, let it not be once named among you, as becometh saints; NEITHER FILTHINESS, NOR FOOLISH TALKING, NOR JESTING, which are not proper: but rather giving of thanks." Ephesians 5:2-5.
1. SPIRIT OF SENSUALITY. Quite often the programs for little children are fraught with sexuality. This comes in the form of either the music…or the actors, who are dressed in a provocative manner. Or perhaps the theme of the program.
2. VIOLENCE. Children's programs often have violence mingled within.
3. GROOMING CHILDREN FOR FURTHER WICKEDNESS. Even those programs which seem "harmless" are only grooming children to eventually watch other shows, even more degrading, which lead children further into sin.
4. ANTICHRIST PHILOSOPHIES TAUGHT. The television makes a very convenient babysitter. The problem is, it is Lucifer, the, "Prince of the Power of the Air", who becomes your babysitter! And his qualities of pride, anger, greed, unbelief in God's Word, atheism, violence, etc., are instilled into the children's minds, causing them to grow up as worldly-minded secularists, who have little or no love for heavenly things!
1. ATHEISM. Many educational programs are produced by atheists, and mingled with atheist philosophies. Atheism is the spirit of "unbelief". Such Antichrist ideologies are like yeast, working themselves imperceptibly through the hearts and minds of viewers. And no matter whether or not the adult or child becomes an atheist as a result, there is nevertheless a spirit of unbelief transferred to the participant, which begins to doubt the power of God to fulfill His promises.
1. COUNTERFEIT JESUS'. As earlier stated, "Satan by any other name, is still Satan". Just because religious television shows are constantly invoking and evoking the name, "Jesus", does not necessarily mean the, "Jesus of Scripture". Paul complained that there were false teachers who proclaimed "Another Jesus, who we have not preached" 2nd Corinthians 11:4.
So when such religious stations misrepresent the true Gospel with a gospel mingled with worldly desires, they are proclaiming, "another Jesus". Let no man deceive you, O Pilgrim!
2. COMMERCIALISM. It is very expensive to produce TV programs, compared to, say, radio or Internet. Television requires a large audience, in order to financially support the stations.
The point is, television must be very entertaining, to maintain such large viewership. So then they often compromise with the world in order to increase ratings. Popular music, excitement, celebrities, theatrical displays, etc., are now the order of the day in the Christian community, because of television.
3. "PROPHESY SMOOTH THINGS TO US" Isaiah 30:10. Furthermore, television must be careful to not offend its faithful audience. So religious stations must be careful what they say, and what they do. What is the result?
4. MILK, BUT VERY LITTLE MEAT. Religious shows usually present the most basic, entry-level Bible concepts. And it's so easy and convenient for Christians to just leave the religious channel on all day. And as a result, the Christian begins to rely more and more upon the religious channel for his or her spiritual food and drink. The problem is, that the Christian begins to slack off on personal Bible study, and allows the religious channel to "feed" him or her. So because it's mostly "milk" and not "meat", the TV-watching Christian's spiritual growth is stunted. And even if the show does happen to give significant passages, they are spoken so quickly, they simply "go in one ear and out the other". There is no replacement for sitting down each day with a concordance and Bible, or even audio Bible readings. Certainly not religious television! Religious shows can be a great time-waster, at best! But at worst, they can deceive the biblically naïve multitudes.
"And many shall follow their pernicious ways; by reason of whom the way of truth shall be evil spoken of. And through covetousness shall they with pretending words make merchandise of you: whose judgment now of a long time lingers not, and their damnation slumbers not." 2nd Peter 2:2, 3. And so these religious shows serve a dual purpose. They deceive their followers into a "Gimme! Gimme!" gospel. But at the same time, they repulse the more savvy general public, causing the truth to be evil spoken of.
And if there's one thing the Devil knows how to do, it's to cast dirt on the Bible!
7. CHRISTIAN MOVIES PRESENT WRONG IMAGE… TV can be very subtle. There are even a few shows about Christians on TV. And so often on these so-called "Christian" shows, compromising and worldly Christians are presented as good and rational and very acceptable, while the serious and dedicated Christians quite often are portrayed as being fanatical, slightly off-balanced mentally; even having a pent-up evil edge, which eventually surfaces as the plot develops. And by exposing ourselves to this subtlety, we become fearful of being considered by others as "fanatical". And so, many Christians try to avoid being stereo-typed, and behave as worldly as possible.
"For the day of the LORD of hosts shall be upon every one that is proud and lofty… and upon all pleasant pictures. And the loftiness of man shall be bowed down, and the haughtiness of men shall be made low: and the Lord alone shall be exalted in that day. And the idols He shall utterly abolish. In that day a man shall cast his idols of silver, and his idols of gold, which they made each one for himself to worship, to the moles and to the bats; To go into the clefts of the ragged rocks, for fear of the LORD, and for the glory of His majesty, when He ariseth to shake terribly the earth! Cease ye from man, whose breath is in his nostrils: for wherein is he to be accounted of?" Isaiah 2:12, 16-18, 20-22.
This above passage really nails down just what the Day of the Lord is all about! We live in a world today, in which the False Prophet, Satan, the Dragon, is using the high-tech devices to present lying images to draw disciples after him. The Internet, the television, radio, magazines, books, movies, etc., are all churning out pleasant pictures, which portray this evil world in a very appealing manner. These pictures often incorporate the beauty of nature together with the glory and beauty of Mankind. Notice that Satan combines the three great sins in these pictures… "The lust of the flesh, the lust of the eyes, and the pride of life" 1st John 2:16.
And so, in hopes of keeping Mankind from returning to God, Satan has given this world a "make-over", in attempt to keep us seeking after some earthly dream.
Whatever the career, whatever the hobby, whatever the romance, whatever the city, whatever the country, whatever the lake, whatever the river or mountain stream, or mansion, or cottage, or car, or boat, or motorcycle, or plane, or vacation resort… Satan now has an image, a pleasant picture just perfect for you to fit into!
And he is the master at presenting this world in the most romantic light with his, "pleasant pictures", as Isaiah 2:12, 16-18, 20-22 says (see two sections above for entire quote). And television is the perfect medium to accomplish this!
Now it should be touched upon, that we humans were created to be, "the temple of the Lord".
This above passage proclaims that the Church-Elect is the Temple of God, spiritually speaking. But individually, Peter declares… "Knowing that shortly I must put off this my tabernacle, even as our Lord Jesus Christ hath showed me." 2nd Peter 1:14.
Now just imagine for a moment if you or I were a priest in the Old Testament Tabernacle. And how long do you think you or I would last if you or I engaged in the frivolous and giddy behavior which is so common among Christians today? If we were to walk into the Holy Place or even the Most Holy Place, and spoke the way we Christians speak today, they would have had to drag us out…feet first!
Well, our mind and heart are an extension of the Holy and Most Holy Place. The mind and heart are where our treasured possessions are stored.
So then, how could we possibly think to defile our Soul-Temple by allowing the immoral filth and worldly dribble to enter into our Most Holy Place, via the TV or radio, or magazines, Internet, etc.? It's really unthinkable, when we consider that our heart and mind is to be a fit dwelling place for the Holy Spirit!
Listen… "Keep thy heart with all diligence; for out of it are the issues of life. Put away from thee a froward mouth, and perverse lips put far from thee, etc…." Proverbs 4:23, 24.
No, God will not strike us instantly dead, as He did to the two priests in this picture. But eventually, we will drive that Holy Dove from our heart, if we persist in defiling ourselves with unholy communications. It will be a spiritual death. And we won't even be aware that He's gone!
How in the world do Christians ever imagine that we can overcome the world, when we defile our Most Holy Place with such worldly graffiti? Rather, the world is overcoming us! And how can we ever expect that we can continue to consume the common-ness and un-Christ-like behavior we see almost every moment on TV and not grieve away the Spirit Of Holiness out of our Soul-Temple?
Does this sound outrageous? Well, just listen to James, talking to Christians… "Ye adulterers and adulteresses, know ye not that the friendship of the world is enmity with God? whosoever therefore will be a friend of the world is the enemy of God. Do ye think that the scripture says in vain, The spirit that dwells in us lusts unto envy?" James 4:4, 5.
Notice that this passage not only says that a friend of the world is the enemy of god, but it also refers to such worldly love as a "spirit" within us.
Well, if I make the unbelievers and worldly Christians who appear on television my daily companions, then I indeed am, "A FRIEND OF THE WORLD".
The above passage reveals that Satan possesses great musical abilities. And do we suppose that he won't use music to deceive the world?
Old King Nebuchadnezzar was pretty clever. He seemed to understand the power of music. When he set up his golden image on the plain of Dura, he put together an orchestra, to add to the moment. The story in the Book of Daniel, Chapter 3, in which the evil king of Babylon set up a golden image, whose height was 60 cubits, and whose breadth was 6 cubits makes a fearful analogy to television.
Remember when the music began, the people of all nations fell down and worshipped the golden image? Obviously Satan was behind all this.
Notice it says in this passage that this scenario concerned the whole world. Listen… "all the people, the nations, and the languages, fell down and worshipped the golden image".
This golden image in the shape of King Nebuchadnezzar was a picture of the image of the beast from Revelation 13. And just as this golden image was a reflection of Nebuchadnezzar (who, by the way, was a picture of Satan, as the above verse points out), so too, television is a reflection of Satan, as has already been discussed in this article.
Just listen… "take up this proverb against the king of Babylon, and say, How hath the oppressor ceased! the golden city ceased!…How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations!" Isaiah 14:4, 12.
One thing that too many Christians do not realize, is that Satan is content with just a small portion of a certain movie or television show, to sow his evil seed.
Christian parents make a great error in thinking that their children are safe by watching a "pretty good" show. Satan laughs at all who buy into such nonsense. The Bible warns Christians… "Your glorying is not good. Know ye not that a little leaven leaveneth the whole lump? Purge out therefore the old leaven, that ye may be a new lump, as ye are unleavened. For even Christ our passover is sacrificed for us:" 1st Corinthians 5:6, 7.
Satan may produce a cute little show for kids, and parents don't realize that just one or two "bump & grind" tunes in that show, is all that Satan needs to sow his evil seed within the heart of that child.
Adult Christians are in no less danger. While a Christian may have to work and live in a worldly environment: yet to needlessly expose one's self to common and low-grade conversation, defiles the Soul-Temple. Listen… "Be not deceived: evil communications corrupt good manners." 1st Corinthians 15:33.
The only safe thing is to realize just whose territory is the television, and pray that God will take it out of one's home. For Christians with an unbelieving spouse, this will be very difficult, and the Believer may have to separate his or her self, during those hours that the family watches those shows.
This next passage from Solomon really clarifies how careful a Christian must be… "Dead flies cause the ointment of the apothecary to send forth a stinking savour: so doth a little folly him that is in reputation for wisdom and honour. " Ecclesiastes 10:1.
In other words, this pearl of wisdom can be applied to many different areas of life, including the things we absorb into our minds.
This above passage presents a great purpose for why we have been called: to be ambassadors for Christ, to reconcile a world, steeped in sin and rebellion against the government of God. But it is not merely telling them about Jesus, that reconciles lost souls. No, God has ordained that we should be transformed by the power of the Spirit of Holiness into the image of Christ. The world needs to see Jesus too…in us! And so, we are to be pure and holy, just like Jesus was pure and holy.
Listen to Peter… "Seeing then that all these things (the heavens and Earth) shall be dissolved, what manner of persons ought ye to be in all holy conversation (words & behavior) and godliness…Wherefore, beloved…be diligent that ye may be found of Him in peace, without spot, and blameless." 2nd Peter 3:11, 13, 14.
By watching television, we imperceptibly become like those we watch… "Be not deceived: evil communications corrupt good manners." 1st Corinthians 15:33.
This verse confirms that what we behold and what we hear have an effect on our personality. So if we desire to become totally and purely Christ-like, then we must separate as far as possible from all ungodly influences.
The world has its own idea of acceptable behavior. By and large, the world has rejected the holiness and reverence of Christ, and has established its own standard. Irreverence, joking and jesting, loud laughter and other common and even cheap talk often have replaced Christ-like holiness and reverence.
The sad part of all this, is that Christians too, have bought into this counterfeit goodness, to a great degree. Christians have rejected such admonitions as this… "I will therefore that men pray every where, lifting up holy hands, without wrath and doubting. In like manner also, that women adorn themselves in modest apparel, with shamefacedness and sobriety; not with broided hair, or gold, or pearls, or costly array; But (which becometh women professing godliness) with good works. Let the woman learn in silence with all subjection." 1st Timothy 2:8-11. Can you imagine what kind of reception such passages as this might have been received in the 20th Century churches?
But for those who wish to enter the Kingdom of Heaven, it will be their joy and delight to forsake any and every impure behavior and conform themselves entirely into the image of Christ. And they will be likewise willing to accept all the mocking and ridicule that such behavior will result in!
WAS THAT GOLDEN IMAGE A PROPHECY OF TELEVISION?
The Lord had set up this story from Daniel, so that He could warn us of what we can look forward to in these last days. Even now, does television and motion pictures combine the proud and sinfulness of Man kind with swelling strains of music, to cause the world to revere the attributes of Satan. For instance TV can take a person who is otherwise greedy, and selfish, and lustful, and conniving, and vulgar, and simply add some beautiful violin strains and make that person appear absolutely wonderful…or brave…or suave, or sophisticated!
For more on the subject of music, You may wish to read the article, "Running The Christian Race (Part 1 Sensual Music)".
The above verse is the testimony by Jacob about his family as they traveled back to their long-lost home. This story is likewise a testimony to how we need to lead our family. We should be inclined to be more like a silent gentle breeze among our family. Not a gale force wind! After all, we appreciate how God has been tender with us. As we look at this painting of Jacob, we recall his gracious words about his family and flocks. He said "I will lead on softly". Jacob saw how God had patiently worked with him through the years. And now Jacob was likewise determined to be gentle with his family.
By prayer, watchfulness, and daily consecration, we can cry out for our loved ones, and have confidence that God hears our prayers. We can cling to God's precious promises about our family, too. As we focus on our own Salvation, we can rest assured that God will work in the lives of others. And if God will peradventure bring a loved one into the fold, then they will also desire to run that Race and fight that Good Fight.


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Priority data needs; sources of national, state, and local-level data and data collection systems
Healthy People 2000 statistical notes ; no. 15
Kim, Insun	; Keppel, Kenneth G.	;
Kim, Insun	; Keppel, Kenneth G.	Less ▲
National Center for Health Statistics (U.S.)
Shipping list no.: 98-0100-P.	Includes bibliographical references (p. 10).
Health Priorities/trends
Health Status Indicators
urn:sha256:3fa848a54c75ea77ad95ba0d3cc64b3924e2afa49829f4633320fb97dc0f718d
Datastream2
Health status indicators for the year 2000
Freedman, Marv Anne
CDC Health Status Indicators Consensus Work Group.. Healthy People 2000 (Group). National Center for Health Statistics (U.S.). Centers for Disease Control (U.S.).
Healthy People 2000 statistical notes ; v. 1, no. 1
DHHS Publication No. (PHS) 92-1237
This report is the first in a series of Statistical Notes that will address technical issues related to assessing progress toward the Y ear 2000 Health Objectives. Future issues will be devoted to topics such as small area analytic methods, denominat...
Developing climate change environmental public health indicators : guidance for local health departments
Houghton, Adele.
Council of State and Territorial Epidemiologists. State Environmental Health Indicators Collaborative Climate Change Subcommittee
Climate change EPHI frameworks have been developed at the state level by the Council of State and Territorial Epidemiologists' (CSTE) State Environmental Health Indicators Collaborative (SEHIC) (available at: http://www.cste.org/?page=EHIndicatorsC...
State and local public health actions to prevent and control chronic diseases
PCD collection
Preventing chronic disease
Publication date from document properties.PCD_StateAndLocal_Collection_FINAL_3-27-18.pdf
Behavioral Risk Factor Surveillance System : 2018 summary data quality report
National Center for Chronic Disease Prevention and Health Promotion (U.S.). Division of Population Health. Population Health Surveillance Branch.
The Behavioral Risk Factor Surveillance System (BRFSS) is a state-based, CDC-assisted health-data collection project and partnership of state health departments, CDC's Division of Population Health, and other CDC programs and offices. It comprises ...
The Behavioral Risk Factor Surveillance System (BRFSS) : complex sampling weights and preparing 2018 BRFSS module data for analysis
The Behavioral Risk Factor Surveillance System (BRFSS) is a state-based telephone survey that collects data on a number of health outcomes, health-related risk behaviors, use of preventive services, and chronic conditions from noninstitutionalized ad...

redpajama_set_name: RedPajamaCommonCrawl