The cruise ships dock in the center of Warnemunde and is only 300 meters from the train station and city center. From there on one can travel to Rostock (20 min) and Berlin (a 2 and a half hour trip) Train schedules. The terminal can accommodate 3 cruise liners at a time. If all occupied, ships dock at the main commercial piers of Rostock at Seehafen on the other side of the river.
Getting to Berlin under your own steam in one day isn't practical, since trains run on specific schedules that may conflict with your ship's time table. Shore excursions use charter trains or coaches, so that is the best way to reach the capital.
Being a center of maritime traffic, the district of Warnemünde comprises numerous navigational aids, the oldest is the lighthouse, which is currently still in use. The lighthouse was built in 1897. In the summer, the tower, approximately 37 meters (121 ft) high, allows visitors to enjoy an impressive view over the Baltic Sea and the northern districts of Rostock. The nearby Teepott (Teapot) with its slightly curved roof, the resort's second famous landmark, is an interesting example of East German (DDR) architecture. Built in the 1960s and renovated in 2002, it today houses different restaurants and a sea voyage exhibition.
Warnemünde's acres of fine sand makes a sure fire hit as a holiday resort and this is where the ship docks. So if your ambition is no more than a touch of sunbathing and a stroll around the resort then all that is very close by.
Yachts at anchor, a jumble of fishing boats, sea, cafes and bars, not forgetting the famous teapot, and a pier all lend character to this small but charming resort.
Trains to Rostock leave about every 10 minutes for Rostock Hauptbahnhof. The train trip is less than 20 minutes, tickets are 1.80 Euro one way, which includes the tram in Rostock. Once you arrive at Rostock Main station, go two levels down and take either tram 5 or 6 to Neuer Markt and you are in the center of this charming town.
The ticket machines at the train station and in the tram (for your return trip) accepts Euro coins and small bills and are automatically time stamped and your tickets are automatically validated. You can also buy a day ticket 4.60 Euro, which allows you to travel on all modes of travel, even ferries, in the municipal area of Rostock.
There are HOHO buses in Warnemunde to Rostock but both cities are so compact it is not necessary. Also the intervals are 2 to 3 hours apart. Everything is within easy walking distance once you are in the center.
Rostock town center is relatively compact so it is fairly easy to take in a number of sites within the course of a day. The place to start is St Peter's Church (St Petrikirche) in the oldest part of the city in the east. It started life as a wooden church in the 13th century but was followed by a brick Gothic construction with an 117m (380ft) tower which served as a landmark for sailors for centuries. Air raids destroyed the tower and part of the church in 1942. After a long wait of 52 years, the tower was rebuilt to a height of 125m (410ft) this time with a modern lift so visitors can ascend to a viewing floor.
You can also take a train from Warnemunde to Lubeck, with a a change in Rostock. Lubeck is a delightful old city to visit. Trains run quite frequently.
Visit Schwerin, about an hour away. You can purchase a Mecklernburg-Vorpommern Ticket 1st person €20 + €3 for each additional person up to maximum 5 people. It is valid from 9 a.m. on weekdays and the whole day on weekends for regional trains (RE or RB) and suburban trains (S).
In Warnemunde in the vicinity of the canal called der Alte Strom (Old Channel), with its various restaurants, pubs and traditional fishing boats is rather touristy but fun to spend a few hours.
Rostock has a wider selection of stores and restaurants and has an more metropolitan atmosphere.
Wifi is sparce in both Warnemunde an Rostock, and often has to be paid for. There is no WiFi in the direct port area.


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text:
\section{Introduction}

\label{intro}

The history of Fermat's Last Theorem (FLT) is so well known, that we
restrict ourselves to remind only some important historical facts.

In 1637 Fermat wrote his famous marginal note in Diophanto's ``Arithmetica",
stating the theorem together with the comment that he ``had found a
remarkable proof, but the margin's space was not enough to write it there"
\cite[p.\,173]{b3}.

Strangely enough, Fermat let elapse 28 years without publishing any proof
until he died in 1665 \cite[p.\,353]{b3}.

His son published the note in 1670 \cite[p.\,172]{b3}, so starting the FLT
saga.

The theorem resisted the efforts of the best mathematicians for a lot more
than three hundred years, so much so, that in the seventies of last century
it was wide spread the opinion that Fermat realized that what he had in mind
was a wrong or an incomplete proof \cite[p.\,202]{b2}.

Finally, in the late nineties, the british mathematician Andrew Wiles
achieved a full FLT proof. A very brilliant and sophisticated one. Indeed,
the way he chose was through a previous proof of Shimura--Taniyama--Weil
conjecture, not yet achieved at that time, considered more general than FLT,
even more difficult and implying the FLT proof. This approach gave Wiles the
opportunity of producing a lot of remarkable contributions mainly in the
fields of elliptic curves modularity, topology and number theory \cite{b1},
\cite{b4}. Obviously, this asked for an extensive use of outstanding modern
mathematical concepts, all this work deserving congratulations, because the
resulting progress of nowadays mathematics. Fermat did a similar thing
regarding the mathematics of his time, but failed in his ``Last Theorem".

Still an interesting historical note is that \emph{FLT in the special case
n=3$, was already known in ancient Greece} under the name of ``\emph{the
cube's duplication problem}". \emph{Mathematically}, the rising of this
question is quite natural. Indeed, Pythagoras, with his fundamental theorem,
had \emph{duplicated the square}. So, why not to start thinking of
duplicating a cube? In other words, given an integer and its cube, to find
two other integers such that the sum of their cubes equals the first cube.
Notorious intellectuals, such as Arquitas, Democritus and many others,
became interested, but none solved the problem. \emph{The situation remained
so for more than two thousand years}. Then, a century after Fermat's
marginal note, \emph{Euler has proved that the problem was an impossible one
.

Reminding all we said now, we kept the opinion that it seems quite
defensible to think that achieving a full and very simple FLT proof still
remains an open and quite challenging problem.

After some time and unsuccessful attempts, we have been lucky enough to find
this way.

\section{Statement}

\label{sec:1}

The equation $z^n=x^n+y^n$ admits no integer solutions in $x,y$ and $z$ if $n
$, also an integer, is greater than 2. This is equivalent to the following.
\begin{equation}  \label{Eq1.1}
\hbox{If $\{y,x,z,n\}\in\N^{+}$ and $n>2$, then $z^{n}\gtrless
x^{n}+y^{n}$\ponto}
\end{equation}

\section{Preliminary considerations}

\label{sec:2}

From now on and just for short, we refer to the theorem writing FLT.

By definition, we say that the inequality between the $z$ power and the sum
of the other two, with the same exponent, is \emph{unreversed} if the signal
is $<$ and \emph{reversed} if $>$.

When it happens $z^{n-1}<x^{n-1}+y^{n-1}$ and $z^n>x^n+y^n$, we call $n$ the
\emph{reversion exponent}. Supposing that there are solutions of the
Diophatine equation form in the statement, its form \eqref{Eq1.1}, implies
z>x$ and $z>y$.

In conformity with these implications are the two hypothesis $z\geqslant x+y
. However, $z>x+y$ remains reversed with $n\geqslant 1$. The same happens to
$z=x+y$ with $n>1$.

The complementar of $z\geqslant x+y$ is $z<x+y$. Now the representative
segments of $x,y$ and $z$ may define a triangle. Triangles can be classified
through the parameter \emph{greatest inner angle, $\alpha$}. If $\alpha>\pi/2
$, $z$ is too large to define a Pythagorean triplet with $x$ and $y$. Hence,
$z^2>x^2+y^2$, so $n=2$.

With $\alpha=\pi/2$ we have a right triangle. Its inequality reverses
through an intermediary equality, $z^2=x^2+y^2$. But, from $zx^2>x^3$ and
zy^2>y^3$ we have $z^3>x^3+y^3$, so $n=3$. We remark that $x=y$ \emph{gives
z$ irrational, not integer}, with exponents one and any other odd number.

It follows $\alpha<\pi/2$.

This subdivides in three cases. One with all inner angles $\alpha=\pi/3$, so
$z=x=y$, contradicting $z>x$ and $z>y$, then no solutions here.
Geometrically, the inequality $z<z+z$ never reverses, whatever the exponent,
thus, also no $n$. Another similar situation happens with two $\alpha$ and
the opposite sides $z$ equal, contradicting $z>x$ and $z>y$. Then again no
solutions and no $n$.

From what have been said and also from the symbology about $x$ and $y$ being
arbitrary, we can assume with no loss of generality,
\begin{equation}  \label{eq2.1}
z>x>y\ .
\end{equation}
Therefore, the only remaining triangle's type is defined by $\alpha<\pi/2$
and all sides different. Now $z$ is not large enough to define a Pythagorean
triplet with $x$ and $y$. Then, the inequations defining this triangle are
\begin{equation}  \label{eq2.2}
\begin{aligned} z&< x+y\ ,\\ z^{2} &< x^{2}+y^{2}\ , \end{aligned}
\end{equation}
the second showing that \emph{to get out of the situation unreversed}, an
exponent, \emph{depending on $y,x$ and $z$ and greater than two} is needed,
\begin{equation}  \label{eq2.3}
n(y,x,z)>2\ .
\end{equation}
What have been said up to now is synthesized in Table \ref{tab:1} below, the
symbol $\triangle$ meaning ``triangle".

\begin{table}[h]
\caption{Triplets' classification.}
\label{tab:1}
\begin{tabular}{|llllllllllll|}
\hline
\multicolumn{6}{|l|}{Set 1} & \multicolumn{6}{|l|}{Set 2} \\
\multicolumn{6}{|l|}{$\nexists\,\triangle\,\leftrightarrow\,z\ge x+y$} &
\multicolumn{6}{|l|}{$\exists\,\triangle\,\leftrightarrow\,z<x+y$} \\ \hline
\multicolumn{3}{|l|}{Subset 1.1} & \multicolumn{3}{|l|}{Subset 1.2} &
\multicolumn{3}{|l|}{Subset 2.1} & \multicolumn{3}{|l|}{Subset 2.2} \\
\multicolumn{3}{|l|}{$z>x+y$} & \multicolumn{3}{|l|}{$z=x+y$} &
\multicolumn{3}{|l|}{$\alpha>\pi/2$} & \multicolumn{3}{|l|}{$\alpha=\pi/2$}
\\
\multicolumn{3}{|l|}{$n=1$} & \multicolumn{3}{|l|}{$z^{2}>x^{2}+y^{2}$} &
\multicolumn{3}{|l|}{$z^{2}>x^{2}+y^{2}$} & \multicolumn{3}{|l|}{
z^{2}=x^{2}+y^{2}$} \\
\multicolumn{3}{|l|}{} & \multicolumn{3}{|l|}{$n=2$} & \multicolumn{3}{|l|}{
n=2$} & \multicolumn{3}{|l|}{$z^{3}>x^{3}+y^{3}$} \\
\multicolumn{3}{|l|}{} & \multicolumn{3}{|l|}{} & \multicolumn{3}{|l|}{} &
\multicolumn{3}{|l|}{$n=3$} \\ \hline
\multicolumn{4}{|l|}{Subset 2.3} & \multicolumn{4}{|l|}{Subset 2.3.1} &
\multicolumn{4}{|l|}{Subset 2.3.2} \\
\multicolumn{4}{|l|}{$\alpha<\pi/2$} & \multicolumn{4}{|l|}{$\alpha<\pi/2$;
\,$z=x>y$} & \multicolumn{4}{|l|}{$\alpha<\pi/2$; \,$z=x=y$} \\ \hline
\multicolumn{4}{|l|}{Subset 2.3.1} & \multicolumn{4}{|c|}{$\nexists\,n$,} &
\multicolumn{4}{|c|}{$\nexists\,n$,} \\
\multicolumn{4}{|l|}{$z^{2}<x^{2}+y^{2}$, \,$n\ge 3$ and} &
\multicolumn{4}{|l|}{$\triangle$ type conserved} & \multicolumn{4}{|l|}{
\triangle$ type and angles} \\
\multicolumn{4}{|l|}{depending on $\{y,x,z\}$} & \multicolumn{4}{|l|}{but
not angles} & \multicolumn{4}{|l|}{conserved} \\ \hline
\end{tabular
\end{table}

It is now clear that proving FLT in general terms is reduced to do that in
the special terms \eqref{eq2.2}.

\section{Proof}

\label{sec:3}

\subsection{A necessary and sufficient condition}

\label{sec:3.1}

One of such conditions is the existence of two consecutive integers, $n-1$
and $n$, \emph{depending on $y,x$ and $z$}, and such that
\begin{equation}
\begin{aligned} z^{n-1}&< x^{n-1}+y^{n-1}\ ,\\ z^{n} &> x^{n}+y^{n}\ .
\end{aligned}  \label{eq3.1}
\end{equation
An alternative and equivalent way of stating \eqref{eq3.1} is the following.
If we imagine the exponent as being the continuous variable in $\mathbb{R
^{+}$, the implicit function
\begin{equation}
z^{s}-x^{s}-y^{s}=0  \label{eq3.2}
\end{equation
defines $s$ in terms of $y,x$ and $z$ and with the requirement
\begin{equation}
s\in ]n-1,n[  \label{eq3.3}
\end{equation}

\subsection{Accessory entities}

\label{sec:3.2}

For $\forall\, i\in N^{+}$, we define
\begin{equation}  \label{eq3.4}
p_i=x^{i}+y^{i}\ .
\end{equation}
From \eqref{eq2.1} $x>y$, then
\begin{equation}  \label{eq3.5}
\begin{aligned} p_{i}\,x &> p_{i+1}\ ,\\ p_{i}\,y &< p_{i+1}\ , \end{aligned}
\end{equation}
so,
\begin{equation}  \label{eq3.6}
\frac{p_{i+1}}{p_i}=\frac{x^{i+1}+y^{i+1}}{x^{i}+y^{i}}=k_{i}\ .
\end{equation}
This, together with \eqref{eq3.5} show that the $k_{i}$ are rational
numbers, increasing with $i$, but always satisfying
\begin{equation}  \label{eq3.7}
y<k_{i}<x\ .
\end{equation}
We can now compare the successions of the $z^{i}$ powers with that of the
p_{i}$,
\begin{equation}  \label{eq3.8}
\begin{aligned} z^{i+1}&=&z^{i}z\\ p_{i+1}&=&p_{i}k_{i} \end{aligned}
\end{equation}
showing that the $z^{i}$ grow ``faster" than the $p_{i}$. Thus, there is a
certain $i$ such that $z^{i}>p_{i}$, and so for any further $i$. By other
words, \emph{when the exponents increase}, $z<x+y$ in \eqref{eq2.2} reverses
and remains so for any further exponent. This allows to define the number
n-1$ in \eqref{eq3.1} as follows:
\begin{equation}  \label{eq3.9}
n-1=\max\{i\in N^{+}: z^{i}<x^{i}+y^{i}\}
\end{equation}

\subsection{Geometrical evolution}

\label{sec:3.3}

When the exponents increase the initial triangle \eqref{eq2.2} changes size
and shape up to exponents $n-1$, with which there is still a triangle whose
inequality is
\begin{equation}  \label{eq3.10}
z^{n-1}<x^{n-1}+y^{n-1}\ .
\end{equation}
With exponents $n$, \emph{be FLT true or false}, there is no triangle,
because $z^n=x^n+y^n$, or $z^n>x^n+y^n$, corresponding the first to FLT
false, and the second to FLT true, \emph{define no triangle}. And, as
already shown by \eqref{eq3.8} and \eqref{eq3.9}, the inequality
\eqref{eq3.10} is reversed \emph{with any exponent greater than $n$}.

This gives two conclusions:

a) without contradiction, FLT can only be supposed false with exponents $n$.

b) with exponents $n-1$ the triangle
\begin{equation}  \label{eq3.11}
T_{n-1}=\{y^{n-1},x^{n-1}, z^{n-1}\}
\end{equation}
can be called ``the last triangle". Its nature may be found squaring the
sides, giving exponents $2n-2$. To the inequality $z<x+y$ being surely
reversed it must be $2n-2>n$, this asking for $n>2$, which is precisely the
case as shown by \eqref{eq2.2} and \eqref{eq2.3}. Then,
\begin{equation}  \label{eq3.12}
z^{2n-2}>x^{2n-2}+y^{2n-2}\ ,
\end{equation}
proving that in the last triangle, $T_{n-1}$ of \eqref{eq3.11}, $\alpha>\pi/2
$; \emph{independent of $y$, $x$ and $z$}.

We remark that the reversion in the squares, \eqref{eq3.12}, is not
``strong" enough to prove FLT, because this theorem \emph{asks for a
reversion of \eqref{eq3.10} in the next integer exponent $n$}.

\subsection{Reversors}

\label{sec:3.4}

About the necessary and sufficient condition \eqref{eq3.1}, we have already
proved the ever existence of the number $n-1$, defined by \eqref{eq3.9}.
Hence, it remains to prove the second of \eqref{eq3.1}, which can be written
in the form
\begin{equation}  \label{eq3.13}
z^n-x^n-y^n>0\ .
\end{equation}
This positive difference, \emph{if FLT is true}, defines an interval in
\mathbb{R}^{+}$, of numbers, $\zeta_n$. Thus, we can write
\begin{equation}  \label{eq3.14}
\text{FLT true} \Longleftrightarrow \exists \{\zeta_n\}\,:\,z^n\geqslant
\zeta_n\geqslant x^n+y^n\ .
\end{equation}
This clearly shows that ``FLT is true" is a proposition \emph{admiting a
continuous infinity of proving ways}, each one through a particular value of
$\zeta_n$. Hence, the next step is to find an algorithm linking $y$, $x$ and
$z$ with the $\zeta_n$. We start to do that searching for a continuous set
of numbers, $\lambda^{\lambda}$, which we call \emph{reversors}, because of
their property of, \emph{despite smaller than $z$}, multiplying by a $\lambda
$ the $z^{n-1}$ in the last triangle's inequality, \eqref{eq3.10}, \emph
contradicts the situation unreversed, and, at the same time, gives the
solution $z^n>x^n+y^n$, to the new situation}.

Formally, as the contradiction of $<$ is $\geqslant$, this property is
written
\begin{equation}  \label{eq3.15}
\lambda\,z^{n-1}\geqslant x^{n-1}+y^{n-1}\Longrightarrow z^n>x^n+y^n\ .
\end{equation}
It is clear that from \eqref{eq3.15}, \emph{to be proved soon}, the
existence of \emph{at least one $\lambda$ is a sufficient condition} of FLT
being true. To have the property \eqref{eq3.15} a $\lambda$ must be of the
form
\begin{equation}  \label{eq3.16}
1<\lambda=\frac{z}{\rho}<z\ ,
\end{equation}
implying
\begin{equation}  \label{eq3.17}
1<\rho<z\ .
\end{equation}
Entering with this in \eqref{eq3.15}, we have
\begin{equation}  \label{eq3.18}
\frac{z}{\rho} \, z^{n-1}\geqslant x^{n-1}+y^{n-1}\Longrightarrow
z^n>x^n+y^n\ ,
\end{equation}
or
\begin{equation}  \label{eq3.19}
\rho(x^{n-1}+y^{n-1})\geqslant x^n+y^n\ ,
\end{equation}
giving
\begin{equation}  \label{eq3.20}
\rho\geqslant\frac{x^n+y^n}{x^{n-1}+y^{n-1}}=\frac{p_n}{p_{n-1}}=k_{n-1}\ ,
\end{equation}
having retaken the use of the $p_i$ and $k_i$, defined in Sec. \ref{sec:3.2
. The $kk$ property \eqref{eq3.7}, $y<k_i<x<z$, confirms that $k_{n-1}$ is a
$\rho$. More precisely, $\rho\geqslant k_{n-1}$ shows that
\begin{equation}  \label{eq3.21}
k_{n-1}=\min\{\rho\}=\underline{\rho}\ .
\end{equation}
by definition of $\underline{\rho}$.

Hence,
\begin{equation}
\exists \,\lambda =\frac{z}{k_{n-1}}\ ,  \label{eq3.22}
\end{equation
\emph{sufficient to prove that FLT is true}. Indeed, entering with $\rho
=k_{n-1}$ in \eqref{eq3.18} and performing the calculations gives
\begin{equation}
z^{n}>x^{n}+y^{n}\ ,  \label{eq3.23}
\end{equation
\emph{like we intended to prove}. As $k_{n-1}=\underline{\rho }$,
\begin{equation}
\frac{z}{k_{n-1}}=\max \{\lambda \}\ ,  \label{eq3.24}
\end{equation
and this rises the question of what could be $\max \{\rho \}=\overline{\rho }
$.

Dividing \eqref{eq3.18} by $z^{n-1}$, we obtain
\begin{equation}  \label{eq3.25}
z>\lambda\geqslant\frac{x^{n-1}+y^{n-1}}{z^{n-1}}=\varphi>1\ ,
\end{equation}
having introduce the symbol $\varphi$, which is greater than one by force of
\eqref{eq3.10}. The signal $\geqslant$ in \eqref{eq3.25} gives
\begin{equation}  \label{eq3.26}
\min\{\lambda\}=\varphi=\frac{x^{n-1}+y^{n-1}}{z^{n-1}}\ ,
\end{equation}
then,
\begin{equation}  \label{eq3.27}
\varphi=\frac{z}{\overline{\rho}}
\end{equation}
and
\begin{equation}  \label{eq3.28}
\overline{\rho}=\frac{z}{\varphi}=\frac{z^n}{x^{n-1}+y^{n-1}}\ .
\end{equation}

To verify \eqref{eq3.26}, we enter with \eqref{eq3.28} in \eqref{eq3.25},
giving
\begin{equation}  \label{eq3.29}
z^n=\overline{\rho}(x^{n-1}+y^{n-1})=z^n\ ,
\end{equation}
confirming, not only that $\varphi=\min\{\lambda\}$, but also that $\varphi$
reverses \eqref{eq3.10} \emph{in the strongest possible way}, because the
reversion's result is $z^n$ itself, the $\max\{\zeta_n\}$. All these
considerations are verifiable by the relations
\begin{equation}  \label{eq3.30}
\overline{\rho}>\underline{\rho}
\end{equation}
or
\begin{equation}  \label{eq3.31}
\frac{z}{k_{n-1}}>\varphi\ .
\end{equation}
Indeed, attending the $k_{n-1}$ form, in \eqref{eq3.20}, supposing
z/k_{n-1}<\varphi$ gives
\begin{equation}  \label{eq3.32}
z^n<x^n+y^n\ ,
\end{equation}
contradicting \eqref{eq3.9}.

The alternative, $z/k_{n-1}=\varphi$ gives
\begin{equation}  \label{eq3.33}
z^n=x^n+y^n\ ,
\end{equation}
i.e. \emph{FLT false, with exponents $n$}, contradicting FLT true, as
already proved by \eqref{eq3.22}. Hence, it only remains the conclusion that
$z/k_{n-1}>\varphi$, as we wanted to verify. Therefore, the main conclusion
is that FLT \emph{is also true} for any triplet of the type \eqref{eq2.2}.

As in Sec. \ref{sec:2} above, FLT has been proved in all other triplets
shown in Table \ref{tab:1}, \emph{this FLT full proof is now completed}.

Another main conclusion \emph{is that FLT admits a not countable infinity of
proving ways}, each one through a particular value of the number $\lambda $
belonging to the set
\begin{equation}
\{\lambda \}\Longleftrightarrow \left[ \varphi ,\frac{z}{k_{n-1}}\right] \ .
\end{equation
\emph{Another way showing the existence of a continuous infinity of proving
ways is the fact that $\lambda ^{\prime }s$ are the solutions of the
compatible opposite sense inequations system \eqref{eq3.25}}.

\subsection{Overreversors}

\label{sec:3.5}

The algorithm linking $y$, $x$ and $z$ with the $\rho ^{\prime }s$, $\lambda
^{\prime }s$, and $\zeta ^{\prime }s$ is the following.

Choosing a $\rho$ from the set
\begin{equation}  \label{eq3.35}
\{\rho\}\Longleftrightarrow \left[k_{n-1},\frac{z}{\varphi}\right]\ ,
\end{equation}
we have the corresponding $\lambda=z/\rho$ and $\zeta_n=\rho(x^{n-1}+y^{n-1})
$.

Double opening the $\rho $ interval, \eqref{eq3.35}, the same happens with
those of the $\lambda ^{\prime }s$ and $\zeta ^{\prime }s$. Therefore, to
\begin{equation}
\forall \,\lambda \in \left] \varphi ,\frac{z}{k_{n-1}}\right[
\label{eq3.36}
\end{equation
corresponds a $\zeta _{n}$ such that
\begin{equation}
z^{n}>\zeta _{n}>x^{n}+y^{n}\ ,  \label{eq3.37}
\end{equation
\emph{logically stronger than} just $z^{n}>x^{n}+y^{n}$.

Because of this property, we call the $\lambda ^{\prime }s$ from
\eqref{eq3.36} \emph{overreversors} and the respective $\zeta _{n}$ \emph{an
overreversion}, because more than needed to prove FLT. For example, if $z$
is large enough as $z^{n}>x^{n}+xy^{n-1}$, $z/x$ is an overreversor.

A numerical example of this situation is the following
\begin{align*}
&\{y,x,z\}=\{2,3,4\}; \\
&4<3+2; \;4^2>3^2+2^2; \\
&n=2;\; n-1=1;\; T_{n-1}=T_1=\{2,3,4\}; \\
&\varphi=\frac{3+2}{4}=\frac{5}{4}; \\
&k_{n-1}=k_1=\frac{3^2+2^2}{3+2}=\frac{13}{5}; \\
&\frac{z}{k_1}=\frac{20}{13}; \\
&\{\lambda\}=\left[\frac{5}{4},\frac{20}{13}\right]; \\
&z^2>k_1(x+y);\; 4^2>\frac{13}{5}(3+2); \; 16>13; \\
&\frac{z}{x}=\frac{4}{3}\in\left]\frac{5}{4}\, \frac{20}{13}\right[; \\
&z^2>x^2+xy; \\
&\zeta_2=x(x+y);\; \zeta_2=15; \\
&4^2>\zeta_2>3^2+2^2; \; 16>15>13.
\end{align*}

\emph{Numerical examples, covering all the possibilities shown in Table \re
{tab:1}, are given in Sec. \ref{sec:6} below, in order to verify the
theoretical results achieved in this work}.

\section{Corollary 1, a general relation between $y,x,z$ and $n$.}

\label{sec:4-Corollary}

We have proved FLT through \eqref{eq3.1}. Taking Neperian logarithms and
solving in $n$ and $n-1$ gives
\begin{equation}  \label{eq5.1}
n>\frac{\log(x^n+y^n)}{\log z}=b
\end{equation}

\begin{equation}  \label{eq5.2}
n-1<\frac{\log(x^{n-1}+y^{n-1})}{\log z}=a\ .
\end{equation}
The first shows that through simple calculations we get $n$, and then $b$,
and again $n$, \emph{as the first integer above $b$}, so
\begin{equation}  \label{eq5.3}
0<n-\frac{\log(x^n+y^n)}{\log z}<1
\end{equation}
is the wanted relation.

To remark that $b$ is never an integer. However, it is possible $a=2$, if
and only if $y$, $x$ and $z$ define a Pythagorean triplet, as easily seen
through \eqref{eq5.2}.

From \eqref{eq5.1} $b<n$, then
\begin{equation}  \label{eq5.4}
z^b=x^n+y^n>x^b+y^b\ ,
\end{equation}
showing that \emph{the inequality \eqref{eq3.10} is already reversed with
exponents $b$}. In parallel terms, apart the Pythagorean triplets, $a>n-1$
and, from \eqref{eq5.2},
\begin{equation}  \label{eq5.5}
z^a=x^{n-1}+y^{n-1}<x^a+y^a\ ,
\end{equation}
proving that the inequality is not yet reversed with exponents $a$.

\subsection{Bounding $b-a$}

\label{sec:4.1}

Through \eqref{eq5.1} and \eqref{eq5.2} we clearly see that
\begin{equation}  \label{eq5.6}
0<b-a<1\ .
\end{equation}
Performing the subtraction \eqref{eq5.1}-\eqref{eq5.2} and reminding the $k_i
$ in \eqref{eq3.7}, one easily obtains
\begin{equation}  \label{eq5.7}
b-a=\frac{\log(k_{n-1})}{\log z}\ ,
\end{equation}
confirming \eqref{eq5.6}, because
\begin{equation}  \label{eq5.8}
y<k_{n-1}<x<z\ .
\end{equation}
By force of $0<b-a<1$, it is also
\begin{equation}  \label{eq5.9}
0<1-(b-a)<1\ .
\end{equation}

Attending \eqref{eq5.7}, we have
\begin{equation}  \label{eq5.10}
1-(b-a)=\frac{\log(z/k_{n-1})}{\log z}\ .
\end{equation}
This and \eqref{eq5.7} ask to compare $z/k_{n-1}$ with $k_{n-1}$. The best
way is through the $k_i$ property \eqref{eq3.7} and the inequations
\eqref{eq2.2} of the initial triangle. This gives
\begin{equation}  \label{eq5.11}
k^2_{n-1}>y^2>(z+x)(z-x)\ .
\end{equation}

As $y,x$ and $z$ are integers, and, from \eqref{eq2.1} $z>x$, $z-x\geqslant 1
$, so $k^2_{n-1}>z$, or
\begin{equation}  \label{eq5.12}
\frac{z}{k_{n-1}}<k_{n-1}\ .
\end{equation}

Entering now with $z/k_{n-1}<k_{n-1}$ in \eqref{eq5.10} and comparing
\eqref{eq5.12} with \eqref{eq5.7}, gives $1-(b-a)<b-a$, or
\begin{equation}  \label{eq5.13}
\frac{1}{2}<(b-a)<1\ ,
\end{equation}
the wanted better $(b-a)$ bounding.

By the same stroke this allows to improve \eqref{eq5.3}, because $n-b$ is a
part of $1-(b-a)$. So we can write \eqref{eq5.3} in the better form
\begin{equation}  \label{eq5.14}
0<n-\frac{\log(x^n+y^n)}{\log z}<\frac{1}{2}\ .
\end{equation}

\subsection{Bounding $s$}

In Sec. \ref{sec:3.2} we have introduced the equalizing exponent $s$,
implicitly defined by $z^s=x^s+y^s$. Taking Neperian logarithms and solving
in $s$, we have
\begin{equation}  \label{eq5.28}
s=\frac{\log (x^s+y^s)}{\log z}\ .
\end{equation}
By force of \eqref{eq5.5} and \eqref{eq5.6}, the $s$ bounds are
\begin{equation}  \label{eq5.29}
n-1\leq a<s<b<n\ .
\end{equation}
The main conclusions about this are synthesized in Fig. 1 below.
\begin{figure}[htb!]
\includegraphics[scale=0.84]{Fig1.eps}
\caption{Inequality's distribution in $\mathbb{R}^{+}$. (No scales)}
\label{fig:1}
\end{figure}

\section{Corollary 2}

\label{sec:5-Corollary}

\emph{The Diophantine equation in Fermat's statement admits no solutions
other than algebraic irrationals and the inherent complexes}.

\subsection{Positive rationals}

\label{Sc7.1}

Supposing this corollary false and letting
\begin{equation}  \label{Eq7.1}
i=1,2,3;\ \ \ \{q_{i},q_{i}^{\prime }\}\in\mathbb{N}^{+}\ \ \hbox{and}\ \
n>2\ ,
\end{equation}
we could write
\begin{equation}  \label{Eq7.2}
(q_{3}/q_{3}^{\prime n}=(q_{2}/q_{2}^{\prime n}+(q_{1}/q_{1}^{\prime n}\ .
\end{equation}
Multiplying by $q_{1}^{\prime }q_{2}^{\prime }q_{3}^{\prime }$, we have
\begin{equation}  \label{Eq7.3}
(q_{3}q_{1}^{\prime }q_{2}^{\prime n}=(q_{2}q_{1}^{\prime }q_{2}^{\prime
n}+(q_{1}q_{2}^{\prime }q_{3}^{\prime n}\ ,
\end{equation}
contradicting FLT, already proved true.

\subsection{Negative integers}

\label{Sc7.2}

We suppose all or some of the integers negative, and, \emph{at least two of
them, equal}, then through preliminary considerations, \emph{mutatis mutandi
}, it is easy to conclude that, with no loss of generality, we still can
assume
\begin{equation}  \label{Eq7.4}
|z|>|x|>|y|\ .
\end{equation}

\subsubsection{All negative}

\label{Sc7.2.1}

If $n$ even, the situation is equivalent to FLT.

If $n$ odd, multiplying by $-1$, we have the same situation.

\subsubsection{Two negative}

\label{Sc7.2.2}

\begin{itemize}
\item[a)] $z$ and $x$
\begin{equation}  \label{Eq7.5}
(-z)^{n}=(-x)^{n}+y^{n}\ .
\end{equation}
If $n$ even, FLT.

If $n$ odd, the second number is a negative number with module smaller than
|z|$. Then \eqref{Eq7.5} is impossible. \vskip15pt

\item[b)] $z$ and $y$
\begin{equation}  \label{Eq7.6}
(-z)^{n}=x^{n}+(-y)^{n}\ .
\end{equation}
If $n$ even, FLT.

If $n$ odd, we have at right a positive number and at left a negative one,
an impossibility. \vskip15pt

\item[c)] $x$ and $y$
\begin{equation}  \label{Eq7.7}
z^{n}=(-x)^{n}+(-y)^{n}\ .
\end{equation}
If $n$ even, FLT.

If $n$ odd, positive at right, negative at left. Impossible.
\end{itemize}

\subsubsection{One negative}

\label{Sc7.2.3}

\begin{itemize}
\item[a)] $z$
\begin{equation}  \label{Eq7.8}
(-z)^{n}=x^{n}+y^{n}\ .
\end{equation}
If $n$ even, FLT.

If $n$ odd, negative at left, positive at right. Impossible. \vskip15pt

\item[b)] $x$
\begin{equation}  \label{Eq7.9}
z^{n}=(-x)^{n}+y^{n}\ .
\end{equation}
If $n$ even, FLT.

If $n$ odd, positive at left, negative at right. Impossible. \vskip15pt

\item[c)] $y$
\begin{equation}  \label{Eq7.10}
z^{n}=x^{n}+(-y)^{n}\ .
\end{equation}
If $n$ even, FLT.

If $n$ odd,
\begin{equation}  \label{Eq7.11}
x^{n}+(-y)^{n}<x^{n}<z^{n}\ ,
\end{equation}
thus, \eqref{Eq7.10} equality is impossible.
\end{itemize}

\subsection{Negative rationals}

\label{Sc7.3}

It is always possible to suppose that the signal of the rationals is that of
the $q_{i}^{\prime }$ in \eqref{Eq7.1}. Then it is easy to see that, after
multiplying \eqref{Eq7.1} by $q_{1}^{\prime }q_{2}^{\prime }q_{3}^{\prime }
, \eqref{Eq7.2} would contain, at least, one negative integer solution, an
impossibility, as already proved in the previous section.

\subsection{Algebraic irrationals and the inherent complex solutions}

\label{Sc7.4}

These exist and can be calculated through index $q>2$ roots of $y$, $x$ and
z$, in triplets admitting an equality with exponents $n\le 2$.

The first case is
\begin{equation}  \label{Eq7.12}
z=x+y\ .
\end{equation}

The candidate to be the solution is
\begin{equation}  \label{Eq7.13}
\{y^{1/q},x^{1/q},z^{1/q}\}\ .
\end{equation}

To begin with, we must know the relation between the $z$ root and the sum of
the other two. It cannot be
\begin{equation}  \label{Eq7.14}
z^{1/q}=x^{1/q}+y^{1/q}\ ,
\end{equation}
because this would imply the equalizing exponent being $1/q$, contradicting
\eqref{Eq7.12}.

The exponent's increasing mechanism is $1/q,2/q,...$ up to $q/q=1$, giving
the equality \eqref{Eq7.12}.

Now, from Section~\ref{sec:3.3} we know that, once reversed with a certain
exponent, \emph{the inequality remains so with any greater exponents}.
Hence, if we admit
\begin{equation}  \label{Eq7.15}
z^{1/q}>x^{1/q}+y^{1/q}\ ,
\end{equation}
this inequality \emph{would remain reversed with the greater exponent $q/q=1
, contradicting \eqref{Eq7.12}}.

Therefore, the only remaining possibility is
\begin{equation}  \label{Eq7.16}
z^{1/q}<x^{1/q}+y^{1/q}\ ,
\end{equation}
so proving that \eqref{Eq7.13} is a solution with exponents $q>2$.

An example is $\{2^{1/3},3^{1/3},5^{1/3}\}$, which, powered to $3$, gives
2+3=5$, in this example with two inherent complex solutions.

The second case is the Pythagorean triplets
\begin{equation}
z^{2}=x^{2}+y^{2}\ .  \label{Eq7.17}
\end{equation
In total parallel terms,
\begin{equation}
\{y^{1/q},x^{1/q},z^{1/q}\}\ \ \ \ \hbox{and}\ \ \ \ q>1  \label{Eq7.18}
\end{equation
and the inherent complexes are solutions, giving \eqref{Eq7.17}, when
powered to $2q>2$.

\section{Numerical verification}

\label{sec:6}

\subsection{Proof}

\label{sec:6.1}

\begin{exmp}\label{Ex6.1}
\ $\{4,5,6\}$.
\begin{gather*}
 6<5+4;\ \ 6^{2}<5^{2}+4^{2};\ \ 6^{3}>5^{3}+4^{3} \ \ \to\ \ n=3;\ \ n-1=2\ponto\\
 T_{n-1}=T_{2}=\{4^{2},5^{2},6^{2}\}\ponto\\
\varphi=\frac{5^{2}+4^{2}}{6^{2}}=\frac{41}{36}=1.1388...\ponto\\
 k_{2}=\frac{5^{3}+4^{3}}{5^{2}+4^{2}}=\frac{189}{41}\ponto\\
 \frac{z}{k_{2}}=\frac{6\timesd41}{189}=1.3015...>\varphi=1.1388...\ponto\\
 \{\lambda\}=\left[\varphi,\frac{z}{k_{2}}\right]=\bigl[1.1388...,\,1.3015...\bigr]\ponto\\
 \frac{z}{k_{2}}\,z^{2}=\frac{6\timesd41\timesd36}{189}=46.8571...>5^{2}+4^{2}=41\ \ \to\\
 \to\ \ z^{3}>k_{2}\,(x^{2}+y^{2})=x^{3}+y^{3}\\
 6^{3}=216>5^{3}+4^{3}=189\ponto
\end{gather*}
\end{exmp}

\begin{exmp}\label{Ex6.2}
\ $\{8,9,10\}$.
\begin{gather*}
 10<9+8;\ \ 10^{2}<9^{2}+8^{2};\ \ ...;\ \ 10^{4}<9^{4}+8^{4};\ \ 10^{5}>9^{5}+8^{5}\ \ \to\\
 \to\ \ n=5;\ \ n-1=4\ponto\\
 T_{n-1}=T_{4}=\{8^{4},9^{4},10^{4}\}\ponto\\
 x^{n-1}+y^{n-1}=9^{4}+8^{4}=10\,657\ponto\\
 \varphi=\frac{x^{n-1}+y^{n-1}}{z^{n-1}}=\frac{9^{4}+8^{4}}{10^{4}}=\frac{10\,657}{10\,000}=1.0657\ponto
   \end{gather*}
 \begin{gather*}
 k_{4}=\frac{9^{5}+8^{5}}{9^{4}+8^{4}}=\frac{91\,817}{10\,657}\ponto\\
 \frac{z}{k_{4}}=10\timesd\frac{10\,657}{91\,817}=1.160678...>\varphi=1.0657\ponto\\
 \{\lambda\}=\left[\varphi,\frac{z}{k_{4}}\right]=\bigl[1.0657,\,1.160678...\bigr]\ponto\\
 \frac{z}{k_{4}}\,z^{4}=11\,606.78...>9^{4}+8^{4}=10\,657\ \ \to\\
 \to\ \ z^{5}>k_{4}\,(x^{4}+y^{4})\virg\\
 10^{5}>9^{5}+8^{5}\ponto
\end{gather*}
\end{exmp}

\subsection{Corollary 1}

\label{sec:6.2}

In each $\{y,x,z\}$ example it is indicated the set it belongs in Table~\re
{tab:1}.

\begin{exmp}\label{Ex6.3}
\ $\{2,5,9\}$.
\begin{gather*}
 9>5+2\ \ \to\ \ \mathrm{Set\ 1.1}\ \ \to\ \ n=1\pvirg \\
 b=\frac{\log(5+2)}{\log 9}=0.885...<1\ \ \to\ \ n=1\pvirg \\
 a=\frac{\log(5^{0}+2^{0})}{\log 9}=0.315...\pvirg \ \ \ \ b-a=0.885...-0.315...=0.570...\pvirg \\
 \frac{1}{2}<0.570...<1\ponto
\end{gather*}
\end{exmp}

\begin{exmp}\label{Ex6.4}
\ $\{2,7,9\}$.
\begin{gather*}
 9=7+2\ \ \to\ \ \mathrm{Set\ 1.2}\pvirg \\
 9^{2}>7^{2}+2^{2}\ \ \to\ \ n=2\pvirg \\
 b=\frac{\log(7^{2}+2^{2})}{\log 9}=1.806...\ \ \to\ \ n=2\pvirg \\
 a=\frac{\log(7+2)}{\log 9}=1\pvirg \ \ \ \ b-a=1.806...-1=0.806...\pvirg \\
 \frac{1}{2}<0.806...<1\ponto
\end{gather*}
\end{exmp}

\begin{exmp}\label{Ex6.5}
\ $\{4,5,7\}$.
\begin{gather*}
 7<5+4,\ 7^{2}>5^{2}+4^{2}\ \ \to\ \ \mathrm{Set\ 2.1}\ \ \to\ \ n=2\pvirg \\
 b=\frac{\log(5^{2}+4^{2})}{\log 7}=1.908...\ \ \to\ \ n=2\pvirg \\
 a=\frac{\log(5+4)}{\log 7}=1.129...\pvirg \ \ \ \ b-a=1.908...-1.129...=0.779...\pvirg \\
 \frac{1}{2}<0.779...<1\ponto
\end{gather*}
\end{exmp}

\begin{exmp}\label{Ex6.6}
\ $\{3,4,5\}$.
\begin{gather*}
 5<4+3,\ 5^{2}=4^{2}+3^{2},\ 5^{3}>4^{3}+3^{3}\ \ \to\ \ \mathrm{Set\ 2.2}\ \ \to\ \ n=3\pvirg \\
 b=\frac{\log(4^{3}+3^{3})}{\log 5}=2.802...\ \ \to\ \ n=3\pvirg \\
 a=\frac{\log(4^{2}+3^{2})}{\log 5}=2\pvirg \ \ \ \ b-a=2.802...-2=0.802...\pvirg \\
 \frac{1}{2}<0.802...<1\ponto
\end{gather*}
\end{exmp}

\begin{exmp}\label{Ex6.7}
\ $\{4,5,6\}$.
\begin{gather*}
6^{2}<5^{2}+4^{2},\ 6^{3}>5^{3}+4^{3}\ \ \to\ \ n=3\ \ \to\ \ \mathrm{Set\ 2.3.1}\pvirg \\
b=\frac{\log(5^{3}+4^{3})}{\log 6}=2.925...\ \ \to\ \ n=3\pvirg \\
a=\frac{\log(5^{2}+4^{2})}{\log 6}=2.072...\pvirg \ \ \ \ b-a=2.925...-2.072...=0.852...\pvirg \\
\frac{1}{2}<0.852...<1\ponto
\end{gather*}
\end{exmp}

\begin{exmp}\label{Ex6.8}
\ $\{6,7,8\}$.
\begin{align*}
 8<7+6,\ 8^{2}<7^{2}+6^{2},\ 8^{3}<7^{3}+6^{3},\ 8^{4}>7^{4}+6^{4}\ \
 &\to&\ \ \mathrm{Set\ 2.3.1}\\
 &\to&\ \ n=4\pvirg
\end{align*}
\vspace*{-4ex}
\begin{gather*}
b=\frac{\log(7^{4}+6^{4})}{\log 8}=3.950...\ \ \to\ \ n=4\pvirg \\
 a=\frac{\log(7^{3}+6^{3})}{\log 8}=3.042...\pvirg \ \ \ \ b-a=3.950...-3.042...=0.908...\pvirg \\
 \frac{1}{2}<0.908...<1\ponto
\end{gather*}
\end{exmp}

\begin{exmp}\label{Ex6.9}
\ $\{2,4,4\}$.
\begin{gather*}
 \mathrm{Set\ 2.3.1}\ \ \to\ \ \forall\,j\ \to\ 4^{j}<4^{j}+2^{j}\ \ \to\ \ \nexists\,n\pvirg \\
 b=\frac{\log(4^{n}+2^{n})}{\log 4}> n\,\frac{\log 4}{\log 4}>n\ \ \to\ \ \nexists\,n\!:\, n>n\ponto
\end{gather*}
\end{exmp}

\begin{exmp}\label{Ex6.10}
\ $\{3,3,3\}$.
\begin{gather*}
  \mathrm{Set\ 2.3.2}\ \ \to\ \ \forall\,j\ \to\ 3^{j}<3^{j}+3^{j}\ \ \to\ \ \nexists\,n\pvirg \\
    b=\frac{\log(3^{n}+3^{n})}{\log 3}=\log2+n\ \ \to\ \ \nexists\,n\!:\, n>\log2+n\ponto
\end{gather*}
\end{exmp}

redpajama_set_name: RedPajamaArXiv


text:
Pen & Paper Roleplaying Central »
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(when) Improv is railroading
Author Topic: (when) Improv is railroading (Read 1255 times)
Re: Improv is railroading
Quote from: Lunamancer on January 11, 2022, 09:46:34 PM
One of my favorite beginnings to a module ever is the one in Dance of the Fairie Rings. Spoilers ahead. The first choice players face is decide which way to go at a fork in the road, the high road or the low road. But if the players take the high road, they find themselves arriving at the same fork in the road. Again and again, each time they take the high road, they keep ending up back on the fork in the road until they take the low road. If that isn't enough, prior to the fork in the road, the "flavor text" that begins the adventure has an old man warning the PCs to avoid the low road.
I think there are a few vital things that separate this from being a railroad.
It's not sneaky. It's in your face. The GM isn't trying hide it.
How easy would it have been to give a straight road with no fork? Why present a choice and not honor it?
For that matter, why were PCs instructed to do something they wouldn't be allowed to do?
And all this adds up to make players feel as though there's some mystery afoot rather than they're being railroaded.
It creates more intrigue than frustration.
By being blatant, I think it makes it clear that you aren't being railroaded by the GM. It's some in-game force that's messing with you. There's some enemy to defeat.
Now for the rare bird who nonetheless does feel railroaded and frustrated by this, there's another surprise. That your annoyance is not justified by the facts because your choice at this fork in the road actually does matter. For it is some NPC that's doing it. The NPC is the prisoner of a dragon, and this is the NPC's way of getting heroes to help. And each time the NPC has to transport the PCs back to the fork in the road, more of that NPC's energy is sapped. And the less energy the NPC has to aid the PCs in confronting the dragon. The longer it takes you to recognize the low road is the solution, the slower you are to adapt, the more reluctant you are to embrace adventure, in other words, the poorer your choices, the less advantaged you are. Isn't that exactly what we expect out of player agency?
My takeaways here.
Reserve judgment regarding railroading. Reserve judgement by a lot.
Railroading isn't railroading when it's an NPC doing. All the railroading GM needs to do to make his or her beautiful plot kosher is hand over the puppeteer strings to an NPC.
NPC villain masterminds, to the degree that they are effective, can rob players of agency. There is no sacred right to agency, other than the existentialist choice to decide what sort of prisoner you will be. Everything else you've got to earn.
I think you're onto something here.
Maybe we could define illusionism as "A term for styles where the GM has control over the a situation (event, NPC, die roll, etc.), by a variety of means, and the players are not aware (or expecting) that the GM has this kind of control."
So, in your example, the PCs are aware that the DM is doing it. But if you fudge a roll, the players aren't aware.
If you all agree that the DM can fudge rolls, it is not illusionism; there is no illusion. The players are expecting this. This is okay.
If you enter a random town, it is expected that the GM can control waht kind of town it is, etc. The GM is not expected to have everything written down beforehand.
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Quote from: S'mon on January 11, 2022, 05:25:24 PM
Railroading is forcing people down a track they don't want to go. The stuff you discuss is mostly bad practice, and may be used to railroad, but is not railroading per se.
/Natural 20
I wanna weigh in here - because it's a very good post and there are a lot of good points being thrown around.
I look at this problem of "Railroading", "Illusionism" as two stages of inevitable growth of being a GM. GMing requires some level of autonomy and agency in its own right - but we rarely talk about it. Most GM's that are relatively new to GMing start with published adventures and I'd say most do not go beyond that point.
Those that hit the top-end of only using published adventures are the ones that want, or are forced because of adventurous players exercising their own player-agency, to go off-roading from the prescribed "path". Invariably these become the Railroaders. And yes, it's a silly skillset unto itself where you learn to finagle players back onto the proscribed path. The degree of hamfistedness is the line between Railroading or Illusionism.
THIS IS BASIC GMING. This is not skilled GMing. This is not the kind of GMing that will run for multi-year campaigns. This is noobcake-to-low-middle-tier GMing skills in practice.
GMing agency requires that you are a fan of the PC's. This doesn't mean you favor them. It means they *are* the stars of the show. And it means that your setting is the unknown PC that lives and breathes with your PC's. It has it's own set of rules filled with NPC's that engage the stars of the show without getting in the way of the PC's agency. And where those two conflict? That's where the game is played.
The idea of improv-as-railroad is true only if the GM in question doesn't understand these principles in practice. This is the hallmark of a GM that doesn't *want* their PC's to enact their own agency in the game. They're passively or actively GMing from a position of being and adversary to the PLAYERS - not the PC's.
GMing is a dance. And that dance requires partners in the affair - the Players. The tacit agreement is We're Playing Together. This requires trust, to boldface say "Improv is Railroading" implies that the GM has not earned the trust of his players. And why is that? Improv is a tool. It's the tool that lets you procedurally color in the paths not painted for you by some other author of your world. That's a skill to be cultivated not shunned.
1) The Players are the STARS of the show.
2) You can kill the Stars of the show.
3) The GM is not passive in the world. The World works according to its own internal logic and the GM is Prime Mover of that logic.
The caveat to this is that these principles are what I use for Sandbox play. But these principles absolutely work for published adventures and one shots.
S'mon
Quote from: Wrath of God on January 12, 2022, 03:36:40 AM
Though many published adventures have enough bad illusions all around that you need to tweak them to make game working anyway.
I stick with location-based published adventures, not plotted adventures. NPC actions such as orcs raiding the village tend to be either randomly generated or GM fiat. If the adventure says "the village may be destroyed while the PCs are away" I'll make some rolls to see if it is attacked and what the outcome is, taking into account PC activity.
Primeval Thule
https://simonsprimevalthule.blogspot.com/2019/01/primeval-thule-campaign.html
Faerun
http://frloudwater.blogspot.com/2020/08/faerun-adventures-beginner-5e-d-game.html
Odyssey of the Dragonlords https://simonsodysseyofthedragonlords.blogspot.com/2021/08/odyssey-of-dragonlords-5e.html
rytrasmi
Revisiting my previous argument, we mostly consider it acceptable for GMs to "balance" encounters when writing before hand. Even if they want to calibrate the balance to easy, average, hard, and run-away! What if the GM makes an error in planning and only discovers that error in real time during play? Is it wrong to correct errors?
GM error is often really player error. If the enemy was stronger than the GM planned, the players still get to choose to fight it or not. The players make the choices, so errors are on them. If the goblin camp was supposed to have 10 goblins but I just described 100 goblins, I have two choices: 1) rewind and correct or 2) run with it. If I run with it, the players get the chance to come up with a creative solution. If they stupidly charge in because of balance, that's their error.
Quote from: SirFrog on January 11, 2022, 08:28:49 PM
I prefer to use two terms to describe my DM'g style: 1) Schrodinger's Goblin and 2) Object Oriented Roleplaying
1) Schrodinger's Goblin is an paradox. I have no idea if there is a goblin behind the door until the players open it. It doesn't matter if it was planned to be there or not. The players don't care either, because until it happens it didn't exist before hand. Just because something is planned or unplanned doesn't make it valid or invalid. You are not cheating the players if they don't know. I am not cheating myself as DM.
2) Object Oriented Roleplaying is exactly what it sounds like. When required a process is run by me that determines what the output in the game is. The process doesn't matter, it's a black box for all intents and purposes. It could be a random table, an encounter pulled from another module, or made up on the spot.
Bottom Line: improv or planned doesn't really matter.
Concerning Schrodinger's Goblin, I'd argue that is does matter. The goblin got there somehow. He had a reason to be there and a trajectory to getting there. If his presence contradicts something else, your players will eventually notice. Maybe not with this goblin, but with the next.
"You are not cheating the players if they don't know." - You're overestimating your abilities. Players are smart and notice a lot. Give them some credit. They will usually go along with it, but don't fool yourself into thinking you're some genius who's crafting perfect illusions. Illusionists always overestimate their abilities. It's a little arrogant to be honest.
Ruprecht
Personally I don't think the quantum ogre is necessarily bad. Yeah, blasphemy I know.
Recycling things makes it easier on the GM, as long as that Ogre isn't boring and the players aren't forced into the fight its not much different then having identical encounters in both locations. Players are unaware of most of what's going on behind the GM screen and wouldn't be aware of the quantum ogres movements anyway.
Civilized men are more discourteous than savages because they know they can be impolite without having their skulls split, as a general thing. ~Robert E. Howard
Actually Railroading can and is performed by players as well on the DM. This came up a year or two ago along the lines of a player declaring they find a shotgun behind a bar. Not roll for to see if anythings there, or the DM saying anything. The player just poofed it into existence. That is a player railroading the DM.
And I've seen far far far far too much of where one player forces an action on another players character.
What I've seen all too often is that its the IC fanatics and storygamers that cause the most trouble with these stunts.
What is IC fanatics? I mean what is IC, I do not recognize this shortcut.
But generally I'd still disagree. Railroad demand certain rails. It generally is term assuming GM has well long term plans and will push or trick players into following strict narrative for long time, at least adventure. So I'd not call fudging one random encounter to be one.
And storygames are different batch. First they generally try to avoid specific rails (while enforcing genre rails, which make doing un-genre stuff generally not important), but yes they ditch rigid setting and give players some elements of power over world itself.
In Character. The types of players who are obsessed with "muh immershun!" not normal sane immersion. But loony fringe stuff more oft than not. For a few its borderline, or full on, method acting. And for others its more like a psychoses far as Im concerned. And very often they will call for, or demand, the removal of rules or systems. Gradually trying to whittle a game down to storygaming, then just storytelling as anything else gets in the way of "muh immershun!"
Railroads demand rails and sometimes its one or more players who try to force everyone else onto their rails.
And hate to burst your bubble. But Storygamers all too often fall into railroading of one form or another. I've seen it time and again. And seen worse from them in the form of rampant abuse of sessions.
Quote from: Ruprecht on January 12, 2022, 12:26:18 PM
I think it's a technique that (unlike railroading) can be good, but needs to be used carefully - and preferably in small doses. If you prep a tower with an ogre and place it in front of the PCs, in principle that's fine. But you need to be careful not to slip into railroading, where the PCs MUST go in that damn tower!
Fearful Symmetry
Some do, some don't. Depends of skill. And assumptions players are smart is... well also wastly overestimating.
I mean games I consider to belong to SG movement/tradition are IMHO vastly opposed to "muh immersion" movement. Immersionists were generally anti-mechanic. Storygames mechanicised narrative elements, for Immersion crowd that's anathema as it take them out of character. Because purpose of SG mechanics is not immersion but keeping ongoing narrative withing genre batch.
Therefore it will cause things happen that are suitable for given genre.
Improvised storytelling is opposite of storygaming, and storygaming movement is like probably godfather of whole "system matters" mentality. They were first to ditch "golden rule" and claiming if you homerule you're not playing this game anymore.
I mean sure you can ditch it for ego-trip and intimidating other players in GM, but it's generally against foundations of whole game design/playstyle philosophy that is called storygames nowadays.
So it's like using simmilar abusive players as argument against classical style.
"Never compromise. Not even in the face of Armageddon."
"And I will strike down upon thee
With great vengeance and furious anger"
"Molti Nemici, Molto Onore"
Shrieking Banshee
Narcissist Undead
Well Id say the quantum ogre/ illusionism is railroading. It may be organic, but it still is. You can defend it for myriad legitimate reasons, but to say its not railroading is denying the truth of the matter.
Because I think all good GMs take the events into their own hands sometimes.
Like there is also 'un-quantum' boredom. Where there are 3 rooms and an ogre is in one of them, but the other two rooms may have just nothing noteworthy in them. So your session has just large periods of nothing happening and afterwards everybody is left unsatisfied.
But you can let them open the room and just skim saying it has nothing of note and you find nothing of note there.
« Last Edit: January 12, 2022, 01:15:05 PM by Shrieking Banshee »
Quote from: Wrath of God on January 12, 2022, 12:51:18 PM
Yeah, well, who's to know for certain? Only the player. A GM that thinks he knows everything his players are thinking is fooling himself.
I dunno man. I've sat there as GM watching my players sweat over a decision and carefully plan for what they think might happen. 5, 10, 15 minutes of discussion and some careful prep to go down path A or B. I can't sit there with a clear conscious the whole time knowing all this discussion and effort makes no difference because paths A and B are the same. It would feel dirty.
« Last Edit: January 12, 2022, 02:06:17 PM by rytrasmi »
It's only really dirty if you make a big deal about one path and then move that encounter to the option that was assumed to be easier. If they are just two roads, one is faster but you'll be seen by enemy spies while the other is slower but you'll be unseen, it doesn't matter that the ogre appears along both. Assuming he's not the boss monster or something. Most of the time travelling to get to the adventure is a hassle designed to make it appear the location isn't next to town where everyone would have picked it clean long ago. I understand the need but I'm not gonna spend a lot of time on it. Instead it's a better planned random encounter.
if the travel is a serious part of the adventure that *could* be a lot different.
« Last Edit: January 12, 2022, 03:32:47 PM by Ruprecht »
I think there is a "fear" that new GM's go through - the fear of being caught off guard, of not having the answers or response to a player's actions.
You know the truth of it is that it's all a learning process. Overcoming that fear of the GMing chair is learning to overcome that fear of "loss of control" or failure, or whatever, and it's also about cultivating the desire to do a "better" game. And I find learning good basic principles about GMing and making a better game removes that fear, and it also, uncoincidentally, removes "railroading" and "Quantum-Ogres" off the table.
Seriously, making great campaigns requires work. Whether that means work in learning how to GM well - which includes Improv, or doing whatever is "good prep" for you, it takes effort. It *seems* effortless when you have a lot of experience, which a lot of my players assume about me and other GM's of my vintage. But that's because they don't understand the work and effort put in to develop the skills we possess. And it's never perfect. It's NEVER EVER perfect.
Improv is just a paintbrush - how well you use it and to what end is up to you. Lets be real - someone that "railroads" their games is going to do it *regardless* of whether they Improv or not. I actually think learning to Improv, and do it well, may lead to freeing one from the Railroad if they put some of that imagination into it.
Of course I also think nothing gets Rookie GM's to be Journeyman GM's than having Veteran GM's around.
Opaopajr
Señor Wences
tendbones, I like how you are placing these on a spectrum of discipline growth. Instead of an antagonistic "one true way" opposition, this organization is an invitation to new GMs to improve their game. Sort of like how Bob Ross gives such an inviting, relaxed aire that removes self-doubt and dogmatic defensiveness with his "Happy little trees," and "No mistakes, just happy little accidents."
We all had campaign struggles and this is sharing what we've learned to avoid (or at least forgive oneself) in the future. The blog writer is sharing a trick to keep harmony at their table. But we are challenging that advice from the perspective of "can you grow further as a performer without the shortcut of easy appeasement?" All disciplines have higher heights to explore, so sharing and learning techniques -- and understanding their limitations -- helps us make new vistas of shared imagination.
Just make your fuckin' guy and roll the dice, you pricks. Focus on what's interesting, not what gives you the biggest randomly generated virtual penis. -- J Arcane
You know, people keep comparing non-TSR D&D to deck-building in Magic: the Gathering. But maybe it's more like Katamari Damacy. You keep sticking shit on your characters until they are big enough to be a star.
-- talysman
Gog to Magog
Yes, growing pains are a part of getting better at something and sometimes there is way too much aversion to experiencing those pains
He said only: "Men shall die for this". He meant the words.

redpajama_set_name: RedPajamaCommonCrawl


Washington State is located at the far West of Northern America and border with Canada. It also neighbor with Idaho State at the East and Oregon State at the South. The best time to visit is during Summer which is from July till September. At this period, visitors can do all sorts of outdoor activities such as mountain hiking, cycling, boating and fishing. The summer season is short, therefore; there will be crowded for just about most of the attractions. Other than this season, the weather are mostly cold and damp. During the winter season, hiking trail are usually closed. Snowshoeing and snow boarding is the popular activities offer on winter.
Located at the North-West of Washington State, the Olympic National Park offers great opportunity to explore the wonderful state. The park covers about one million acres. It is a wilderness preserve for different ecosystems such as alpine mountain, glacier-capped mountains and more than 70 miles of ocean coastline. The park is selected as a worldwide UNESCO Heritage site with many highlights including SolDuc Hot Springs and Hoh Rain Forest.
The Hoh Rain Forest is the top highlighted spot where it offers a challenging landscape to hike on Mount Olympus. Along the journey, there are many great scenery where the visitors can also watch the elks wander freely in the park. With the uniqueness of natural landscape, hiking is the best activity for adventurous visitors to explore the park. There are hiking trails designated for different fitness levels. Alternatively, visitors can go biking, canoeing, and kayaking to see the lakes in different angles. Tour on Lake Quinault with some cruises, visitors can enjoy seeing the wildlife such as black bears and birds.
Another important attraction that are not to be missed, visitors could enjoy a relaxation session at the SolDuc Hot Spring where they offer one freshwater pool and three hot springs with different minerals.
There are four famous National Park of Washington State, which are located from North to South. Mount Baker-Snoqualmie, North Cascades, and Mount Rainier. Starting from Mount Baker-Snoqualmie and North Cascades, both runs on the gradients of the Cascade Mountains from the Canadian boundary. There are broad range of outdoor activities such as water ski, hiking, mountain climbing and forest cabin rental. Glacier is the small town nearest to the peak that provides limited amenities such as lodging and restaurants. The total length of 60 miles of scenery stretch gives visitors opportunities to stop at different places to enjoy the beautiful scenery. Another popular stops are Heather Meadows, Artist Point and Nooksack Falls, where the best time to visit is during August and September. North Cascades provides a 400 miles hiking trails which is suitable for visitors with elderly or children with a great chance to enjoy wildlife watching. For instance Wildlife such as gray wolves and grizzly bears, while camping and picnicking. Diablo Lake, is a reservoir dam offers boat tours where visitors get to enjoy the stunning view of the lake with turquoise hue which is surrounded by glaciers.
Continue heading to the South, Mount Rainier is the tallest mountain in Washington, also another volcanoes chain of Cascade Mountains. Mount Tacoma is also known by the name Mountain Reinier. It is a visible landmark from Olympia and Seattle. This park is open all year round, permitting visitors to do summer hiking and winter snowshoeing.
Paradise Vista is one of the more popular easy hiking trail especially for kids and elderly. Also, there are more than 40 different trails available to adventurous lovers. Cycling is another popular activity, however, it is not allowed on the hiking trails. There are several campgrounds available for camping where visitors can enjoy and get some rest under the stars.
Spent a little time at Downtown Seattle to feel the local fresh food, cultural and historical background of Seattle. Pike Market is famous among tourists and even the local residents. The market offers a large variety of kiosks and eateries around. Ranging from fresh seafood, farm produce and beautiful flowers. Enjoy the cultural craft and art items and listening to very talented street musicians performance is truly one of the best activities to do. There are also numerous museums that fit almost all different visitor interests such as Wooden Boats Center, EMP Museum, Museum of Flight and Living Computer Museum. To get the full experience of the entire Seattle, visitors should visit the Space Needle, which was launched on 1962 World's fair.
Another unique Washington attraction would be Leavenworth, or also named as Bavarian Village. The Bavarian heritage is remained in this community where the local residents are still wearing the cultural costume, lederhosen and playing musical instruments named alphorn. The entire community is adapted to Germany architectural culture, where German festival such as Oktoberfest is celebrated annually in the month of October. This is definitely a great time to enjoy German delicacies and beers during that month. If you are a history lover, don't forget to explore the Market Square (Der Markt Platz) and learn about the town's history.


text:
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Spotlight on giving - who are Australia's most charitable?
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Email CBA Media Team
Phone CBA Media - 0291186919
Commonwealth Bank analysis reveals the types of Australians most likely to donate to charities and the causes about which they are passionate.
The research finds that those aged over 50 years are responsible for half of all donations while those aged over 65 give away the most in a year at $425 on average, compared to $147 for those aged under 30.
Females as individuals are more likely to give to charity than men but men provide slightly greater amounts when they do donate. The majority of donations come from couples and families.
And the types of charities which attract the most financial support are humanitarian services at 44 per cent of all donations, followed by health and disability services (21 per cent), children's services (11 per cent) and animals and environment (9 per cent).
Commonwealth Bank Head of Not for Profit Sector Banking, Julienne Price, said the analysis provided rich insights into the charitable habits of Australians.
"The analysis is based on electronic payments made over a two-year period from 2013/2014 to 2014/2015 involving 18.5 million transactions by more than two million Commonwealth Bank customers to 185 charities," she said.
"We found that customers who donate across several charity types generate more value for those organisations than those who donate to only one brand. A total of 11 per cent donate to more than five brands, generating 33 per cent of the total value."
"There is virtually no difference in the population share and donation values from State to State but the analysis found that Queensland recorded the greatest donation value increase from one year to the next. And rural and regional centres recorded greater charitable growth than metropolitan centres over the study period."
In fact, the top three suburbs by number of donors were all in Victoria at Reservoir, Frankston and Berwick, while the top three suburbs by value were Mosman in NSW followed by Victoria's Camberwell and Kew.
"Many of our NFP clients are looking for insights and advice to help them with the various challenges they face which of course includes fund-raising and this analysis can really help them," Julienne said. "This is an example of using our very extensive data base to illustrate what's happening in the market place to help our customers plan and work more effectively. Apart from the important demographic details, one insight we know from this data is that aggregators are responsible for eight per cent of all donations but just three per cent of the value, so potentially that represents an opportunity or challenge to increase the value derived from that source for charities."
"We also found the average donation size is around $50 and that the winter months are the most popular time for donations. These sorts of insights can help charities better plan and target both existing and prospective donors in their fund raising efforts."
Key study highlights:
Demographic breakdown of donation sizes
Demographic group
Average donation size
Annual donation
Couple/family
Income type
Middle 50%
Bottom 25%
State breakdown
Customer numbers
Donation value
NT/SA


text:
KLBB may refer to Lubbock Preston Smith International Airport (ICAO code KLBB).

KLBB may also refer to a number of different radio stations in the United States

KLBB (AM), a defunct radio station (1220 AM) formerly licensed to serve Stillwater, Minnesota
KLBB-FM, a radio station (93.7 FM) licensed to serve Lubbock, Texas
KLBB-LD, a low-power television station (channel 19, virtual 48) licensed to serve Lubbock, Texas
KMNV, formerly KLBB, a radio station (1400 AM) licensed to serve the Minneapolis-St. Paul area of Minnesota
KXTQ-FM, formerly KLBB-FM, a radio station (107.7 FM) licensed to serve Idalou, Texas

redpajama_set_name: RedPajamaWikipedia


Nature Heals, a new meditation CD by South Korean-born author Ilchi Lee, was released today by Sedona-based publisher BEST Life Media. The meditations for self-healing include natural sounds, soothing music, and guided visualizations that will help you relax, reduce stress, and connect with the healing energies of the earth.
For centuries, ancient mystics and indigenous shamans knew what modern science is only now beginning to recognize—nature heals. By tapping into the natural elements, we can step into the flow of nature and balance our body, mind, and spirit. Many of us can attest to the soothing effects we feel when walking a sun-baked hiking trail, meandering through a shaded forest, or relaxing by a cool, rushing stream. This is earth wisdom at work.
This new 78-minute audio CD features six elemental properties of the planet—rain, water, sun, trees, wind, and earth—that are connected by the cycles of nature. The rain falls, streams fill, sun emerges, soil nourishes, plants grow, and the air is oxygenated. It is a never-ending cycle and circle of life, of energy. By tapping into this energy, we can unleash our own natural healing ability.
Nature Heals features six tracks that can be listened to one at a time or in a single continuous session. It can be used indoors or outside. Each meditation uses a specific natural element as the focal point while leading the listener through a guided meditation designed to enhance a particular human quality such as acceptance, purification, personal power, communication, freedom, and gratitude.
The meditations are read by Michael Munson, a Dahn Yoga and Brain Education Trainer who travels worldwide, leading seminars and workshops for individual self-mastery and empowerment. Munson has been a student of energy healing and Ilchi Lee's teachings for nearly ten years.
Nature Heals will enhance your capacity to experience and communicate with the tremendous living world that exists all around and within you. By immersing yourself in the elemental properties of the plane, you can encounter the earth's wisdom and witness principles of life that are both hidden and pervasive in the natural world.


text:
Q: Test Local Service Against Production Clients At our company we have a variety of microservices and web clients that make up our SaaS (software as a service) product.
When modifying the behavior of a specific service (usually written in C# WebApi). We would like to spot check the integration behavior against a client that makes calls to that service. As the developer working on a C# service locally, I would prefer not to have to clone and build that specific web client (with local settings to point to the local server) in order to see how it interacts with my local server changes. Ideally I could navigate to a deployed version of the client (develop, rc, prod) and redirect the requests that client is sending to the deployed version of my service to my local server instead.
I've attempted this with tools such as requestly. However this just results in a 307 response and the following error:

XMLHttpRequest cannot load http://localhost:59517/api/users. Response for preflight is invalid (redirect)

While we are verifying the correct behavior on the server via TDD unit tests. There are occasions where it would be nice to be able to use an already deployed client to test a local server to get a better feel for what might break in the integration tests during the automated build. Are there standard ways of doing this sort of microservice testing that does not involve local buildin/configuring of the web client?

redpajama_set_name: RedPajamaStackExchange


text:
Albin Pelak (nacido el 9 de abril de 1981) es un exfutbolista bosnio que se desempeñaba como centrocampista.

Albin Pelak jugó 2 veces para la selección de fútbol de Bosnia y Herzegovina entre 2002 y 2005.

Trayectoria

Clubes

Selección nacional

Estadística de equipo nacional

Referencias

Futbolistas de Bosnia y Herzegovina
Futbolistas de la selección de fútbol de Bosnia y Herzegovina
Futbolistas del FK Sarajevo
Futbolistas del Cerezo Osaka
Futbolistas del Građanski Nogometni Klub Dinamo Zagreb
Futbolistas del FK Željezničar Sarajevo
Futbolistas del FK Olimpik Sarajevo


Credit Vouchers to give to your friends!
NB Credit Vouchers will usually be actioned within 1 working day but may take longer at busy periods.
Gift vouchers will now be given in the form of credit on the persons account. Please put details of the recipient in the comments.
If no recipient is mentioned then the credit will be put on the purchasers account.


text:
Пелещук Василь (? — ?) — начальник дивізії Дієвої Армії УНР.

Біографія

У 1914 році був мобілізований з запасу у званні прапорщика, служив у 166-му піхотному Рівненському полку, у складі якого брав участь у Першій світовій війні. Був нагороджений Георгіївською зброєю (4 березня 1917, за бій 31 січня 1916 року). Останнє звання у російській армії — капітан.

У 1917 році — командир батальйону 1-го Українського запасного полку військ Центральної Ради. З листопада 1917 року — командир 3-го Сердюцького полку ім. П. Дорошенка військ Центральної Ради. У лютому 1918 року деякий час перебував на посаді командира 1-го Запорізького куреня Окремого Запорізького загону військ Центральної Ради. З серпня 1918 року — помічник командира зі стройової частини Окремого Чорноморського Коша Армії Української Держави. З кінця жовтня 1918 року — командир цього Окремого Чорноморського Коша. Під час Гетьманату П. Скоропадського був підвищений до звання військового старшини. З грудня 1918 року і до лютого 1919 року — начальник Чорноморської дивізії Дієвої Армії УНР.

Подальша доля невідома.

Джерела

Вояки Армії Української Держави
Офіцери Армії УНР


Most Canadian millennials haven't started saving for a home, despite wanting to own one, according to a new poll from CIBC.
The vast majority of respondents of the survey released Thursday (94 per cent) who rent or live with family said they plan to buy a home, but 67 per cent of them haven't started saving yet.
Almost two-thirds (65 per cent) of millennials polled currently rent or live at home with parents or family. Less than half of renters (45 per cent) and one-third of those who live with family (39 per cent) see the appeal of home ownership but don't think it's realistic.
"While most still dream of owning a home one day, higher house prices, the prospect of higher rates, and new qualifying rules are prompting some millennials to pause and question whether being a homeowner is realistic or even desirable for them," said Grant Rasmussen, senior vice president of mobile advice at CIBC, in a release.
Sixty per cent of respondents said they believe "renting is just as costly as homeownership," even though the poll found millennial homeowners still manage to save more each month than renters do ($566 versus $368).
But the majority of respondents (58 per cent) who own a home said they're concerned rising interest rates will make it more difficult to cover household expenses.
Nearly half (46 per cent) of those who intend on buying property said they plan to do so within five years, but the majority of respondents in that category (76 per cent) haven't started saving or have less than one-quarter of a down payment.
CIBC's survey was conducted online between March 19-26 among 1,471 randomly-selected Canadians aged 18 to 37.
What's your advice for millennials who dream of home ownership?


text:
Q: How to set a keepalive in PgAdmin4? It was possible in PgAdmin-III to set a keepalive through the ~/.pg_services.conf file. Looking at the docs for version 4, it doesn't seem to use libpq and there is no mention of a keepalive setting in the documentation.

A: TCP settings could be configured in : postgresql.conf

*

*On Ubuntu it would be found in: /etc/postgresql/13/main/ (note that "13" refers to postgresql version)

Set the tcp_keepalives_idle based on official document and your experience on how much does it take to disconnect. Example: 480
Based on my experience, using SSH-Tunneling is the best way to keep the connection alive.

*

*You might either set up a SSH-Tunneling using PuTTY (windows) or terminal (Ubuntu) like: ssh -L 63333:localhost:5432 user@VPS-IP/Domain
and then use localhost and port 63333 to connect from pgAdmin.

*Or you can use the pgAgmin built-in SSH-Tunneling.
Note: The SSH itself should be kept alive by creating a config file in .ssh/ and proper settings like:
Host (VPS-IP)
   Hostname (VPS-IP)
   Port 22
   User (your username)
   ServerAliveInterval 180
   ServerAliveCountMax 2


Having beaten expectations in July (and printed notably higher than payrolls), ADP employment growth was expected to slow in August and it did - more than expected. ADP printed +163k against expectations of +200k (down from July's revised +217k).
"The job market is hot. Employers are aggressively competing to hold onto their existing workers and to find new ones. Small businesses are struggling the most in this competition, as they increasingly can't fill open positions."


Are you looking to change how your body looks and feels forever?
Want to improve your self confidence, mental outlook and instill habits that will last you a lifetime?
Want to know exactly what steps to take in terms of training and eating and have EVERYTHING laid out in front of you so you can't possibly fail?
This offer is limited to just 4 clients in total because of the high level of personal service you receive.
Right now, we have 2 new spots open. Don't miss out.
PS. We totally understand that this offer isn't for everyone, you might not be in the right head space yet, but that's ok.
PPS. This is your chance to actually get that summer body you've been talking about, since you know, forever.
Go on, commit to changing your life.


My ECM Giotto ( premium? ) from year 2004 starts to sound like a machine gun.
I guess it´s time to replace the pump right?
1. Is it the ULKA EX5 pump I´m going to purchase for the replacement?
2. Please refer to pic in below link - How to I disassemble the connection marked in the picture?
2. Undoes. Lefty loosy, righty tighty.
May need to remove pump first.
Confirmed it was a ULKA EX5 pump.
no special tools required, just disamble the sides and the pump it's just with some rubber mounts.
2 electric cables, unplug and plug in the new pump.
Reminds me of a joke from the old country (a bit of background to it - we had a factory which half was manufacturing AK47s and the other half sewing machines): No matter how you assemble your sewing machine you still get an AK47.
Perhaps your coffee machine was manufactured in similar conditions... certainly gives a new meaning to "coffee shots" - just beware of ricochet ristretto.


text:
using System;

namespace Nohros.Configuration
{
  /// <summary>
  /// A <see cref="RepositoryNode"/> is a container for pathnames. It is used
  /// to resolve relative pathnames to absolute pathnames using the application
  /// base directory. This allows applications to associate constants to
  /// configurable pathnames.
  /// </summary>
  public interface IRepositoryNode : IConfigurationNode
  {
    /// <summary>
    /// Gets or sets the path pointed by the repository.
    /// </summary>
    string RelativeDirectory { get; }

    /// <summary>
    /// Get the full path pointed by the repository.
    /// </summary>
    string AbsoluteDirectory { get; }
  }
}

redpajama_set_name: RedPajamaGithub


text:
The world tilted, Sir Hossein Yassaie steps down
Creator of the GPU IP industry, Sir Hossein Yassaie passes the baton Sir Dr. Hossein Yassaie has stepped down as Chief Executive of Imagination Technologies, and Andrew Heath, one of the non-executive directors, has been appointed Interim Chief Executive. Imagination is also announcing details on restructuring initiatives. These include the sale of Pure, its consumer electronics business, and the expectation ...
Creator of the GPU IP industry, Sir Hossein Yassaie passes the baton
Sir Dr. Hossein Yassaie has stepped down as Chief Executive of Imagination Technologies, and Andrew Heath, one of the non-executive directors, has been appointed Interim Chief Executive.
Imagination is also announcing details on restructuring initiatives. These include the sale of Pure, its consumer electronics business, and the expectation at this stage that The group expects to reduce total operating costs of its on-going businesses by £15 million in the next financial year ending April 2017, with a modest impact in the current financial year. Of this, £2 million will be re-invested in PowerVR, further strengthening the Group's flagship multimedia product.
The group believes there are potentially more appropriate owners for Pure, given the economies of scale in the consumer electronics market, who will be able to leverage its leading technologies and brand. Imagination will treat the Pure division as a discontinued operation with immediate effect. Imagination will also initiate a full operational review, including all R&D expenditure. This review, which is expected to last several months, will ensure investment is focused on core activities that are set to deliver attractive returns.
What do we think?
Yassaie has left Imagination after 18 years as chief executive,. He has been our friend for longer than that, and it is correct to say the company (or "the group," as they like to call themselves) will not be the same. Hopefully it will be OK, but it certainly won't in my opinion be better.
SIR DR. Hossein Yassaie.
Granted, the Pure product didn't fit well with the company's main efforts or strengths; although it helped Imagination to become number one digital radio IP supplier, it became a cash and man-agement drain. Imagination would not be the first, nor the last, to have some structural problems (look at Intel or AMD, or Nvidia's abandonment of modems, or Qualcomm's sell-offs).
I think the investors got impatient with Hossein's timetable amidst a major industry downturn; he did have a plan to spin off Pure after the refocusing that started a year ago. And all the other actions the company has taken, including the £15 million cost-reduction restructuring, emanated from his plan. However, he choose to step down as the alternative of a full-blown public row with some investors and a board disagreement that would have damaged the very thing he cared the most about: the people and the company.
Hossein was born in Iran and moved to the U.K. in 1976, where he became a professor at University of Birmingham. He joined STMicroelectronics/Inmos, setting up and managing the DSP and digital video developments. I met him in 1992, when he joined Video Logic. That was the year Martin Ashton developed the tiling approach for a graphics processor, two years before Chappell Hills' famous Pixel Flow machine was lit up, and four years before Microsoft's Talisman. The concept came from flight simulator design Ashton developed.
The moment of truth gets closer –
Real or virtual—is it legal?
Recent AR developments and hints
What Apple, Qualcomm, and Google have revealed
Streaming needs a strong dash of social involvement
Social media is Gen Zers' top choice for entertainment.


Churchill Downs Incorporated (NASDAQ: CHDN) ("CDI" or "Company") today announced that T. Kevin Flanery has been named the 13th track president of Churchill Downs Racetrack ("Churchill"), home of America's greatest race, the Kentucky Derby.
Flanery will report to Bill Carstanjen, chief operating officer of CDI, and will remain a Company senior vice president.
Flanery joined CDI in December 2005 as vice president of national public affairs, and was named senior vice president of national public affairs and communications in March 2008. While leading the Company's legislative and communications initiatives, Flanery headed the successful 2008 campaign to permit Calder Race Course, the Company's racetrack in Miami, to operate slot machines.
Before joining CDI, Flanery held a number of key positions in government and private business, including secretary of the Kentucky Finance and Administration Cabinet and president of Hagan Properties, a real estate development company based in Louisville, Ky. A 43-year-old native of Louisville, Flanery has been active in a variety of community activities and currently serves on the board of trustees of Norton Healthcare and the board of directors of St. Francis De Sales High School. He holds a bachelor's of arts degree in psychology from Bellarmine University and a juris doctor degree from the University of Kentucky College of Law, where he was inducted into the Order of the Coif.
CDI will conduct a search to fill Flanery's prior roles as head of national public affairs and communications.
Churchill Downs, the world's most legendary racetrack, has conducted Thoroughbred racing and presented America's greatest race, the Kentucky Derby, continuously since 1875. Located in Louisville, the flagship racetrack of Churchill Downs Incorporated (NASDAQ Global Select Market: CHDN) also operates Trackside at Churchill Downs, which offers year-round simulcast wagering at the historic track. Churchill Downs will conduct the 136th running of the Kentucky Derby on May 1, 2010. The track's 2009 Fall Meet is scheduled for Nov. 1-28. Churchill Downs has hosted the Breeders' Cup World Championships a record six times, and will host the international racing championship again on Nov. 5-6, 2010. Information about Churchill Downs can be found on the Internet at www.churchilldowns.com.


Art Rx now serves two communities: those with chronic pain and those who serve as caregivers for patients or loved ones facing the end of life. These individuals along with their guests are invited to enjoy facilitated group conversations about select pieces of art with a trained docent. The goal of Art Rx is to encourage positive experiences that reduce the burden of chronic pain and caregiver stress. No prior art knowledge is necessary. Advance registration is required. Call (916) 808-1962 or email education@crockerart.org with questions. First-time participants: Please arrive 15-20 minutes early for check-in. Art Rx is presented in collaboration with the Center for Pain Medicine's Integrative Pain Management Program, part of the UC Davis Health System.
The Crocker Art Museum is committed to reducing barriers and increasing accessibility to the Museum and art experiences. The Art Access initiative provides programs and services to help ensure art is available to everyone. Funding for programs is provided by the National Endowment for the Arts.
Purchase tickets by clicking the REGISTER button above, visiting the Museum Admission Desk, or calling (916) 808-1182.


It seems I have been away from blogging for almost two weeks now! Tsk tsk. I have been making lists and checking them twice trying to get all in order for the upcoming holiday which is now just 17 days away! Eee! You can imagine my to-do list with so many little ones to make Christmas magical for.
Mr. and Mrs. Claus seem to always get the job done though, so I should not worry as much as I do.
Little Evangeline took her first romp in a leaf pile with her sisters!
My two Hope monkeys for Craft Hope's latest project safely arrived at their destination.
I made the black one to replace the blue one that captivated Grace's heart.
I made a new ruffled tree skirt using this tutorial from Prudent Baby!
Forgive that the photo does not show the finished binding at the top.
It has now been completed and looks awesome under our decorated tree!
to help my brother get a tree for his apartment!
Now I am off to have a cup of good cheer ( some green tea with honey )!
Hope to see you all sooner than later!
I have a little niece that loves sock monkeys...yours are so cute I might try to make her one before Christmas(fingers crossed). Thanks for the inspiration!!


I'm attracted to the market opportunity within large, established markets. These markets already have huge spend, they have established dominant players with an inertia resistant to major change, most of the innovative talent and money is off in new market spaces, and innovation within these spaces tends to be evolutionary in nature and follow predictable paths.
The revolutionary innovation that occurs in many of these markets is often serendipitous. That means someone isn't looking to solve the end problem, but something they did is applicable to it. See, for example, Viagra or Post-Its.
More often than not, however, the real revolutionary innovation is in line with the evolutionary. Therefore, pick a really big market and do something revolutionary within the natural evolution of the space.
So the key question becomes: what is it that successful inventors do to be revolutionarily successful within an evolution?
—Design for how people work.
—Consolidate and reduce core concepts to a ridiculous minimum; a core concept is anything the customer has to learn or understand in order to successfully use your product.
Mobile phones, e-mail on Blackberries and Treos, MP3 music players—all of these existed separately and with ever-expanding feature sets. The race toward consolidation had been going on for some time; but it carried with it the complex, rich feature sets of each independent device.
experience one that requires the customer to learn nothing new. There is no way to mess up, no configurations to understand, no compatibility to sweat. And, let's get rid of everything but one button. Nothing forces simple concept consolidation like the absence of knobs to turn. That's why the bottom line for innovation success in a crowded converging market is the reduction and consolidation of core concepts.
There is a close parallel to the iPhone story in this saga. The approaches taken by the companies vying for the prize have fallen into different categories, each of which has its special purpose, and each of which continues to pile on the features to stand out above the noise. There are wikis for data collection and discussions, there are project management tools for structured deliverables tracking, there are online office applications to solve the sharing dilemma among many people, there are simple task management tools for personal to-do's, and so on.
All of them are overkill in their category, and all of them are applicable to only a minority few with special needs for their deep feature set. Many understand the need to consolidate and bring the disparate functions together. However none is capable of doing the transformational work necessary to reduce and consolidate all the core concepts in their products to something universally simple and consistent across each. It would mean starting over entirely in almost all cases.
—Online is a big enabler.
—Account-based (individually-centered) services are better understood.
—Salesforce.com has made team SaaS tools mainstream.
—Workforces are increasingly more distributed.
—Outsourcing of component deliverables is increasing.
—Pressure to coordinate across multiple people and multiple sources of information is only getting greater.
A consolidation of the core concepts in the five major approaches to work collaboration is inevitable. Designing that consolidation for how people actually work is the other half of the revolution in this evolution, but that's for another post.


A comfortable office chair can comes in all sizes, colours, and shapes. Ergonomics implies a chair has a healthy design. Chairs may come with adjustable parts.
All of the whilst, the body comes in several different sizes and styles. Some could be tall, other short. Some need a huge chair, while others like a smaller width. As much as we may need it to, the body isn't as flexible as an ergonomic chair.
Though it's not feasible to find the ideal office chair for everybody, it's quite possible to get adjusted to every kind of seating. Even if you are not capable of finding the perfect office chair, you can always use methodologies to make the maximum of the situation.
They can help in making correct use of the body and even augment your coordination too. The idea here, is to hold your neck in such a fashion the length of your backbone and neck are not shortened or curved in any way. There's no ergonomically designed comfortable office chair that will force your body into the right position it should be in.
It's up to your body and mind to sit in an a healthy demeanour. When it comes down to it, finding the ideal office chair is all a matter of what's best for you. Office chairs come in all different styles and sizes,eg human body's.
If you try out many chairs, you will find the ideal chair for your special body size. Once you have found your ultimate office chair, you can relax like never before.
In the office, finding the ideal chair for yourself is something that you must do. Finding your ideal office chair isn't that hard – all you must do is look around.
The standard of your reception chairs will reflect that old proverb "you only get one chance make a good impression". In your office, you'll be wanting to ensure that guests and clients are as comfy as they can be whilst they wait for an appointment.
Reception chairs are well-liked outside the office as well, as faculties and even churches use them. Reception chairs are actually an asset to have around, as they're going to provide a friendly atmosphere and leave a long lasting impression on your visitors.
By trying these chairs in your office, guests will feel comfortable and right at home in your dwelling.
You might also place your chairs around a desk or occasional table in the waiting area with a heap of mags for your visitors to read. When purchasing reception chairs, one of the most vital calls will be finding chairs that may make folks of all height and weight costly.
What you will need to do, is provide chairs that offer adjustable options for the height, depth of the backrest, and even the arm rests.
The average reception chair is really sturdy and can last fifteen years – with each guest on the way being snug and each time they sit in the chair. Virtually all reception chairs have a robust and stable frame that may offer your back the maximum quantity of ergonomic benefits.
These chairs will supply the "home away home" feeling, and give your office the appearance your visitors will like to come back to.
Chairs with mesh backs are quickly changing into a must have in the business world. They are catching on quickly in numerous meeting rooms, home offices, and offices around the US.
The explanation for their achievement is the extra comfort the mesh back provides. When you sit at your desk all day, it can become quite boring.
Sitting in a cubicle all day for hours and hours can leave you feeling a bit stuffy with a cramped back and legs. A regular office chair can make this worse, as it'll cut off the airflow to your back, causing your body temperature to rise.
Mesh back office chairs stop this by permitting your back room to respire.
The mesh material allows for the exchange of air thru the chair, making your day in the office less stuffy. You can spend hours and hours in a mesh chair and your back will not even know it.
Another excuse for the popularity of mesh back office chairs is their design. By offering a contemporary design, the mesh back chair lets your customers know that you are to cruising speed with your office. You can even get your own design and material, customizing your chairs the way you would like.
Sellers and shops give you the opportunity to customize your mesh back chairs, permitting you to mix them in with your meeting room.
You can turn your conference room or office into a work of art with mesh back office chairs. Most of folks are worried that mesh back chairs don't offer the support an ordinary office chair will be offering.
All mesh chairs have lumbar back support built right in and are designed for support and comfort.