Update
The problem appears only with the edges. A possibility is to scale only the edges. Firstly we get the coordinates, then we divide them by 10 and finally we scale the coordinates by 10. I changed some styles from the original code.
\documentclass[onlymath]{beamer}
\usefonttheme{serif}
\usepackage[orientation=portrait,size=a0,scale=1.0]{beamerposter}
\usepackage{eulervm}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows,positioning,matrix}
\begin{document}
\begin{frame}[t,fragile]{}
\begin{block}{Big TikZ Test}
\begin{center}
\begin{tikzpicture}[blk/.style= {rectangle,draw,text width=2in,text centered},
edge/.style = {draw =black!50 ,line width=3pt,->}]
\matrix[row sep=1cm,column sep=1cm] {%
\node[blk] (a) {A};
&
\node[blk] (b) {B};
&
\node[blk] (c) {C};
&
\node[blk] (d) {D};
&
\node[blk] (e) {E};
&
\node[blk] (f) {F};
&
\node[blk] (g) {G};
&
\node[blk] (h) {H};
&
\node[blk] (i) {I};
&
\node[blk] (j) {J};
\\
};
\path[edge] (j) edge [bend left=30] (i)
edge [bend left=30] (h)
edge [bend left=30] (g)
edge [bend left=30] (f)
edge [bend left=30] (e);
\path (a.south);
\pgfgetlastxy{\ax}{\ay}
\path (b.south);
\pgfgetlastxy{\bx}{\by}
\path (c.south);
\pgfgetlastxy{\cx}{\cy}
\path (d.south);
\pgfgetlastxy{\dx}{\dy}
\begin{scope} [scale=10]
\path[edge] (j) edge [bend left=30] (0.1*\dx,0.1*\dy)
edge [bend left=30] (0.1*\cx,0.1*\cy)
edge [bend left=30] (0.1*\bx,0.1*\by)
edge [bend left=30] (0.1*\ax,0.1*\ay);
\end{scope}
\end{tikzpicture}
\end{center}
\end{block}
\end{frame}
\end{document}
There is another problem, when we crate the edges, in the log I see
Missing character: There is no ï in font nullfont!
Missing character: There is no ¿ in font nullfont!
Missing character: There is no ¼ in font nullfont!
Missing character: There is no ï in font nullfont!
Missing character: There is no ¿ in font nullfont!
Missing character: There is no ¼ in font nullfont!
Missing character: There is no ï in font nullfont!
Missing character: There is no ¿ in font nullfont!
Missing character: There is no ¼ in font nullfont!
One warning for one edge
update 2
Perhaps it's a bug in 'to'. I try with controls and the code compiles without errors. I used some control points but without calculations.
\begin{tikzpicture}[blk/.style= {rectangle,draw,text width=2in,text centered},
edge/.style = {draw =black!50 ,line width=3pt,->}]
\matrix[row sep=1cm,column sep=1cm] {%
\node[blk] (a) {A};
&
\node[blk] (b) {B};
&
\node[blk] (c) {C};
&
\node[blk] (d) {D};
&
\node[blk] (e) {E};
&
\node[blk] (f) {F};
&
\node[blk] (g) {G};
&
\node[blk] (h) {H};
&
\node[blk] (i) {I};
&
\node[blk] (j) {J};
\\
};
\path[edge] (j) edge [bend left=30] (i)
edge [bend left=30] (h)
edge [bend left=30] (g)
edge [bend left=30] (f)
edge [bend left=30] (e);
\path[edge] (j) .. controls ([{shift=(210:20)}]j) and ([{shift=(-30:20)}]d) .. (d);
\path[edge] (j) .. controls ([{shift=(210:25)}]j) and ([{shift=(-30:25)}]c) .. (c);
\path[edge] (j) .. controls ([{shift=(210:30)}]j) and ([{shift=(-30:30)}]b) .. (b);
\path[edge] (j) .. controls ([{shift=(210:35)}]j) and ([{shift=(-30:35)}]a) .. (a);
\end{tikzpicture}
I don't really get the question so I hope this is what you wanted. If you include a full document (such that we copy paste and see the problem on our systems) things are much more easier.
Here, you can change the default setting within a scope but your block
style had a node distance
which was resetting every time it is issued. I've made it 2mm such that we can see the difference easier.
\documentclass[tikz]{standalone}
\usetikzlibrary{arrows,shapes.geometric,positioning}
\begin{document}
\begin{tikzpicture}[decision/.style={diamond, draw, text width=4.5em, text badly centered, node distance=3.5cm, inner sep=0pt},
block/.style ={rectangle, draw, text width=6em, text centered, rounded corners, minimum height=4em, minimum height=2em},
cloud/.style ={draw, ellipse, minimum height=2em},
line/.style ={draw,-latex'},
node distance = 1cm,
auto]
\node [block] (1st) {1st};
\node [block, right= of 1st] (2nd1) {2nd1};
\begin{scope}[node distance=2mm and 10mm]%Here we change it for everything inside this scope
\node [block, above= of 2nd1] (2nd2) {2nd2};
\node [block, below= of 2nd1] (2nd3) {2nd3};
\node [block, right= of 2nd1] (3rd1) {3rd1};
\node [block, above= of 3rd1] (3rd2) {3rd2};
\node [block, above= of 3rd2] (3rd3) {3rd3};
\end{scope}
\node [block, below= of 3rd1] (3rd4) {3rd4};
\node [block, below= of 3rd4] (3rd5) {3rd5};
\path [line] (1st) -- (2nd1);
\path [line] (2nd1) -- (2nd2);
\path [line] (2nd1) -- (2nd3);
\path [line] (2nd2) -- (3rd3);
\path [line] (2nd1) -- (3rd1);
\path [line] (1st) -- (2nd1);
\end{tikzpicture}
\end{document}
Best Answer
As percusse has noted (answer now deleted) the problem is with completely empty nodes. Filling them with a space element such as
\,
would add an empty terminal node, which would remove the error, but also yields extra vertical branches in the tree, which is not really what you probably want. A better solution is to add empty node labels instead of using spaces as terminal nodes:Personally, as a linguist, I would just leave the empty nodes out of the tree altogether:
(code omitted)