Subject: Re: [BoundaryPoint] Jungholz<br/>
Date: Mar 14, 2001 @ 23:22<br/>
Author: Brendan Whyte (&quot;Brendan Whyte&quot; &lt;brwhyte@...&gt;)<br/>
<a href="1756.htm">Prev</a>&nbsp;&nbsp;&nbsp;&nbsp;Post in Topic&nbsp;&nbsp;&nbsp;&nbsp;<a href="1767.htm">Next</a>&emsp;[<a href="topic1754.htm">All</a> Posts]<br/>
<a href="1765.htm">Prev</a>&nbsp;&nbsp;&nbsp;&nbsp;Post in Time&nbsp;&nbsp;&nbsp;&nbsp;<a href="1767.htm">Next</a><br/>
<br/><br/>
<div id="ygrps-yiv-1714893815"><blockquote><span title="ireply">&gt;Jungholz is connected to the rest of Austria by a single point. That is <br/>
&gt;alrady established.<br/>
&gt;<br/>
&gt;On the other hand Germany is also connected with herself at that point. <br/>
&gt;Right?<br/>
<br/>
 </span></blockquote>Right<br/>
<br/>
<br/>
So if Germany is connected is then Jungholz disconnected ie an enclave?<br/>
<blockquote><span title="ireply"> &gt;<br/>
 </span></blockquote>No. BOTH are connected there, and yet both disconnected. That is why single <br/>
points are called singularities, because they are truly singular!<br/>
<br/>
<br/>
<blockquote><span title="ireply"> &gt;Who owns the point?<br/>
 </span></blockquote>BOTH<br/>
<br/>
<br/>
No man&#39;s land or a condominium? If point is a no man&#39;s land then Jungholz is <br/>
a fragtment (as it is touched by no man&#39;s land and Germany).<br/>
<blockquote><span title="ireply"> &gt;<br/>
&gt;If condominium then Jungholz is also a fragtment as it is touched by <br/>
&gt;Germany/Austria and Austria!<br/>
<br/>
 </span></blockquote>It is 100% surrounded by Germany, and at the same time is not disconnected <br/>
fomr Austria.<br/>
It is not a fragment, or an enclave as it is not disconnected.<br/>
<br/>
Let&#39;s take another exmaple. On the Dutch-German border, the border must be a <br/>
string of points. Who owns them? If Germany owns them, then the border is <br/>
the NEXt set of points to the west. And vice versa if Holland owns them.<br/>
If neither own them then Germany does not border Holland, it borders a <br/>
neutral zone and you have to ask what about the points along THAT border...<br/>
A border is an infinitely thin line, but it must be a point. It must exist. <br/>
It is not the gap between a German point and a Dutch point. Because if there <br/>
is a gap, there must be ap oint to fill it.<br/>
For every point m and n, where n&gt;m, there exists a point p such that m&lt;p&lt;n. <br/>
Ad infinitum.<br/>
We get into mathematics here. It&#39;s beutiful. Even if you were only as wide <br/>
as a single point, you could not get to Jungholz fomr austrai without <br/>
violating German sovereignty (which is probably not a wise thing to do ;)  <br/>
).<br/>
And vice versa for crossing the point from Germany to Germany.<br/>
Even more so for objects in the real world that DO have width.<br/>
<br/>
So while Jungholz cannot access austrai without violating Germn soil, yet at <br/>
the same time Germans cannot encircle Jungholz without leaving Germany and <br/>
violating Austria.<br/>
<br/>
It&#39;s a paradox!<br/>
<br/>
It&#39;s a frozen snapshot of that instant in time when two waterdrops join to <br/>
one, or one splits into two. It is quite remarkable.<br/>
<br/>
B<br/>
_________________________________________________________________________<br/>
Get Your Private, Free E-mail from MSN Hotmail at <a rel="nofollow" target="_blank" href="http://www.hotmail.com">http://www.hotmail.com</a></div>