## [spr] Re: dimensions

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nThomas Cuny &lt;tec@highstream.net&gt; wrote\n\n&gt; Are dimensions fundamental?\n&gt; Dimensions don\'t seem to exist when the universe is in the big bang\n&gt; state,the big crunch state, or in black holes.\n&gt; Perhaps dimensions don\'t really exist.\n\nDimension, like many other, is not an absolute concept, so whether it =\ndoes exist or not, depends on the perspective taken. Basically, given a =\nset, you introduce a dimension if you can factorize the labels assigned =\nto its elements. The deeper such factorization, the higher dimension can =\nbe ascribed to the set. If the procedure is based on some particular =\ndistance relation between the elements it is not guaranteed to succeed. =\nThis is well familiar to anybody having to do with a fractal, where it =\nis impossible to factorize the labels, and thence the \'dimension\' gauged =\nby embedding the set in a bigger one (for which a factorization is =\nknown), is \'found\', or rather defined non-integer.\n\nregards\npg\n\n\n----------------------------------------------------------------------\nStartuj z INTERIA.PL!!! &gt;&gt;&gt; http://link.interia.pl/f1837\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Thomas Cuny <tec@highstream.net> wrote

> Are dimensions fundamental?
> Dimensions don't seem to exist when the universe is in the big bang
> state,the big crunch state, or in black holes.
> Perhaps dimensions don't really exist.

Dimension, like many other, is not an absolute concept, so whether $it =$
does exist or not, depends on the perspective taken. Basically, given a =
set, you introduce a dimension if you can factorize the labels assigned =
to its elements. The deeper such factorization, the higher dimension can =
be ascribed to the set. If the procedure is based on some particular =
distance relation between the elements it is not guaranteed to succeed. =
This is well familiar to anybody having to do with a fractal, where $it =$
is impossible to factorize the labels, and thence the 'dimension' gauged =
by embedding the set in a bigger one (for which a factorization is =
known), is 'found', or rather defined non-integer.

regards
pg

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