[MD] are theism and mysticism mutually exclusive notions?

Case Case at iSpots.com
Sun Oct 1 17:15:34 PDT 2006


[SA]
     So eternity and void do not exist according to
what you say.  I'm not quite sure if this is true or
not, but as I prepare to go outside to enjoy the
chilly blue sky day I'm also not sure if it matters if
eternity and void need to be known to me at this
moment.  
     No, I haven't explored the Mandelbrot set.  I did
try out that other game you linked.  It was a bunch of
dots moving around exploding and relocating, until
they all disappeared.  That wasn't the Mandelbrot set,
was it?

[Case]
Charles Seife in the Biography of Zero claims that the Greek banned zero
from mathematic on philosophical grounds. The ban stood until the middle
1600's. Even Descartes who invented graph paper did not include negative
numbers in his coordinate system. Zero and Infinity are scary ideas even
today. If you are a computer programmer a divide by zero error can mess up
your morning.

The Game of Life shows how complicated organic looking behavior can result
from very simple rules. The dots you saw exploding did so because rules
established three simple relationships or conditions that would govern their
behavior on each iteration of the screen. Steven Wolframm has extended this
process on a more complicated level by experimenting with different sets of
rules to see even more organic behavior in three dimensions over time.

The Mandelbrot shows: self similarity across scale. The whole set lies on a
graph with the X axis at 0 and between -2 and 1 on the Y axis. As you
examine the object on a computer screen you can zoom in on the line around
the edge. No matter how much you zoom in you will see the same level of
detail. 

One real world example frequently given is to consider the coastline of
England. How long is it? If you use a ruler a mile long as a standard unit
you would get a particular number. If you measured again with a half mile
long ruler you would get a bigger number because you could measure into
nooks and crannies the bigger ruler could not measure. As your ruler gets
smaller, that is more and more precise; your coastline gets longer and
longer. In fact the coastline of England is infinitely long. 

Another property of the coastline of England is self similarity across scale
If you use Google Earth and zoom in on the coastline of England I bet you
will see this clearly. Actually any coastline will do. Many things in nature
both in the inorganic and biological realms show self similarity across
scale. If you cut a branch off of a tree and hold it up is looks like a
small tree. Cut off another branch and the same deal. This works down into
the structure of the leaves. 

Animals have self similar interacting structures like this in their lungs,
nervous systems and circulatory systems. Clouds are self similar. So are
streets and highways, rivers and telephone networks, spider webs and sand
dunes. 




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