It does interest me :) , in fact... I have written a few programs based on the paradigm often called "evolutionary algorithm"... is it essentially a probabilistic search technique for optimal values. Evolutionary algorithms don't produce anything new, just find different parameters..
x[t+1] = s( v( x[t]) )
where x[t] is the population under a representation at time t, v(.) is the variation operator(s), and s(.) is the selection operator
These algorithms are nifty but only if the selection operator and variation operator, and termination condition are very carefully designed. "But it takes intelligence to create the evolutionary algorithms!" You are absolutely correct....In fact I know from experience that it is actually easy to write one which will never converge on the optimal set of parameters especially if the search space doesn't have natural "hills and valleys" (doesn't fit hill climbing algorithms). These algorithms require a highly ordered/designed computational device capable of running the same set of designed instructions over and over and over again with out error.
An interesting probability model is calculating the probability of trying to assemble life from non-life purely by chance and natural process:
http://www.freerepublic.com/focus/f-news/1689062/posts?page=185#185
a) Calculations of Sir Fred Hoyle and Chandra Wickramasinghe for random generation of a simple enzyme and calculations for a single celled bacterium.
b) Calculations of Hubert Yockey for random generation of a single molecule of iso-1-cytochrome c protein.
c) Calculations of Bradley and Thaxton for random production of a single protein.
d) Calculations of Harold Morowitz for single celled bacterium developing from accidental or chance processes.
e) Calculations of Bernd-Olaf Kuppers for the random generation of the sequence of a bacterium.
Ah man, you started out so strong and got me all excited.
Evolutionary algorithms are surprisingly strong... if made correctly. I have alot of experience with them. Of course they've made new things. They've redesigned computer chips by manipulating everything from the layout to the number, type, and sequence of logic gates. I've used them in simplier hypercubic minterm applications as well as condensed matter optimizations. I even worked with a guy who wanted to apply them to make new quantum computing algorithms.
I'm well aware of the problems stochastic algorithms have with local minima in the fitness landscape of the search space. I have two problems with your interpretation:
(1) The search space doesn't have to be bounded. In many applications the actual search space is so buried in abstract mathematics (A fun little section called Matroid Theory) that its unreasonable to describe changes as simply changing parameters within a space.
(1) As many have said, "New" or "New genetic information" is subjective and, as far as I can tell from the rather ambiguous and ever-changing definitions put forward by Creationists, is environment dependent.
Think of the fitness landscape (environment/time dependent) of the genetic search space (which potentially has infinite dimension, but in practice only has a couple of billion dimensions - 750B base pairs in an amoeba is the highest found). First of all, note that all known life is contained (approximately) in this search space. All evolution is doing is changing parameters... there's no "information" involved.
and then you did the turn to "But the results are impossible to construct randomly even though we're talking about a stochastic process (very different)." which was disappointing.