Re: is free, open source software ethical?

In article <d330t3t97il90vdl0n4dps5nk4ajigg7um@[EMAIL PROTECTED]
>,
 Steve Schafer <steve@[EMAIL PROTECTED]
> wrote:

> On Thu, 06 Mar 2008 09:56:56 +1300, Barb Knox <see@[EMAIL PROTECTED]
> wrote:
> 
> >In what sense do you believe that random data can be compressed?
> 
> What he's getting at is the difference between the concepts of "random
> data" (where "random" ~ "arbitrary") and "a particular set of data,
> producing using a random process."
> 
> Given a specific set of data--regardless of how it was produced--there
> is an algorithm that will compress it, obviously.

No, this is not obvious.  In fact, it is provably wrong.  The proof is 
elementary.  There are 2^n possible data streams of length n bits.  
Therefore to compute them all you need 2^n distinct programs (where 
"program" here means the aggregate of code and data).  To produce 2^n 
distinct programs, at least one of them needs to be n bits long.  
Therefore at least one of the 2^n possible bits streams of length n 
cannot be represented by a program of length less than n, and is 
therefore incompressible.

Note that this proof is non-constructive.  It does not tell you *which* 
of the 2^n data streams are incompressible.  In fact, it can be proven 
that it is not possible to know whether a given bit stream is 
compressible or not.  See http://www.flownet.com/ron/chaitin.html
for 
the proof.

Notwithstanding the above, there are numbers (called Chaitin Omegas) 
which are mathematically well defined but which are provably 
uncomputable, and hence provably uncompressible.  I have a power point 
presentation about that but it's not on line.  If there's interest I'll 
put it up.

rg