Re: [Phys-l] ill-posed problems

[John Denker <jsd@av8n.com>]

On 03/15/2010 05:00 PM, Quist, Oren wrote:
>   Physics cannot produce a solution to a
> problem that does not have unique results.

Along that line: Einstein said "God does not play dice."

However, the overwhelming preponderance of the 
evidence is that God *does* play dice.  There 
are some things that are just random.  They are
random for all practical purposes, and as far
as anybody can tell they are random in principle.

Random implies that any particular instance of
the problem "does not have unique results."

Let's make this really specific.  Suppose I build
a random number generator based on the Johnson
noise (thermal noise) in a resistor in accordance
with the laws of thermodynamics.  The machine puts
out numbers *and* a lower bound for the entropy
thereof.  Suppose people are literally staking 
their lives on the proposition that these random 
numbers are unpredictable.  Can you defeat this 
random number generator, so that it puts out 
numbers that are less random than I claim they
are?  Can you use physics to make Johnson noise 
predictable?

  Note that the RNG machine is protected against
  tampering.  Also, a denial-of-service attack
  such as annihilating the whole machine does
  not count as a defeat since the guarantee goes
  to zero, and the machine is not violating its
  guarantee.