On Thu, May 14, 2015 at 04:47:21PM -0400, John Clark wrote: > On Wed, May 13, 2015 at 8:01 PM, Russell Standish <li...@hpcoders.com.au> > wrote: > > > > >> Both Og and the daemon are deterministic but even if we ignore > >> chaos deterministic is not the same as predictable. A very simple program > >> can be written to look for the first even number greater than 2 that is not > >> the sum of 2 primes and then stop, the program is 100% deterministic but > >> nobody has been able to predict if it will ever stop or not, and even worse > >> Turing tells us that there is a chance nobody will even ever be able to > >> predict that someday somebody will be able to predict if it will stop or > >> not. > > > > > > > > > Are you arguing that Laplace's daemon is impossible? > > > > Yes. Laplace didn't know that calculation takes energy and produces > entropy,
Sure, so we now know the daemon cannot be physical. I'm not sure that Laplace thought they had to be physical to make his non-physical thought experiments go through though. After all, even though Laplace made his famous quip to Napoleon, most people at the time believed in a non-physical God person. > and he thought deterministic was the same as predictable and it > isn't. How on earth do you expect the poor daemon to know if a program to > find the first even integer greater than 2 that is not the sum of two prime > numbers and then stop will ever stop if Goldbach is true but has no proof?? > Deterministic means you can predict what will happen at some given time t_1 after the origin. So you can just run the program for t_1 seconds, and it will tell you whether the proigram has halted by that time or not. If you want to actually predict the outcome, use a 10x faster computer. To determine the outcome of the program in the above circumstance, you need a more powerful beast than Laplace's daemon - it would need to be a Halting Oracle - ie someone who knows the decimal expansion of Chaitin's Omega to say a few thousand decimal places. But a Halting Oracle can never predict the outcome of FPI, the latter is truly random. > > > >> That is incorrect it matters a great deal. The daemon must keep > > his prediction of Og's behavior secret from Og or lie about what he > > really thinks Og will do. If Og is DETERMINED to do the opposite of > > whatever the daemon predicts he will do and Og is told what the prediction > > is then the daemon's prediction will never be correct. > > > > > What does DETERMINED mean here? > > > Deterministic clockwork. > Right - so you're setting up a logical contradiction. You haven't really proved anything by it, other than Laplace daemons cannot influence the system they study. You haven't shown the impossibility of Laplace daemons, for example. You may have shown the impossibility of Maxwell's daemon though, although I suspect Slizard got there some time ago... but I've kind of lost interest already, this is so much of a digression already, which was about demonstrating a real distinction between FPI and dynamical chaos. > > Sounds an awful lot like Og's free will. > > > Determined in your sentence was clearly ambiguous. I was interpreting it as meaning that Og was resolute, not that "It is determined that Og does...". -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
