On Mon, Sep 29, 2014 at 8:29 PM, Tim Tyler via AGI <[email protected]> wrote: > On 29/09/2014 15:41, Matt Mahoney via AGI wrote: >> >> On Mon, Sep 29, 2014 at 7:15 AM, Tim Tyler via AGI <[email protected]> >> wrote: >> >>>>> There's no known speed limit on evolution. >>>> >>>> Yes there is. Copying one bit of information in any form including DNA >>>> requires at least kT ln 2 energy, or about 3 x 10^-21 J at room >>>> temperature. >>> >>> That's the cost of *deleting* a bit of information (from Landauer's >>> principle). Copying is a reversible operation that doesn't require >>> deleting anything. This has been proven - for example by >>> building reversible self-reproducing cellular automata. >> >> Copying information requires storing it somewhere. That requires >> overwriting the information that was stored there before. > > > Nope. Again, think of a reversble cellular automaton capable of supporting > self-reproducing systems > (of which there are plenty in the literature - e.g. see: "Logical > universality and self-reproduction in > reversible cellular automata" by Kenichi Morita and Katsunobu Imai).
I just read the paper and found it fascinating. I am tempted to write some programs to play around with this. It would be interesting to see whether evolution is possible in a reversible cellular automaton. Evolution requires some source of randomness to induce mutations. We could use repeated encryption as a reversible pseudo-random source. It seems like it must be possible because we evolved in a universe with reversible physics. (Strictly speaking, you also have to reverse charge and parity along with time to make the weak nuclear force reversible). The entropy of a closed, reversible system cannot increase. You can always find the the Kolmogorov complexity of a reversible system by running it backward and measuring the length of the original program. Of course this is not what we observe. Entropy is indeed increasing. We cannot make it decrease. Time has a direction. Heat flows one way until everything is the same temperature. Why? We can blame quantum randomness, but I don't like that explanation. Schrodinger's equation gives an exact solution when you include the observer. We only prefer probabilistic approximations like the Copenhagen interpretation because it makes the computation tractable. Another problem is that Morita and Imai are describing CA with infinite memory. You can always store bits without deletion by moving all of the existing bits to the next higher address and writing to address 0. You can't do that with finite memory. But finite systems can still be reversible. Any finite state machine must eventually repeat. At that point, no more information can be lost even though memory bits are still being written. -- -- Matt Mahoney, [email protected] ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
