On Fri, Dec 19, 2014 at 4:42 PM, Matt Mahoney via AGI <[email protected]> wrote: > I realize there are some programs that are reversible, for example {A > -> B, B -> A}. In this case, entropy remains constant.
Significantly, the 'entropy' of a computer (program) is relative to some 'frames of reference', like whether the previous state of a variable is retrievable. > A computation taking input is equivalent to a computation whose input > is part of its initial state. But again, the 'entropy' is relevant to some 'frames of reference' so your last statement must be an over-generalization. This isn't a quibble. (Or maybe, from another angle, it is a quibble, but it is a good one.) You are using a defeasible notion of logical equivalence to produce a conclusion about 'entropy'! It is like a perfect storm of an inappropriate use of logical equivalence. Even if a program that reacts to input is equivalent to a program with that input as part of an initial state, how could it be true that the entropy of the programs are equivalent? You can't dismiss the potential for the entropy of input as a mere representation of a particular path reproduced in a closed program. But even ignoring the question of whether the frame of reference of looking for sources of 'entropy' might override some equivalence argument, what about the question of a closed computation that looks for solutions to equations where some solution searches might produce chaotic evaluations. You cannot say that the entropy of the solution is decreased by an excursion into chaos because there may be more such excursions. For a strong example, if the 'equation' might itself be chaotic then the search for a solution to some 'equations' may not produce reductions in 'entropy' via any iteration. Extrapolations of a concept like 'entropy' is ok as long as you make a real effort to examine the limitations of such extrapolations realistically. Jim Bromer On Fri, Dec 19, 2014 at 4:42 PM, Matt Mahoney via AGI <[email protected]> wrote: > On Fri, Dec 19, 2014 at 2:13 PM, Jim Bromer <[email protected]> wrote: >> On Thu, Dec 18, 2014 at 9:52 PM, Matt Mahoney via AGI <[email protected]> >> wrote: >>> On Wed, Dec 17, 2014 at 1:27 PM, Abram Demski via AGI <[email protected]> >>> wrote: >>>> My current understanding of time is "the direction of computation". >>> >>> That is actually quite precise. The entropy of a computer can only >>> decrease. In a state transition diagram, states can merge but not >>> fork. Operations like writing a bit of memory cannot be reversed >>> because the previous bit was erased. >> >> That reasoning is confused. The reference to a state transition >> diagram is not directly related to the discussion up until that point, > > Suppose a finite state machine has 2 possible states, A and B. The > program is {A -> B, B -> B}. The initial state can either be A or B. > The next state will be B. The entropy of the computer (the number of > bits you need to describe the state) has gone from 1 to 0. > > If the computer is in state B, you do not know the previous state. You > cannot run the program backward. > > The same argument applies to Turing machines. Writing a symbol to the > tape is not reversible in general because the previous symbol is > erased. > > I realize there are some programs that are reversible, for example {A > -> B, B -> A}. In this case, entropy remains constant. > >> and I don't believe anyone was talking about a computer program that >> could not respond to input. > > A computation taking input is equivalent to a computation whose input > is part of its initial state. > > -- > -- Matt Mahoney, [email protected] > > > ------------------------------------------- > AGI > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/24379807-653794b5 > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com ------------------------------------------- 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
