Act II of Manthey's little drama should have read: The man now extends his hand and it contains *a bunch of* identical coins.
Stipulating that the* bunch of* coins are in every relevant respect identical to the coins we saw earlier, we now know that there are *"more than one coin"*, that is, *we have received one bit of information*, in that the ambiguity is resolved... On Mon, Jan 6, 2020 at 3:47 PM Matt Mahoney <[email protected]> wrote: > I show you n coins. How much information did I transmit, as a function of > n? > > Of course the answer depends on what probability distribution you were > assuming over the nonnegative integers. But whatever it is, it must favor > small numbers over large, in the sense that there are an infinite number of > larger and less likely possibilities, but only a finite number of smaller > or more likely possibilities. That is the fundamental reason why Occam's > Razor and Solomonoff induction work. > > On Sun, Jan 5, 2020, 9:56 PM James Bowery <[email protected]> wrote: > >> An excerpt from "Awareness Lies Outside Turing's Box" by Michael Manthey >> >> *Act I. A man stands in front of you with both hands behind his back. He >> shows you one hand containing a coin, and then returns the hand and the >> coin behind his back. After a brief pause, he again shows you the same hand >> with what appears to be an identical coin. He again hides it, and then >> asks, “How many coins do I have?” * >> >> Understand first that this is not a trick question, nor some clever play >> on words - we are simply describing a particular and straightforward >> situation. The best answer at this point then is that the man has “at least >> one coin”, which implicitly seeks *one bit* of information: two possible >> but mutually exclusive states: *state1* = “one coin”, and *state2 *= >> “more than one coin”. >> >> One is now at a decision point - *if *one coin *then *doX *else *doY - >> and exactly one bit of information can resolve the situation. Said >> differently, when one is able to make this decision, one has *ipso facto* >> *received* one bit of information. >> >> *Act II. The man now extends his hand and it contains two identical >> coins. * >> >> Stipulating that the two coins are in every relevant respect identical to >> the coins we saw earlier, we now know that there are two coins, that is, *we >> have received one bit of information*, in that the ambiguity is >> resolved. We have now arrived at the demonstration’s dramatic peak: >> >> *Act III. The man asks, “Where did that bit of information come from?” * >> >> Indeed, where *did *it come from?! >> >> The bit originates in the *simultaneous presence* of the two coins - >> their *cooccurrence* - and encodes the now-observed *fact *that the two >> *processes*, whose states are the two coins, respectively, do not >> exclude each other’s existence when in said states. >> >> Thus, there is information in (and about) the environment that *cannot *be >> acquired sequentially, and true concurrency therefore *cannot *be >> simulated by a Turing machine. Can a given state of process a *exist >> simultaneously* with a given state of process b, *or* do they *exclude* >> each other’s existence? In concurrent systems, *this* is the fundamental >> distinction. >> > *Artificial General Intelligence List <https://agi.topicbox.com/latest>* > / AGI / see discussions <https://agi.topicbox.com/groups/agi> + > participants <https://agi.topicbox.com/groups/agi/members> + delivery > options <https://agi.topicbox.com/groups/agi/subscription> Permalink > <https://agi.topicbox.com/groups/agi/Tc33b8ed7189d2a18-M76f69db78bd53391d8821a05> > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Tc33b8ed7189d2a18-M1320d0ce3293de5ba5bc393e Delivery options: https://agi.topicbox.com/groups/agi/subscription
