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-M55a127306c5bb18333aa528f> > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Tc33b8ed7189d2a18-M76f69db78bd53391d8821a05 Delivery options: https://agi.topicbox.com/groups/agi/subscription
