Matt said, "A string is random if there is no shorter description of the string."
That is a conjecture, or a hypothesis. Matt said, "... but there is no general algorithm to distinguish them in any language. "Encrypted data appears random if you don't know the key. But it is not random because it has a short description (compressed plaintext + key). Kolmogorov proved that there is no general algorithm to tell the difference." if there is no general algorithm to distinguish or detect them then the hypothesis cannot be validated. While you might present a string and declare it to be "random" the fact that you cannot prove that it is the shortest description of the string and therefore purely random, or random, then the conjecture cannot be sustained. Jim Bromer On Thu, Oct 11, 2018 at 1:37 PM Matt Mahoney via AGI <[email protected]> wrote: > > On Thu, Oct 11, 2018 at 12:38 PM John Rose <[email protected]> wrote: > > OK, what then is between a compression agents perspective (or any agent for > > that matter) and randomness? Including shades of randomness to relatively > > "pure" randomness. > > A string is random if there is no shorter description of the string. > Obviously this depends on which language you use to write > descriptions. Formally, a description is a program that outputs the > string. There are no "shades" of randomness. A string is random or > not, but there is no general algorithm to distinguish them in any > language. If there were, then AIXI and thus general intelligence would > be computable. > > > From an information theoretic (and thermodynamic) viewpoint in your mind > > what happens when you see the symbol for infinity? Semi-quantitatively > > describe the thought processes? > > The same thing that happens when you see any other symbols like "2" or > "+". Mathematics is the art of discovering rules for manipulating > symbols that help us make real world predictions. > > -- > -- Matt Mahoney, [email protected] ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T55454c75265cabe2-M2822e026919b850bade7c01f Delivery options: https://agi.topicbox.com/groups/agi/subscription
