Wesley R. Elsberry
Posts: 4928 Joined: May 2002

Quote (OgreMkV @ April 02 2015,13:04)  Prepare for the onslaught of misrepresentation of this article
http://researcher.ibm.com/researc....TMX.pdf
Quote  Logical Depth and Physical Complexity Charles H. Bennett IBM Research, Yorktown Heights NY 10598, USA pp. 227257 in The Universal Turing Machineâ€“ a HalfCentury Survey, edited by Rolf Herken, Oxford University Press (1988) Abstract Some mathematical and natural objects (a random sequence, a sequence of zeros, a perfect crystal, a gas) are intuitively trivial, while others (e.g. the human body, the digits of Ï€) contain internal evidence of a nontrivial causal history. We formalize this distinction by defining an objectâ€™s â€œlogical depthâ€ as the time required by a standard universal Turing machine to generate it from an input that is algorithmically random (i.e. MartinLÂ¨of random). This definition of depth is shown to be reasonably machineindependent, as well as obeying a slowgrowth law: deep objects cannot be quickly produced from shallow ones by any deterministic process, nor with much probability by a probabilistic process, but can be produced slowly. Next we apply depth to the physical problem of â€œselforganization,â€ inquiring in particular under what conditions (e.g. noise, irreversibility, spatial and other symmetries of the initial conditions and equations of motion) statisticalmechanical model systems can imitate computers well enough to undergo unbounded increase of depth in the limit of infinite space and time. 

There was brief discussion of "logical depth" in the original UD thread, and I brought it up with Dembski once, I think at the 2006 GreerHeard Forum. There hasn't been any stampede among IDC advocates to take it up.
 "You can't teach an old dogma new tricks."  Dorothy Parker
