Wesley R. Elsberry
Posts: 4991
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. 227-257 in The Universal Turing Machine– a Half-Century
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 π) contain internal evidence
of a nontrivial causal history.
We formalize this distinction by defining an object’s “logical depthâ€
as the time required by a standard universal Turing machine to generate
it from an input that is algorithmically random (i.e. Martin-L¨of
random). This definition of depth is shown to be reasonably machineindependent,
as well as obeying a slow-growth 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 “self-organization,â€
inquiring in particular under what conditions (e.g. noise, irreversibility,
spatial and other symmetries of the initial conditions and equations of
motion) statistical-mechanical 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 Greer-Heard 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
|
