Models
A model of the above example is a left-ended Post-Turing machine tape with its fixed "head" located on the left-end square; the system's relation is equivalent to: "To the left end, tack on a new square □, right-shift the tape, then print ■ on the new square". Another model is the natural numbers as created by the "successor" function. Because the objects in the two systems e.g. ( □, ■□, ■■□, ■■■□ ... ) and (0, 0', 0, 0', ...) can be put into a 1-1 correspondence, the systems are said to be (simply) isomorphic (meaning "same shape"). Yet another isomorphic model is the little sequence of instructions for a counter machine e.g. "Do the following in sequence: (1) Dig a hole. (2) Into the hole, throw a pebble. (3) Go to step 2."
As long as their objects can be placed in one-to-one correspondence ("while preserving the relationships") models can be considered "equivalent" no matter how their objects are generated (e.g. genetically or axiomatically):
- "Any two simply isomorphic systems constitute representations of the same abstract system, which is obtained by abstracting from either of them, i.e. by leaving out of account all relationships and properties except the ones to be considered for the abstract system." (Kleene 1935:25)
Read more about this topic: Object Theory
Famous quotes containing the word models:
“French rhetorical models are too narrow for the English tradition. Most pernicious of French imports is the notion that there is no person behind a text. Is there anything more affected, aggressive, and relentlessly concrete than a Parisan intellectual behind his/her turgid text? The Parisian is a provincial when he pretends to speak for the universe.”
—Camille Paglia (b. 1947)
“Today it is not the classroom nor the classics which are the repositories of models of eloquence, but the ad agencies.”
—Marshall McLuhan (1911–1980)
“The parents who wish to lead a quiet life I would say: Tell your children that they are very naughty—much naughtier than most children; point to the young people of some acquaintances as models of perfection, and impress your own children with a deep sense of their own inferiority. You carry so many more guns than they do that they cannot fight you. This is called moral influence and it will enable you to bounce them as much as you please.”
—Samuel Butler (1835–1902)