An invariance is something that stays the same while other aspects of the system change, or if it changes, it always changes in the same way with respect to its environment. The modeling process always looks for factors which remain the same or are predictable. This is true whether the system is deterministic (a ball dropped will fall to the floor) or probabilistic ( a fair die will fall on a particular face one sixth of the time). We may speak of invariances with varying degrees of rigor. The relationship of pi to the radius of a circle can be carried out thousands of places to the right of the decimal point if there is any need but we can easily agree that 3.14 will be adequate for our purposes. In a less precise manner, we know the shape of a learning curve and have little expectation of further gain after we are told that such a curve has leveled out. Many invariances depend on a context for their validity. Such contexts include the physical, the biological and the social. They may be stated with varying degrees of formality from 'it's always crowded here at the holidays' to a set of axioms and postulates. In some cases whether or not an invariance holds depends on the level of abstraction or on a time scale, e.g. the pattern of a marketing campaign may be invariant although the products offered vary. # SOURCE Invariance is the negative of variance which comes from the same Old French word as variety. See also Chapter 2: Beer, S. (1979). Heart ofEnterprise. Chichester: John Wiley & Sons, # EXAMPLES • the boiling point of water at sea level • the progression of the seasons • die upper level of a machine's capacity • the recognition of an identity • an established ratio of output to input
# NON-EXAMPLES • next year's fashion • the outcome of a fair election • the behavior of the stock market • next week's weather PROBABLE ERROR • observing the system for too short a time to establish the correct pattern • making incorrect assumptions about the initial state of a system • misjudging the context in which an invariance holds # SEE Coenetic Variable; Identity; Model