Uncertainty is a condition which is met whenever we leave the confines of closed or deterministic systems. It occurs in a general sense whenever probability is a factor. Later, it enters specifically as an inherent characteristic of experiments.
The first place we meet uncertainty is in our daily lives. The probability that the light will go on when we flip the switch is close to 1 (or certainty) but the bulb may have blown, the switch may have failed or the power may have been disrupted at source by an accident. If it is terribly important that the electricity not fail, e.g. a hospital operating room, an emergency power supply will be installed to support the* whole system. For the rest of us, a few candles or a flashlight may do to take care of the gap between highly probable and certain. The idea of probability is implicit in many activities. Seeds planted in the spring are expected to yield summer flowers, but a late frost may kill the young plants. On the other hand, waiting until all chance of frost has passed guarantees a late blooming garden so most of us choose to run some risk. If our business is agriculture, we will probably take steps to make the implicit probabilities explicit on the basis of recorded weather trends. In other areas we are familiar with uncertainty with respect to the limits of accuracy of predictions: the poll which is correct to within four percentage points 19 times out of 20 or the message which can be transmitted to an arbitrarily high (but never absolute) degree of accuracy. * In physics, we meet one type of uncertainty as soon as we leave Newton to consider the statistical theory of heat. In quantum mechanics, uncertainty is endemic in the design of experiments or the choice of the 'observation situation'. To quote Heisenberg, " ..in quantum theory the uncertainty relations put a definite limit on the accuracy with which positions and momenta, or time and energy, can be measured simultaneously." Further, it became apparent that while the experiment itself could be designed to take objective (and reproducible) measurements, that the inferences and conclusions drawn from the experiments could no longer be accepted without qualification because the measurement iiself intrudes into the event and cannot be separated from it.
This concept of uncertainty has been found to be applicable to many areas outside of physics where the choice of an observation situation and the act of observation cannot be separated from the phenomena observed. In behavioral and social sciences, not only the act of measurement but the self-consciousness of the individuals observed intrudes on the objectivity of the findings. Another dimension of uncertainty has been explored through the mathematics of fuzzy sets, pioneered by Zadeh. He noted: "As the complexity of a system increases, our ability to make precise and yet significant statements about its behavior diminishes until a threshold is reached beyond which precision and significance (or relevance) become almost mutually exclusive characteristics."
Zadeh was particularly concerned with the extension of set theory to applications where the boundaries of the set could not be crisply defined. Sometimes the fuzziness was due to the lack of precision of natural language such as described by 'a good journal article' 'or a satisfactory paper'. Sometimes the dependency on context is a factor. Tall and short, or fat and thin describe very different situations depending upon whether you are speaking of a team of gymnasts or the customers for a men’s clothing store. Finally, the number of relevant variables may be too large to be conveniently specified such as is the case where a quick decision must be taken in a high variety situation.
# SOURCE Heisenberg, W. (1959). Physics and Philosophy. London: George Allen & Unwin. The Physicist's Concept of Nature. Westport, CN: Greenwood Press, 1958. L. Zadeh in Information and Control, Vol. 8 (1965) pp. 338-53.. # EXAMPLE • the effect of observation on the results of an experiment • the natural language definition of most sets • the planning of an action in a high variety environment # NON-EXAMPLES • an exploration in abstract mathematics • the application of Newtonian mechanics (in fuzzy sets) • the presence of random variables # PROBABLE ERROR • Noting the conditions of observation at the beginning of a report of an experiment and not following through on their implications • Confusing undeddibility with uncertainty # SEE Complementarity; Boundary; Observer