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To master complexity, we can organize it or discard it. The Art of Insight in Science and Engineering first teaches the tools for organizing complexity, then distinguishes the two paths for discarding complexity: with and without loss of information. Questions and problems throughout the text help readers master and apply these groups of tools. Armed with this three-part toolchest, and without complicated mathematics, readers can estimate the flight range of birds and planes and the strength of chemical bonds, understand the physics of pianos and xylophones, and explain why skies are blue and sunsets are red.
The effect on the mean-variance space of restrictions on a variable is investigated in this
paper. A restriction may be the placing of upper and lower bounds on a variable.
Another limitation is the loss of the continuity of a variable.
Average marks for Examinations are considered in an application of this limited meanvariance
space. In this case, the bounds are given by the highest and the lowest possible mark (e.g. 1.0 and 5.0). The limitation of the mean-variance space depends on the number of students who participate in the examination. The restriction of the loss of continuity is shown by the use of discrete marks (e.g. 1.0, 1.3, 1.7, 2.0, …). Furthermore,
the Target-Shortfall-Probability lines are integrated into the mean-variance space. These
lines are used to indicate the proportion of students who have good or very good marks in the examination. In financial markets, Target-Shortfall-Probability is used as a risk criterion.