Final answer:
Some limits associated with the use of normals include the ambiguity in directional choice when applied to surfaces, difficulties in estimating extreme values in statistical distributions due to inadequate sample sizes, and the potential for bias in historical analysis.
Step-by-step explanation:
The use of normals is critical in various areas of mathematics and physics, particularly in analyzing surfaces and in studies involving distributions like the log-Normal. However, there are limits associated with the use of normals that one should be aware of.
Limits in Surface Normal Direction
Since n is a unit normal to a surface, it can point in two possible directions. This duality can pose a limit because choosing the wrong direction can lead to incorrect interpretations, particularly in the computation of flux through a surface in physics.
Limits in Statistical Distributions
In statistical analyses, particularly when dealing with distributions, normals are often assumed to follow a certain distribution such as the log-Normal. However, determining extreme values characterized by the tails of distributions can be challenging. The accuracy of characterizing these extremes suffers when the sample size is not adequate or when variability is high, making the distinction between pattern and noise difficult.
Limits in Historical Contextualization
Social scientists caution against labeling contemporary times as 'abnormal' without basis. Doing so may introduce bias and oversimplification of complex, nuanced historical contexts. Nevertheless, it is acknowledged that exceptions exist when quantifiable data regarding human impact on planetary resources support the uniqueness of the current age.