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These transformations produce similar shapes, which is the basis of trigonometry.In contrast, angles and ratios are not invariant under non-uniform scaling (such as stretching).
In “Toward a Theory of Race, Crime, and Urban Inequality,” Sampson and Wilson (1995) argued that racial disparities in violent crime are attributable in large part to the persistent structural disadvantages that are disproportionately concentrated in African American communities.
They also argued that the ultimate causes of crime were similar for both Whites and Blacks, leading to what has been labeled the thesis of “racial invariance.” In light of the large scale social changes of the past two decades and the renewed political salience of race and crime in the United States, this paper reassesses and updates evidence evaluating the theory.
A simple example of invariance is expressed in our ability to count.
For a finite set of objects of any kind, there is a number to which we always arrive, regardless of the order in which we count the objects in the set.
We conclude by charting a dual path forward: an agenda for future research on the linkages between race and crime, and policy recommendations that align with the theory’s emphasis on neighborhood level structural forces but with causal space for cultural factors.).
Race and Economic Opportunity in the United States: An Intergenerational Perspective. The Equality of Opportunity Project, Available at:
Uniform semiclassical approximations and their applications.
[PDF: ~5.9 MB](Gabrielse) ROESER, CHRISTOPHER ALLAN DEWALD, B.
In so doing, we clarify key concepts from the original thesis, delineate the proper context of validation, and address new challenges.
Overall, we find that the accumulated empirical evidence provides broad but qualified support for the theoretical claims.