Outdoor Lighting and Crime - Amper

where Q is the total annual light energy loss per unit area. If the total light energy loss of a
city is T and its area is A, then Q = T/A. If the population is N, then the total light energy loss
per person, L, is T/N, or
T = L N, so that
Q = L N/A.
Thus, the English regression equation can be put into a form closer to that of the USA
equation by using the English variable for light energy loss per person, provided it is
multiplied by N/A, the population density for each city. 66 This does not mean that population
density matters in England but not the USA. If the English result had been used to start with,
the USA result could have been made more like it by including the inverse quantity, area per
person for each city. This does not explain or change the difference, but it does indicate that
in both countries, the crime rate increases with total light energy loss T divided by some
factor involving city population and area. The factor could have the form (a N + b A), where
the present dichotomous values of a = 1 and b = 0 for the USA, and a = 0, b = 1 for England,
might be replaced by non-zero real numbers or mathematical operators. Investigations of this
may uncover some physical or economic connection between the variables, idiosyncratic for
particular countries.
5.4 CURVE E AND THE CRIME VERSUS LIGHT ENERGY LOSS
GRAPHS
An objection could be made that the zero-light value of crime rate implied by the regression
equation in Figure 13 contravenes the statement above that negative crime rates do not exist in
the real world. 67 It might be thought that the regression equation should be constrained to a
zero or positive intercept on the vertical axis, and that the regression equation should be nonlinear.
These constraints may be sufficient to get around the problem but they are not
necessary, however. The theory in Section 4.2.2 can be used to explain how the negative
value might arise in particular studies without the actual crime rate ever being anything but
positive. The plots of crime against light energy loss per unit area can be related to the curves
shown in Figure 6. Curve E is used as it best explains the situation.
If a city has a really bright lighting system, Curve E indicates that crime at night there would
be hardly less than the daytime rate. The total or overall crime rate for day and night would
be just under that represented by 100% of the day rate. If some of the bright lighting is
removed, Curve E might indicate that the night crime rate, after the end of twilight, will drop
to say 90% in due course. The effect on the overall crime rate over the first 12 months, day
and night, will be to drop it by less than half as much because the night rate is integrated over
fewer hours than the day rate is, on average. The day rate will also tend to follow the night
rate to some extent according to the hypothesis, so the equilibrium overall crime rate will end
up at say 95% or lower. Successive reductions in ambient light at night will each result
66 Some readers will see this at a glance but the detailed steps will be useful to others.
67 Nor do coins exist with a negative face value, but negative money amounts are an everyday
part of accounting. Negative crime rates do have a useful existence in theory.
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