Note that the mere existence of these assumptions do not render the simpler dating methods entirely useless.
In many cases, there are independent cues (such as geologic setting or the chemistry of the specimen) which can suggest that such assumptions are entirely reasonable.
(Rocks which include several different minerals are excellent for this.) Each group of measurements is plotted as a data point on a graph.
The X-axis of the graph is the ratio of in a closed system over time.
However, the methods must be used with care -- and one should be cautious about investing much confidence in the resulting age...
especially in absence of cross-checks by different methods, or if presented without sufficient information to judge the context in which it was obtained.
Each such age would match the result given by the isochron.
The "generic" method described by Gonick is easier to understand, but it does not handle such necessities as: (1) varying levels of uncertainty in the X- versus Y-measurements of the data; (2) computing an uncertainty in slope and Y-intercept from the data; and (3) testing whether the "fit" of the data to the line is good enough to imply that the isochron yields a valid age.
There are minor differences between isotopes of the same element, and in relatively rare circumstances it is possible to obtain some amount of differentiation between them. The effect is almost always a very small departure from homogeneous distribution of the isotopes -- perhaps enough to introduce an error of 0.002 half-lives in a non-isochron age. but it is rare and the effect is not large enough to account for extremely old ages on supposedly young formations.) as minerals form.
This results in a range of X-values for the data points representing individual minerals.
An additional nice feature of isochron ages is that an "uncertainty" in the age is automatically computed from the fit of the data to a line.
A routine statistical operation on the set of data yields both a slope of the best-fit line (an age) and a variance in the slope (an uncertainty in the age).