(This topic will be discussed in much more detail below.) Where the simple methods will produce an incorrect age, isochron methods will generally indicate the unsuitability of the object for dating.
Now that the mechanics of plotting an isochron have been described, we will discuss the potential problems of the "simple" dating method with respect to isochron methods.
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.
Unfortunately, one must wade through some hefty math in order to understand the procedures used to fit isochron lines to data.
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.
Note that the mere existence of these assumptions do not render the simpler dating methods entirely useless.
The X-axis of the graph is the ratio of in a closed system over time.
It is not easily explained, in the general case, in any other way.
There is no good way to tell how close the computed result is likely to be to the actual age.
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.