Carbon dating problem
It is not easily explained, in the general case, in any other way.The data points would be expected to start out on a line if certain initial conditions were met.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.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.Since the data points have the same Y-value and a range of X-values, they initially fall on a horizontal line: half-lives will include zero within its range of uncertainty.(The range of uncertainty varies, and may be as much as an order of magnitude different from the approximate value above.
For further information on fitting of lines to data (also known as regression analysis), see: Note that the methods used by isotope geologists (as described by York) are much more complicated than those described by Gonick.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).Each such age would match the result given by the isochron.Gain or loss of In order to make the figures easy to read (and quick to draw), the examples in this paper include few data points.