# Carbon dating contreversy

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Details about linear regression are available in any elementary statistics book, or online -- see [Linear2013].Here are just four examples of isochron graphs, which are entirely typical among the tens of thousands of examples that could be mentioned.

Also, such a calculation does not provide us with any statistical error margin to double-check the result.Of course, in real scientific research, scientists do not rely on manually drawing points on graph paper to determine a best-fit straight line or to determine the line's slope or y-intercept.Instead, they use a statistical technique known as linear regression, which computes the least-squares best fit of a straight line through a sequence of points.Along this line, a kickstarter-funded firm known as Consumer Physics has designed a handheld, consumer-oriented optical spectrometer, which can be used to measure the molecular constituents of an item (food items, etc.) that you shine its built-in light upon.This cannot be used for radiometric dating, but it does suggest advanced technology such as this is rapidly advancing and soon will be available to consumers.Note how breathtakingly close these points are to the fitted lines (thus confirming with high statistical confidence the validity of the resulting dates): The data for the first graph (upper left) is a set of measurements of basaltic achondrites (meteorites) in [Basaltic1981, pg.

938]; the data for the second graph (upper right) is from early Archaean gneisses rocks near Isua, Greenland [Morbath1977]; the data for the third graph (lower left) is from ancient gneiss rocks in Swaziland [Carlson1983]; the data for the fourth graph (lower right) is from lunar dunite rocks gathered during Apollo 17 [Papanastassiou1975]. For many years, fairly large samples were required to produce statistically reliable results.

This technique, which is used in virtually all disciplines of modern social science, physical science and engineering, is entirely straightforward, and computer software is widely available to do the requisite calculations and, in fact, is built in to most spreadsheet programs.

An important fact is that linear regression, in addition to giving the best fit of the slope of the line (which then leads immediately to the date), also gives a statistical confidence interval as to the possible error in the determination of the slope.

In mathematical terms, radioactive decay is governed by a simple exponential formula, taught in many high school math classes: P is the amount after time t, and L is the decay constant for the radioactive isotope.

This decay constant L can be expressed in terms of the half life T (the time it takes for one-half of the material to decay) as L = log(2) / T, where log(2) = 0.693147... In other words, if we know P, or even merely their ratio, we can solve the above equation for the time t.

The half-life T of this decay has been measured in careful laboratory measurements as T = 48.8 billion years.

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