# The Apes—Points To Ponder

### Extrapolation

Mathematically, extrapolation is where you extend a method (say a formula or a technique) outside the range of proven real world applicability, and logically deduce that it applies to all areas outside the range. Mathematics even has a specific kind of proof (the inductive proof) that works by extrapolation.

This is fine in the domain of mathematics, as it does not need or even care for real world confirmation. It is correct axiomatically, and thus an inductive proof applies all the way to infinity. All mathematical extrapolation is valid for the mathematical map, but the map is not the territory.

As soon as you apply extrapolation in science you are on shaky ground. Consider, for example, an activity as fundamental to geology as estimating the age of rocks. Such ages are calculated on the basis of radioactive decay. For example, the element Uranium 238 decays to become Thorium, which in turn decays until it becomes Lead. There are many steps to this process. The geological dating of a specimen can be achieved by estimating the original content of Uranium 238 and all the elements and associated isotopes in the rock sample when the rock was formed. The rock’s age is deduced according to the quantities of those elements and isotopes. The known proven-in-the-laboratory pattern of decay of Uranium 238 is applied. This is an extrapolation.

The accuracy of the calculation suffers from three problems:

1. The estimate of the original content of U238 and the elements and radioisotopes it decays into could be incorrect.
2. The rock could have been contaminated during its long life in a way that altered the ratios.
3. The normal (predictable) process of radioactive decay could have been accelerated or decelerated by unusual conditions some time during the lifetime of the rock.

One example of an anomaly is sufficient to demonstrate this problem. Radioactive dating on recent (roughly 50-year-old) lava flows at Mt. Ngauruhoe, New Zealand, have yielded a rubidium-strontium “age” of 133 million years, a samarium-neodymium “age” of 197 million years, and a uranium-lead “age” of 3.9 billion years. In each case, the dating method gives a wildly incorrect result and, as you can see, they are not even close to agreeing among themselves.

But what is the geologist to do? There are no better methods for estimating the age of rocks. It may even be that some of these estimates are correct in some cases. However, there is good reason to doubt.

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