Radiometric Dating
I like to think about radiometric dating. When I consider, say Carbon-14 dating, this relatively young science and learning potential are amazing and, while these processes of dating are not without their flaws, let's talk about them anyway.
Today, we observe Carbon 14 (C-14) next to Carbon 12 (C-12) in a ratio of one to one trillion respectively (remember, these are molecules; a trillion isn't very many). C-14 dating is a reliable dating method (to about 25,000 years) only in organics.
Well, that last sentence was wrong, or almost right depending on how we look at it. More correctly, C-14 dating is a reliable dating method (to about 25,000 years) only in material that contains carbon; the difference is subtle, but important. Plants take in Carbon Dioxide (C02) from the atmosphere, we eat the plants and that C-14 ratio ends up in us.
There is only one geological sample (that I know of) that deals with C-14 and it is diamonds, because they are pure carbon. The conversation about C-14 dating and diamonds is controversial, but it serves to identify weaknesses not commonly relayed when C-14 is used.
For instance, we only see the ratio of C-14 to C-12 today. There's no observable science to verify what that ratio was 5,000 or even 1,000 years ago.
Current science tells us that the decay rate of C-14 is between 5,730 and 5,770 years. Again, there's no way of knowing if this rate has increased or decreased over the millennia.
All radiometric dating suffers from the "initial amount" syndrome. How much carbon did the sample being test contain initially? I'm not opposed good guesses and scientific speculation if stated so in the result, but, more often than not, these non-scientific assumptions go unmentioned.
Lastly, influence from surrounding geology is largely ignored or classified as contamination by detractors of these weaknesses. Igneous, metamorphic, and sedimentary are all influenced by their surrounding geology.
Radiometric dating is wonderful science to stimulate and investigate when its strengths and weaknesses are properly categorized and calibrated to their samples and science.
These are things I like to think about.