You could call this technique "complexity dating". First you show there is exponential growth (or decay) occuring naturally. The actual changes occur randomly but the mean rate is fixed. Then you plot on log scale and voila you have complexity dated life itself. The only argument you can make against is that the laws of physics are somehow not constant, but I think everything froze out by the time molecules were forming.
So in your cartoon, the bride can marry a random normally distributed number of husbands each time. We would determine the average rate of husband accretion. Then given the number of husbands at any time we could determine when the rapacious bride began marrying.
Inaccurately, with recent revisions to the tune of hundreds of millions of years.
> The age of rocks?
Surprisingly inaccurately, despite the smooooooooth exponential curve of radioactive decay.
Evolution is not smooth.
> Do you not accept carbon dating?
I do, within its error range. Which is large. Like tens of percent in common scenarios.
1. The rate of change-per-generation is very much not constant, as described by the Punctuated Equilibria theory. Sudden changes in the environment can cause sudden bursts of evolution. We don't know if there were any (and how many) mass extinctions / sudden change events before the fossil record starts, which is already hundreds of millions of years into the existence of single-celled life existing!
2. The time elapsed per generation has changed over time too, and we have virtually no direct evidence of the actual rate for the earliest epochs of life, before multi-cellular life.
These are particularly bad problems for any theory trying to extrapolate backwards, with compounding issues that can blow out any naive error estimates massively.
For example:
RNA-based vs DNA-based life. We know that DNA is more stable and resistant to mutation than RNA, which was the foundation of the earliest life forms. But we have no idea how that difference specifically affected early life evolutionary rates! We can guess... but only guess. However, almost certainly, early life had a much higher mutation rate per generation than modern life AND a consistently short generation time.
