May I ask you two questions?

1. Why did you jump to carbon dating when it wasn’t mentioned in the post?
2. Where did you get the idea that there are two different things named “observational science” and “historical science”?

First, there is no such thing as historical science. All science is based on observation. Based on the observations, models are made to make predictions and theories are structured to explain what we see and suggest how the world works. Again, based on observed facts. Theories then grow in strength over time as 1. It survives continuous efforts to falsify key assumptions that must be true for the theory to hold. And 2. Further facts are discovered that aligns with the assumptions of the theory. Both contributing to decreasing the likelihood that we’ve arrived at the theory by mere accidence. So, if I say that humans and chimpanzees share a common ancestor, or that the world is close to 4.5 billion years old, those statements are based on observational science. I didn’t have to be there to make the observations. I can make them today and still know that it happened.

As for carbon dating, I’ve heard what you said many times before from people who deny the evidence for an old earth or for evolution. But it makes no sense to even bring it up since we don’t rely on carbon dating to estimate either the age of rocks nor of fossils (it is useful when you dig up remnants from older human civilizations like from the Viking era, Roman era, etc that are more recent). Instead, when an archaeologist discovers fossils that are very old, they will instead examine the rocks above and below the fossil-containing elements such as potassium with a half-life time of 1,250,000,000 years.

Today, millions of fossils have been documented, and the location of their discovery with regards to geological layers has always fitted the model of evolution and it with the estimated age of the earth. In other words, we’ve never found rabbit bones in the Pre-Cambrian.

Now, you may say – and indeed did say – that perhaps these laws may have changed. After all, we were not there to see and observe, right? Well, there’s two issues with that. First, we have now relied on these methods for decades and they have not changed one percent of one percent (such a change would have actually added many meters added inaccuracy over time to our satellites which rely on atomic clocks due to the fact that they never change). Second, this is not intellectually honest, and you are doing exactly what the people in the documentary are doing, which is to respond to evidence contradicting your beliefs by coming up with some alternative explanation – for which there is no evidence – in order to not have to change your mind according to new observations.

If you are going to always ask “but what if”, then you are never going to change your mind and never going to learn anything. Because you can always resort to saying that. I don’t think I can put it better than Bertrand Russell when he gave his thoughts on it here.

So finally, how come I am so confident to say that I know that evolutions are true and the age of the Earth? Because we have completely independent branches of research that support the same theory and because the resulting model allows us, continuously, to make accurate predictions of future events. In genetics, we can now look at the DNA of different species and literally count our way back to the common ancestor. Computers have done this now for millions of species to make cross-examinations and judge how old a species is and how long ago it is since it shared a common ancestor with any other of the millions of species. The result can be plotted as a family tree. Guess what? It matches, perfectly, with the tree you get based on the dated age of all the discovered fossils.

So what is the likelihood, not only that each of these would produce consistent results on their own, but jointly by accident? It’s about as likely as you are winning the lottery every single week for the rest of your life, and then realizing that everyone in the states chose the exact same numbers when choosing theirs at random. Except, I haven’t even mentioned the also confirming evidence from RNA, geological distribution of species and how they match continental changes etc.

So yes we can know these things, no we don't need carbon dating to know them (which you're right about) and no there is no such thing as historical science, models that accurately predict the future should be used to assume the past until otherwise is proven.