There is a crucial difference between radiocarbon dating manuscripts and radioisotope dating rocks.
Nitrogen in the earth’s atmosphere occasionally becomes Carbon 14. Both carbon 12 and carbon 14 are present in the earth’s atmosphere. Plants regularly “trap” carbon through photosynthesis, some of this carbon is carbon 12 and some is carbon 14. Animals eat plants or other animals that ate plants. In this way and perhaps other ways as well animals and plants usually contain a certain percentage of carbon 12 and a certain percentage of carbon 14 while they are alive. Occasionally carbon 14 turns back into nitrogen. It is assumed that when animals and plants are alive there is a certain ratio of carbon 12 to carbon 14. When animals and plants die, they no longer put carbon 14 into their system through digestion and photosynthesis. The longer an animal or plant has been dead theoretically the less carbon 14 is present per carbon 12 and a mathematical estimation of how long the organism has been dead can be calculated through this ratio. There are many assumptions, to this method because of these assumptions it is not valid to determine the age of a manuscript by carbon dating alone, historical methods should also be used. None the less carbon dating can add credibility to the date estimated by historical methods and historical dating methods of manuscripts have shown that carbon dating sometimes works fairly well.
Carbon dating can sometimes work because, we have reason to start with an assumption of what percent carbon 14 we started with. The reason to assume is what makes carbon dating manuscripts completely different than radioisotope dating rocks.
Many times in math class we did radioisotope dating problems where we were given a certain percentage of parent and daughter isotopes in a rock and given a half life for the parent isotope. (A math book writer would typically be less qualified than a physics or chemistry book writer in such matters.) We were then asked to use differential equations to calculate the age of the rock. The problem is we were told to assume 100% of the parent isotope was present. Do rocks only become rocks when 100% of the parent isotope is present? No! So there is no basis to choose 100% as the starting point, what about another percentage? How do you know what percentage, it started with? You must be there when the rock was formed, because rocks do not only form when the material they came from is a specific percentage of parent isotope. Now if you were there when the rock was formed you would already know how old it is and have no need for radioisotope dating. Furthermore there is a disturbing problem if mass and energy are conserved in the universe then before the rock existed it must have come from something else, and if you keep track of every molecule that came from what formed the rock eventually 100% of the molecules that later formed the rock would have been parent isotopes (looking backward in time.) But what were they before they were 100% parent isotopes? What were they before that? Is it possible to go on backwards throughout all eternity? If not we must reject a non-supernatural origin of the universe or change our science laws, because mass and energy must be conserved in a non-supernatural origin of the universe and therefore everything must have came from what was before it forever. If on the other hand, we find that we can keep on going back forever (in theory) which direction will we be going, towards heavier or lighter isotopes, more or less protons per atom/ion more or less neutrons per atom/ion or both ways (the path may be more complicated than any of the combinations I mentioned but the path is still either reversible or irreversible.) If it is only one way (irreversible) we cannot go back forever in time (forcing us to reject the non-supernatural hypothesis or change our science laws) on the other hand if it is both ways (a reversible path) it will cast severe questions, as to why we choose the percent of parent isotope we did.
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