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By what means are things dated?

Folks whose religious faith informs them that there have been only "10,000 years of existence" will never accept the answer to your question. This is because faith is unquestioning belief and acceptance without proof, whereas science is constant questioning, and a continual search for proof and knowledge. Religion and science are not incompatible except to religions wherein the teachings are rigidly fundamentalist.

A perfect example is found in those religions which teach that their adherents should not obtain medical help for illness or injury, but that one should only pray for whatever outcome God wills. Those religions are certainly entitled to their beliefs, but the rest of us are grateful for modern advances in medical science.

Similarly, religions which hold that the world is about 10,000 years old are perfectly entitled to their beliefs. The rest of us are grateful for scientific advances that enrich our knowledge of the grand sweep of earth and human history stretching billions of years into the past. God gave human beings brains capable of moving humanity from cave-dwellers to spacefarers in only about 100,000 years, and I, for one, think that's one of the most beautiful aspects of His creation.

Dr. Willard Libby, the founder of the carbon-14 dating method, assumed this ratio to be constant. His reasoning was based on a belief in evolution, which assumes the earth must be billions of years old. Assumptions in the scientific community are extremely important. If the starting assumption is false, all the calculations based on that assumption might be correct but still give a wrong conclusion.

In Dr. Libby’s original work, he noted that the atmosphere did not appear to be in equilibrium. This was a troubling idea for Dr. Libby since he believed the world was billions of years old and enough time had passed to achieve equilibrium. Dr. Libby’s calculations showed that if the earth started with no 14C in the atmosphere, it would take up to 30,000 years to build up to a steady state (equilibrium).

If the cosmic radiation has remained at its present intensity for 20,000 or 30,000 years, and if the carbon reservoir has not changed appreciably in this time, then there exists at the present time a complete balance between the rate of disintegration of radiocarbon atoms and the rate of assimilation of new radiocarbon atoms for all material in the life-cycle.

2Dr. Libby chose to ignore this discrepancy (nonequilibrium state), and he attributed it to experimental error. However, the discrepancy has turned out to be very real. The ratio of 14C /12C is not constant.

The Specific Production Rate (SPR) of C-14 is known to be 18.8 atoms per gram of total carbon per minute. The Specific Decay Rate (SDR) is known to be only 16.1 disintegrations per gram per minute.

3 What does this mean? If it takes about 30,000 years to reach equilibrium and 14C is still out of equilibrium, then maybe the earth is not very old.

“God gave human beings brains capable of moving humanity from cave-dwellers to spacefarers in only about 100,000”

Actually it is not until Christ that mankind advances - we were still cave dwelling at 0 AD.