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Tree rings are normally the annual growth rings of trees. Their thickness varies with moisture. The number of rings is supposed to equal the age of the tree in years. The study of these rings is called dendrochronology. However some types of trees have been known to produce up to 5 rings in a single year. Further more trees of the same type, growing near each other; can have different size rings for the same year. The thickness of the same ring can vary significantly with in a tree.
The matching of tree rings is used to extend "dates" beyond living tree. Often C14 dating is also used to help match rings. This process is used extrapolate the C14 clock backwards. This process ignores the possibility that C14 ratios rose rapidly after the Genesis Flood. It also fails to recognize that ring patterns are not unique, not even is same tree. Further more the best matches are often rejected in favor of less exact matches that agree with C14.
Bradford Pear Tree
I have had a chance to study several Bradford pear trees from the same area that were cut down with in days of each other.
The trees are labeled by the numbers given trees on site.
These are the stumps of two Bradford pear trees both were cut down on the same day. Their cores were 103 feet 8 inches a part. They are close enough that their rings should match. Both cores were off center by about 1/4 inch, so their rings could not be internally consistent.
According to theory since both trees lived near each other, were the same type, and were cut down the same day, their outer most rings should match. However when I tried to match them, I could not find an objective match. Both trees were cut down the same day.
This is the stump of a Bradford pear tree, what is notable about this tree is that the number of rings varies with direction. If one counts one way, the number is 20. If one counts another way, the number is 23. This is because some of the rings don't go all the way around the tree. This would throw off the ring count if one did not have an entire cross section of the tree.
This is the stump of a Bradford pear tree, what is notable about this tree is the clear lack of uniformity in ring pattern. The pattern is so chaotic that there would be no objective way of matching it with another tree. If cut in to slices, it could be confused for different trees. Further more if one had a small enough segment, the chaos of the ring pattern would not be known. Such trees make dates extrapolated form more than one tree questionable.
The result is that tree rings are not an objective and independent dating method, it can't be used to confirm or calibrate C14 dates. Since the oldest living bristlecone pines based on tree rings is about 4,600 years and they are the oldest living things in the world. So real tree ring data fits with in the Biblical time frame for the flood.
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Tree ring dating (dendrochronology)
The Oldest Tree
Brown, R. H. --- Can Tree Rings Be Used to Calibrate Radiocarbon Dates?
Tree Rings and Biblical Chronology