Hugh Pickens writes: "Contrary to previous beliefs, identical twins are not genetically identical. Researchers studied 19 pairs of monozygotic, or identical, twins and found differences in copy number variation in DNA which occurs when a set of coding letters in DNA are missing, or when extra copies of segments of DNA are produced. In most cases, variation in the number of copies likely has no impact on health or development but in others, it may be one factor in the likelihood of developing a disease (pdf). "Those differences may point the way to better understanding of genetic diseases when we study so-called discordant monozygotic twins....a pair of twins where one twin has a disorder and the other does not," says Carl Bruder, Ph.D. "If twin A develops Parkinson's and twin B does not, the region of their genome where they show differences is a target for further investigation to discover the basic genetic underpinnings of the disease.""
We warn the reader in advance that the proof presented here depends on a
clever but highly unmotivated trick.
-- Howard Anton, "Elementary Linear Algebra"