Many interesting questions can be asked about the genetic code, including why the pattern of redundancies in the code exists. Furthermore, there is the question of to what extent this code applies to all life forms, from the most simple to the most complex. While at one time it was thought that the code was totally universal, this has proved not to be true. For certain bacteria and in other situations the universality of the code breaks down. Cellular life forms are classified according to whether they are prokaryotes or eukaryotes. Prokaryotes are cellular organisms where the genetic material is not a part of a membrane-enclosed nucleus, while in eukaryotes the genetic material is contained in a nucleus. At one time life forms were classified as either bacteria or eukaryotes. A group of bacteria like organisms, found in very hot environments such as undersea vents, were initially classified as bacteria. However, when Archaea's genetic makeup was studied, its members were found to have an amazingly large number of genes that were not known to exist in other organisms. They seemed to be surprisingly different from the bacteria with which they had been formerly classified. It has become standard in recent years to list the Archaea in a separate category from the bacteria and eukaryotic organisms. Use of phylogentic trees was in part a tool that led to this change.
It is tempting to believe that, because human beings are as complex as they are, other species will have less genetic material than humans. However, chromosome number (and the total size of the genome) varies with species in a way that seems to have no rhyme or reason. Thus, chimpanzees have 48 chromosomes, cats 38, dogs 78, rabbits 44, rats 42, turkeys 82, and horses 64. (I purposely am not listing examples for plants which forms a complex subspecialty within the complex environment of genetics. The genome of some plants have been sequenced, however.) Perhaps when the genomes of many different and varied species are sequenced it will be possible to get insight into these wildly varying numbers.
This brief introduction to biological and genetic ideas should help the reader to understand the terminology and ideas in other parts of this essay as well as the literature of mathematics when applied to genome research.
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