If all 'living things' can be described with 'Descriptors' comprised of any 4 integers, and there is no (obvious) limits to the combinations, sequences, repetitions, and/or locations ... how many types of 'organisms' are possible?
Any Genetic guru's around? About all I know of the human gene map is that there are about 30 to 40 thousand 'genes' and each of these consists of the above mentioned descriptor sequences. (how many descriptors per gene? I don't know. Lets assume > 10^5 and < 10^8 .
Note: It really gets more complex when you realize that these 30-40 thousand genes are just the instruction sets to the really complex protein sets that make life... anyway...
Unknown... Is the human map a simple, medium or complex gene set? In all the universe, are we the king or are we the amoeba?
In our funny little part of the universe, we are the top of the complexity chain. Assume that this is unknowable and that organisms N times more complex might be possible, where N is any Real number < 1000. This will preserve our self worth a bit, you see. <grin>
My guess is that it is a countable union of countable sets... with the upper limit of 1000 imposed.
Now watch me go down in flames!
PS... this is REALLY a COMPLEX post. I am just curious to get some mathematical sense of 'the possiblilities of DNA structured life'. <Pun's are good>