Narrow Results

This paper investigates the dimensionality of genetic information from the perspective of optimal representation. Recently it has been shown that optimal coding of information is in terms of the noninteger dimension of e, which is accompanied by the property of scale invariance. Since Nature is optimal, we should see this dimension reflected in the organization of the genetic code. With this as background, this paper investigates the problem of the logic behind the nature of the assignment of codons to amino acids, for they take different values that range from 1 to 6. It is shown that the non-uniformity of this assignment, which goes against mathematical coding theory that demands a near uniform assignment, is consistent with noninteger dimensions. The reason why the codon assignment for different amino acids varies is because uniformity is a requirement for optimality only in a standard vector space, and is not so in the noninteger dimensional space. It is noteworthy that there are 20 different covering regions in an e-dimensional information space, which is equal to the number of amino acids. The problem of the visualization of data that originates in an e-dimensional space but examined in a 3-dimensional vector space is also discussed. It is shown that the assignment of the codons to the amino acids is fractal-like that is well modeled by the Zipf distribution which is a power law. It is remarkable that the Zipf distribution that holds for the letter frequencies of words in a natural language also applies to the rank order of triplets in the code for amino acids.

Scientific discoveries, especially over the last six decades, have left no doubt that ‘information’ plays a central role in biology. Specialists have thus sought to study the information in biological systems using the same definitions of information as have been traditionally used in engineering, computer science, mathematics and in other disciplines. Unfortunately, all of these traditional definitions lack aspects that even non-specialists recognize as being essential attributes of information — qualities such as meaning and purpose. To remedy that deficiency, we define another type of information — Universal Information — that more accurately embodies the full measure of information. We then examine the DNA/RNA protein synthesizing system with this definition of Universal Information and conclude that Universal Information is indeed present and that it is essential for all biological life. Furthermore, other types of information, such as Mental Imaging Information, also play a key role in life. It thus seems inevitable that the biological sciences (and science in general) must consider other-than-the-traditional definitions of information if we are to answer some of the fundamental questions about life.