The Origin of Digital Information

June 8, 2012 Leave a comment

The second half of the 20th century was the era of the computer and DNA. Their common feature is digital information. As mentioned in “Properties of Digital Information“,  it has properties of the natural number one: equality, invariability and indivisibility. Let us seek the origin of digital information.  The computer is invented in the 20th century. In contrast, scientists discovered 419 million-year-old DNA intact. It is the known oldest digital data.

Let us consider DNA. DNA is a chemical compound. By contrast, the natural number one is the concept. There is the definitive difference between them. Plato emphasized the distinction between the real matter and the abstract concept. He described in Phaedo “Then we must have known absolute equality previously to the time when we first saw the material equals, and reflected that all these apparent equals aim at this absolute equality, but fall short of it? ” That is, DNA cannot have ideal properties. However, lives try to make DNA close to the ideal digital information.

For example, a large set of DNA repair enzymes are required for the storage of genetic information. Even under normal cellular conditions, each nucleotide of DNA is modified by spontaneous  reactions: oxidative damage, hydrolytic attack and uncontrolled methylation by the methyl group donor S-adenosylmethionine.  Furthermore, DNA undergoes modifications by many other reactions. Hence, the life evolved the DNA repair system for preserving genetic information. This example shows that digital information is produced by life for survival. That is, the life can change the grade of the completeness of digital information. However, because the mutation is necessary for evolution, DNA will never be identical to ideal digital information.

As I mentioned in “What is digital information?“, we can define digital information as the substantial entity, which is the replica of the Platonic number and has the possibility of determining life or death of a living organism. The most important thing is that digital information determines the survival rate of  a life. How long a DNA sequence is close to the ideal digital information is determined by its importance for survival.

Let us consider the maintenance of DNA sequences. The mutation rate of bacteria is 1 nucleotide change per 109 nucleotides per cell generation. On the other hand, under laboratory conditions, E. coli divides about once every 30 minutes. Under these conditions, more than half nucleotides will change about 40,000 years. That is, if all mutants survived, all genetic information would be rapidly changed. This change speed is good for evolution, but is inappropriate to preserve genetic information. However, natural selection excludes disadvantageous mutations in reality. Thus, the rate of evolution varies according to a gene. Because the mutation of the important gene for survival is likely to fatal, its rate of evolution is slow. In contrast, if mutations within a gene are likely to tolerate, it will rapidly evolve.

Finally, let us consider an extreme example. The most conserved gene is the ribosomal RNA. Especially, strongly conserved regions of 16s rDNA are shared by all known cells. Nucleotides in them have close properties to the natural number one: equality, invariability, indivisibility. They might be the nearest real thing to the natural number one on the Earth. Because properties of the natural number one are abstracted from life, their properties are come from the life itself.

If you want to know the more detailed discussion, please read “Natural Selection Protects Information against Entropy”

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Properties of Digital Information

May 28, 2012 2 Comments

The digital computer can recognize only 1 and 0. Because it distinguishes only two signals, the intermediate signal cannot exist. This is the remarkable feature of digital information. According to Wikipedia, historical digital systems are the written text, Morse code and etc. They are the serial sequence of restricted characters. They can be converted into each other. The alphabet can be converted into 1 and 0.

The above figure is the example of the conversion. The upper row represents alphabets, and the lower row represents corresponding binary digits according to the ASCII code. Why is the conversion possible? Each character of any kind of digital information has common features, which are properties of the natural number one. As I say in “What Is the Natural Number One?“, it is indivisible, invariable and equal to each other. These properties are the basic property of  digital data. However, there are some differences between digital data and natural numbers.

Digital data consists of multiple characters. In contrast, the natural number is the set of the natural number one only. Furthermore, we can add two natural numbers. However, we cannot apply the calculation rule to the ASCII code. Rather, 0 and 1 of the ASCII code are regarded as mere symbols. Especially, the digital data 0 and the number 0 are very different. Though digital data 0 is indivisible, the number 0 is divisible.

0=0+0+0+•••+0

Thus, the digital data and the number is different. Still, they can be converted reciprocally. Especially, as mentioned in “the concrete basis of the number theory“, the ordinal number has the basic property of digital data, which is the basis of the conversion of digital data. Therefore, the basic property of digital data is necessary for the interconversion of the digital data and the interconversion between the digital data and the number.

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