A Life Is the Original Form of the Natural Number One

October 14, 2013 1 Comment

The modern science began from the statement of Descartes: I am thinking, therefore I exist. He said in Discourse on the Method as follows:

Lastly, I decided to pretend that everything that had ever entered my mind was no more true than the illusions of my dreams, because all the mental states we are in while awake can also occur while we sleep and dream, without having any truth in them. But no sooner had I embarked on this project than I noticed that while I was trying in this way to think everything to be false it had to be the case that I, who was thinking this, was something. And observing that this truth I am thinking, therefore I exist was so firm and sure that not even the most extravagant suppositions of the sceptics could shake it, I decided that I could accept it without scruple as the first principle of the philosophy I was seeking.

His statement means that anyone cannot deny the existence of oneself. The premise of his statement is the unity of the self. That is, the self has properties of the natural number one.

Eqn286

The above equation is the starting point of all science. Then, I consider more deeply.

What is the natural number one? Ancient Greeks quested this problem most profoundly since the dawn of history. There were great discussions about this issue in Ancient Greece. Among these arguments, Plato described three important properties of the natural number one in the Republic. Socrates said “there is a unity such as you demand, and each unit is equal, invariable, indivisible.” The natural number one has these three properties.

Next, I shall compare the self to the object with respect to three properties of the natural number one. Firstly, any object can be divided. Even, a diamond is crackable. Secondly, any object is not eternal. Geographical features of the geosphere have always changed through the history of the earth. Even, continents moved. Thirdly, there is no pair of objects, which are completely equal to each other. In contrast, the self has properties, which are close to  the natural number one. Firstly, even though there are various people on the earth, everyone is a human. This is the basic principle of democracy. Everyone is equal in the sense that we identify everyone as a human. That is, humans instinctively regards that selves are equal to each other. Secondly, a human usually keeps ego identity from birth to death. That is to say, the self of is invariable. Thirdly, the self cannot be divided. If a self of a person is disturbed, the person might have a mental illness: schizophrenia or multiple personality. A self of a human, who is mentally healthy, is indivisible. Therefore, the self has similar properties of the natural number one.

Phylogenetic_tree.svg (1)

I shall pursue the origin of the similarity between the self and one. When I phylogenetically trace back to the origin of the self, I reach the last common universal ancestor. Most biologists believe that life on Earth arose only once. Hence, all lives are descendants of the first single cell. The basis of the dogma is as follows. All living things are composed of cells, which have common features. All cells have DNA, plasma membrane, cytoplasm and ribosomes. Additionally, the  basic biochemical system is identical in all lives. DNA preserves genetic information. Next, it is transcribed  into RNA. Subsequently, RNA is translated into the amino acid sequence of the protein. Especially, The most astonishing fact is the universality of the genetic code of all lives. Genetic code is the code, which is required for the translation of the genetic information to the amino acid sequence. Thus, the human insulin gene can be put into E. coli genome. Now, human insulin is made by E. coli.

When we accept the universality of all lives. we can abstract the equality of all lives. Also, basic featureｓ of lives have been invariable since the arising of the first life. Furthermore, if a cell is divided by force, the cell will die. A cell is indivisible. The death of a life is the only irreversible process on the Earth. Therefore, a life is the original form of the natural number one.

Filed under Philosophy Tagged with , , , , , , , , ,

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”

Filed under Information Tagged with , , , , , , , , , ,

The Origin of the Natural Number One

June 3, 2012 Leave a comment

The natural number one is the most fundamental concept of mathematics.  Certainly, the number anyone knows very first is one, which is equal, invariable and indivisible.  Moreover, as I say in “Properties of Digital Information“, these properties are the basic property of digital data. Let us consider the origin of these properties. Firstly, Plato says in Phaedo as follows.

But what would you say of equal portions of wood and stone, or other material equals? and what is the impression produced by them? Are they equals in the same sense as absolute equality? or do they fall short of this in a measure?
Yes, he said, in a very great measure, too.
And must we not allow that when I or anyone look at any object, and perceive that the object aims at being some other thing, but falls short of, and cannot attain to it-he who makes this observation must have had previous knowledge of that to which, as he says, the other, although similar, was inferior?
Certainly.
And has not this been our case in the matter of equals and of absolute equality?
Precisely.
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?

So, we have never seen absolutely equal objects. Hence, we might be inherited the concept of the absolute equality from our ancestors.  However, probably equal objects have never existed. If we want to seek for the origin of the complete equality, we must trace back to the evolutionary tree without limit. Therefore, I think that life might have the built-in equality.

Let us consider the drastically simplified life.

The above figure represents the simplified cell. A circle represents a cell, and capital letters represent the base sequence of DNA. The left circle represents a cell with DNA, and the right circle represents a cell without DNA. Almost all features of a cell are encoded in DNA. However, the most remarkable feature of  life might not be encoded in DNA. It is the irreversibility of the death of a life. When any life dies, it cannot revive. This is the only absolutely irreversible process, which we know. As mentioned in “Natural Selection Protects Information against Entropy“,  this is the necessary property for preserving information. Another important fact, when a cell dies, its whole body is dead.

Next, let us consider a thought experiment. If we removed DNA and products of DNA from a cell, there would be an empty container, which consists of the lipid bilayer. The function of it is the separation of the inside of the cell from the outside.  That is, it gives unity to a cell.

According to the cell theory, Virchow said that every cell originates from another existing cell like it (Omnis cellula e cellula). Hence, common properties of every cell might be inherited from the first cell on the earth. Among them, the property of this hypothetical container is important. It is identical to the natural number one. Plato described “there is a unity such as you demand, and each unit is equal, invariable, indivisible” in Book Ⅶ of the Republic. These three properties are the basic property of the natural number one.

Let us consider each property. Firstly, the indivisibility is the most remarkable feature of life.  A cell can be divideｄ into two cells only in the final stage of the cell division. Usually, a cell is indivisible. If a cell is divided severely, it would die.  If it is cut off a part, it would repair the part. This principle can be applied to a human being. If a man is divided, he would die or survive with serious injury. However, one human being is never divided into two human beings. Thus, we can regard one generation of a cell corresponding to an entire life of a human. So, both a human and a cell correspond to the natural number one.

Next, let us consider the equality and the invariability. Because the difference of cells is due to the variety of DNA, the common feature of all cells might be inherited from the first cell. Especially, properties of the hypothetical container might have been invariable. It is necessary for the unification of the whole cell. Furthermore, if it is broken, the cell dies. If we consider the abstract container, it is indivisible, invariable and equal to each other. Therefore, the natural number one is abstracted from properties of the cell.  If you want to read the more detailed description, please read “What Is the natural Number One?”

Filed under Number Tagged with , , , , , , ,