The Biological Foundation of Mathematics 1

Any scientific theory cannot be absolute. Even Newtonian mechanics were corrected by physicists. The theory of relativity and quantum mechanics replaced it. There is no absolute truth in science. That is, all scientific theories are hypotheses. However, scientists have considered that mathematics is the absolute truth. Is this belief sure truth? Probably, if the human were the creature of God, mathematics could be the absolute truth, because it is a product of the human brain. However, the molecular biology provides many evidences, which support Darwin’s theory of evolution (1). Now, most biologists accept his evolutionism.  So, they consider that species have evolved by natural selection and random mutation.

The evolution usually chooses the ad-hoc solution. Surviving for the time being is important for a living thing. Necessarily, the structure of the human brain is the great piles of ad-hoc solutions. It is not elegantly designed by the great engineer. The pioneer molecular biologist François Jacob said “Evolution is a tinkerer, not an engineer (2).” David Linden described in The Accidental Mind that the human brain has the primitive systems in our distant evolutionary past (before mammals) and that have been supplemented by newer, more powerful structures. Furthermore, Dean Buonomano described in Brain Bugs as follows:

Human beings, of course, not the only animal to end up with brain bugs as a result of evolution’s kludgy design process. You may have observed a moth making its farewell flight into a lamp or the flame of a candle. Moth uses the light of the unreachable moon for guidance, but the attainable light of the lamp can fatally throw off their internal navigation system (3). Skunks, when faced with a rapidly approaching motor vehicle, have been known to hold their ground, perform a 180-degree maneuver, lift their tails, and spray the oncoming automobile. These bugs, like many human brain bugs, are a consequence of the fact that some animals are currently living in a world that evolution did not prepare them for.

When the human brain cannot be trusted, what should we trust? Descartes tried to answer this question. He doubted everything in DISCOURSE ON THE METHOD. Surely, all our experiences during the waking period can be replicated in dreams. Moreover, we cannot distinguish them. Hence, all realities may be illusions. However, Descartes described ” whilst I thus wished to think that all was false, it was absolutely necessary that I, who thus thought, should be somewhat; and as I observed that this truth, I think, therefore I am (COGITO ERGO SUM), was so certain and of such evidence that no ground of doubt.”  His statement is  the starting point of all science. The surprising point of it is the independence from the brain bugs. Even if all sensory inputs are illusions, it is true.

Why could it have the surprising universality? I shall consider profoundly. Firstly, the important premise of  it is the unity of the self, which depends on the indivisibility of a human. If a man is divided, probably he will die. Even if he survived, he lost a part of his body. However, he cannot be divided into two persons. Similarly, animals cannot be divided. Although many plants are divisible, the cell is indivisible. As I mentioned in A Life Is the Original Form of the Natural Number One, this principle is due to the unity of a life. Secondly, the important feature of Descartes’s statement is the easiness of acceptance. Everyone thinks that it is applied to oneself. This means that the self has common properties. Since all human beings are 99.9 percent genetically identical, naturally the basic structure of the self is constant. Probably, the common structure of the human self is the base of declaration of Descartes.

However, the declaration of Descartes is based on the language and the logic. When we consider the self of an animal or a human, who don’t have the ability of the language, we need the more universal definition of the self. German psychiatrist Jaspers defined the self-awareness clearly in general psychopathology (4).

 Jaspers lists four formal aspects of self-awareness: the feeling of activity, i.e. the awareness of being active, the awareness of unity, the awareness of identity, and the awareness of being distinct from the outer world.

Jaspers’ definition of the self is practical in psychiatry. The most severe state of the schizophrenia is called the catatonic stupor. When a schizophrenic patient falls in it, he cannot move, talk and eat. Because his self is disturbed, his ability of the movement is lost. So, Jaspers’ definition of the self is applicable to the schizophrenic, who cannot speak the language. As pointed out by Vittorio Gallese and Francesca Ferri, Japers’ self contains the bodily self, which might be the base of the motion of the human body.

Firstly, when a human wants to move, he must be active. Secondly, if the right side and the left side of a human body moved to opposite directions, the human would be divided. Hence, the unity of the whole body is necessary for the motion. Thirdly, when a human walks forward to take a food, he has to move forward consistently. That is, he, who found a food, is identical to himself, who walks toward food. Thus, the identity of the self is required for the coherent　movement. Fourthly, in order to exercise correctly, a human must recognize the boundary between oneself and the external world. Therefore, the intact self defined by Jaspers is required for the movement.

This principle can be applied to not only animals but also unicellular organisms. Especially, the paramecium has been well studied. When a paramecium swims to a direction, it moves all cilia systematically. Even if there are foods and blockades, the paramecium will choose the most appropriate direction. It seems that  the paramecium has the intact self defined by Jaspers. Furthermore, he defined the self so that the intactness of the self could be judged only by the objective observation. Hence, we have no choice to accept that the paramecium has the self defined by him.

Paramecium

Because the self defined by Jaspers is conserved from paramecia to human beings, the basic structure of the self is identical. The basic part of the self is invariable and equal to each other. Furthermore, the self is indivisible. While, 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.” Then, we can regard the basic structure of the self as the prototype of the natural number one. The natural number one is the foundation of all science.

References

1.  Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P. Molecular Biology of the Cell 4th ed. New York, Garland Science; 2001 How Genomes Evolve
2.  Jacob F. Evolution and tinkering. Science. 1977; 196: 1161-66
3. Dawkins R. The God Delusion. New York, Bantam Press; 2006
4. Vittorio G, Francesca F. Jaspers, the Body, and Schizophrenia: The Bodily Self. Psychopathology. 2013; 46(5): 309-19