Let us suppose that a human being is software placed on hardware called a human body. The software has at least the level of OS (operating system) and the level of specific word-processing software which is to be acquired later. The former also exists in other living things and lets them act subconsciously. The latter may also exist in other living things, but in human beings its enormous operation obviously lets you bring into high-grade conscious activity.

All the living things on the earth can be regarded as the system of self-extension and self-reproduction destined to produce offspring, which maintains homeostasis of their inner circumstances while reacting to outer impetus. This is a biological demand for self-extension which is already performed even in the OS level of human beings. And in the case of the latter where human beings use languages consciously, the conclusion made by linguistics is said to be that the demand for self-extension appears as far as languages are used. Furthermore, that reflects the endlessness of languages and enhances impulse up to the limit of "world-recognition," "world-grasping," and "world-control." In other words, as far as human beings have word-processing software, you cannot help trying to practice "world-recognition," "world-grasping," and "world-control." As those three are closely related, let me use just "world-grasping" in this paper. And, although I will omit a detailed explanation, this may be a theory of modernism in a broad sense originated from humanism.

Then, how can you practice the "world-grasping"? The answer is by a language. Concretely speaking, by the extension of the language-world by the act of naming, and by a tautological deductive operation in the language-world following generative grammar. The former will result as the group of vocabulary which languages possess as langue. And the latter will result as an effective theorem of an operation, as philosophy (and religion and science and art). In this paper, from the above-stated premise, let us consider about the theory of the world-grasping especially from the standpoint of natural philosophy.

As present computer environment before you is an artificial one, it may faithfully reflect the system of the world-grasping by human beings. However, as the environment is also nature before you to which you have been thrown out without notice, it will also become the subject of natural philosophy.

In my case, I first bought a computer just as a tool for drawing pictures, so my encounter with the computer was the latter case, "nature before you." In other words, it was for me "a discovered new digital continent." And especially through the actual working process of CG (computer graphics), I have reached a conclusion that having a thorough knowledge of the essential qualities of the CG's two big opposing concept, "bitmap-mode" and "object-figure-mode," perfectly corresponds to the very effective previous theorem, not only in digital environment but also in art history and furthermore in the whole range of the world-grasping.

Let me first give you a rough sketch of why the theorem is so effective: As CG is, from the start, a technique for describing (=grasping) the world view with 0 and 1, the theory of CG has already directly connected with that of the world-grasping. And as it is a deduced result of genuine symbolic logic called programming, it has already been a basic theorem without any impurity. Furthermore, the essence of the opposition between two things dates back to the opposition between "atomism and idea-ism" in ancient Greece, and on the other hand it was a persuasive term for telling the present digital world. Generally speaking, thought history is always to be renewed according to the newest knowledge of natural history.

Now let me explain the new concept of opposition between two things in the level of CG's original meaning.

The bitmap-mode grasps the world as a gathering of minute color units. It is paint-type tools that treat the mode. In this mode, the world is given at first as a statical system of coordinates. At that moment, minute color units appear as obvious objects at each individual coordinate value. A unit is usually a same-sized square dot. In the initial stage, there appears a vacant world, which does not mean that "there is none," but that "there are white dots." (In the three-dimensional world, that means that "there are transparent dots.") Actual graphic drawing can be done by replacing the color attribute given to a dot with a different one. As that process can be done freely with any dot unit, it well influences on coloring by hand. But if you want to draw a circle using this mode, what you can get is only "an approximate circle" however cleverly you gather those square color dots. That means that the dot's jagginess has already existed at the data level. On the other hand, it is easy to make a wormhole in the circle. The reason is that a perfect circle did not exist from the start, and that the circle was only a gathering of dots which was possible to be edited. Namely, this mode originally has no conception of a form, and what it has is only a coloring action.

On the other hand, the object-figure-mode grasps the world as a form shown by a certain numerical formula. Draw-type tools treat the mode. In this mode, you have to make firstly a single topology-suface-form before the system of coordinates as the whole world using an equation with an equal mark. (As there exists no system of coordinates,) any numerical value is a variable, and it is originally dynamic. The screen shown in the initial stage is not the whole world, but it is nothing but a window through which observers peek who are living in the coordinate world. Therefore, if there is no equation, there exists nothing but a situation of "there is none" which is impossible to refer. Actual graphic drawing can be done by making or changing a single equation. For example, in order to draw a form of a circle, you just make an equation of a circle. This will be a genuine circle with no jagginess at the data level. But at the printout level, sometimes it is inevitable to have jagginess depending on its resolving power. And it is difficult to make a wormhole in the circle because you have to destroy the topological circle-equation in order to do so. As is shown in the above-stated basic form, theoretically coloring action by hand is impossible. The reason is that this mode has originally no concept of color; it has only the action of making forms. However, almost all draw tools are able to treat through a single window more than two topology-surface-forms at the same time, that is, to treat different worlds shown by more than two equations concurrently. In addition, they can give each specific color to each individual form, and they can also paint out the inside of a figure shown as an inequality area. It is this option that makes it possible to perform pseudo-coloring-by-hand.

Now let me interpret here about the opposition between two things. As is mentioned above, the strong and weak points of these two things are perfectly opposite each other. This fact will suggest that it is not the level of the matter that which is wrong or which is right. It is the two ways of the world-grasping, which becomes more effective by understanding both of them. For example, at the practical level, it is sometimes convenient to have paint tools with strengthened draw functions, or draw tools with strengthened paint functions. And if you practice the world-grasping using these two ways together as a theorem, the world will appear before you as a chimera of a compound of the two.

Setting aside the original meaning of the concept of opposition between two things in CG, let me show you some practical examples of the world-grasping by means of concrete oppositions between two things. Here I use only "bitmap" and "object" without sticking to the programming terms. And from the above-stated reason, a word "tautology" may be rather preferred to "practical examples."

[a] Atomism and Idea-ism

As for the opposition between two things in Greek traditional philosophy, there were atomism by Democritus and idea-ism by Plato. If you correspond an obvious minute color dot to an atom which cannot be divided any farther, and likewise a numerical formula to idea, that will become homologous with the "bitmap and object." Although atomism by Democritus was criticized of being unable to describe motion, the stationary state of the system of coordinates is rather the characteristic of the bitmap. Plato put idea of a chair higher than a real chair, and that is the same thing with the matter that the data of a circle made by draw tools is often more perfect than a circle printed out. From that matter, it is also possible to interpret that the system of the bitmap, which naturally accepts dots or atoms, takes an affirmative view of the world, and that the system of the object, which puts a high order to a numerical formula or idea, takes a negative view of the world. As Aristotelianism concluded atomism and idea-ism as mass and form, so it is not necessarily to have the alternative of the bitmap and the object.

[b] Chemistry and Physics

Chemistry tries to grasp the world from the viewpoint of material, and physics tries to grasp it from the viewpoint of a body. By the way, you can regard a red area, which was drawn as a gathering of red dots by paint tools, as red material composed of a gathering of red atoms. And a fan shape or a cone made by draw tools are the same objects (=bodies) as the fan shape or the cone. Therefore, "chemistry and physics" is homologous with the "bitmap and object."

Chemistry is a study which clearly approves the level of atoms, and it becomes atomic physics when you try to study the atom itself as an object. Likewise, a dot which is clearly approved by the bitmap is actually defined as an object in the level of a program.

[c] Plants and Animals

As both plants and animals are living things, their system is that of self-extension and self-reproduction as stated above. Now, let us remember the hypothesis of the origin of plants and animals: The origin of plants is considered to be a gathering of many unicellular living things which eventually became multicellular living things; and the origin of animals is considered to be a single cell which differentiated into a multicellular living thing in order to strengthen its function. From that, you can schematize as follows: A plant as a gathering of many cells is the bitmap; an animal as an enbodiment of a function-form is the object.

Actually, plants maintain homeostasis by taking root to the system of coordinates of land surface, and nourish themselves through chemical photosynthesis. As plants have no topological identity, getting wormholes is not fatal and you can perform a cutting or a division easily. On the other hand, animals, though they are free from the system of coordinates, hold homeostasis by maintaining topology of skin surface, and nourish themselves through physical ingestion. Getting injuries is often fatal, and having surgery is a serious matter. By the way, when plants want to move, they become objects called seeds, and when animals want to exchange gases, they use a bitmap organ called a lung which is composed of germinal cells. So the world is already a chimera.

[d] Venetian School and Florentine School

Venetian School which put higher priority to colors and Florentine School which put higher priority to forms appeared in the Renaissance period when humanism was a main stream, and they remained for a long time in the Western art history as a schema of the opposition between two things. The dogma of the former is what the bitmap advocates, and the doctrine of the latter is the very thing of the object. Let us survey it using keywords.

Tiziano of Venetian School regarded colors as a painting itself and thickly put colors as color material leaving powerful strokes of his brush. In respect of putting emphsis on material, later, Rodin took the similar style using clay in his "sculpture to be piled up." Rodin believed that the essence of sculpture lay in an unfinished state, the reason of which was his dislike of its surface being fixed as topology. Later in Venetian School, there appeared Seurat of pointillism who grasped the world-scape as a gathering of color dots, and there also appeared Fauvism which advocated the color revolution. After the war this stream produced minimalism which showed the repetition of colored basic forms.

On the other hand, for Leonardo da Vinci of Florentine School, a painting was a window which trickily reflected the topology's surface of models who were on the far side of the picture. Therefore, he gave higher priority to shading than an individual color, and put colors very thinly often leaving his works unfinished. The same Florentine artist Michelangelo gave higher priority to drawings than oil paintings, and established his own aethetics of "sculpture to be chipped," directly taking out topology's surface from marble saying that "I release the soul." Later in Florentine School, there appeared Cezanne who said that "You must recognize a landscape as a ball, a column, or a cone," and there also appeared cubism which advocated the form revolution. After the war this stream produced conceptualism which defined works using words.

[e] Others

"Polytheism and monotheism," "anarchism and totalitarianism," "harmonic compositional technique and line-like compositional technique," etc.

When you want to draw a circle by way of the bitmap, instead of thinking that "it is impossible to draw it, as it will become jaggy," fractionate dots infinitely, or raise the resolving power infinitely, and you will finally get a real circle. This is a rough idea of infinitesimal calculus. And the history of infinitesimal calculus since Archimedes, who dealt with the mensuration questions by putting two things side by side, that is, "the (bitmap-type) way of discovering and the (object-type) way of squeezing out," has turned out to be the history of the theory of the world-grasping which aims at the unity of the bitmap and the object. Although I will omit a detailed explanation, there are related interesting stories such as that Archimedes was one of the disciples of the atomist Democritus, and that Leibniz who was one of the originators of so-called infinitesimal calculus advocated monadology which can be said to be the atomism of spirit, and that Leibniz's discovery that the world was able to be described only by 0 and 1 actually establised the foundation of today's symbolic logic and present digital environment.

And likewise, I will not go deep into such subjects as the game of go whose real charm is to move back and forth between the bitmap and the object, and as music players who take out the object called melody from the Western scores which are written in a bitmap way.

Although idea-ism takes a negative view of the world, its attitute is of natural philosophy's just like atomism, as it affirms an ideological idea-world and bases the world-grasping principles on it. By the way, it was Socrates who thoroughly pointed out the ineffectualness of a tautological deductive operation in languages. Although Plato was one of the disciples of Socrates, in that point Plato's strength in thought made less progress than that of Socrates's. Socrates was death itself because he denied both this world and the next, while Plato praised the world after death averting his eyes from death itself. That bears a close resemblance to the relation between Dadaism and surrealism in art history of 20th century.

I have written about two ways of grasping the world as natural philosophy, but what I have written seems quite ineffective before the questions presented by Socrates who completely became tautology itself.

(Written in August, 1997)