Significance of "Digital Nendo" in Visual Art History

By Hideki Nakazawa (multimedia artist)


"Digital Nendo," a 3D tool, was recently published by Ask Koudansha Company, and the reason I named it "Digital Nendo" (Japanese "nendo" means "clay") is that I wanted to emphasize its being a material. The world's first bitmap 3D software, "Digital Nendo," can freely define the 323=32768 3D-section unit, the fact of which means that we now have a gravity-free and topology-free 3D world for the first time in the world. That is really an epochal and significant event which could never possibly happen with conventional object-figure-mode 3D tools. And, in addition, it is very significant as well in the art history, that is, in the long-lasted opposition, "Venetian school vs. Florentine school." I, Hideki Nakazawa, who invented the software and designed it, will write about it.


  • 1. What Motivated the Invention?

  • 2. Bitmap Concept vs. Object-Figure-Mode
  • 3. Two Conspicuously Opposite Figures in Art History
  • 4. World's First Gravity-Free and Topology-Free 3D Sensation
  • 5. "Futurism" of Digital Nendo (Introduction of the Time-Axis)

  • 6. Pseudo-Cubes Made by Fukan-Mode

  • 7. Sense of Possession in the Definition System

  • 1. What Motivated the Invention?
  • When I first thought of the gist of this software, I had the least idea that I myself would become its developer, because it was so ordinary and convenient an idea that some other person may surely already have actualized it. In 1991, five years ago from now, I drew pictures every day in the style of bitmap-jaggyish "BAKA CG," around when some one said to me, "Use a 3D tool. It's so easy to use." So I used then main-stream 3D tool, "Swivel 3D," for the first time, which was the motivation of my engaging in the software. Frankly speaking, "Swivel 3D" was far from to be easy-to-use. You can make using it such objects as a ball or a cube very easily, but once you want to make some indeterminate forms like stool, it turns out very difficult-to-use. Instantly when I felt its inconvenience, I realized that "Swivel 3D" was a tool based on the draw-system concept in the plane graphic field. But, quite contrary, what I first imagined instantly from the word of the person who said that a 3D tool was so easy to use, was a 3D-version of a bitmap-type paint tool like MacPaint.

    "Somewhere in the world there must exist such bitmap 3D tools as I have in mind. There surely must exist some of them, as even I myself thought of it so easily. Anyway what is so clear is that 'Swivel 3D' is never the one of them. . . ." I said such things to myself at that time. After that, all people but one whom I asked about it answered they didn't know. The only person told me about a similar concept called voxel in the field of fluid analysis but he added that there were no graphic-use tools with which you could edit without restriction. So far I understood, and yet I still thought that it was unbelievable that there existed no bitmap 3D graphic tools in the world, and that what it would be like if there existed such kind of tools in the world. And finally I came to convince that it would be possible to actualize my idea, a simple one. As a bitmap in a plane is represented by a section, so a bitmap in the third dimention, by a 3D section. And you will perhaps be able to make an object like stool easily, although objects created may become a little jaggy. You might feel unsatisfied with calculating speed, but, even if what you can handle is such a small 3D world as a16-dot cube, wouldn't it seem interesting? In order to designate individual cubic dot in the third dimention, you can input the x-axis and the y-axis using a mouse with your right hand, and your left hand can input the z-axis by touching a key board.

    Such an idea occurred to me so soon, but I didn't do anything more as I was too busy in attending to my business as an artist.

    Last year, early in 1995, I got an offer of some CD-ROM work from Ask Kodansha Company. Instead of doing some CD-ROM work, I suggested the idea of my application tool, "Digital Nendo." As such a simple, ordinary, and non-special idea has not actualized yet in this world, I decided to develop it myself. Programming was undertaken by Simple Systems Co. And now here is the product, "Digital Nendo."

  • 2. Bitmap Concept vs. Object-Figure-Mode
  • Now let's consider the most particular characteristic of "Digital Nendo," that is, a bitmap concept, by contrasting it with the object-figure-mode which is a directly opposite one. Some people might think that a bitmap, if given higher resolving power, can not be different from the object-figure-mode. But it is wrong. The opposition between both of them is a fundamental one lying in our concept of the world. By the way, let me reconfirm special terms used here: A "paint tool" is a tool for drawing graphics which is based on the bitmap-concept. A "draw tool" is a tool for drawing graphics which is based on the object-figure-mode.

  • Section vs. Equation (How to Obtain the World)

  • The world consists of a whole and a part. In order to recongnize and obtain the world, there are two ways.

    Firstly, you consider a whole as a complex unity of parts, and describe every part precisely, and you naturally obtain the whole as a complex unity of parts. To regard a bitmap as a section is just based on the idea, and a "paint tool" is the very one with which you can obtain the world by painting each section. Now let's think of a big circle drawn based on that concept. The circle will apparently seem like a circle but it is nothing but a united sections. So, seen carefully, it is jaggy, but, conversely speaking, you can make any worm-holes in it so easily and simply.

    The second way to obtain the world is like this: you consider a part as a part of the whole. It is the way that once you describe the whole nature precisely, you can guess the nature of each part from that of the whole. To regard object-figure-mode as an equation is just based on that idea, and a "draw tool" is the very one with which you can obtain the world by directly making an equation of describing figures. A circle drawn based on that concept is a perfect circle, which you cannot examine by reducing it. So, even seen carefully, it is not jaggy, but, conversly speaking, when you want to make a worm-hole in it, you have to rewrite algorism of the whole circle, which is very troublesome and inconvenient.

    You can reach both of the methods through God's magic, the concept of infinity, the idea known as infinitesimal calculus. But, to tell the truth, its ability is limited only in an acquisition system called scanning. In other words, it is limited in the case of forcibly drawing toward us the world which naturally does not exist around us, by making a section-unit minimum and resolving power maximum. (It is evident from the fact that some people spontaneously think that they can approach "truth" by making resolving power higher.) So let's stop thinking of such an acquisition system and turn toward a definition system which outputs the world existing around us as it is. In the definition system, whatever defined as a section is to be always a section and whatever defined as an equation is to be always an equation. It is the bitmap jagginess that is important, so such trial to delete jaggy parts is nothing but absurd. Conversely speaking, in the object-figure-mode, however high resolving power a printer has, it always outputs just "an approximate figure." You now know the striking conceptual difference between the bitmap-mode and the object-figure-mode.

  • Material vs. Body (or Atomism vs. Idea-ism)

  • The two conspicuously opposite concepts can also be explained through a dialogue, "material vs. body." A material is cognition of the world seen from the viewpoint of atomism. A body is cognition of the world seen from the viewpoint of idea-ism. Therefore, you can have an explanation as seen below.

    A bitmap-concept which regards a section as a minimum unit of the world, and the world as a gathering of sections is fundamentally the same with a Dimokritos-like concept of atomism which regards an atom as a minimum unit of the world, and the world as a gathering of atoms. In atomism, the gathering of atoms is called a material. A material does not have any particular formal attribute but has an optical scientific attribute. For example, it is nonsense to consider the form of material called bronze, but it is sure that its color is bronze. Therefore, you can regard the gathering of sections as a material and, essentially, bitmap-pictures as the gathering of colors. By the way, I chose a word "nendo" (which means "clay") for my software, "Digital Nendo," to emphasize its being a material. Or if it was called "Analogy of color nendo", it would have been more precise.

    On the other hand, the concept of the object-figure-mode, which regards an equation as the world's first principle and as that everything can be solved by an equation, is fundamentally the same with the concept of an ancient Platonic idea-ism which first recognizes the dimention of the idea and considers that all the real world originates in the nature of the idea world. In idea-ism, idea takes the figure of a body. (A cup's idea takes the shape of a cup.) And a body does not have any particular optical scientific attribute but has a formal attribute. For example, it is nonsense to consider the color of a body called a cup, but it is sure that it has a certain form to contain water. Therefore, you can regard an equation as a body and, an object-figure-mode drawing as a appearance of a form. By the way, it goes without saying that an object means only a body and the level of the essential nature of a body's molding is diferrent from that of its surface coating, as you can analogize from the fact that draw-tool functions such as a color-specifying function or a texture function are nothing but added functions after molding.

    These two terms used in "material vs. body" are just the same with Aristotle's two oppsite concepts, "matter (hyle) vs. form (eidos)." If you review the two concepts of atom's and idea's very carefully, you will understand more clearly the meaning of a unit-section which the bitmap-concept (optimistically) takes as self-evident, and the meaning of an equation which the object-figure-mode (pathetically) takes as a premise.

  • Plant-tic vs. Animal-tic (Coordinate System and Topology)

  • Now let's turn to one of the theories of the origin of multicellular living things. It is said that the origin of plants can be "the gathering of many unicellular living things which started to act as if it were a single living body," and that the origin of animals can be "that a single living body of a unicellular one differentiated into a multicellular living thing." If you remember the theory, you can also think the opposition of "bitmap concept vs. object-figure-mode" from the viewpoint of the theory, "plant-tic vs. animal-tic."

    The identity of being a living thing is said to be the maintaining of homeostasis (constancy). Plants maintain homeostasis by their most conspicuous characteristic, that is, being fixed to the system of coordinates. Not by topologically completing as a single living body.

    On the other hand, the most conspicuous characteristic of animals is that they are not fixed to the system of coordinates. They maintain homeostasis by topologically completing as a single living body.

    By closely examining which identity a living body takes, the system of coordinates or topology, you can conclude as follows: In the viewpoint of a plant~bitmap-concept, there is no concept of a background, and all the "canvas=the whole world," which is shown by the coordinates position, is considered to be filled with "units of sections=materials." Plain canvas of the two-dimentional paint-tool does not mean that nothing is there but it is a gathering of "white sections." In the case of a 3D paint-tool, "Digital Nendo," a vacant world is considered to be filled with "transparent sections." Just think of an artificial flower which "blooms" when immersed in water. Transparency is also one of colors. In bitmap pictures, it is impossible to cut out the foreground from the background, and similarly, it is impossible to take out a plant as a simple substance, and the only way is to take it out with its flowerpot, that is, with the coordinate system. You can see that the flowerpot is always filled with soil.

    In the viewpoint of the animal~object-figure-mode, there is no concept of the whole world, and "a single and completed topology is the all." In other words, a draw-tool's window is nothing but an eyehole, and so, when you only see a part of a ball, you can just change the visual point in order to see the hidden part of it. To understand it more easily, please think like this: Each individual file does not have any meaning but an animal's cage, and each individual figure is gathered into one by chance and saved in a file. The meaning of "topology is the all = no restriction except topology" is, conversely speaking, that you can enlarge, reduce, transform, and rotate an object with a draw-tool, as long as you don't change the topology. An animal's identity will not be changed even if it stretches itself or turns itself. That point differs very much from the nature of a fixed-coodinate paint-tool which cannot enlarge, reduce, transform, nor rotate an object but only in a false way (except enlargement by integral times and rotation by 90 degrees). Changing topology with a draw-tool, however, is very difficult, and you need a surgery-like work just to make a worm-hole, which is so easy a task for a paint-tool. That is the same matter as that plants are so topology-free that they can easily grow from a cutting or a grafting, or even sprout out from a rootstock made by dividing themselves, while animals cannot do anything like that.

  • Concerning the Chimera-tic World

  • Hitherto I have explained the world from the viewpoint of those two opposite principles for convenience, but, actually, we cleverly use the two things in different ways on the case-by-case basis in order to recognize and treat the world. In other words, the world is interpreted as a chimera-tic thing.

    For example, an iron kettle is usually an object which "can contain water and can be carried with its handle," but in the case when a war breaks out and you find yourself in dire need of resources, the kettles will be collected as a material of iron. Likewise, you conveniently recognize the same object, that is, in some time as a body and in some other time as a material.

    Similarly, a paint-tool is fundamentally based on the bitmap-concept and on the idea which regards all the sections equal. But, its rasso function regards a certain specified-and-encircled group of sections as like a single object and moves it or changes its shape, which is, as it were, a draw-type function. (It actually is a function that cuts out an object with the coordinates, like a flowerpot, and changes its direction or moves it.) On the other hand, a draw-tool is fundamentally based on the object-figure-mode and on the method of making a single simple figure from a few specified dots. But, its free-hand function is, as it were, a paint-type function, because its purpose is to get a figure which is algorismically hard to understand by recognizing many specified dots through continuous handwriting movement of a mouse. (What is a free feeling for your hand is an opposite feeling of free for topology, that is, it is a function that hinders an animal to go back to its normal topologic form, as if by putting excessive handcuffs and shackles on it.) As seen above, the tools already resemble our concept which tends to recognize and treat the world as a chimera (regardless whether it is good or bad). I here explained that all the functions of the paint tools are not necessarily based on the bitmap-concept, and all the functions of the draw tools are not necessarily based on the object-figure-mode.

    In addition, it can be said that the world is already a chimera of the two before you recognize and treat it. For example, a plant's seeds are, as it were, like animals, as they have a complete topology without being fixed to the coordinates. And an animal's lung is, as it were, like a plant (planted in a pot), as a lung itself and air complicatedly entangle themselves. As things are such, that is a reason why I put "plant-tic vs. animal-tic" instead of "plant vs. animal" in the previous chapter. If you think this tendency phiolosophically, you can go as far as that "you can not completely divide an iron kettle into a genuine kettle form and a genuine iron material." In short, you can say that the world can not exist from the start but just in the form of a chimera. And that will finally reach the area of dividing spirit from flesh.

    Therefore, conversely speaking, the opposition of two things like "the bitmap concept vs. object-figure-mode" or similar ones seen above can be said to be the two opposite conceptions produced in order to explain the originally chimera-tic world by all means without doing "epoche," which probably is opposite of the recent tendency which thinks that nothing can be obtained from the opposition of two things. The concept is not the one that takes a chimara as a chimera itself, but the one that takes it after reducing it into two things. And, in addition, the opposite mode of two things (which will fill the world) is not completed yet, as seen in a vacant area of a 3D bitmap-tool which has been left untouched.

  • 3. Two Conspicuously Opposite Figures in Art History
  • If the invention of perspective can be a big event in art history, art itself can also be the result of a continuous quest for the way of how to make the world visual and how to describe it. The opposite figures seen in the previous chapter, "Bitmap Concept vs. Object-Figure-Mode," is the very two forms of describing the world in this computer generation. Its origin, I think, may date back to the opposite figures of "Venetian school vs. Florentine school" which had constantly formed the Western art history since Renaissance. Therefore, in this chapter, I also intend to re-grasp the art history more clearly and precisely, which is considered to be a chimera of the tradition of Venetian school and that of Florentine school, using the opposite form seen in programming terms, "bitmap concept vs. object-figure-mode." First let's survey the Western art history from that point of view, and next, let me refer to "some fallacy" about the dimention which was made by analog days people.

  • Venetian School vs. Florentine School

  • Venetian school is an art school born in Venice in Italy, in the golden age of Italian Renaissance, whose representatives are Giorgione and Tiziano. Venetian school expressed their idea by grasping the world with colors, and by thickly putting them on the canvas in free styles. On their canvas there certainly exist some forms, but the main quality is their colors, and so, if you think their pictures beautiful, it may be just because of the beautiful luster of the colors which were put there. You can see powerful strokes of his brush in Tiziano's works in his later days, and it is the true material of colors seen in his brush strokes that was the essence of art for him. It goes without saying that his concept was almost the same with that of the bitmap.

    On the other hand, Florentine school is an art school born in Florence in Italy, in the golden age of Italian Renaissance, whose representatives are Leonardo da Vinci and Michelangelo. Florentine school expressed their idea by grasping the world with forms, and they composed their art using many sketches of forms obtained from such studies of the dissection of human bodies. On their canvas there certainly exist colors, but the main quality is their forms, and so, if you think their pictures beautiful, it may be just because of their full knowledge of how to express the topology of a model's surface as if it were real. The techniques invented by Leonardo da Vinci, such as chiaroscuro technique (the gradation treatment of light and dark parts in a picture by thinly putting colors) and sfumato technique (the treatment of gradating outlines), can even be said to be a trick of making colors perform as forms. And furthermore, it is the illusion of forms made by the trick that was the essence of art for him. In some way, it can be said to be the object-figure-mode.

    With the change of times, the opposition form of "Venetian school vs. Florentine school" has been reborn many times until today each time as a new art ideology underlying the art history. The opposition form seen in "Romanticism vs. neo-classicism" in modern ages, and "Fauvism vs. cubism" in recent times, are just the examples.

    For example, Matisse, a representative artist of Fauvism, which is called the revolution of colors, used from the start the technique of pointillism which originated in neo-classicism. Pointillism which grasps the world as the gathering of light and expresses it by putting colors' dots thickly on the canvas easily reminds you of the bitmap concept. Matisse's Fauvism was born by putting colors' dots more emphatically.

    On the other hand, cubism, which is called the revolution of forms, is said to be born by what Cezanne said, an artist of post-impressionism: "You must recognize a landscape as a ball, a column, or a cone." Those words of his seem to be the very copy for explaining the object-figure-mode. Cubistic pictures painted by Braque or Picasso were born through really actualizing his words.

    And furthermore, the opposition form seen in "minimalism vs. conceptualism," which appeared in the post-war American modern art world, may have originated from those of "Venetian school vs. Florentine school." In short, the former is the ism which protrudes toward the anonymous material, and the latter is the ism which protrudes toward an idea of the non-material. The former, Donald Jadd is one of its representatives, has such a characteristic as monotonously repeating the same color-plane and the same unit of a cube, which, as you understand, is really a big-dotted bitmap. As for the latter, let me introduce a work by Joseph Kosuth, one of its representatives. What is important for him is the visualizing the ism itself, and what you see in his work, "One and Three Chairs," is composed of a panel on which the definition of a chair is written, and a photograph of a chair, then three real chairs put side by side. And what you should pay attention here is that Kosuth made a sharp distinction between a body and a word (an equation), although both of which are fundamentally the same. On the one hand, he put higher priority to a word than a body, while he mixed a body and material, which is the reason why such an interpretational confusion arose as minimalism is to be set in the previous stage to conceptualism. (Actually, there seems to be no hierarchy between them.)

    In France in the same age, there arose a "support/surface" movement. The movement, which is considered to be reductionism as a whole, is an interesting example having the two opposite sides, that is, one is the side of "surface," a type of the bitmap concept, and the other is the side of "support," a type of the object-figure-mode. Claude Viallat, a representative of the former, displays a canvas-size pattern of horsebean which has lost its support, and Daniel Dezeuze, a representative of the latter, starts by displaying the support which has lost its canvas, and then later displays such things as a fence which expands and contracts like an animal, or a work of walls which lean at any angle. You can find here a different type of " minimalism vs. conceptualism" which was born in America. And the side of "support" in this case is a body rather than a word, which is in accord with the form of the "material vs. body" shown above.

    In Japan in the same age, there arose Japanesque schools such as "thing school" and "Japan-concept school," both of which can be interpreted as another opposite cencept in accord with the two opposite figures seen in "minimalism vs. conceptualism" and even in "Venetian school vs. Flolentine school." Nobuo Sekine, who belongs to "thing school," succeeded in leaving plenty amount of indeterminate-form of clay in the gallery (Vacant layer--Clay), which was the result of his having interest in topology. Yutaka Matsuzawa, who belongs to "Japan-concept school," after performing "a ritual of extinguishing material," at last made a work which is just announced by words that "Look there! Look at just that white circle," which is a work just displaying an object-figure-mode equation. The titles of Matsuzawa's works, such as "White-Circle Fundamental Picture," or "Invisible Circle," may well represent such essence of the object-figure-mode as what you can print out is only its approximate figures.

    As Japanese "thing" means both material and an object, so "thing school" sometimes chimeratically displays not only material but also an object just like reductionism. The characteristic of the bitmap concept is an optimistical self-evident unit of sections, and in Japan, Kishio Suga, for example, intentionally used such a frigile section unit as paraffin, and Katsuro Yoshida's work which was made of lumber, a rope, and a stone, is no more of the section unit but rather a collage, a mixture of objects made of different materials. (By the way, the "collage" used here is analogous to the form, "Put animals in a cage and let them leave as they are," invented by cubists, who are on the side of the object-figure-mode, and Robert Raushenberg, who invented a special collage called conbine-painting, declared that he learned the way of just putting objects nonchalantly side by side, from Leonardo da Vince's pictures.) If the number of section units becomes too few, the section units are no more self-evident and they will take object-like appearances, that is, chimeratic appearances. (The individual section unit of "Digital Nendo" is, in fact, defined by a draw-concept.)

    Though such a thing happens as you cannot make a distinction between the two of them at the fundamental point, it is still clear that the opposition form of "bitmap concept vs. object-figure-mode" has always been a basic idea in the art history, borrowing the form of "Venetian school vs. Florentine school." And you will notice that the form of "bitmap concept vs. object-figure-mode" in this digital days is more than a programming term and that it should be more highly recognized from the viewpoint of the art history. Furthermore, you will understand that the 3D bitmap paint-tool invented by myself, which is based on a universal idea, was born in order not only to be used for programming but also to bury the vacant place in the art history. And, as the result, it has turned out to induce a new state of things, which will be exlained next.

  • Analog Day's Misunderstanding of the Dimention

  • "Digital Nendo," which is fundamentally a tool based on a universal idea, has, on the other hand, come to display world's first totally new physiological sensations (that is, "gravity-free" and "topology-free" sensations which will be explained in the next chapter) and to correct the misunderstanding of the dimention which human beings have long conceived. Following the context, let me explain the analog day's misunderstanding of the dimention first from the viewpoint of the Western art history.

    In the context of the Western art history, the misunderstanding is, in short, that, "material~Venetian school" has often been considered as the two-dimentional characteristic, and "body~Florentine school," as the three-dimentional one. In other words, as they are expressed by using color-material called paints, the various natures of the "material" seen above (that is, the way of thinking of the bitmap concept), are pictures, or, two-dimentional things, and, as they are expressed by cutting a form out of marble, the various natures of the "body" seen above (that is, the way of thinking of the object-figure-mode), are sculptures, or, three-dimentional things. Such interpretation has been used in the tendency trying to expel illusion of magic-like things from the pictures, especially after artistic works in modern times came to tend to be those of reductionism. Nowadays, in digital times, you know that you can apply the both ways of the bitmap concept and the object-figure-mode in equal manner to the both of two-dimentional and three-dimentional ones, but, in analog days, such way of thinking was thought to be impossible.

    Let's think of the form of "Venetian school vs. Florentine school" once again, following that way of thinking seen above. By doing so, you will understand such a misunderstanding in analog days was not so unimaginable.

    Firstly, if the essence of "Venetian school" exists in the second dimention, you can easily understand those plane pictures by Tiziano. He pursued the truth of colored material called paints as if it were of the bitmap concept. And that is a situation which, if considered from the viewpoint of a digital graphic tool, is equivalent to the first bitmap two-dimentional paint-tool called "MacPaint."

    Next, if the essence of "Florentine school" exists in the third dimention, you can also easily understand Michelangelo's sculptures, as he hierarchically thought that pictures were nothing but rough sketches for sculptures, and that it is in sculptures that truth existed. He pursued the truth of a body cut out of marble as if it were of the object-figure-mode. He, a neo-Platonist, had an idea of releasing the form of "soul=body" from a prison of a hard block of marble, which also fits well if seen from a spiritual level. And that is a situation which, if considered from the viewpoint of a digital graphic tool, is equivalent to a once-popular object-figure-mode 3D draw-tool called "Swivel 3D."

    Now, let's take up Leonardo da Vince who belongs to Florentine school, which gave higher priority to pictures than sculptures. As above stated, he pursued the trick-nature of material called paints, that is, he did not pursue the truth of it. He had a great interest in the magic-like illusionism which he produced from material called paints using a technique of erasing its material-ness. If seen from the viewpoint of a digital graphic tool, his illusionism corresponds to a two-dimentional paint-tool, "Photoshop," whose main function is to erase the sections as much as possible, staying in the bitmap concept. "Photoshop," in some sense, can be said to be a paint tool for "procuring" the object-figure-mode.

    I wrote, in a previous chapter, that "Florentine school" is, in a sense, of the object-figure-mode, but, more strictly speaking, it probably should be like this: "The plane pictures of 'Florentine school' correspond to an object-figure-mode 3D draw-tool, 'Camera Function,' for the purpose of the two-dimentional projective technique." "Photoshop," as a tool for "procuring," literally aims the function of a camera. It is true that a conventional camera function in 3D tool is to let a program do automatic calculation of "an object-figure-mode 3D draw-tool, 'Camera function,' for the purpose of the two-dimentional projective technique," but in that case it is you that regulate those various magic effects to some direction, with some intention, using "Photoshop," which can be considered to belong to the two-dimentional graphic-tools. I mentioned above that Leonardo da Vince gave higher priority to pictures than sculptures, but, strictly speaking, it should be corrected like this: Leonardo da Vinci gave higher priority to 3D photographs than real 3D objects. And as the times go on, a real camera was invented, and "magic-like illusionism with paints" shown in those plane pictures by impressionistic artists, which performed like a camera, came to be expelled. And when a huge canvas was invented, Clement Greenburg and others, advocators of American Abstract Expressionism, totally expelled that illusionism, from the theoretical viewpoint as well.

    Now let's return to the main subject. As I alluded to the examples of "Floretine school" in the second dimention, so now let's see the examples of "Venetian school" in the third dimention. Let me take up the sculptures by Auguste Rodin, contemporary with impressionists. What he intended to express was bulk of 3D materials, not topology of a body's surface, and he made an artistic creation, fleshing out his works with malleable wax or clay, which was completely different from Michelangelo's, who used hard blocks of marble as material. But, once the work finished and its surface turned to be cold and completed topology, the malleable nature of material, which the artist once touched and felt while creating, must have extremely been injured. Therefore he invented the technique of "leaving the works unfinished." As he thought that being unfinished was the principle of art, he left his surfaces unfinished, rough and irregular. In such a point, he may have something in common with Tiziano who left powerful strokes in his works. But, though we directly see in Tiziano's plane pictures all the material he used, in Rodin's solid sculptures we only imagine those malleable material indirectly through the roughness of the surfaces. (That is because of topology's powerful restriction as will be detailed in the next chapter.) Though Rodin's sculptures are certainly of Venetian school's, the indirectness is always seen in his works, not being able to be direct like Tiziano's. And, if seen from the viewpoint of digital graphic tools, a bitmap-concept 3D paint-tool, "Digital Nendo," is the very thing that properly succeeded for the first time in what Rodin tried to fulfil and that perfectly solved the "indirectness" which annoyed Rodin. It is "Digital Nendo" that gives you world's first new sensation.

    As you have seen the relation between the two opposite figures and the dimention, now you wil understand why such misunderstanding occurred in analog days when there were no digital tools: the misunderstanding that the truth of material is in the second dimention, and that the truth of a body is in the third dimention. And you should pay attention to the loss of recognition of the world, for example, as seen in Japanese ukiyo-e, which was unable to explain in the above situation concerning the post-Renaissance Western art history. Different from the works of Leonardo da Vinci, ukiyo-e, a wood-block print, can be considered to correspond to the first two-dimentional draw tool, "MacDraw," which, instead of giving up to reflect the three-dimentional solid topology on the two-dimentional plane, obtained the true plane topology in the two-dimentional world. Indeed, an idea of a plane body must have been difficult to conceive in the real world, which may have been a cause of such misunderstanding and of ukiyo-e having been put in a blind spot in the Western art history.

    In addition, in the works of post-impressionistic Western artists, who were influenced by ukiyo-e, you can find a true type of the two-dimentional object-figure-mode, like "MacDraw." Some slate-printed posters by Toulouse-Lautrec or Kandinsky's later works after he invented "hot abstraction" can be given as examples, but the former was not able to display the important ism in the art history. The latter is interesting when compared with Mondriaan, and what is special for him is that he recognized plain canvas only as vacancy not as the system of coordinates. But he was less powerful in the attempt of just leaving a body of the object-figure-mode than Hans Arp, a dadaist as well as "objet" artist, who expressed it in a relief or a solid sculpture. Kandinsky's works in his later days do not seem to have a strong inevitability of being a plane.

    In the next chapter, let's think about "new physiological sensation arisen by 'Digital Nendo,'" which clearly shows the two opposite concepts in the art history and its relation with the dimentions.

  • 4. World's First Gravity-Free and Topology-Free 3D Sensation
  • "Digital Nendo," which was just invented based on a general idea, turned out to be a tool which displays world's first utterly new physiological sensation, by which the misunderstanding of the dimention conceived by human beings came to be corrected. To be precise, "Digital Nendo" actualized the world's first "gravity-free and topology-free 3D sensation" as new physiological sensation. It is the fact that can be compared to the discovery of the negative number. As the discovery of the negative number, which was obtained through a faithful operation of the four rules of arithmetic, enlarged our sense toward the number more correctly, so "Digital Nendo," whose purpose is just to arrange the material faithfully, did enlarge our sense toward the third dimention, and did correct the analog-days' inadequate recognition of the third dimention.

    In the previous chapter, we considered the analog-days' fallacy of the dimention from the viewpoint of the art history. In this chapter, the world's first new physiological sensation and its fallacy will be interpreted from the real mathematical viewpoint of the program.

  • New Gravity-Free Sensation

  • As above stated, the characteristic of the bitmap is that it is thoroughly fixed to the system of coordinates. Conversely speaking, it has no unnecessary restriction except the system of coordinates. When an artist puts red color on his canvas at the upper left corner, the color stays on the given coordinates as he wishes. It will never fall. That is one of the grounds why you tended to think the analog two-dimentional world by the bitmap concept.

    In the analog third dimention, you usually cannot get free from the restriction of gravity. So an artist cannot put red clay in space so easily. In other words, it often used to be useless to try to put material on the space-coordinates. On the contrary, for a sculptor, the restriction of gravity is not so big a problem. Topology will be kept in any degree as it is put. What meaning will it have if an animal moves around in a cage? That is one of the grounds why you tended to think the analog three-dimentional world by the idea of the object-figure-mode.

    Thus we first experienced the feeling of being set free from the restriction of gravity in a computer, which is really worthy of close attention, especially in the bitmap system of coordinates. When I explain the feeling of using "Digital Nendo," I often say, "it is as if pushing mayonnaise out of its tube in the cosmic space," which is different from putting decorations on a Christmas tree, and which must be the world's first experience. So, even without any intention to create something, and just touching the tube-tool, you will get a new sensation. An the added special function, "Whole world falling by gravity," will be found to be fresh.

  • New Topology-Free Sensation

  • The explanation of topology hitherto was done in the meaning that you can freely draw a thing like stool by handwriting and that you can make a worm-hole easily. That free paint-feeling in this sense was first established by "Digital Nendo" in the third dimention. In comparison with the analog third dimention, the matter of being topology-free induces the more important new situation. To be precise, you can freely see and draw the inside structure of the three-dimentional object for the first time. In short, being topology-free means two things, that is, free handwriting as above stated, and ability of handling a body's inside as is now going to be stated. And the latter is more important.

    In mathematical viewpoint, you can never reach the space closed topologically from outside. An ant on the two-dimentional space can never reach the sugar placed in a rubber band on the plane. But if the ant is on the three-dimentional space, it will easily climb over the rubber band. Likewise, human beings on the three-dimentional space need not to pay much attention to the restriction of the two-dimentional topology in the two-dimentional pictures. That is one of the grounds why it was difficult to grasp the analog second dimention by the object-figure-mode.

    But, in the analog third dimention, the restriction of the three-dimentional topology becomes very huge for us. We, living on the three-dimentional space, can never reach the contents of a can closed three-dimentionally, without breaking the can's topology. When you see Piero Manzoni's "An Artist's Stool," a work of a can in which he put his own stool, you will feel just like the ant on the two-dimentional space which cannot climb over the rubber band. That enormous topological restriction in the analog third dimention was what even Auguste Rodin could not solve directly, and that is one of the grounds why we tended to think the analog third dimention by the idea of object-figure-mode.

    In the beginning of developing "Digital Nendo," I said to the programmers, "You can settle the users on the four-dimentional space." Even before developing, it was naturally expected that a mouse pointer would be able to go through a body's surface into the deep inside coordinate. Of course you can stop it by programming at the front section-unit so that it cannot go farther, but why should this software be resemble to the analog third dimention? You need not to say, "I cannot deduct 7 from 5." Like the idea of "5-7=-2," the mission of the world's first bitmap 3D tool may be like this: you can enjoy topology-free sensation in the bitmap system of coordinates where there is really no topological restriction, and you can fix any solid coordinate equally. To "fix any solid coordinate equally" cannot be attained in the analog world unless it is on the four-dimentional space, and so I dared to say like the above. And now you can put colors on the inside solid sections through the surface or make them transparent again, as if you were in the four-dimentional space.

    The above story is related with "Fukan-mode," and so, let me also refer to "Slice-mode" which will remind you of CT scan. Personally, I am a doctor, and when I was a medical student, I was trained to solidly grasp the human body's inside structure through CT-scan pictures put side by side. The very mode, which apparently does not seem to be a solid object, may also bring you the three-dimentional sensations, as CT- scan pictures do, if you are used to its appearance. And furthermore, as it will always be monitored by "Para-para Window," you can say like this: The sculptors in analog third dimention, even Auguste Rodin, only had responsibility on the surface topology, but the users of "Digital Nendo" will not be satisfied unless they pay attention to the inside structures. The three-dimentional sensation will necessarily be enlarged to a totally new sensation.

    Thus, because of the perfect possesion of the space coordinate world gained by the "gravity-free," and because of the reference to the body's inside world gained by "topology-free," you can get a new and true three-dimentional sensation for the first time, which is a very remarkable happening, if seen in the history of human physiological sensation, or in the art history, especially in the opposite form seen in "Venetian school vs. Florentine school," or rather in human history of grasping the world.

  • 5. "Futurism" of Digital Nendo (Introduction of the Time-Axis)
  • You have already seen various natures which are naturally induced by the type of a "bitmap conceptual 3D paint-tool," that is, the type of "Digital Nendo." Now from here I will write about a few devices only the very software can do. In other words, up to the previous chapter you saw the common characteristics of its type, and from here you will see different expected characteristics of each different software which will be born imitating the very software.

    Firstly, let me introduce one of the devices seen in "Digital Nendo," that is, the introduction of the time-axis for sensational understanding of 3D objects. Conventional draw-type 3D tools usually do lighting and shadowing, and the introduction of the perspective expresses statically 3D sensation or perspective feeling. With the very software, the lighting and shadowing are just for convenience, and no introduction of the perspective was done. Instead, the two windows are always open by default, that is, "Guru-guru Window," where a 3D object of "Fukan-mode" keeps rotating, and "Para-para Window," where each layer of "Slice-mode" keeps showing itself in turn just like the CT-scan animation. So, the 3D sensation can be shown through those windows' kinetic animation.

    Let me first state the reason why I did not put much strength on showing static 3D objects. For one reason, I wanted to put strength on the fact that each material has its own peculiar color in the bitmap type, different from in the object-figure-mode. In other words, I wanted the users to renew the recognition that the very software has the peculiar colors for your own to prevent colors from going on changing by the light-up. For the second reason, I wanted to appeal that each individual 3D section (which is called "voxel" in the very software) has the same and equal form and size. No introduction of the perspective means that you see it from an infinite distance, and each voxel is shown in the same form and the same size. And, for example, to one red voxel I did not give six red colors but only three red colors, that is, just to the front, the top, and the side, and I fixed the direction of the light-up for convenience' sake just from the front, so that the users can concentrate in putting colored material wherever you want without caring about lighting or shadowing.

    Thanks to the animation of "Guru-guru Window," you can have the three-dimentional feeling very strongly, just by turning it by 90 degrees non-continuously. It is not a special thing to express the three-dimentional feeling by just turning, and so the very software emphasizes it by showing it by default. Let me remind you that the turning is the one shown in "Fukan-mode" which is based on the special method of projections as will be stated below, and it gives you a different feeling from the other usual presentation of 3D objects. Conversely speaking, you can enjoy creating 3D objects and watching them through "Guru-guru Window." (You will find several examples in the Stamp's Preset which is my own creation.)

    Next, "Para-para Window" is analogous to 3D CT-scan animation. The animation of the Window is necessarily emphasized by showing it by default. And the body's inside, to which you topologically did not have to refer up to the present, is now always monitored, and so you must want to have responsibility even for the inside as I already mention.

    As "Para-para Window" may remind you of the para-para manga, you can make it through "Slice-mode" and enjoy it through "Para-para Window." It is quite possible to make animation as a 3D object, which is completely opposite from creating a 3D object on the time-axis. A "para-para manga : 3D object" made like that can be appreciated as a queer 3D object through "Fukan-mode" or "Viewer," especially when its background is fixed to be transparent. The precedent of the "para-para manga : 3D object" is a bronze sculpture, "The Flight of a Gull," made for a scientific purpose by a French scientist called the father of the cinema, Etienne Marey. Italian "futurism" was born much infuenced by Marey's studies, and it is probably the first group in the art history that created works the most precisely referring to the time-axis. The artists of futurism, who admired power and speed, tried to visualize the time-axis and created many queerest works such as a picture of a dog with many feet. The feeling of the reality held by a small number of those futuristic artists can now be universally possessed by everyone through the very software nearly a century later. Such idea as it would be "a tool to actualize futurism" has long been conceived by myself since before its developing.

    To be more precise about "Para-para Window," it was born through applying time to the z-axis of coordinates, that is, through regarding the z-axis as the t-axis. As a monitor screen itself is on the second dimention having only the x-axis and the y-axis, it is not easy to show the third dimention. For example, the introduction of lighting or the perspective as is seen in conventional draw 3D tools, like the study by Leonardo da Vinci, is nothing but a trick to produce a perspective-like illusion. If the t-axis replaces the z-axis, however, it is not illusion but real, (although it was also approached from the fourth dimention.) The idea of replacing the z-axis with the t-axis is based on the experience of a stereoscopic view by the naked eye, a fad appeared around 1993, in which you found that you can get the stereoscopic view not only using two plane pictures taken from different angles but also using two pictures taken in different times. Not actualized yet, I invented a mode for making 3D objects through cross-viewing by the naked eye.

  • 6. Pseudo-Cubes Made by Fukan-Mode
  • The conspicuous invention concerning the very software is, in fact, the method of "Fukan-mode," which apparently does not seem so conspicuous. If seen carefully, it is completely different from "Viewer," and it takes the form of the cubes of the "whole world," a different world from the real one. It consists of layers of 32 square planes arranged from the back toward the front, and all the squares seem square and correspond with the xy-plane on the monitor screen. And from the front to the back, as it goes one layer inner-side, it goes 45-degree upper left, a half voxel away in distance. In other words, two layers inner-side of the voxel of (1, 1, 32), there is a voxel of (2, 2, 30) which just piles upon the other.

    As you see, that is the method of "pseudo-cubes," and it is the introduction of the method of "pseudo-cubes" that brought you the real feeling of possession and easy-handling of the system of coordinates. The reason is that the system of peculiar coordinates of the whole world and the system of visible coordinates completely correspond with each other on the xy-plane. And the direction of the z-axis is so easy-to-understand that you need not the z-axis of the visible coordinate, and so the mouse pointer can only follow the system of peculiar coordinates of the whole world. To be clearer, however freely your right hand moves the mouse, the indicated coordinate by the mouse pointer always stays on the same layer of the z-axis, as far as you do not change the z-axis with your left hand touching the cursor keys. From that you will understand that the pseudo-cubic display in "Fukan-mode" is nothing but the transformation of the display in "Slice-mode." So you can use the same tool in the same way both for "Fukan-mode" and "Slice-mode," (which makes the frequent users of "Slice-mode" feel a new 3D sensation.)

    Although you may not think the pseudo-cubic display so remarkable, it took a long time to get the idea. By that time, I had been preparing for the editing task from the same oblique angle taken for making "Viewer," and it had been a great question that, when you moved the mouse pointer following the visual-point coordinates, where it would stay on the world's peculiar coordinates, and that how easy-to-understand it would be, and so forth. Often deep into midnight, the programmers and I discussed the problem, and sometimes even such an idea came forth, "You may need nothing but 'Slice-mode.'" At that time I was also engaged in another work asked by Ask Kodansha Company (it was a CD-ROM, "KIDS BOX"), which once completely occupied myself for nearly two months, making it impossible for me to have a meeting of "Digital Nendo." And at last, just the previous day of the first meeting after two months, while taking a shower, I thought, "Oh, it's tommorow that we'll meet after a long time," and at that moment the idea of the pseudo-cubic display came across my mind. Once I had the idea, I wonder why I did not think of it earlier, because it is so simple and useful an idea. In pioneering stage for a new field, there may often happen such a thing that you cannot think of such simple matters.

    As the algorism here used is not the special one for the pseudo-cubic method (actually it is made for "Viewer"), there exists a small opening between each two layers in "Fukan-mode." As you see, the small openings were not made intentionally. And if you get used to seeing the mode, you will feel another special 3D sensation which can be had only through the pseudo-cubic method. Let me recommend you to see Figure Series in Stamp Preset l, and all kinds of Stamps of Stamp Preset 5, which are my company's own products, through the pseudo-cubic method of "Fukan-mode" (and even through "Guru-guru Window") rather than through "Viewer."

    After I finished writing the above sentences, someone who read those sentences told me that the method of the pseudo-cubes here used is precisely a kind of projective technique called the oblique method of projections. I learned that the ordinary oblique pictures seen in "Viewer" were of the one called the oblique-axis projective method, which could be understood mathematically as the difference of projective technique.

  • 7. Sense of Possession in the Definition System
  • Let me simply refer to the definition system once again. To draw a picture in the bitmap mode is to put a color on each dot or to erase it. If you have made an icon 32 by 32, you will probably understand that the smaller a picture's size becomes, the heavier the dot's weight becomes, and you must put more spirit in a single dot.

    In the art history, as times go on, the each section-unit of pictures by "Venetian school" became bigger. In other words, as times go on, it tended toward reductionism and the number of dots, the whole world which artists intended to define, became smaller. That means the sense of world's possesion is strengthen for the smaller world. I noticed that idea around when I drew two-dimentional illustrations under the slogan of "BAKA CG," and it has become my theme since then. It is the same reason that makes me often declare that it is the jagginess that is important.

    And now here is "Digital Nendo," which was born through my coworker's kind understanding of my idea, especially of Ask Kodansha Company. Usually people will think that 32678 (32 by 32 by 32) is too low of resolving power that it cannot be put to practical use, for example, for such a minute description of the inside of human body. But, I once tackled the work called "A Floppy Disk with Limit-Point Icons," which has as many as 424 icons, a critical capacity with space of 0K, and so I felt that the size of 32 by 32 was big enough for describing as the definition system. Therefore I asked them to put the highest priority to the feeling of easiness and speed in handling the mouse, limiting the kinds of colors to the nine logically basic ones, that is, the six colors of RGBCMY plus white, black, and transparent. I also asked them to put high priority to "Guru-guru Window" and "Para-para Window" as well.

    And, let me add one more thing for the reason why you can get a stronger feeling of possession when the size gets smaller. If the world's size is big, when arranged by "Slice-mode," it will surpass your acknowledging ability sensationally. If it becomes like the size of a 320-dot cube, you have to see 320 layers at one time, which is sensationally impossible. In that case, a kind of a method of displaying them by a group of ten layers might be taken, but, if so, the feeling of possession in the definition system would be decreased. Of course, it would be more convenient for the procuring system, though.

    Such being the case, in spite of my advocating "nendo/clay," it turned out to be like a "block" because of its big section-unit. Later, even if a similar software of higher resolving power appears, the wonderful feeling of possession gained by the 32-by-32-by-32 sized "Digital Nendo" will continue to be irreplaceable.

    For the last, let me write about my obsession of the fundamental issue, "the possession of the whole world." I think that it would be analogous to the issue of modernism, that is, how you would feel if you found a new world. I do not take a totally positive position of modernism, and at the same time, I do not take it negatively from the start. Probably, the very software was created from the standpoint of modernism in order to fill the blank which is left undone by the modernistic aesthetics. If I continue to write about this issue, it would take a large amount of words and go farther from the main idea, so I will take it up in another chance.

    By Hideki Nakazawa
    Publishing date of the third edition: August 12, 1996

    ** The text, "Significance of Digital Nendo in Visual Art History" was first written on July 1, 1996, (it is the first edition), and on July 31 of the same year I changed the contents a little, that is the second edition, and I revised furthermore on August 12 of the same year, which is the third edition.
    *The first edition (1996.07.01) --- The full text is recorded in the style of text data in a CD-ROM, "Digital Nendo," (Macintosh version) published by Ask Kodansha Company on July 18, 1996.
    *The second edition (1996.07.31) --- Appeared in the print distributed on the occasion of the display of "Digital Nendo" (from August1 to September 23 of 1996) at Tokyo Metropolitan Museum of Photography.
    *The third edition (1996.08.12) --- Since August 12, 1996, appeared in HIDEKI NAKAZAWA's home page: (http://shrine.cyber.ad.jp/~nakazawa/NAKAZAWA). Also recorded in a CD-ROM, "Digital Nendo," (Windows version) published by Ask Kodansha Company on November 8, 1996.
    *Before finishing the full text of the first edition, its excerpt was published in the Users' Guide of "Digital Nendo," and also in the magazine, "Super Designing" (No. 16).

    **Please read the three suplements together with this text :
    "Supplement 1 : The new way of making 3D objects using 'Digital Nendo.'" , "Supplement 2 : Inside story of why it is called 'Digital Nendo.'" , "Supplement 3 : Concerning 3D Printer."

    **In HIDEKI NAKAZAWA's homepage, you can find a home page of DIGITAL NENDO by HIDEKI NAKAZAWA himself: (http://shrine.cyber.ad.jp/~nakazawa/NAKAZAWA/nendo). Ask Kodansha Company's home page: (http://www.ask.object-design.co.jp).

    **ENGLISH version: Translated by Rubiko Nakazawa.

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