1. SUBSTANCE OF CYBERSPACE



1.1. The substance of cyberspace

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In order to understand the nature of matter in cyberspace, we need to move away from looking at matter as something that is constant as we see it in the physical world. In the case of cyberspace, we need to refer to the associations with the mind's space—a place of abstract reasoning where matter equals image, information, and idea. The notion of "substance" rather than "matter" better reflects the nature of the intangible electronic environment.

Substance completely fills up cyberspace and constitutes its existence. Cyberspace cannot exist where there is no substance. The substance is consciousness, idea, code, the law and lawlessness of cyberspace. It saturates space with information, not with objects and forces.

Cyberspatial substance is a cybernetic database with a bionic control system. [1]
 
Space, especially the electronic space as a substantial material, has an inexhaustible means of morphological and structural possibilities. The dynamic structure of substance determines the character of cyberspace as liquid, temporary and nonlinear. Cyberspace in this respect is part of the pulsing biological environment, an integral part of the biosphere:

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The space where we live is not a hostile emptiness, but in the broadest scale—the biosphere, the matrix from which derive all forms of life, understood not only biologically but also culturally. This means that the basic material for these processes is simply the space itself, influenced by various factors that shape it into endless mutations and systems. [2]

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Cyberspace saturates the biosphere with electronic information.

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​1.2. To sculpt cyberspace

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​Cyberspace is an integral part of existential space. It is derived directly from the mind and it is an electronic extension of the mind’s space.

Sculpting/carving cyberspace means giving form to the substance of cyberspace, forming information. It is the continuous and constant process of creation and evolution of the electronic environment. Forming information in cyberspace happens on two levels. The first level is forming an interface—the dialogue between the transmitting device and a man. (i.e., designing the medium that enables communication with the device.) The second level is giving form to the communication that is passed through this device to other users, thus forming the information.

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1.2.1. Formation of the interface 

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For a computer (device) it simply doesn’t matter whether it is dealing with images, music or film because the way the binary electronic world operate is reduced to ones and zeros. However, for a man it does matter, so he uses the interface to maintain control of the computer. Cyberspace, in this sense, is thus the interface between man and device. Designing the interface is part of the process of creating the face of cyberspace, establishing and designing points of intersection of the physical world with cyberspace.

1.2.2. Shaping the message  ​

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Cyberspace is not just an interface. It is also considered to be a communication medium. Thus, the main value of cyberspace is not the device but the message. (The device is only an intermediary in the communication process.)  Formation of the message in cyberspace usually means the creation of a visualization of an idea. Or, in other words—the process of imagining. Imagining, thinking with images instead of words, expresses the visual nature of human imagination. Creativity is usually connected to the act of imagining (shaping images and its manipulation) and is largely based on visual stimuli:

Keeping in mind the astonishing variety of phenomena occurring in the spatial systems that arise in the human imagination, that is constantly enriched by experiencing surrounding world, we could assume that everything that imagination absorbs and emits is nothing but a visual reflection of the endless resources of the environment—which is simply based on formation of flat or spatial images. Therefore, the fundamental notion, which reflects the concept of imagination, is not an image but the process of imagining. [3]

The process of imagining is the driving force that creates cyberspace. Simulation of the real and unreal world through imagining evolves into the reality of an electronic environment. Creation of visual representations and transferring meanings through images constitutes the basis of the construction of the cyberspatial substance.

1.3. Structure of cyberspace



Cyberspace, like any other human space (or any part of existential space) requires organization and structuring. Cyberspatial structures are logical ways of organization of the substance of cyberspace and, like the structures of the physical world, can be represented by certain forms, clusters of matter, or constructions reflecting logical plans, analysis and diagrams.

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1.3.1. The order of space

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Space is an element of human existence and the order of the space is a necessary part in determining the structure of being. Spatial structures should therefore fit into a certain order in the space. The order of cyberspace is associated with certain dynamics of formation and evolution of idea, but also, as shown by Schmidt, with the dynamics of the bionic system itself:

From the variability of spatial phenomena occurring in nature, comes the basic observation: the natural order of things is dynamic, and any attempt to create a static, seemingly inviolable system within it that, sooner or later will fail. [4] 

Structures of cyberspace are thus dynamic systems, which come directly from the dynamic nature of thought itself. Creation of the cyberspatial structures should be based on this assumption.

1.3.2. Spatial coordinates 

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The organization of space requires determination of its spatial coordinates. The basic organizational models of the physical man’s world consist of: establishing the centers—in the sense of places (to establish proximity), directions—ways (to establish continuity) and the territories—zones (to establish limitations).

Spatial coordinates define the organizational model of man’s physical universe, determined by the establishment of proximal centers, directional force to delimit continuity and boundary.

In the case of cyberspace, the situation is similar; its organization also requires creation of places, directions and territories, but in a completely different sense than in the physical world.

The cyberspatial electronic environment is governed by rules closer to the spaces of the mind than the laws of physics. Therefore, the creation of cyberspatial coordinates should be initiated by analyzing the resources available to the mind spaces.

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These resources can be divided into two groups. The first group is connected to the process of creation meanings, metaphors, language, with intuition and cognition. We can call this group the Right Hemisphere Structures. The second group is associated with logic, analytical thinking, mathematics and geometry, and process of analyzing and sorting. This group can be called the Left Hemisphere Structures.

1.3.3. Right Hemisphere Structures

The right brain hemisphere, which controls the emotional life, gives our experiences immediate expression, enables true multi-dimensional learning, and the perception of space. There is no sense of time; it is oriented towards the here and now. It is creative, emotional, and it encompasses the whole of the perceived phenomenon.  In this group of cyberspatial structures, the metaphor and symbol provide tools for imagining, visualizing and creation of cyberspace.

1.3.4. Left Hemisphere Structures

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The left hemisphere is the logical hemisphere. It is responsible for analysis, attributing facts, perception and sense of time, control on the word, verbal communication and counting. It is oriented towards the future, and is aimed at sorting facts and listening. It is based on the so-called “short memory” and the perception of individual elements of the phenomenon.

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In the group of left hemisphere logic structures and mathematics are the tools of planning and structuring the cyberspace, enabling the identification and description of the spatial coordinates. It is the mathematics in this group that provides the tools of perception and creation of space. 

Mathematics, as the science about structures, their relationships and dependencies,[5] for centuries has perceived the objects of its studies as existing for and within them. Most importantly, these studies determine the relationship between “unidentified mathematical objects” and the rules that govern operations on them:

In the field of mathematical science one cannot and must not discuss what points, lines and numbers effectively are. What is important, and what corresponds to “verifiable’ facts are structure and relationships, that two points determine a straight line, that numbers combine according to certain laws to form other numbers etc. [...] [6]

Mathematics creates forms whose substance is an idea. It is an abstract, logical tool. This is why it makes mathematics a perfect tool for forming the substance of cyberspace:

Mathematics is moving through a vast, free world of thought. The mathematician, like the painter and poet, is a creator of forms. If the forms he creates are more durable than theirs, it is because his are made of ideas. [7]

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Mathematics allows using abstraction, not only for describing physical phenomena, but also in the process of creating reality, allowing us to go beyond the limits of reality and the mind. Abstraction is an invaluable cognitive tool, possessing the power of universality that allows the application of a single rule in very different circumstances, allowing us to go beyond the world of nature. Another advantage is that allows our imagination great liberty, permitting us to devise new and alternate versions of reality; versions that may not correspond to something in the real world.

Mathematics and geometry are creative and cognitive tools: logic and intuition, analysis and construction, generality and individuality. Mathematics is a kind of expression of the human mind, "reflects the active will, contemplative reason and desire for esthetic perfection." [8]

The substance of cyberspace consists of information and image. The process of formation of cyberspace should be based on formation of its electronic substance using logic and abstract tools of mind, creation of images, meanings, symbols, and finally, a new language of an electronic cyberspace. Structures of cyberspace are dynamic, are variable, temporary, interactive, and liquid as the biosphere itself.

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[1] Ostrowicki M., Wirtualne Realis. Estetyka w epoce elektroniki, Universitas, Kraków 2006, (s. 93)

[2] Szmidt B., Ład przestrzeni, PIW, Warszawa 1981, p. 34.

​[3] Szmidt B., op.cit., p. 114.

[4] Ibidem, p. 70.

​[5] Mathematics as a system, serves the process of exploring the surrounding reality. Without mathematical structures, according to Emmer, nature could not be understood. He says that the Greeks were the first to realize that nature can be understood using mathematics, and geometry can be applied also to its discovery, not only to describing it. Mathematics is in some sense the translation of the language of nature, translation of the surrounding reality. Euclid, through the 'Elements', opened a window through which the nature of the universe has been noticed. Euclid, using the two-dimensional space of thought, without referring it to the physical world, contributed to a revolution in the concept of space, to the birth of abstraction and the idea of mathematical proof. Later, thanks to Descartes, and the invention of the frame of reference, mathematics gave mankind the tools of simulation, visualization and prediction. These tools are the basis for the creation of cyberspatial structures.

​[6] What is mathematics?  R. Courat, H. Robbins

​[7] Emmer M., Mathland, From Flatland to Hypersurfaces, Birkhäuser Basel, 2004, p. 20.

[8] What is mathematics?  R. Courat, H. Robbins