Space composition II for Green x (2022–)

Study for geometry: the stereographic projection and the gnomonic projection

"Silence surround us, silence around us" - Green x is my solo research project from the aspect of biology in the 21st century.

Study for P (Phenomenology)

Study for A (Articulation in arts)

Study for N (Natural science)

Subject: projection and reflection

Subtheme: Visible and invisible space and their space in between

Leitmotifs: near and far

Scientific exploring

Materiality in post-materiality

# Hidden Dimensions: Exploring Hyperspace

How did he solve the enviromental issue of projection and reflection in materiality and environment?

- Three-dimension in "High" and its weight and form

- Time and body (biological movement) in space

- Communication between space and space

Limitation of topology

Limitation of geometry

Multi-modularity

## 3. Philosophy of Mathematics and Natural Science

It was noted above that Cassirer’s early historical works interpret the development of modern thought as a whole (embracing both philosophy and the sciences) from the perspective of the philosophical principles of Marburg neo-Kantianism, as initially articulated in [Cohen 1871]. On the “genetic” conception of scientific knowledge, in particular, the a priori synthetic activity of thought – the activity Kant himself had called “productive synthesis” – is understood as a temporal and historical developmental process in which the object of science is gradually and successively constituted as a never completed “X” towards which the developmental process is converging. For Cohen, this process is modelled on the methods of the infinitesimal calculus (in this connection, especially, see [Cohen 1883]). Beginning with the idea of a continuous series or function, our problem is to see how such a series can be a priori generated step-by-step. The mathematical concept of a differential shows us how this can be done, for the differential at a point in the domain of a given function indicates how it is to be continued on succeeding points. The differential therefore infinitesimally captures the rule of the series as a whole, and thus expresses, at any given point or moment of time, the general form of the series valid for all times,

Cassirer’s first “systematic” work, Substance and Function [Cassirer 1910], takes an essential philosophical step beyond Cohen by explicitly engaging with the late nineteenth-century developments in the foundations of mathematics and mathematical logic that exerted a profound influence on twentieth-century philosophy of mathematics and natural science. Cassirer begins by discussing the problem of concept formation, and by criticizing, in particular, the “abstractionist” theory characteristic of philosophical empiricism, according to which general concepts are arrived at by ascending inductively from sensory particulars. This theory, for Cassirer, is an artifact of traditional Aristotelian logic; and his main idea, accordingly, is that developments in modern formal logic (the mathematical theory of relations) allows us definitively to reject such abstractionism (and thus philosophical empiricism) on behalf of the genetic conception of knowledge. In particular, the modern axiomatic conception of mathematics, as exemplified especially in Richard Dedekind’s work on the foundations of arithmetic and David Hilbert’s work on the foundations of geometry, has shown that mathematics itself has a purely formal and ideal, and thus entirely non-sensible meaning. Pure mathematics describes abstract “systems of order” – what we would now call relational structures – whose concepts can in no way be accommodated within abstractionist or inductivist philosophical empiricism. Cassirer then employs this “formalist” conception of mathematics characteristic of the late nineteenth century to craft a new, and more abstract, version of the genetic conception of knowledge

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing is not allowed.

Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that are related with distance, shape, size, and relative position of figures.[1]

I am exploring the techniques of schablone and assemblage, the question is in mechanics, includes material and its character, as well as environment includes gravity. Thereby collage technique does not apply. (I showed the description for this draft to an architect, I think that he understood my explanation in the terms of artistic techniques of schablone and assemblage. - a collaboration between fine arts and architecture which relates to topology and geometry with the material on the subject of "projection and reflection". Because he gave me back this description with a sentence. His role is for functionality critically, and my task is for Gestaltung/design in the social context critically. - Space, Time and Body) ->  In the case of the theory of topology, for example, to deformed a non-shrinkable metal plate, usually assembled as a body. In the new technique for the deformation of a non-shrinkable metal plate today. -> spherical form

-> From a 21st-century perspective, I agree with his theory of Substance and Function Einstein's theory of Relativity [Cassirer 1910]. So I have been explored it with artistic mediums practically. And instead of "the mathematical theory of relations" I explore "relativity".  Artist, we don't need to create an object absolutely, such as a designed robot. What we artists create, that is a fiction. Even if a sculpture, a three-dimensional object, that is a fiction. So, it originated nonsense-art by DADA, which was critical toward the philosophical empiricism.