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The purpose of this paper is to introduce the cybernetics audience to the fundamental interdisciplinary concept of hyperseeing and its application to hypersculptures.

Briefly, hyperseeing is seeing from multiple viewpoints in a very general sense. In particular, the author first discusses hyperseeing a sculpture. A sculpture is defined as an object in a fixed position relative to a horizontal plane (base, ground). Two sculptures are congruent if they consist of the same object. A hypersculpture is a set of congruent sculptures. A hypersculpture is a more complete presentation of the sculptural possibilities of an object.

A specific example is given of hyperseeing a knot sculpture made of copper tubing.

The paper demonstrates how the study of hypersculptures facilitates gaining a deeper understanding and appreciation of sculpture.

The paper aims to research the applications of topological geometry to the architectural concept design process and their combination with the modern digital technology to find novel architectural spaces and forms which are dynamic, easily adaptable to the context and surroundings.

The article uses the method of studying the existing literature on topological geometry and architectural design theory including design thinking, architectural design methods and architectural compositions to analyze and compare them with architectural practices and suggest new topological design tools and methods. Moreover, the paper tests the proposals with a number of preliminary design research experiments. In addition, graphic design software, parametric design, building information modeling (BIM) and digital development trends in architecture were explored and experienced to reveal the application potential of topological design thinking and methods in the trend of architectural digitization.

The paper has analyzed, synthesized and systematized the basic theories of topological geometry in order to clarify their applications in the architectural concept design process. On that basis, the paper proposes a novel topological design thinking and method for finding rich diversified architectural ideas and forms based on original invariant design constraints. Finally, the paper clarifies the combination as well as the mutual, motivating relationship between topological geometry and modern digital technologies when applied to architectural design.

The research contributes a novel design thinking and method based on topological geometry combined with modern digital technology to the architectural design theory. It will be a valuable tool capable of suggesting architects how to think and innovate in architecture in the era of industrial revolution 4.0.