Higher dimensional space Essay

We spend eighty percent of our lifetime in indoor spaces, and the evolution of indoor spaces is being adaptable to the surrounding and the environment, but moving towards a technological future, which is being mostly influenced by virtual other than reality, it is a need for the population to know how their indoor spaces are going to be evolved. what I mean by virtual And reality in architecture is considering reality as a three-dimensional world which we are living in And virtual as higher-dimension which is an upstep of three dimensions to which architects are having their own interpretation. the world has witnessed the evolution of two dimensions to three dimensions in the technological aspects. but what will the evolution of third to the fourth dimension in architecture and spatial aspect be like?

To understand the future and the higher dimension in architecture, we need to go through the evolution and the design process of the hyperspace and cyberspace which are closely related to the higher dimensional space and its representations. And its influences and realations from past to present for a better understanding of the future.


Internal spaces define the experiences of architecture. Having a beautiful facade or elevation is just the container in architecture, the four walls of the container the void is where the man lives, is the key element in architecture. Internal space is not easily represented in the drawings or plans, even if it does the architecture can end up being unsuccessful. To understand the voids itself, it should be developed in concepts and theoretical understandings. space is determined by the dimensions and its relation between space and human. The invention of the fourth dimension is a cubist revolution which leads to the exploration and advancement of the space. This emphasizes that space is the successive viewpoint for the architecture.

A Primer of Higher Space by Claude Bragdon

Claude Bragdon in his A Primer of Higher Space, he starts off with a question to readers that line is bounded by dots and lines bounds planes, in turn, it bounds the Solids." what then do Solids bound?" and after this question the author Claude says "if you answer that a solid cannot be a boundary we parted company". And from there he starts his analogy about the fourth dimension, from one dimension which is a point, to the fourth dimension which is a Tesseract or a hypercube.

To raise a number to any given power arithmetically it's achievable but for the Tesseract or the hypercube, humans don't have the visual or sensory knowledge of it. To represent the fourth-dimensional space, building the space to visualize and analyze is the only option here, but the mathematicians don't have the geometry for this.

The fourth-dimensional space gives a feeling of unfamiliarity and shock because of the reason where the people's experience has been only in three-dimensional spaces. Claude says that when there is an increase in dimension, it add-ons to an additional way of movement, for example, he compares the movement of caterpillar and butterfly as caterpillars movement is two dimensional it can only see things as two dimensional even if the objects are three dimensional, but for the butterfly as it has an extra movement compared to caterpillar which is flying the visual is three dimensional. so from this example can understand that a new power of movement can be the expression of the fourth-dimensional space. Claude Bragdon relates time and movement to the fourth dimension as the one undefined movement form the three dimensions leads to the fourth dimension the author states that the direction can be towards "the principle of growth, of change, a measure of relations which cannot be expressed in terms of length, breadth, and thickness". and from here can understand that fourth dimension is a space that changes in time. The time, in the fourth dimension, is powered by movement if we pause all the movement there is a halt in the fourth-dimensional space.

Joe Durben Education: Augsburg College - M.Ed., Augsburg College - Bachelor of Arts - Summa cum laude - Minneapolis College of Art & Design

joe Durban an artist exploring and reflecting four dimensions in his work.

All those motions created by flashing and blinking of fluorescent bulbs and lights, from top of the buildings to the moving cars creates energy to the streetscape of the city. which represents the four-dimensional movement to Joe Durben, for an example Iluma by WOHA architects, the facade was filled with lights and it creates an illusion calming movement to the streetscape by having multiple movements from the moving cars to the facde. and the next example is the work by Ned Kahn which shows that the four-dimensional movements can be created without electricity, for an example, The articulated cloud on the Pittsburgh children's museum where Ned Khan use multiple numbers of metal sheets, which are powered by wind to create a wavy movement in the facade. and the next example joe Durban explains the vision of David Fisher's dynamic architecture, where every floor of the building is moving independently to create ultimate views from the windows that are ever changing. which is considered to be a four-dimensional building. From all this, case studies and elements of the fourth dimension in architecture, the fourth dimensions are implicated through time and movement.

La Grande Arche by Danish architect Johann Otto von Spreckelsen

La Grande Arche was built with the properties of a four-dimensional cube. The cube consists of 32 edges with 16 connecting points. and the distance along its edges are not uniform because of the reason where the cube itself is a shadow of four-dimensional space and according to Claude Bragdon when a cube cast its shadow a dimension is lost in that process. accordingly, the La Grande Arche is a shadow of the four-dimensional cube.



Spatial fourth-dimensional was trying to prove its existence from the 19the century, which was supported by the Albert Einstein "Theory Of Relativity". But the quality of the four dimensions being as hypercube was not successful, with the typical representation methods of that time period. This exploration and invention of the higher dimension created a focus and trend in art and architecture to explore it and resulted as Dadaism, cubism, constructivism, and futurism movements, These movements were constantly looking of conceptions of spaces and its other possible ways of representing. These styles of movements integrated the concept of movement and time into it. whereby time has been interpreted as the spatial dimension. The development of computer and software for Virtuality known as cyberspace helps to visualize hyperspace and non-euclidean geometries, which made the hyperdimensional spaces easy to visualize with the help of cyberspace. As this development and evolution in the virtuality of computers, it has a great impact on the architects affecting their visualizations and designing process and design methods by, designing with the parameters and algorithmic as an integral part of it, by designing network parameter they are able to create a higher dimension along the immateriality to space, as there is no connection to the physical world.which is being more focused on the possibilities of geometrical elements other than the materials in architecture.

“An architecture of warped multidimensional space would

move beyond the mere manipulation of shapes and forms into

the realm of events, influences, and relationships of multiple


Branko Kolarevic, “Introduction",” in Architecture in the Digital Age: Design and Manufacturing, ed. Branko Kolarevic, New York: Spon Press, 2003.p.15.

The nth-dimensional geometries were developed from the time period of the nineteenth century. Visualizing of this higher dimension was a challenge and it remains hypothetical. which changes the preconceived idea about geometry in architecture and spaces. after the researches and exploration of the nth dimension, hypercube became the popular figure. However, during the 20th century, there was an alternative approach to the fourth dimension considering it as time in a temporal dimension. and this approach of time as the fourth dimension has been visualized through slicing the third dimension and overlaying them or combine the multiple objects to represent the whole object. Example of this exploration is reflected in the projects of Eero Saarinen, Eric Mendelsohn, Le Corbusier, and Gaudi. And time as the approach of the fourth dimension brought considerations about mobility duration and instance.

The Concept of Hyperspace

During the end of the nineteenth century, the concept of hyperspace made a trending topic on society with the various attempts of representing forms, geometries, and concepts.which also had a great impact on architecture together with sculpture, painting, and literature. and made them explore and visualize the fourth-dimension hyperspace.which also made Charles Howard Hinton form the philosophy on the foundations of hyperspace. hinton was the first person to explore and represent a way of seeing the four-dimensional object, not in a mathematical expression, he invented a learning system by using the multicolored cube and connecting the same color faces to each other to forme the hypercube.


cyberspace is easy to visualize structures and spaces compared to the hyperspace. Cyberspace is considered another way of idealizing space. Which is done with the help of computers and software (virtuality) without any connections to the physical or material world. which changed the game of the designing process and the ability to visualize space, which carries the ability to be precise and functional. The preciseness helps to visualize complex structures and spaces along with the higher dimensional spaces representation.

William Gibson, Neuromancer

The sky above the port was the color of television, tuned to a dead channel.

....Night city was like a deranged experiment in Social Darwinism, designed by a bored researcher who kept one thumb permanently on the fast forward button.

Neuromancer a sci-fi novel takes place in Japan, which depicts a vision of the near future at 1984, which is turning out to be witnessed in our day to day life, how we are merged with technologies in an irreversible way. In the novel Neuromancer people live in two worlds with two lives, one is the physical world and the other one is the matrix world which takes place inside the computer(virtuality) with futuristic technological spaces and unlimited movement and forces, by making the community brain interacting with the computer matrix by using electrical impulses and sensory. The author William Gibson names the matrix world as cyberspace because space exists without any relation to the physical world and being generated and designed by computers. The author describes the cyberspace (the second world inside the novel)

"A consensual hallucination experienced daily by millions of

legitimate operators, in every nation, by children being taught

mathematical concepts… A graphic representation of data

abstracted from the banks of every computer on the human

system. Unthinkable complexity. Lines of light ranged in the

nonspace of the mind, clusters, and constellations of data"

William Gibson, Neuromancer, p.51.

The Neuromancer was the first novel to talk about the cyberspace, it's a virtual world designed with the elements that are extending in all three dimensions witha grid system concept to it. The community of the cyberspace gets to enjoy the functions and forms that are adapting themselves to multiple needs. Spaces are futuristic but the way William Gibson explains the futuristic part in his novel is in a way that the technology and the virtuality are those fused together with evolution and development, and the community tends to spend more time in the cyberspace (virtuality) other than the reality which cant be refused by this generation itself. can see that architecture and spaces are being generated and eveoled with technologies.

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