" Tout dans la nature se modèle sur la sphère, le cône et le cylindre, il faut apprendre à peindre sur ces figures simples, on pourra ensuite faire tout ce qu'on voudra ". Paul Cézanne

manicone description

manicone is a humanoid form in 4 spatial dimensions (i.e. a "4D avatar"). The construction is based on the symmetries of geometrical primitives like the cone, the cylinder and the sphere, which are called quadrics. Quadrics are often used as building blocks for more complex forms like in particular humanoid forms.

Due to the internal symmetries of quadrics their extension to higher dimensions exists within mathematics. However humans cannot directly perceive four spatial dimensions.
In addition the special inherent mathematical form of quadrics implies that the cut of a quadric with a plane results in a quadric of a lower dimension. In particular slicing a quadric in 4 dimensions with a 3 dimensional hyperplane results in a slice which gives back the usual quadrics, i.e. the cone, the sphere, ellipsoid etc. In other words - this 3 dimensional slice is again perceivable to our senses.

This "slicing mechanism" can be compared to what a 3D scanner (watch e.g.the nice example of the milkscanner) does in 3 dimensions. I.e. here an object in 3 dimensions is sliced by cutting it with a 2 dimensional plane. The computer then reconstructs the object in 3 dimensions by concatenating the 2 dimensional slices. Likewise the brain can concatenate the forms (at least to some extent) and reconstruct the original form in 3 dimensions.

The "slicing mechanism" works analogously in a higher dimension, for example an object in 4 dimensions can be sliced by 3 dimensional (hyper-) planes.

The question is how good can the brain "reconstruct" this form.

There had been a lot of visualizations of the 4 dimensional hypercube as projections or as a 3 dimensional slice like e.g. Dalis famous example. These are visualizations of one geometrical primitive namely the cube. We were asking ourselves how more complex (and rather nonsymmetrical) forms in 4 dimensional space will be perceived and how in particular a humanoid form will be perceived, since it is one of the most direct accessible forms for human perception. This resulted in the construction of manicone.

manicone can be deformed via a discrete Traktixmechanism which extends to 4 dimensions.

We used color in order to tag the primitives and allow for an easier and visually richer perception in the online 2D environment. Colors may be different in a virtual 3D theater (see also remark below).

manicone was done with jreality a mathematical visualization kit, which enables -among others - an easier implementation of 4D applications and likewise for more unusal space forms like a hyperbolic space. The modularity of jreality allows in principle for experiencing manicone e.g. in a 3D cave-like virtual environment or for high-quality print-outs rendered e.g. with RenderMan®.

->more details in the 10 min. video description of Manicone on youtube