Re(Calibrator) Phase1 part2

In 1783, Kant wrote: "That everywhere space (which is not itself the boundary of another space) has three dimensions and that space in general cannot have more dimensions is based on the proposition that not more than three lines can intersect at right angles in one point. This proposition cannot at all be shown from concepts, but rests immediately on intuition and indeed on pure intuition a priori because it is apodictically (demonstrably) certain." (page 38. Prolegomena to any future metaphysics).
For centuries, many have been contemplating about the other spatial dimension and in recent decades the contemporary science and physicists are developing theories that will explain all the existing forces and the mystery of matter.
In forth, extra spatial dimension, the simplest geometric object is assumed to be the tesseract. In geometry, the tesseract, also called an 8-cell or regular octachoron or cubic prism, is the four-dimensional analogue of the cube.

A square, a cube, a hypercube

However, it is not as easy to visualise a tesseract, or even more complicated multi-dimensional objects. In the past, many scientists tried to picture this with a pen and paper, but now with the emergence of the new technologies, we can see these multi-dimensional forms in motion as animated sequences.

  An animation showing multi-dimensions

And yet, even with the animated view, it is hard to imagine the forth spatial dimension. We are in three dimensional equivalent of the fictional world called "Flatland: A Romance of Many Dimensions" by English schoolmaster Edwin Abbott Abbott.

A house in a Flatland

Here the author is describing "a two-dimensional world referred to as Flatland which is occupied by geometric figures. Women are simple line-segments, while men are regular polygons with various numbers of sides. The narrator is a humble square, a member of the social caste of gentlemen and professionals in a society of geometric figures, who guides us through some of the implications of life in two dimensions. The square has a dream about a visit to a one-dimensional world (Lineland) which is inhabited by "lustrous points."

The Lineland

He attempts to convince the realm's ignorant monarch of a second dimension but finds that it is essentially impossible to make him see outside of his eternally straight line. He is then visited by a three-dimensional sphere, which he cannot comprehend until he sees Spaceland for himself."

(http://www.geom.uiuc.edu/~banchoff/Flatland/).

Similarly, we find it difficult to comprehend anything that is simultaneously perpendicular to all our known x, y, z axis. Having said that, I find myself equally incapable of portraying the Lineland or the Flatland as well.

Did anyone ever try to build a tesseract house? There is a science fiction story "And he built a crooked house" by Robert Heinlein, in which an ambitious architect Quintus Teal, attempts to build a four dimensional house, and once it is built, very strange things start happening to the occupants, as the house does what seems to be a teleportation from one point of a universe to another, or a movement in four dimensional space. Perhaps this story inspired another artist and architect Paul Laffoley, to put together detailed plans of a tesseract house. (http://paullaffoley.net/paullaffoley/)

Tesseract house plans by P. Laffoley

This house has actually been built by Seifert Surface, but only in a virtual realm of the "Second life".

Heinlein inspired tesseract house in Second Life

Leaving the room we are in, walking straight through four doors and ending up back where he began. And so a graduate student in Stanford’s math department has managed to create, more than 60 years after Heinlein first conceived it, a home that seems to exist in more than three dimensions.  http://nwn.blogs.com/nwn/2011/06/tesseract-crooked-house-in-second-life.htmlThere are however other more complex multidimensional object.

Multidimensional objects

Although mathematicians can work with the fourth dimension abstractly by adding a fourth coordinate to the three that we use to describe a point in space, a fourth spatial dimension remains difficult to visualise.

Sculpture of a shadow of a four dimensional object

Above is a sculpture designed by Penn State professor of mathematics Adrian Ocneanu (http://science.psu.edu/news-and-events/2005-news/math10-2005.htm/), which measures about six feet in every direction, presents the three-dimensional "shadow" of a four-dimensional solid object. Ocneanu's sculpture similarly maps four-dimensional solid into a space perceptible to the human observer. His process, radial stereography, presents a new way of making this projection. He explained the process by analogy to mapping a globe of the Earth onto a flat surface.
"Four-dimensional models are useful for thinking about and finding new relationships and phenomena," said Ocneanu. "The process is actually quite simple- think in one dimension less." To explain this concept, he points to the two-dimensional map of the three-dimensional world. The interview with the professor and the overview of the sculpture can be found here (http://www.youtube.com/watch?v=viKTj78ge-0)