A cut through the wooden cube with the glass  plane creates the red something in that plane.  A cut through that red something with the black line, creates something on that line: a kind of Morse coding that holds some information about the original wooden cube.

A cut through a 4 dimensional hyperobject by our familar 3 dimensional space creates a 3 dimensional section in that space. All things we observe in our ordinary space might in fact be 3-dimensional sections  of things in 4 and higher spaces! Maybe.

In 1884, E.A. Abbott (Edwin Abbott) wrote Flatand: A romance of many dimensions.  Its main character is a square living in a 2-dimensional plane. Many strange phenomena observed by the square are explained as the passing of 3-dimensional objects through the plane of Flatland (see also Cat. Nr. 52 ). One could simply disappear and reappear in Flatland, by making a jump into the 3rd dimension. Or from some position above the plane of Flatland, one could see the inside of a flatland house, or any other object for that matter. Why not make the hypothesis of the existence of a fourth dimension, to explain certain phenomena like clairvoyancy or “appearances” in our ordinary 3-dimensional world? 

In our 3-dimensional space all things have a length, a width and a height. But they also have an extension in time: they have a duration or age. We see, because we experience,  that “fourth” dimensions as independent from the 3 spatial dimensions: it is not because that we move back and forth between the table and the wall, that our watch will go faster or slower or even backwards, our watch will always run forwards.

H.G. Wells (Herbert George) was the first to popularize the idea that time could be imagined as a fourth spatial dimension in which one could move back and forth. According to Wells, what we see now in this very moment, are 3-dimensional sections of 4-dimensional objects that stretch out also in time. Well’s Time Traveler had in fact built a Time Machine, already in 1895, with which he could go and see how the world changed between past, present and future, in the same way he could go and see how the world changed when travelling from London to Paris. And of course, having been in the future, back in the present he could see the invisible and foretell the future.

Not long after the publications of Abbott and Wells, Albert Einstein developed his theories of relativity, the special and the general one, in which the 3 spatial dimensions and time were indeed to be seen as the 4 equivalent dimensions of a 4-dimensional space. (This is not to say that Einstein had been inspired by Abbott and Wells. More likely is that all three of them had been inspired by mathematicians like Gauss and Riemann who had developed mathematical tools to deal with hyper-dimensional and curved spaces.)  Anyway,  only when time and space were treated equally, could certain observations of cosmic magnitude be explained. To include the description of the sub-atomic world in one general theory, which is the same as saying to explain the evolution of the universe from the Big Bang onwards, physicist now propose a space of at least 10 dimensions. Dimensions are simply the different facets of what we perceive to be reality, physicists say. With 10 dimensions they arrive at the point in which everything possible and imaginable is covered. Beyond this, nothing can be imagined by us lowly mortals, which makes it the natural limitation of what we can conceive in terms of dimensions.