Suppose the Big Bang was not actually big at all, but rather it was small. The very first life forms that arose from this “small bang” were strings. When they were born, they were quite big relative to the size of the universe. Then as time went on, relative to us, who grow bigger in proportion to the world around us, strings have slowly become the smallest things that exist.
At the time of the “small bang” the strings were so large in proportion to the universe that people now think they have left imprints, like fossils of the universe, but even harder to see than the fossils in the seabed. Their imprints would lie in between stars and in places in the galaxy we have not even discovered yet.
On Earth, in a place called CERN, scientists try to find ever smaller things, building super machines to conduct their experiments. Not so long ago, scientists at CERN thought that they had observed a particle travelling faster than light. Since the time of Albert Einstein’s Special Relativity, it is believed that nothing can travel faster than light. The only explanation for this that people could imagine would be that the particle had escaped through a higher dimension and taken a shortcut from A to B. In fact, the explanation turned out to be that there had been a mistake in the experiment. Special Relativity is a precursor to Einstein’s General Theory of Relativity, which is a theory of gravitation. The latter tells us how large objects – people and aeroplanes, for example – are affected by gravity; that is why we can’t float around and why spacecraft can orbit the earth.
Theories evolve and there is a more recent theory for tiny particles that incorporates Special Relativity; it is called “Quantum Field Theory”. An even more recent theory that lots of scientists are working on now is called “String Theory”. Since strings are thought to be the smallest pieces that form all other matter, if anyone can understand how strings work, then we will all understand the world better.
We are used to thinking about the world we live in as made of three spatial dimensions plus time. In string theory there are ten dimensions: nine spatial plus time. We cannot experience these spatial dimensions in the way we know our own three dimensions because they are too small.
To begin to grasp the idea of nine spatial dimensions, imagine three levels of space. The outer level is our three-dimensional space, then curled up inside our big three dimensions are three smaller dimensions. At every point in our three-dimensional space, we pass through them, but we do not know it … and, curled up again inside those, are three smaller dimensions still … the inner space of the strings … the last of the Russian dolls.
The idea of spaces nested inside other spaces is not so unfamiliar to us; just imagine the pregnant woman with the embryo curled up inside, and, inside the embryo again, eggs for a future generation.
There are half a billion possible geometries that we know about for the inner space of the six additional dimensions. One way to get a sense of the shape of the inner space is to zoom out until the three smallest dimensions become invisibly small, until we are left with a 3D space that looks exactly like the outer 3D skin of a 4D polytope (a 4D polytope has an outer 3D skin, just as a 3D polytope has an outer 2D skin). In this house, you see the unfolded 3D skin in sculptural form and the projected 3D skin in my drawings. These 3D skins represent the spaces that the strings could inhabit. If we zoom back into these 3D skins the sharp edges and corners get smoothed out and the additional three smaller dimensions come back into sight. The resulting six-dimensional space is the inner space.
Four-dimensional polytopes are fascinating in them- selves. Although we cannot directly experience them, we can intuitively imagine them folding and unfolding, and we can draw projections of them in two and three dimensions. Because we can unfold a four-dimensional form to create a three-dimensional form, we can say that the fourth spatial dimension precedes the third spatial dimension. The skin facets of an unfolded four-dimensional form may appear to be separate from each other in three dimensions, but in the fourth spatial dimension they would be folded up, in full connection with one another.
I often feel a bit like one of these four-dimensional polytopes, unfolded in my daily life, living out many different roles … mothering twins, doing art, writing emails, managing the struggle against the disorder of home, self, family. But I carry a sense that it is the same “me” behind all these activities … and sometimes I just wish to be folded up.
Every now and then I imagine that all these facets of the polytope represent different people, and all living beings, in our little worlds – messy entangled processes that we are – still living an illusion of separateness from each other. Even so, we are aware that, on a deeper level, we are connected. Through meditation on four-dimensional forms, we can contemplate the multi-dimensional nature of reality and our limited experience of its fullness. We can imagine ourselves folding and unfolding and know that whatever our fleeting experience of wholeness may be, it is tapping into something real. Perhaps the mathematical object is more “alive” than we give it credit for.