Shape
&
Movement

From the simple shapes of their early understanding,

with solids that could be seen and touched,

humans take their ideas inside their heads

and lead them into different dimensions.

They quickly learn how to understand

the 3d meaning of a 2d illustration.

And from a need to be able to distinguish mountains or canyons

from flat land in maps of the landscape,

they learned to imagine 3 dimensions from marks on a 2d page.

This ability is so common that they tend to forget just how special it is,

being able to imagine things with depth.

And from maps tracking flat paths for roads or canals,

they took to imagining upwards, through buildings and air traffic control

and space travel,

and imagining downwards through pipes and tubes for power and water

and sewage, and underground railways,

and further below them

studying geological layers.

Of course,

with the invention of electronic screens,

allied to silicon chips,

the use of paper rapidly declined

as it became possible to represent depth in layers,

so that a representation of a 3d object

could be manipulated on screen

so as to be seen from different viewpoints.

And as a series of viewpoints

could then be viewed in sequence,

they could be used to create animation and game worlds

representing three dimensions on a 2d screen.

Game and movie animation can also be seen as an exercise in moving 3d objects in time,

sequences that can be seen as imagining 4d through a 3d illustration,

itself illustrated on a 2d screen.

Humans can see such extraordinary things

through their imaginations,

and it is a talent they enjoy,

as can be seen in the way that they see beauty in symmetry.

There is a certain pleasure that is gained

from seeing something and being aware of

an ability to transform one side into its opposite

by simply using imagination

to flip it through another dimension.

There is a sense of balance.

And with minds that can travel into dimensions beyond those they can sense,

the idea of symmetry can lead to some extraordinary places,

with some extraordinary numbers.

And so it was with the discovery

of the number that is known as 'The Monster'.

A strange thing indeed,

needing some tricky multidimensional mathematics to discover,

but like any real number, imaginable.

What use it might be in the tangible world is yet to be imagined,

but we can be sure that it is in the imagination

that the power of the intangible lies.

imagining 5d in 4d in 3d in 2d knots and topology

symmetry and the monster