Different
Dimensions

You know,

people need to use numbers

to map the world of physical experience

in 2 and 3 dimensions and more,

because human senses are not only insensitive,

they aren't always to be trusted.

Can we trust our eyes with regard to shapes in 3d,

when all we have to assess distance is binary vision

and eyes with a slight variable focus.

Touch is better for small things,

but as with the blind men and the elephant,

to assess the shape of larger things by touch

can depend on which bit of the thing you have a hold of.

Sight gives a bigger picture,

but things seem smaller when they are further away,

so how can we make sense of what we see in front of us?

How is it that we can look at a jumble of wires

and see something that we understand to be a mesh cube,

a crystal like net we can understand in our imagination,

but we can only be sure of what it is when we move around it.

When we stop we just see one shape before us,

though of course with the slight variation that comes from having two eyes.

But on a sheet of paper or a screen

humans can draw the extraordinary worlds

they can conjure up in their imaginations.

A simple sheet of axonometric graph paper

can quickly lead to representing the pathways of a platform game,

or a complex Diablo style dungeon,

and even the most subtle of scenery and character CGI creations

can in the end be seen to be

the ordered arrangement of a vast collection of polygons.

But not all those 3d imaginings stay behind the flatness of a screen.

A collection of polygons can form the panels of a football,

or the structure of a geodesic dome.

Things get really useful when they go from 2d to 3d.

It's not just origami.

But what about 4d?

What use can we make of that?

Well, we can imagine trying to follow a specific line of action

over a period of time.

That is imagining 4d in 3d.

You don't have to be a bobsleigh pilot

imagining the winding line through the upcoming high speed corners,

to know the need to plan ahead.

Moving platforms in games follow regular sequences of moves in space and time,

as do most bosses that need to be battled.

For all forms of combat on the chess board

or the battlefield,

there is need for prediction of events in time and sequence.

Strategy is planning ahead

imagining in 4d.

Of course, once we get up from 2d to 3d

it isn't all just straight lines and polygons,

there's all those curvy shapes that lie between.

But maths has something to deal with that,

a way of comparing objects simply in terms of their surfaces,

their holes and bubbles,

topology,

useful for tele- communications,

computer graphics,

and face recognition software.

And one branch of mathematics was in practical use

long before it was thought of as a branch of mathematics.

Knot theory is the study of closed curves

embedded in 3 dimensional space,

how they compare and link together,

but people have been using knots for a very long time.

Sailors had to learn their different knots,

and strung them together to form nets,

which also proved useful for tennis nets,

and goal nets,

and circus safety nets.

And linked knots are at the heart of so many woolcrafts,

like those of the islands,

knitted stitches forming patterns that go back in time

as part of the history of the place that they came from

and linking to the people that lived there.

And now, knot theory is used in biology

to describe configurations of DNA

and related long proteins.

and God is the Maker, the Shaper.