Hyperspace:Home Intro Time Width Walls Bridges Rounds
If beings of diverse dimensions are made to share the same time and the same gravity, then they share the same forwards/backwards and the same up/down. Any other dimension that exists must become those of width, or across the direction of forward.
The Square¹ has no feeling of width, since this is part of his hyperspace. The Sphere has width, she being of the same world as we are. Yet the square can appreciate the notion of width, just as we shall experience the notion of a two-dimensional width.
A method often used to explore the higher dimensions is sectioning. What this entails, is for the Sphere to toss things through the plane of the Square, so that one sees a sequence of cross-sections.
The nature of sectioning brings on some inappropriate idioms, which make it harder to understand the nature of dimensions. Firstly, it introduces a temporal sequencing, where we are trying to get away from the use of tine in this fashion.Secondly, we do not visit random objects but whole vistas. There are much better idioms to look at the higher dimensions, such as maps and pictures.
This is much like trying to guage the shape of a figure by watching its outline as it passes through the surface of the water. It is not how we see things, and there are correspondingly much better things around for the hyperspace as well.
Instead, we use maps and pictures to display hyperspace. That is, we use the mapping of 2D, 3D onto 3D, 4D.
To appreciate how a floor-plan works, we first consider what a 2D floor might look like. All-space is the plane, so we lie on the floor, with our feet on a wall. We must stay on that wall, so you will appreciate that it is very hard to have furniture that sticks out from the floor. You're forever climbing over it. Note also that you are no longer a largish dot on the floor, but a very tall thing.Now look at the whole room as a floor plan. You are now a roundish dot about the size of your projection on the floor. Imagine this moving around the room, going to bits of furniture that are on any of the six walls (including the 3D floor and roof). The doors need only be small. Put furnature in the middle of the space, like a table in the room.
Let your mind drift around the house. You would then make other rooms the same, you can create a hallway that does not take lots of room.
What we have is a multistory building made in a one-floor bungalow. You can make stairs if you want to, but for this exercise, we shall stick to a single floor.
We can continue this exercise outside as well. One does not have to cross linear things, such as railways, roads, and rivers. A whole city the size of Brisbane can exist, such that one can drive across it, or walk across it or whatever, without ever having to cross a river, road or railway.
Likewise, there would be no intersections: roads would effortlessly merge in much the same way that the blood stream, lymp system, air tracts, nervous system, and digestive tracts co-exist without any signalled crossing.
We make use of a kind of holographic approach, based on the equation of the Square's solid space as a diagram we can look at, a map or picture. The Square's notion of a solid wall is to us a thin line surrounding,We see the Square, not as its skin, but as a mess of its innards. Its clothing is to us just a crumpled line around itself, and its lunch is plainly visible to ourselves.
So is it in 4D to us.
The notion of numbers as a feature of width is to us strange, but it is useful to reflect on how these numbers form. We are, essentially biological creatures in three dimensions, and the sorts of numbers has as much to do with space as anything else.
Natural fingers
size Some representive numbers in the
different dimensions, expanded as
geometric objects.
2D * * * 1+1 = 2
base 4 Note for example, that we have
the dimensions, while not necessarily
* * all-space, is none the less made as
a relation as solid.
3D * * * 1+4 = 5
base 10 Natural Size is something to deal with
* * the order of things that animals can
deal with in an instant, or the number
of major players that can be dealt with
4D 13 1+14 = 15 at once.
base 30
fingers is roughly based on the sort
of decimal-like base one might expect in
these dimensions.
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1 We make use of Abbot's Square and Sphere characters to represent the two- and three-dimensional figures.
Hyperspace:Home Intro Time Width Walls Bridges Rounds