General theory on dimensions

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Postby wendy » Wed Aug 01, 2007 7:21 am

While a fence might _appear_ to be a 2d thing, it is really a fat line, rather like a ribbon. The height of the fence serves to provide evidence of division.

The height of the fence is in no way dependent on the area to enclose, so it really is a latrous affair - that is, line-like-shaped. The reality is that the fence divides ground. The height of the fence is a measure of how the division ought be seen, while the length (alone) is related to the area to enclose.

The fence, then provides a "surface" to the ground enclosed, and so in higher dimensions too: the surface of a portion of ground in Nd, is then N-2 d, because the ground is N-1d, and the division is N-2.

The actual crossection can be a solid square, for what it matters.
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Postby bo198214 » Wed Aug 01, 2007 2:06 pm

Oh come on Wendy!
The discussion becomes absolutely fruitless.
For everyone here it is clear that a fence is 2d (in our 3d world).
To climb or jump over a fence is not the same as to cross a line; similarly for n-dim worlds.
You are the only one who tries to create your own deviating language by philosophical finickiness about "what really is" or the "true nature/purpose". Language shall serve for communication, not for confusion.

There are other words to express what you mean, in 3d it would be called perhaps "separating/dividing/boundary line". In 4 dimensions you can use "ground division area" or "boundary on the ground" in n dimensions or similar words.
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Postby wendy » Thu Aug 02, 2007 7:33 am

It is not all that fruitless.

A ribbon is clearly two-dimensional, having length and width, but it is used to substitute a one-dimensional string. In practice, these are three-dimensional things, with one free dimension - length. For this, one might use the word 'latrid' (1d-ish).

A fence is essentially a replacement for a line on the ground. The height of the fence is not dependentant on the area it encloses, but rather the effort of the closure.

It is a line around an area, with height. The pan-dimensional thing is that a fence is a bound of surface (area), with height. If you think the height is part of the figure then you would count it as N-1 dimensional.

However, it is best to regard the ground as N-1 dimensions, and any dividing space as N-2. This is how it appears on maps. Since we already understand the idiom that the real world is map + height, the use of the map notion serves to better visualise it.

For a fence, it really does not matter how long it is, for the purpose of visualising it. The height and width of it is more to do with dealing with stopping crossings, while only the portion of it on the map says where the crossings are not permitted.

A fence, then is rather like a ribbon, in that given a cross section, it can be usefully repeated in just one dimension, and therefore is a latrid thing.
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Postby bo198214 » Thu Aug 02, 2007 9:14 am

wendy wrote:A ribbon is clearly two-dimensional, having length and width, but it is used to substitute a one-dimensional string.
...
A fence, then is rather like a ribbon,

So we agree that a fence is 2d (in our 3d world) but for various aspects merely its 1d baseline is of importance.
Generalized to n dimensions a fence is n-1 dimensional but for various aspects merely its n-2 dimensional intersection with the ground is of importance.
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