A question about page 4 of this site

[scrub1942]

Hi all -
I am new to this site, but intensely intrested. I have a question... on page 4 of this site, when Bob puts the nail through Fred's 2-d world, it says that Fred sees a circle appear in mid air. Wouldn't Fred actually see a line segment? If the 3-d Nail penetrated the 2-d plane at 90 degrees, wouldn't Fred see a line? I think that understanding the relation betweeen the 2-d and the 3-d world is integral to my understanding of the 4-d and 3-d relationship.

Thanks for your input!

[wendy]

Have a look at the set of "hyperspace" pages from my polygloss, at

http://www.geocities.com/os2fan2/gloss/index.html

This is an insight into how to use hyperspace (relation between N and N+1 dimensions) to explore 4 dimensions. The idea is to think in terms of

pictures + maps have 2 dimensions

things fall in pictures but not in maps

So when you do interesting things like design cities etc in 4d, the idea is to keep focus on "what things do" rather than what shape things are.

A road connects: it is a 1d thing. On a map of 4d (which is 3d), a line does not divide. On a map of 3d (which is 2d) a line divides. So you have to cross streets in 3d, but not in 4d.

A sword divides: specifically moving the sword makes something that divides, so the blade-tip is (solid space) - 1 dimension [we're spliting, not squashing] - 1 dimension [because motion makes this up]. It is 1d in three dimensions (ie a line), but 2d in four dimensions.

[Chaos]

He would see a line, but it would make sense to him in a way we can't imagine. If you think about it, planespace is supposed to be infinitely flat, so the line he sees would therefore be infinitely thin, generally making it almost invisible. Imagining what it would be like to live in planespace is almost as difficult as comprehending tetraspace.

[pat]

I have a question... on page 4 of this site, when Bob puts the nail through Fred's 2-d world, it says that Fred sees a circle appear in mid air. Wouldn't Fred actually see a line segment?

Push a nail through a piece of paper. Now, pull the nail out of the paper. What shape is the hole?

It is a circle. If you were living on the piece of paper, you'd be able to walk all around that circle and verify that it's actually circular. From a distance away, it may just look like a segment that's the length of the diameter. But, if you still had perspective vision... or shadows... or some other depth cue... you would be able to see that it's not a flat line segment.

[sup2069]

He would see a line, but it would make sense to him in a way we can't imagine. If you think about it, planespace is supposed to be infinitely flat, so the line he sees would therefore be infinitely thin, generally making it almost invisible. Imagining what it would be like to live in planespace is almost as difficult as comprehending tetraspace.

Or think about what emily, or a tetrabeing would feel like trying to imagine themselves living in 3d space. It would drive them mad!