A third dimensional object has length, width and height

[Yaho1974]

A third dimensional object has length, width and height. Taking a cross-section of this object anywhere along one dimension results in a two dimensional object, i.e. a line segment with length and width.

A two dimensional object has length and width. Taking a cross section of this object anywhere along one dimension results in a one dimensional object, i.e. a point with only one measurement.

Is that to say that the cross section of a fourth dimensional object should be a three dimensional object? Taking a cross section of an object moving through time and space throughout it's life would result in a three dimensional object.

Is that to say that the cross section of a fifth dimensional object would be a single object moving through time and space? If you took every object that exists, while moving through time and space, in relation to each other and took a cross section you would be left with a single object moving through time and space.

Is that to say that the cross section of a sixth dimensional object would result in every object that exists moving in time and space in relation to each other? Calculating any given alternative of everything that exists at anyone given point would result in a single instance of every object that exists moving through time in space in relation to each other.

Is that to say that the cross section of a seventh dimensional object would be every possibility that could occur when everything that exists moves through time and space in relation to each other?

 

[EL]

Hi Yaho1974.

A third dimensional object has length, width and height. Taking a cross-section of this object anywhere along one dimension results in a two dimensional object, i.e. a line segment with length and width.

"The cross-section" is a two-dimensional object.
I wouldn't call something with length and width for a "line", since a "line" is a 1-dimensional object.

A two dimensional object has length and width. Taking a cross section of this object anywhere along one dimension results in a one dimensional object, i.e. a point with only one measurement.

A point is a zero-dimensional object. In this case it's more accurate to call the cross-section a "line".

Is that to say that the cross section of a fourth dimensional object should be a three dimensional object? Taking a cross section of an object moving through time and space throughout it's life would result in a three dimensional object.

That's pretty much true, although I'm not really sure what you mean by "result in"?


I'm not even sure how to start replying to your other questions...usually when you talk about higher dimensional objects (as in string theory) all the extra dimensions are spatial, and no one of them temporal.

 

[petm1]

A point is a zero-dimensional object.

Would you think of this zero dimensional object as an infinite number of small points or as just one point when using our visible universe as a scale? In other words; In the case of our visible universe, would we think of just one point or an infinite number of points when you think of a dimensionless point?

 

[wilgory]

A point isn't really an object. It represents a position in space or on a grid. It is dimensionless because it does not exist. Since it doesn't exist, to call it infinite would not be correct.

 

[petm1]

A point isn't really an object. It represents a position in space or on a grid. It is dimensionless because it does not exist. Since it doesn't exist, to call it infinite would not be correct.

A point represented as a position in space is not a dimensionless point, it is a point named the zero dimension for mathematics purposes. A dimensionless point could be anything that relative to us has no measurable value, like a photon at rest. A dimensionless point does exist we just can't measure it. Think of space as what we can measure between objects using our ruler of EMR with time itself as the dimensionless point that the EMR is traveling through. Our visible universe can be measured but outside of our visible universe is an even larger dimensionless point. A small point or an infinite number of points all appear the same to me, as just one dimensionless point. This is why I think of time as the expanding aether and space as what we measure via EMR.

 

[christianjb]

OK, follow up question.

The intersection of two lines is a point (except when the lines are colinear).
The intersection of two planes is a line (except when the planes are co-planar)

By extension- the intersection of two volumes is a surface (except when the volumes exist in the same 3D space).

So if I intersect two 3D spheres of radius 1 in 4D space, what surface would I get?