A third dimensional object has length, width and height

  • Context: Graduate 
  • Thread starter Thread starter Yaho1974
  • Start date Start date
  • Tags Tags
    Height Length Width
Click For Summary

Discussion Overview

The discussion explores the properties of dimensional objects, particularly focusing on the implications of cross-sections as dimensions increase. Participants examine how cross-sections of objects in various dimensions relate to one another, including the transition from three-dimensional to higher-dimensional objects, and the nature of points and their dimensionality.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that a cross-section of a fourth-dimensional object should yield a three-dimensional object, suggesting that this aligns with how lower-dimensional objects behave.
  • Others argue that the terminology used to describe dimensions and their cross-sections may be misleading, particularly regarding the definition of a "line" versus a "point."
  • A participant questions whether a zero-dimensional point should be considered as a single point or an infinite number of points when viewed at the scale of the visible universe.
  • Some participants assert that a point is dimensionless and does not exist in a physical sense, while others challenge this by suggesting that a dimensionless point could represent measurable phenomena.
  • A later reply introduces a question about the intersection of two three-dimensional spheres in four-dimensional space, seeking to understand the resulting surface from such an intersection.

Areas of Agreement / Disagreement

Participants express differing views on the nature of points and dimensions, with no consensus reached on the definitions or implications of dimensionality. The discussion remains unresolved regarding the interpretation of higher-dimensional objects and their cross-sections.

Contextual Notes

There are limitations in the assumptions made about the nature of dimensions and the definitions of terms like "point" and "line." The discussion also reflects varying interpretations of dimensionality in relation to physical and mathematical concepts.

Yaho1974
Messages
1
Reaction score
0
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?
 
Space news on Phys.org
Hi Yaho1974.

Yaho1974 said:
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.
 
Last edited:
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?
 
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.
 
wilgory said:
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.
 
Last edited:
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?
 

Similar threads

Graduate What Insights Does the Fourth Dimension Offer About Our Universe?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How do we know space is expanding?
  • · Replies 24 ·
Replies
24
Views
2K
Undergrad Is the universe actually just mass and length?
  • · Replies 7 ·
Replies
7
Views
1K
Flow rate needed to lift object inside a vertical pipe
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How do we say that the universe we live is 3 dimensional?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad An Imagined Diffraction Grating
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Question about geometrical engineering (placeholder name)
  • · Replies 32 ·
2
Replies
32
Views
2K
High School Using energy principles to find equilibrium depth of floating object
  • · Replies 8 ·
Replies
8
Views
891
Graduate Alternative topology of our 3D space
  • · Replies 1 ·
Replies
1
Views
2K
High School A Valid Position on Time Theory?
  • · Replies 2 ·
Replies
2
Views
2K