What do you mean by 'multi-dimensional'?

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Discussion Overview

The discussion revolves around the concept of 'multi-dimensional' spaces, specifically in relation to tesseracts and higher dimensions. Participants explore the nature of dimensions beyond the familiar three spatial dimensions and one time dimension, touching on theoretical implications and interpretations.

Discussion Character

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

Main Points Raised

  • Some participants define 'multi-dimensional' as a space with more than one dimension, seeking clarification on its context.
  • One participant asks how to conceptualize a tesseract as a 4-D object and what the foundational basis for constructing it is.
  • Another participant explains that visual representations of higher dimensions can lose information, noting that a 3D representation of a tesseract will have intersecting lines and non-right angles.
  • One participant mentions that in spacetime, four dimensions are necessary to define a position, with additional spatial dimensions proposed by string theory, although their existence remains controversial.
  • A participant queries how to describe dimensions beyond the four of spacetime, prompting a response that refers to them as "extra dimensions."
  • Another participant suggests that characteristics of dimensions beyond the four could potentially be explained using only the x, y, z, and t coordinates, which is challenged by another participant who asserts that these extra dimensions are distinct from the conventional coordinates.

Areas of Agreement / Disagreement

Participants express differing views on the nature and characteristics of dimensions beyond the four of spacetime, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

There are unresolved questions regarding the definitions and implications of higher dimensions, as well as the relationship between these dimensions and the established coordinates of space and time.

upkiran
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What do you mean by 'multi-dimensional'?
 
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Welcome to PF!

Hi upkiran ! Welcome to PF! :smile:

"multi-dimensional" simply means that a space has more than one dimension.

What is the context? Does this come from a particular book?
 


Hi..

I want to know how do you realize multi dimensions. For example when you say that a tesseract is a 4-D object how do you expain its dimensions. what is the base to constructing a tesseract?
 
hmm … what's a tesseract? :rolleyes:

ah … one of those … http://en.wikipedia.org/wiki/Tesseract" .​


ok … you can "draw" a 3D version of a tesseract (eg the http://en.wikipedia.org/wiki/File:Schlegel_wireframe_8-cell.png" )

but like a 2D copy of a cube, you lose some information.

In a 2D copy of a cube, some of the lines intersect (in 3D they don't), and the angles between the faces aren't 90º.

Similarly, in a 3D version of a tesseract, some of the faces intersect (in 4D they don't), and some of the angles aren't 90º.

Four dimensions are the minimum necessary to have all the angles 90º, and to have none of the faces or "hyperfaces" intersecting where they shouldn't. :smile:
 
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In spacetime you need 4 dimensions to define a position - 3 spatial and one of time. Extra dimensions, mainly spacial, are posited by string theory. The need for these extra dimensions is controversial and no observational evidence for their existence has yet emerged.
 


Hi...

Ok now let's go a step further... Consider an object said to have more than 4 dimensions... If space and time constitute four of these dimensions how would you describe the remaining dimensions?
 
You just call them "extra dimensions". :smile:

(you can give them names if you like … but "what's in a name?" :wink:)
 


The name is not important...

I was talking about its existence or characteristics... i mean any dimension other than "THE FOUR" are said to be of the order of Planck length, right.. If so can't those dimensions be explained using only the x,y,z and t coordinates?
 
No, they have nothing to do with the x,y,z and t dimensions.

(just like t has nothing to do with the x,y and z dimensions :wink:)
 

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