What does N-Dimensional mean?

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Discussion Overview

The discussion centers around the meaning of the term "n-dimensional" and its implications in both mathematical and physical contexts. Participants explore the concept of dimensions beyond the familiar three, touching on theoretical models and the use of "n" as a variable in describing dimensions.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants note that "n-dimensional" refers to models that extend beyond the three dimensions of our physical world, with examples including 4, 5, and even 11 dimensions.
  • Others argue that the term "n" is a mathematical construct that generalizes the concept of dimensions, similar to how one might refer to n-player games.
  • A participant suggests that a meaningful explanation of "n-dimensions" may require mathematical context, questioning the feasibility of a non-mathematical explanation.
  • Several participants provide examples of how dimensions can be used to describe various states or conditions, such as a 6-space that includes latitude, longitude, altitude, temperature, and humidity.
  • There is a question raised about the appropriateness of using "n" versus "x" to denote dimensions, with some suggesting that "n" typically denotes an integer in mathematics.
  • Some participants clarify that "n" is simply a variable representing any number of dimensions, which could include 2D, 3D, 4D, etc.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of mathematical context for understanding "n-dimensional" and whether the term has a specific meaning or is merely a variable. The discussion remains unresolved regarding the best way to conceptualize and explain "n-dimensions."

Contextual Notes

Some limitations in the discussion include the challenge of providing a non-mathematical explanation for a fundamentally mathematical concept and the ambiguity surrounding the specific meaning of "n" in different contexts.

nomisrosen
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What does "N-Dimensional" mean?

What exactly does the term "n-dimensions" mean? I've also seen "n-space". Please, no math, just a simple explanation!

Thanks!
 
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We seem to live in a 3-dimensional world. There are models that are 4-dimensional, 5-dimensional and even 11-dimensional. This number, when unspecified, is generalized simply as n-dimensional.


Just like you might say there are 1 player games, 2 player games, 3 player games, all the way up to n-player games.
 


nomisrosen said:
What exactly does the term "n-dimensions" mean? I've also seen "n-space". Please, no math, just a simple explanation!

Thanks!

I would add to Dave's statement the following: since it is a fundamentally mathematical concept once you get past our familiar world of 3 dimensions (4 if you count time as the 4th) so an answer without math doesn't seem to be a meaningful concept. Or maybe the answer that would be meaningful to you would be "it is a mathematical construct" (and some values of n may describe physical space, but many, and certainly those above a dozen or so, certainly do not seem to).
 


nomisrosen said:
What exactly does the term "n-dimensions" mean? I've also seen "n-space". Please, no math, just a simple explanation!
This is like asking for an explanation of the term "quixotic" that doesn't use words, so you may want to rethink the "no math" request.
 


If someone asks where you were at 3 hours GMT yesterday you can tell them latitude, longitude and how far above the surface of the earth. So there are 4 numbers used to specify your location in spacetime. Consider that we also what to know what the temperature and humidity are at that location (generally at any location) then that's another 2 numbers for a total of 6 numbers. Each of these numbers is independent of the other and each number is needed to characterize what we're interested in. This is a crude example of a 6-space.

You can imagine other kinds of information that you might want to relate to one another such as the volume of each of 12 different petroleum products that result from distillation based on the concentrations of 5 different catalysts and over a range of temperatures and pressures. This might be thought of as a 19-space modeling a petroleum refinery - crudely.
 


xristy said:
If someone asks where you were at 3 hours GMT yesterday you can tell them latitude, longitude and how far above the surface of the earth. So there are 4 numbers used to specify your location in spacetime. Consider that we also what to know what the temperature and humidity are at that location (generally at any location) then that's another 2 numbers for a total of 6 numbers. Each of these numbers is independent of the other and each number is needed to characterize what we're interested in. This is a crude example of a 6-space.

You can imagine other kinds of information that you might want to relate to one another such as the volume of each of 12 different petroleum products that result from distillation based on the concentrations of 5 different catalysts and over a range of temperatures and pressures. This might be thought of as a 19-space modeling a petroleum refinery - crudely.

Well, yes, but I interpreted the question as asking about physical space dimensions extending beyond 3 we know and live in.

nomisrosen, what were you really asking?
 


phinds said:
Well, yes, but I interpreted the question as asking about physical space dimensions extending beyond 3 we know and live in.

nomisrosen, what were you really asking?

I was wondering what is meant by n-space or n-dimensions in physics. I guess it means anything more than our familiar 3, but why the term n? Wouldn't "x-dimensions" be more appropriate?

My main question was whether the term "n-dimensions" has a specific meaning (specified number of dimensions in a specific type of space) or if it is just a variable.
 


nomisrosen said:
I was wondering what is meant by n-space or n-dimensions in physics. I guess it means anything more than our familiar 3, but why the term n? Wouldn't "x-dimensions" be more appropriate?

My main question was whether the term "n-dimensions" has a specific meaning (specified number of dimensions in a specific type of space) or if it is just a variable.

Well, n usually denotes an integer in math... that might have to do with it...
 


nomisrosen said:
I was wondering what is meant by n-space or n-dimensions in physics. I guess it means anything more than our familiar 3, but why the term n? Wouldn't "x-dimensions" be more appropriate?

My main question was whether the term "n-dimensions" has a specific meaning (specified number of dimensions in a specific type of space) or if it is just a variable.

Yes, n is just the variable. So if I say n-dimensional, i may mean 2d, 3d, 4d and so on and so on.
 
  • #10


Thank you!
 

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