Representing a 4th dimention on paper

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Discussion Overview

The discussion explores the representation of the fourth dimension, particularly in relation to visualizing higher dimensions on paper and the implications of time as a fourth dimension. Participants engage in theoretical reasoning, drawing connections between dimensions and concepts from relativity and quantum physics.

Discussion Character

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

Main Points Raised

  • One participant describes a method for visualizing the transition from lower dimensions to the fourth dimension by drawing shapes and connecting them with lines.
  • Another participant confirms the drawing method but notes the distinction between orthographic and perspective views in representing dimensions.
  • A participant proposes that if time is considered the fourth dimension, all events exist simultaneously, and movement through this dimension is continuous, suggesting that faster movement in space correlates with faster movement through time.
  • Another participant challenges this idea, stating that objects moving faster in the first three dimensions actually experience time more slowly.
  • Further discussion introduces the notion of multiple possible pasts leading to the same future, suggesting a fifth dimension to represent these possibilities, which is met with skepticism by others.
  • One participant attempts to clarify their analogy regarding numbers and causation, asserting that different actions can lead to the same effect, and questions the existence of multiple versions of reality stored in a higher dimension.
  • A later reply discusses the nature of causes and effects in classical and quantum physics, emphasizing the complexity of the topic and the need for a consistent model to derive meaningful answers.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between movement through space and time, with some asserting that faster movement leads to slower time passage, while others propose alternative interpretations. The discussion on the existence of multiple pasts and dimensions remains unresolved, with competing perspectives presented.

Contextual Notes

Participants reference concepts from relativity and quantum mechanics, but there are limitations in the assumptions made regarding time and causation. The discussion does not resolve the complexities of these theories or their implications for understanding dimensions.

JPC
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This is just a little observation , if you could confirm, or explain a theory behind it
=>

if we start with one dimension we have one line
to get to 2D we draw the shape (here a line) somewhere else, and draw lines that connect them (here 2)
then to get to the third, we again draw the shape (here a rectangle) somewhere else , and draw line to connect them (here 4)

So i was thinking for going to the 4th dimension, i draw a cube somewhere else on the paper, and draw the 8 lines that connect them

here is a little drawing i made to explain what i mean
http://i73.servimg.com/u/f73/11/43/46/43/draw10.jpg
 
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That's correct.

You can do a google image search for more pictures. The Wikipedia page is a pretty good introduction.

Note, though, that your drawing uses an orthographic view (like building plans drawn on CAD). Some pictures you will find will look like a small cube inside a large cube, and these are done with a perspective view, where points farther away appear closer together.
 


ok thank you

this gives an other idea
i am just going to think my way with the few things i know about relativity, so feel free to correct me if i am wrong, or completely off the point

if we consider time as the 4th dimension, it means that everything that will happen and that has happened already exists. And we are in a continuous movement in this 4th dimension. If i understood well, objects with faster movements (bigger speed) in the first 3 dimensions, also travel the 4th dimension (time) faster. Meaning that it is possible to change our speed in this 4th dimension. But as it seems we can only travel it in one way, not the other way round.
And we know that different "pasts" can create the same future. For example by the application "power of 2", we have 2 possible pasts for 9 (-3 and 3). Meaning that there would exist a 5th dimension which would represent all the possible pasts there could have been leading to this present.
 


If i understood well, objects with faster movements (bigger speed) in the first 3 dimensions, also travel the 4th dimension (time) faster

Actually, objects traveling faster in the first 3 dimensions travel slower through time (at least, as far as the object can tell)
 


JPC said:
ok thank you

this gives an other idea
i am just going to think my way with the few things i know about relativity, so feel free to correct me if i am wrong, or completely off the point

if we consider time as the 4th dimension, it means that everything that will happen and that has happened already exists. And we are in a continuous movement in this 4th dimension. If i understood well, objects with faster movements (bigger speed) in the first 3 dimensions, also travel the 4th dimension (time) faster. Meaning that it is possible to change our speed in this 4th dimension. But as it seems we can only travel it in one way, not the other way round.

This isn't how it works. Things moving faster through space move *slower* through time. But it's more complicated than that, and you should go to the relativity forum for that.

And we know that different "pasts" can create the same future. For example by the application "power of 2", we have 2 possible pasts for 9 (-3 and 3). Meaning that there would exist a 5th dimension which would represent all the possible pasts there could have been leading to this present.

This *really* isn't how it works. When you "square" a number, you aren't changing the number you started with. Numbers don't have a "past", because they don't change. Numbers stand perfectly still in mathematics. It makes them (slightly) easier to work with.

The idea of "a 5th dimension to represent all possible paths" is pretty ridiculous. It's like saying a circle on a plane is three dimensional because you need an extra dimension to represent all possible points on it. You don't.
 


I know numbers don't change, i was just using that as an image. I just meant there are different actions that can have the same effect.

But do we consider that the past and future already exist, and that we have a speed in the 4th dimension that make us see a future ?

If so,
Do you agree that there are different possible causes that can have the same effect, and different possible effects that can have the same cause ?
And the way i think, these different "versions of the movie" must be stored somewhere.

Like for example you have "one movie" representing the 4 dimensions, how the position of the objects evolved with time.
And you have in a 5th dimension, all the different versions of the "movie", all the different plots their could have been in the movie.

///////////

Now from what you tell me, i know there is something wrong in my thinking here,
how does quantum physics see and explain all this ?
( i know, i realized at the end, i should have posted this in the physics section)
 


Are there two possible causes for a single effect? That question really depends on what you mean by "cause" or "effect".

If you're talking about a mechanical system in classical physics, then you can run time backwards and such an event never happens. In quantum mechanics, any process between measurements is similarly completely reversible, and so causes and effects are again strictly one-to-one.

Now, somewhere in there entropy comes along and ruins things. Uniform states spread out to random ones. Things heat up and never cool down without heating something else even more. Time seems to be very much to favor one direction over another.

I hope you see your question could have all sorts of interpretations. You can't really speak generally on the subject. You need to stick with one model (physical or mathematical, it doesn't matter) before you can get a meaningful answer out of it.
 
ok, yes i see what you mean
since i started by posting in the maths section, better stick to the mathematical model
 
JPC said:
if we start with one dimension we have one line
to get to 2D we draw the shape (here a line) somewhere else, and draw lines that connect them (here 2)
then to get to the third, we again draw the shape (here a rectangle) somewhere else , and draw line to connect them (here 4)

So i was thinking for going to the 4th dimension, i draw a cube somewhere else on the paper, and draw the 8 lines that connect them

You could also start with a zero-dimensional object, the point. Draw another point (the shape) somewhere else, and connect them with a line. Now you're at 1-dimension (a line segment) and can proceed as you did.

FYI:
http://en.wikipedia.org/wiki/Hypercube

You can also google "hypercube" and see what comes up.
 

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