Can anyone define the fourth dimension geometrically?

  • Thread starter shawnr
  • Start date
  • #1
20
0
I know about the tessaract and I'd like to understand more about it from a Euclidean perspective so I may translate it algebraically.
 
Last edited by a moderator:

Answers and Replies

  • #2
PeterDonis
Mentor
Insights Author
2020 Award
32,901
11,391
I'd like to understand more about it from a Euclidean perspective
I'm not sure what you mean by this. A manifold with a Euclidean metric works the same regardless of the number of dimensions, so if you understand how 2- and 3-dimensional Euclidean spaces work, you understand how 4-dimensional Euclidean spaces work. What else do you need to know?
 
  • #4
34,675
6,386
My goal is to find ways to start linking the dimensions for a few book hypotheses I have written.
Per the rules of this forum (https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/ ):
Non-mainstream theories:
Generally, in the forums we do not allow the following:
  • Discussion of theories that appear only on personal web sites, self-published books, etc.
  • Challenges to mainstream theories (relativity, the Big Bang, etc.) that go beyond current professional discussion
  • Attempts to promote or resuscitate theories that have been discredited or superseded (e.g. Lorentz ether theory); this does not exclude discussion of those theories in a purely historical context
  • Personal theories or speculations that go beyond or counter to generally-accepted science
  • Mixing science and religion, e.g. using religious doctrines in support of scientific arguments or vice versa.
  • Philosophical discussions are permitted only at the discretion of the mentors and may be deleted or closed without warning or appeal.
 
  • #5
20
0
Well I just want some help and answers, but since you brought it up.

"Generally, in the forums we do not allow the following"
Generally meaning it is due to the tone of the message and not the letter.
My questions don't have to relate to my book at all. I am asking about 4-dimensional space on a three dimensional graph. In much the same way that you put a straight line (1 dimensional) on any chart. I'm asking about an already established idea. You can forget the book, I was just asking questions.

Back to the post: Can someone answer my last threads question or expound on manifolds for me please.
 
Last edited by a moderator:
  • #6
PeterDonis
Mentor
Insights Author
2020 Award
32,901
11,391
I don't know what a Manifold is, I'll look it up.
Ok, good.

Perhaps you can help my other thread question.
If you don't understand what a manifold is, then you need to learn that on your own first. Trying to answer your questions at this point would amount to giving you a course in geometry and topology, and that's beyond the scope of PF.
 
  • #7
PeterDonis
Mentor
Insights Author
2020 Award
32,901
11,391
Generally meaning it is due to the tone of the message and not the letter.
No; "generally" meaning it's a rule unless a particular exception is made, and any exceptions to the rule are at the discretion of the moderators.

I am asking about 4-dimensional space on a three dimensional graph. In much the same way that you put a straight line (1 dimensional) on any chart.
These are not the same thing at all. A 1-dimensional straight line has fewer dimensions than a chart (at least as long as the chart has 2 or more dimensions). A 4-dimensional space has more dimensions than a 3-dimensional graph.

Can someone answer my last threads question or expound on manifolds for me please.
As I said in my previous post, you need to learn the basics for yourself first. That includes manifolds, per my previous post; it also includes coordinate charts and projections (since in order to represent a space of n dimensions on a graph of fewer than n dimensions, you need to do some kind of projection). The questions you are asking are too general at this point to be answered within the scope of PF. Thread closed.
 
  • #8
34,675
6,386
Well I just want some help and answers, but since you brought it up.
No, actually, you brought it up when you said this (which I quoted):
My goal is to find ways to start linking the dimensions for a few book hypotheses I have written.
You're a new member here, so might not be aware of our rules, especially those on personal theories and the like.
 

Related Threads on Can anyone define the fourth dimension geometrically?

Replies
6
Views
1K
Replies
5
Views
13K
Replies
5
Views
5K
Replies
1
Views
1K
Replies
12
Views
894
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
10K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
8
Views
2K
Top