How to imagine the 4-space
$begingroup$
We represent 1-space by a straight line, 2-space by two perpendicular line and 3-space by 3 perpendicular line.
Do we represent 4-space by 4 perpendicular line?
If it is, how can I imagine it ?
linear-algebra vectors
asked Dec 14 '18 at 12:22
SmyraSmyra
71
$endgroup$
add a comment |
$begingroup$
We represent 1-space by a straight line, 2-space by two perpendicular line and 3-space by 3 perpendicular line.
Do we represent 4-space by 4 perpendicular line?
If it is, how can I imagine it ?
linear-algebra vectors
asked Dec 14 '18 at 12:22
SmyraSmyra
71
$endgroup$
add a comment |
$begingroup$
We represent 1-space by a straight line, 2-space by two perpendicular line and 3-space by 3 perpendicular line.
Do we represent 4-space by 4 perpendicular line?
If it is, how can I imagine it ?
linear-algebra vectors
asked Dec 14 '18 at 12:22
SmyraSmyra
71
$endgroup$
We represent 1-space by a straight line, 2-space by two perpendicular line and 3-space by 3 perpendicular line.
Do we represent 4-space by 4 perpendicular line?
If it is, how can I imagine it ?
linear-algebra vectors
linear-algebra vectors
asked Dec 14 '18 at 12:22
SmyraSmyra
71
asked Dec 14 '18 at 12:22
SmyraSmyra
71
asked Dec 14 '18 at 12:22
SmyraSmyra
71
asked Dec 14 '18 at 12:22
SmyraSmyra
71
asked Dec 14 '18 at 12:22
SmyraSmyra
71
71
add a comment |
add a comment |
1 Answer
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$begingroup$
Yes you can represent any n-dimensional space by its values along n to each other perpendicular lines.
But since we are beings living in a 3 dimensional space, we can not really imagine such a space where n is greater then 3. I find it the easiest to just think of it in an abstract sense, in that each position point just has n values which describe it completely and uniquely.
For 4 dimensions you could imagine being somehow outside of time itself and looking down on it. Then every event would have a unique position due to its physical position and the time it was happening. But as I said there is ultimately no way to really imagine a higher dimensional space.
answered Dec 14 '18 at 12:44
BörgeBörge
1,057415
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1 Answer
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1 Answer
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$begingroup$
Yes you can represent any n-dimensional space by its values along n to each other perpendicular lines.
But since we are beings living in a 3 dimensional space, we can not really imagine such a space where n is greater then 3. I find it the easiest to just think of it in an abstract sense, in that each position point just has n values which describe it completely and uniquely.
For 4 dimensions you could imagine being somehow outside of time itself and looking down on it. Then every event would have a unique position due to its physical position and the time it was happening. But as I said there is ultimately no way to really imagine a higher dimensional space.
answered Dec 14 '18 at 12:44
BörgeBörge
1,057415
$endgroup$
add a comment |
$begingroup$
Yes you can represent any n-dimensional space by its values along n to each other perpendicular lines.
But since we are beings living in a 3 dimensional space, we can not really imagine such a space where n is greater then 3. I find it the easiest to just think of it in an abstract sense, in that each position point just has n values which describe it completely and uniquely.
For 4 dimensions you could imagine being somehow outside of time itself and looking down on it. Then every event would have a unique position due to its physical position and the time it was happening. But as I said there is ultimately no way to really imagine a higher dimensional space.
answered Dec 14 '18 at 12:44
BörgeBörge
1,057415
$endgroup$
add a comment |
$begingroup$
Yes you can represent any n-dimensional space by its values along n to each other perpendicular lines.
But since we are beings living in a 3 dimensional space, we can not really imagine such a space where n is greater then 3. I find it the easiest to just think of it in an abstract sense, in that each position point just has n values which describe it completely and uniquely.
For 4 dimensions you could imagine being somehow outside of time itself and looking down on it. Then every event would have a unique position due to its physical position and the time it was happening. But as I said there is ultimately no way to really imagine a higher dimensional space.
answered Dec 14 '18 at 12:44
BörgeBörge
1,057415
$endgroup$
Yes you can represent any n-dimensional space by its values along n to each other perpendicular lines.
But since we are beings living in a 3 dimensional space, we can not really imagine such a space where n is greater then 3. I find it the easiest to just think of it in an abstract sense, in that each position point just has n values which describe it completely and uniquely.
For 4 dimensions you could imagine being somehow outside of time itself and looking down on it. Then every event would have a unique position due to its physical position and the time it was happening. But as I said there is ultimately no way to really imagine a higher dimensional space.
answered Dec 14 '18 at 12:44
BörgeBörge
1,057415
answered Dec 14 '18 at 12:44
BörgeBörge
1,057415
answered Dec 14 '18 at 12:44
BörgeBörge
1,057415
answered Dec 14 '18 at 12:44
BörgeBörge
1,057415
1,057415
add a comment |
add a comment |
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