- #1
Antonio Lao
- 1,440
- 1
Dimensions Defined without Coordinates?
Mathematicians, I'm sure, have solidly clear idea of dimension but not to me. So allow me to ask some questions for all who have a clear understanding of the concept of dimension.
Can we define dimension without the use of so called multidimensional reference frames with their equal number of coordinates? 3 coordinates in Cartesian system. 4 coordinates in Einstein's relativities. 10 and 11 coordinates(?) in superstring and M-theory.
What is the true relational correspondence between dimension and direction?
How can direction be defined without a coordinate system or a reference frame?
What is the physical meaning of angles (plane, solid and abstract phase angle)? Can direction be defined without angles?
Mathematicians, I'm sure, have solidly clear idea of dimension but not to me. So allow me to ask some questions for all who have a clear understanding of the concept of dimension.
Can we define dimension without the use of so called multidimensional reference frames with their equal number of coordinates? 3 coordinates in Cartesian system. 4 coordinates in Einstein's relativities. 10 and 11 coordinates(?) in superstring and M-theory.
What is the true relational correspondence between dimension and direction?
How can direction be defined without a coordinate system or a reference frame?
What is the physical meaning of angles (plane, solid and abstract phase angle)? Can direction be defined without angles?