3-d geometry is not math., it is theoretical physics

[Yuri]

For physics it is important to know math. We all know real numbers - very important. What advances in math. do we have since the real numbers? Geometry? No, 3-d geometry is not math. -- it is theoretical physics, theory of unmoving physical bodies where math and physics welded together in some inseparable complex. It became clear when 4-d "geometry" became immanent. I put quote because the math that is implicitly used in 3-d geometry should carry another name and should be formulated for n dimensions. Is it Riemann n-d geometry – yes, but: a) I do not feel comfortable with the name geometry. I would rather say “math theory of n-dimensional numbers”. b) For the most physical applications including special relativity (SR) we do not need curvature. That means some simplification.

The problem we have is that only elite knows “Riemann geometry”. We are in a situation like if would only elite knew real numbers. Starting with Einstein, we are trying to build some inseparable compound of 3-d geometry and Einstein's postulates in SR. We need to stop that and study math theory of n-d numbers so that majority who discuss physical problems knows it and uses it.

[Edge]

3-D geometry is math. Is 2-D geometry with, say, another dimension.

[Yuri]

Originally Posted by Edge

3-D geometry is math. Is 2-D geometry with, say, another dimension.

2-D Riemann geometry included in 3-D Riemann geometry when everything does not deepend of one of the coordinates (or one of the coordinates assign to zero). Also can be considered independently as 2-D Riemann geometry. It is math. When either of them is applied to explain physical objects (like a triangle drown on the board) -- it becomes theoretical physics. In schools they teach how explain point, line, triangle only. Mathematics has nothing to do with physical objects -- it is only about numbers!

[Edge]

Originally Posted by Yuri

2-D Riemann geometry included in 3-D Riemann geometry when everything does not deepend of one of the coordinates (or one of the coordinates assign to zero). Also can be considered independently as 2-D Riemann geometry. It is math. When either of them is applied to explain physical objects (like a triangle drown on the board) -- it becomes theoretical physics. In schools they teach how explain point, line, triangle only. Mathematics has nothing to do with physical objects -- it is only about numbers!

Geometry is not math then?

[Yuri]

Originally Posted by Edge

Geometry is not math then?

Geometry is a demonstration how math can be applied to the resting physical objects. But what is the math itself? The math itself should be called "math theory of n-d numbers" (my opinion) and taught before geometry.

[Pyrotex]

Originally Posted by Yuri

For physics it is important to know math. We all know real numbers - very important. What advances in math. do we have since the real numbers? Geometry? No, 3-d geometry is not math. -- it is theoretical physics, theory of unmoving physical bodies ...

If we are going to 'play games' with the definitions of well understood concepts, then we can make any conjectures we want and generate as much confusion as we can tolerate. For example, 3-D geometry is theoretical bunny breeding, or, 3-D geometry is just mechanical drawing.

Math has several closely related definitions. One is: a rigorous set of relationships between symbols that represent integers, real numbers, complex numbers, points, lines and curves; and a set of rigorous rules for manipulating those symbols such that self-contradictions do not occur.

Since 3-D geometry fits that definition, it is a 'math'.

Your confusion may arise because among all the maths, the ones we find most useful are those that accurately 'model' some aspect of the real world we live in (Physics). The Calculus, for example, is spectacularly successful at modeling the movements of physical objects, especially where those movements change with time. That doesn't mean that The Calculus "is" Physics. It is still a math -- and -- you can't "do" real Physics without The Calculus. You can say much the same for 3-D Geometry.

Does this help, or have I misunderstood your question?

[Yuri]

If we are going to 'play games' with the definitions of well understood concepts, then we can make any conjectures we want and generate as much confusion as we can tolerate. For example, 3-D geometry is theoretical bunny breeding, or, 3-D geometry is just mechanical drawing.

I agree. It is better not to touch the deep-routed traditional concepts unless it is really urgent. And it is urgent: 100 years past since the theory of special relativity (SR) was created and still more than a half of professors of physics do not understand it (say nothing about students). I claim 3-d geometry responsible. Theoretical physics uses mathematics as a tool. One has to know the tool itself separately from its application and before its application.

Math has several closely related definitions. One is: a rigorous set of relationships between symbols that represent integers, real numbers, complex numbers, points, lines and curves; and a set of rigorous rules for manipulating those symbols such that self-contradictions do not occur.

I agree with 'integers, real numbers, complex numbers'. I do not agree with 'points, lines and curves'.
In Math Dictionary: point -- one of the basic undefined elements of geometry possessing position but no nonzero dimension; line -- …one of the basic undefined terms in Euclidean geometry,… A line has infinite length, but zero width and zero thickness.

It is the definitions of physical objects. The math definition would be: point -- becomes definite if 3 ordered real numbers (x,y,z) are given; line -- multitude of points that becomes definite if 3 ordered (x=…,y=…,z=…) linear functions of a one parameter are given.

Since 3-D geometry fits that definition, it is a 'math'.

Your confusion may arise because among all the maths, the ones we find most useful are those that accurately 'model' some aspect of the real world we live in (Physics). The Calculus, for example, is spectacularly successful at modeling the movements of physical objects, especially where those movements change with time. That doesn't mean that The Calculus "is" Physics. It is still a math -- and -- you can't "do" real Physics without The Calculus.

The Calculus happen to be math because it deals with numbers.

Does this help, or have I misunderstood your question?

Thank you!
***************