What is the "dimension" of the world in which we live?

ByMichelSmolders

We are usually said to live in 3 dimensional space. In the first place, the following movie explains the question as to what the "dimension" is and what we are acquiring "why we are living in three dimensional space".

What is a dimension? In 3D ... and 2D ... and 1D - YouTube


We know that the world in which we live is three dimensional, but how do you know about that? We usually use three coordinate axes such as a combination of three numbers x, y, z or latitude, longitude, and altitude to point to a specific coordinate, but for that reason I think it is three dimensional It is not.


For exampleSpace filling curveIt is proved mathematically that if you use a mysterious curve called so, you can fill a plane or solid with a single line. What is drawn in this moviePeano curveIt is a curve called.


Even without using three numbers, using this space filling curve makes it possible to point to a specific coordinate with only one number. It can not be said that it is a three-dimensional space because it shows coordinates with three numbers.


Although it seems to be strange to say, this is made up of the reason that "the number of points in a square is the same as the number of points included in the straight line of that square is.


But we do not think that we are living in a single line folded into a mess. So why are we able to perceive that they are living in 3 dimensional space?


We do not perceive the three-dimensional space itself clearly, but we know only empirically that we are living in three-dimensional space.


Let's assume for example a diffusing gas. Gas spreads more and more with time. At this time, measure the radius of the gas spreading area and the volume of the gas.


If this world is a one-dimensional space, the volume is proportional to the radius, the volume is proportional to the square of the radius if it is two-dimensional, proportional to the cube of the radius in the case of three dimensions, ... From the relationship between volume and radius, you can see the dimensions.


Actually, for example, if the radius doubles after a certain period of time, the volume has expanded by 8 times. Because the volume is proportional to the cube of the radius, we know that we live in three dimensional space.