2021-09-26

## Collisions - Dimensions - Forms

Yoshigasaki Sensei
talks about collisions, dimensions and forms.
"Well this here, this is a collision ..."

Video:
00:00 This is a collision. That's in one dimension.
00:04 Dimension means using a (new) dimension to make possible what was not possible before.
00:14 So he comes here. Now the collision can be avoided. That is the second dimension. That is the meaning of dimension. The new dimension makes possible what was not possible before. But with point mathematics.
00:32 Then he does that, right? Now there is no collision. But if I now stretch out my arm and he does not want to collide, then he has to look for the third dimension. This is the third dimension. This is Euclid, the geometry of Euclid. That is enough to cover all the points in this room. Then there is time as a dimension. So these are dimensions.
01:01 On the other hand, there are no dimensions in the mathematics of forms. Because they are forms. So, if he comes like that... or so... or? ... you understand. It is only form, there is no dimension. There are forms with which collisions occur and there are forms where there are no collisions. In the mathematics of forms, therefore, there are no dimensions. Everything is possible.

Comment:
This example makes shows what Yoshigasaki Sensei means with point mathematics and the mathematics of forms.
Point mathematics is working with the idea that space consists of points. This theoretical concept comes from physical mechanics. You quickly realize that you always need three values/numbers to describe the position of a point in space. These are the three dimensions of a Euclidean space. In addition, time can be defined as the fourth dimension.
In the first example (00:02), two people collide that go directly to each other. The straight direction is a one-dimensional line.
To avoid the collision, the person evades sideways (00:17), so he uses a second dimension.
With the arm outstretched, the person has to duck down (00:17) and thus uses the third dimension.
Avoiding collisions can also be understood as a change in the form of the body instead of change of positions in space (01:12-01:22). This is the so-called mathematics of forms. Seemingly it does not need the concept of dimensions.
According to Yoshigasaki Sensei, mathematics is the correct description of relationships and the mathematics of forms allows a better imagination of reality.
Bernhard Boll