THE CONCEPT OF THE OAWOO
Having defined the IBOZOO UU as an elementary entity composed by a beam of orthogonal axes which cannot cross each other, we intentionally introduced (for teaching purposes) a concept which you must reject: that expressed by a very familiar word on Earth: AXIS.
If you associate our word OAWOO (AXIS or DIRECTION) with a straight line that has direction, we must start over again because you will not have understood any of our preceding explanations.
Obviously there is a serious obstacle there for we speak different mathematical languages, languages conditioned by a set of different psychological perceptions between you and us.
So we invite the laymen in mathematics to imagine the IBOZOO UU as a series of axes (indefinite, ideal straight lines), whose DIRECTIONS could never be compared to axes or real or ideal lines.
D59_FG22
We wish to insist on the fact that an isolated IBOZOO UU is illogical to conceive, i.e. that it has no reality. We say AIOOIEDOO (false concept, absurdity, has no reality).
We will take an example for the laymen of the Earth.
Imagine that we wish to obtain a closed enclosure (container) and that we have a certain number of cylindrical vases. Obviously, an insulated vase will never constitute a closed space, but if we close its opening by another (D59_FG23)
D59_FG23
We will obtain a small CLOSED ENCLOSURE. A series of such vases would form a chain of sealed enclosures, as in D59_FG24
D59_FG24
Before we continue, it would be useful to go into more detail about the concept of a STRAIGHT LINE. The distance from one point to another must be interpreted as a succession of IBOZOO UU whose EIDIIU (angles) or more precisely, whose IOAWOO (1) differ between them as dq. (see D59-fg17). The difference between EIDIIU and IOAWOO is very important: EIDIIU is our translation of the familiar concept of an angle. Thus an EIDIIU is the right angle formed by a vertical wall and the floor of a room.
IOAWOO would be " the ANGLE " formed by two OAWOO (" AXES ") of two associated IBOZOO UU (D59_FG11); if in both cases we use the word " ANGLE ", whereas they are two very different concepts, it is because there does not exist in your language a corresponding word (NdR: To our knowledge the concept of "angle "formed by two axes in space, axes which do not intersect, does not exist in our geometry, which requires, for the definition of these two axes, a projection onto planes, or the measurement of two angles compared to a trihedron of reference. Which geometrician will formulate the IOAWOO?)
We said to you that between two points (D59_FG15) we can consider not one, but an infinity of different chains of IBOZOO UU (for various three-dimensional reference systems). In other words, it would appear that one of them is actually " geodesic " (the shortest line a body would follow between two points of a hypersphere located within a framework of four dimensions) D59_FG25 A.
D59_FG25
But this is insufficient. Any other arc located in this sphere (representating for instance a larger apparent distance as in D59_FG25 B) is represented by the SAME chain of IBOZOO UU, which it would be incorrect to qualify as GEODESIC; we thus prefer to qualify it as GEOIDIC, even if the two words have an similar etymology on Earth.
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