Reciprocal System Research Society

MWells wrote:

Space and time have the same properties by definition.

The only property that space and time have is "magnitude invariance".

MWells wrote:

Counterspace and space are the same thing.

Space and Counterspace are reference systems, based on different assumptions (for example, space has a plane at infinity; counterspace has a point at infinity). Hence, they have different invariants and properties. They are not the "same thing", but subclasses of the reference system class.

MWells wrote:

Therefore a linear translation and angular rotation ("turn") must be equivalent.

Analogous, not equivalent, since each is a function of measure within different reference systems.

MWells wrote:

This means that *both* linear translation and turn are primary.

Within their specific set of assumptions created by the relevant reference system.

MWells wrote:

That is, these two geometrical constructs are at the exact same ontological level.

Yes. Space and counterspace are also at the same ontological level, but just being on the same level does not make them identical.

MWells wrote:

There is no condition that allows a linear translation to not be primary.

...within the reference system of "space."

"Linear" is only one aspect of translation; "angular" is another. Given the assumptions of the RS, there is no condition that allows a translation (linear, angular or other) to not be primary, but those are dependent upon the reference system used by the observer.

Quote:

But one other problem creeps up... counterspace is polar, hence ANGLES, not linear translations, are PRIMARY.

Space and time have the same properties by definition. Counterspace and space are the same thing.

Therefore a linear translation and angular rotation ("turn") must be equivalent.

This means that *both* linear translation and turn are primary. That is, these two geometrical constructs are at the exact same ontological level.

There is no condition that allows a linear translation to not be primary.

But there are no other "subclasses". Why emphasize them as belonging to a set of two? Space and time are a duality ("motion"). There really is only one primary reference system which is also a duality ("mind"). It is impossible for the reasoning process to entertain the two qualities of space and time simultaneously. So, for purposes of convenience only, this one reference system has been split into two distinct methods of interpretation. It is this arbitrary separation that changes the order of the representation from primary to secondary. Secondary in the sense of attempting to express one in terms of the other - where they are indeed analogs.

As soon as we start believing that this separation is somehow real, we fall into the trap of thinking these two distinct prefaces are primary. The result is the creation of of concepts such as "time region", which does not preserve the inherent mutual identity of space and time - the qualities of which are supposedly to be represented as accurately as possible by the two reference systems.