In the previous post, I ended with the suggestion that, in the study of the RST, we ought to seriously consider replacing the LST's algebra, based on the imaginary square root of -1, with the new algebra, based on the real square root of 2. There is a subtle play on words here, because the meaning of the word real can be taken in two ways, both of which are relevant to the discussion: The first meaning is real vs. imaginary, while the second meaning is real numbers vs. integer numbers.

As I have been explaining here, on the LRC site, and elsewhere, Larson's work has brought us to the nexus of science and mathematics.

For mathematicians, the term "multi-dimensional scalars" is an oxymoron. Scalars, by their definition in the legacy system of mathematics (LSM), have no dimensions and the pseudoscalars are not normally thought of as numbers.

Arguably, the most profound consequence of the first fundamental postulate is that the theoretical universe is a universe of numbers, because, as I explained in the last post, all counting numbers can be represented as simple ratios. Another way of stating this is to assert that the set of counting numbers consists of one component, ratio, existing in three dimensions, in discrete units, and with two reciprocal aspects, numerator and denominator, an exact parallel to the first postulate of the RST.

Two of the most important concepts of Larson's work, though exceedingly simple, are some of the least understood. They are the concepts of unit progression and unit speed-displacements. The progression algorithms (PAs) are even less understood, even though they are mathematical expressions of these two fundamental concepts of the RST.

Larson explains the concept of the unit progression in Chapter II of The Structure of the Physical Universe (SPU). He writes:

In contemplating the postulated scalar, or magnitude only, motion of the universe of motion, we are assuming that it exists in three dimensions, in discrete units, with two reciprocal aspects, space and time. One of the first questions that arises then concerns how to express this motion, or even illustrate it, appropriately.

In the previous post, I explained how the second postulate, like the third postulate, is not really needed, if one understands that the assumptions it makes explicitly are really a consequence of the logic of the first postulate; That is, if it is assumed that the units of space-time are all that exist, and that they exist as reciprocals, and the only way a non-unit ratio of these units can be formed is if the scalar "direction" of their increase can change to a scalar decrease, and thereafter alternate between an increase and a decrease of scalar magnitude, then it follows that t

On the RS2 site, here, Bruce Peret discusses the history of Larson's development of the fundamental postulates from which he deduced his universe of motion. Bruce makes some interesting observations on the evolution of the postulates, which started me thinking about some fundamental issues in geometry and mathematics.

One of the most important, and most mysterious, elements of the Reciprocal System of Physical Theory is what Larson called the "inter-regional ratio." Evidently, it was the subject of some conversation at the 1984 ISUS conference, in Salt Lake City, because afterwards, each ISUS member was invited to "write a statement of his ideas on the subject for publication in Reciprocity." In Larson's statement he writes: