Fundamental Postulates

One of more interesting facets of Dewey Larson's Reciprocal System is that an entire Universe can be derived from two, fundamental postulates. Larson based these postulates on everyday life—not mathematical theory:

“They [The fundamental postulates] have not resulted from a search for the absolute truth, whatever that may be, but from an effort to establish a working basis by which the ordinary phenomena of everyday life could be explained qualitatively and quantitatively.”¹ [emphasis mine]

Larson intended that his “physical universe” be the ordinary Universe in which we live—one of three, spatial dimensions and clock time. Over the course of the development of the RS, Larson has updated the postulates a number of times. Prior to the 1959 publication, The Structure of the Physical Universe, the postulates were:

Pre-1959 Postulates

1. The physical universe is composed entirely of a single entity: space-time, existing in three dimensions, in discrete units, and in two reciprocal forms: space and time.

2. Space-time conforms to the relations of ordinary mathematics, its magnitudes are absolute and its geometry is Euclidean.

3. (Exact wording has been lost, but concerned the scalar, magnitude-only, non-geometric nature of space-time).

Larson also included some “Laws” to clarify the Postulates:

1. Every physical event is accompanied by a reciprocal event equal in magnitude and opposite in space-time direction (General Law of Reaction).

2. The total amount of space-time displacement cannot be altered by any process within the physical universe (General Law of Conservation).

3. Where a physical event may have more than one possible result, the proportionate number of each alternative resulting from a number of events of this kind is equal to the mathematical probability (General Probability Law).

After consideration, Larson dropped the third postulate as unnecessary:

“In the early stages of this investigation the scalar nature of space-time was embodied in an additional postulate. Further study indicated that it was a necessary consequence of the previous assumptions, as indicated in the preceding paragraph, and it was therefore eliminated from the list of postulates.”² [emphasis mine]

He also dropped the General Laws as being a natural consequence of the Fundamental Postulates. This may not have been a good idea, as students of the Reciprocal System often confuse fundamental, scalar motion with the Euclidean motion of the physical universe. In Larson's view, it was obvious that "scalar space-time" was of magnitude only and as such, could not include any concepts such as a point, line, circle or plane—scalar motion has no geometry!

The first official publication of the Fundamental Postulates was in the 1959 publication, The Structure of the Physical Universe:

1959 Fundamental Postulates (from Structure of the Physical Universe)

1. The physical universe is composed entirely of one component, space-time, existing in three dimensions, in discrete units, and in two reciprocal forms, space and time.

2. The physical universe conforms to the relations of ordinary mathematics, its magnitudes are absolute and its geometry is Euclidean.

Most notably is the absence of the concept of motion—Larson started with the concept of space-time, which was nothing more than a ratio of two scalars: a magnitude of space inversely related to a magnitude of time. In later works, he changed space-time to motion, which was the same concept—a ratio of absolute, scalar magnitudes (again, NO GEOMETRY involved).

In the 1965 publication, New Light on Space and Time, Larson altered the 2^nd postulate to include the “commutative” adjective to mathematics:

1965 Fundamental Postulates (from New Light on Space and Time)

1. The physical universe is composed entirely of one component, space-time, existing in three dimensions, in discrete units, and in two reciprocal forms, space and time.

2. The physical universe conforms to the relations of ordinary commutative mathematics, its magnitudes are absolute and its geometry is Euclidean. [emphasis mine]

“Commutative” was added to counter the non-commutative mathematics becoming popular with the Relativity theory of the time. Larson was aware that conventional scientists did not comprehend the temporal nature of the atom, and he was able to approximate atomic properties quite closely with his “commutative” slide rule, so he converted it to a general statement.

It should be noted that the “commutative” adjective applies to the physical universe—NOT “space-time,” which has no concept of the number line on which the commutative property is based, being magnitude-only. Another facet missed by most RS students is that scalar motion can be increased or decreased through the mathematical concepts of evolution and involution—not added or subtracted, which are Euclidean, number-line based concepts.

By the time 1979 rolled around, Larson revised the Fundamental Postulates yet again, moving away from the idea of “space-time” and substituting the concept of “motion,” primarily because space-time had too many hard-core connotations with conventional scientists:

1979 Fundamental Postulates (from Nothing But Motion)

1. The physical universe is composed of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.

2. The physical universe conforms to the relations of ordinary commutative mathematics, its primary magnitudes are absolute, and its geometry is Euclidean.

When Larson wrote Beyond Space and Time, he discovered that his Fundamental Postulates did not apply to the non-physical Universe³, which was obvious by the opening remarks concerning the fact that he created the Postulates to reflect ordinary life—and metaphysics was hardly “ordinary.” To correct this, he added the set of Metaphysical Postulates:

1995 Metaphysical Postulates (from Beyond Space and Time)

1. There are existences in the metaphysical region of a more general and less restricted type than the units of motion that are the basic constituents of the physical universe.

2. The metaphysical existences are logical, orderly, and rational.

3. Metaphysical existence conforms to a specific set of laws and principles different in some respects from those of the physical universe.

4. The metaphysical existences of which we have evidence are intelligent.

As demonstrated by the need for Metaphysical Postulates, the Fundamental Postulates are not complete and all-encompassing of the Universe, in general, but only applicable to what Larson describes as “Level I—Inanimate” in Beyond Space and Time. Larson identified three levels of existence, which means that his Fundamental Postulates only describe approximately ⅓ of the known “ultimate truth” of the Universe, which is where RS2, the reevaluation of the Reciprocal System, steps in:

“… At best, therefore, what we term knowledge is merely an approximation and the advancement of knowledge is essentially a process of arriving at even closer approximations to the ultimate truth.

“Fundamental 'laws' and principles are no exception. Even though they may have served us well and faithfully in those fields wherein we have utilized them thus far, time comes that greater accuracy is needed we must replace them with closer approximations in order that progress may continue unimpeded. The carpenter's rule serves its own limited purpose very satisfactorily but the marvels of modern machinery would be impossible without micrometer calipers or their equivalent. From time to time, therefore, it is well that we should undertake a critical reexamination of our fundamental theory in order to determine whether it is still adequate to carry the additional burdens that our more advanced facilities for observation and measurement have placed upon it. Perhaps the branches of the tree may have become too numerous and heavy for the trunk to support.”⁴ [emphasis mine]

RS2 is the “critical reexamination of fundamental theory,” using modern tools developed by the computer industry, such as matrices, quaternions, projective geometry and the resulting virtual reality—commonplace tools we use and experience daily that were inconceivable when Larson published his first book in 1959.

In keeping with Larson's intent, you cannot have one set of rules for one situation, and another set of another. Larson was able to accurately define the physical universe in terms of space and time—he did not need one set of rules for the atomic configuration space, another for astronomy and another for mechanical interactions. But when he encountered the living realm, his "Level II—Biologic", the postulates fell apart.

Part of the RS2 reexamination effort is to find out why the Fundamental Postulates are not generally applicable to the other levels of existence and to find what can be done to correct that situation so they ARE of general applicability again. Larson changed the Postulates at least 5 times before they settled on their final form, then had to use a new set of postulates to continue from that point. RS2 believes that is unnecessary; that a simple modification of the Postulates, once again, can open the door to a generalized set of Postulates to include the other levels of existence that Larson documented, as well as to clarify some of the inherent problems identified with his “Level I” research.

Clarification of Larson's Fundamental Postulates

First off, some clarification of Larson's Fundamental Postulates are in order. For that, we will use a modern technique called an “ERD”—an Entity-Relationship Diagram—which graphically represents how the various components of the Postulates relate to each other:

The two postulates clearly describe two different realms in the Reciprocal System. The First Postulate delimits the behavior of motion, what Larson originally called “space-time” and is purely scalar—magnitude only. The Second Postulate delimits the behavior of the physical universe, which is based on the “ordinary phenomena of everyday life,” as Larson so aptly described it. A third realm was included, the Manifest Realm, to show the “observables” of the physical universe, since ordinary phenomena are what is observable—we cannot SEE a magnetic field, only the effect it has on real “observables.”

First Postulate: the Scalar Realm

Larson always used the mathematical definition of the scalar, “a quantity possessing only magnitude.” A scalar, as in motion or space-time, cannot have any associated geometric relationships. It is impossible for “5” to be at a right angle to “3.” But it can have attributes, such as integer or real values, can be contained in sets and can exist in mathematical relationships. Larson defines these explicitly in the First Postulate:

• “Discrete Units” refer to the set of integers, but note that Larson did not say “integers” or “whole numbers.” By using discrete UNITs, Larson is referring to the set of counting numbers, as a “unit” is a countable quantity with a minimum quantity of one. And we also know that Larson's “natural datum” is Unity, so there are no integer values less than 1 in the scalar realm.

• From observation, which is Larson's premise, the observable universe has 3 dimensions, so he limits the set of scalars to three dimensions. Note that these are independent dimensions, as there is no geometry to create a dependent relationship between them.

• Finally, he defines that there are two magnitudes involved in motion (or space-time), one aspect call space and the other, time, that exist in an reciprocal (inverse) relationship to each other, what is commonly known as a ratio. Note that the ratio of motion is also scalar, and has no geometry associated with it.

Second Postulate: the Coordinate Realm

The Second Postulate clearly defines the behavior of the “physical universe,” the realm of ordinary experience, by listing some of its basic character as a set of rules:

• It conforms to Euclidean geometry, which means it HAS GEOMETRY and hence cannot apply to the scalar realm of motion. It can be seen from Euclid's Postulates that this is, indeed, a coordinate realm being described:

  1. A straight line segment can be drawn joining any two points.

  2. Any straight line segment can be extended indefinitely in a straight line.

  3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.

  4. All right angles are congruent.

  5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate.

• Primary magnitudes in the physical universe are “absolute,” which has two meanings:

  1. Unchanging, in that the coordinate motion is dependent upon the uniform, scalar magnitude composing it and

  2. The magnitudes are always positive⁵. (Having a natural datum of unity, there cannot be “nothing” (zero), so the absolute magnitudes are the set of positive integers.)

• Commutative, because the coordinate realm is based on Euclidean, linear relationships—the number line. Again, Euclidean geometry and the commutative property only apply to the coordinate realm defined in the second postulate—not the scalar motion of the first!

The Manifest Realm

The physical universe can be seen as two, independent sectors: the material (the ordinary realm of 3D space and clock time) and the cosmic (3D time and clock space), which conventional science refers to as “antimatter.”⁶

Having material consciousness, we can only directly observe the material sector. In simpler terms, we use "space" to measure "space" and cannot directly measure any temporal event, such as a gravitational, electric or magnetic field, nor any cosmic structure. This limits our observable realm to only half of the manifest, physical universe, but we CAN get some idea of the cosmic side, by how time affects space. We cannot see a magnetic field, but we can see how it influences iron filings on a sheet of paper.

To clarify, in the material sector, we have "locations" containing time (scalar motion of atoms, 1^st Postulate), geometrically oriented in space (2^nd Postulate).

The New Micrometer: Virtual Reality

The field of computer imaging has produced some very precise and detailed tools for the construction of virtual realities—objects and images that appear so real, one has difficulty separating them from the real, observable objects in the physical universe. This is a big clue that these computers must be doing something right… when reduced to their simplest form, computers are nothing but binary bits, which are grouped into scalars, starting with integers—“magnitude only” that somehow manages to create virtual buildings, people, planets and galaxies. Sound familiar? It should—it's the SAME PROCESS that Larson documented as the Reciprocal System, from scalars to physical universe, but with millions of man-hours of effort refining the details of the process.

RS2 applies this new “micrometer caliper” of computer imaging techniques to replace Larson's carpenter's rule of the 1950s and expands upon Larson's request that the system be reexamined regularly to see what these new tools can do to refine and clarify the system.

The primary tool in this virtual toolbox is that of Projective Geometry, a technique that explicitly defines the process from converting a scalar magnitude, sitting in the memory of a computer, into a virtual reality that is nearly identical to that which we observe. Projective Geometry has actually been around for a long time.⁷ It became popular with the advent of computers and computer imaging and was used by the military to convert photographs into 3-dimensional scale models, so they could figure out what the enemy was building and determine its abilities and limitations.

Larson never provided a mechanism to convert scalar motion into coordinate motion, other than probability. Projective geometry provides this solution, in enormous detail.

The second tool in the virtual toolbox is the use of complex quantities to represent linear and rotational motion concurrently, as homogeneous coordinates and quaternions. Everyone is familiar with how you can define a point in space to determine a direction. There is also another process—using roll, pitch and yaw, as any flight simulator will demonstrate. The computer imaging process discovered that they are actually geometric reciprocals of each other; polar geometry is the inverse of linear geometry, and what better tool than a “geometric reciprocal” for a Reciprocal System of theory?

One Giant Leap for Larson-Kind

It is obvious that the biological realm, documented in Larson's book Beyond Space and Time, is composed of the same stuff everything else is made of. So why did Larson need to define Metaphysical Postulates?

Studies in the biological realm by Nick Thomas⁸ show that the geometric relations are not Euclidean in nature, as you find in the inanimate realm, but Affine—they appear as a scalar recursion. Some of the geometric assumptions made by Euclid do not hold true in living forms. This is because the type of motion is different. Larson's Postulates define the inanimate realm, where you have motion in EITHER space OR time. When it comes to the animate, living realm, a new kind of motion is introduced, a motion that is BETWEEN space AND time, which Larson roughs out as a “life unit.”

By using the tool of Projective Geometry, we can now clearly identify that the "Level I—Inanimate" realm of Larson's Postulates is in the Euclidean geometric stratum, the "Level II—Biologic" is in the Affine geometric stratum, and Larson's scalar motion (or space-time) sits cleanly in the Projective stratum, prior to geometric assumptions. All that is required to make Larson's original Postulates function in the biological realm is to acknowledge the different strata of geometry, each having applicability to a particular “level of existence,” as Larson calls them in Beyond Space and Time.

Larson's “Level III—Ethical” realm becomes a consequence of the stratification of geometry, defined by Projective geometry techniques in virtual models. It actually defines seven possible levels, of which Beyond Space and Time documents the first three.

By removing these limitations, Larson's postulates work for the biological and ethical realms—no additional postulates are needed. This is what RS2 has done in the reevaluation:

RS2 Fundamental Postulates

1. The universe is composed of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.

2. The universe conforms to the relations of ordinary mathematics, its primary magnitudes are absolute, and its geometry is Projective.

What did we change? No more “physical”—the Postulates now function for the non-physical, or “metaphysical” Universe. Euclidean geometry was changed to Projective geometry, to allow for the stratification into the Levels of Existence, and “commutative” was dropped, as it is inapplicable to motion that occurs in more than one dimension, such as the polar geometry of the life or ethical unit.

Now that we are using a micrometer caliper and computer instead of a yardstick and slide rule, a larger and more-encompassing model can be developed from Larson's original work while retaining the best of what Larson has already accomplished.

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