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Space : Time
The tree is not caused by events in space and time. The tree itself is space and time.
Space and time are life.

- Robert Campbell, Fisherman's Guide To The Cosmic Order (pg. 153)
An Introduction To The Reciprocal System

Dewey Larson was an engineer who formulated what he called The Reciprocal System of Theory. Here is a quote from his book Nothing But Motion that describes its humble beginnings from his research into the chemical elements:
As might be expected, the task that I had undertaken was a long and difficult one, but after about twenty years I had arrived at some interesting mathematical expressions in several areas, one of the most intriguing of which was an expression for the inter-atomic distance in the solid state in terms of three variables clearly related to the properties portrayed by the periodic table of the elements. But a mathematical expression, however accurate it may be, has only a limited value in itself. Before we can make full use of the relationship that it expresses, we must know something as to its meaning. So my next objective was to find out why the mathematics took this particular form. I studied these expressions from all angles, analyzing the different terms, and investigating all of the hypotheses as to their origin that I could think of. This was a rather discouraging phase of the project, as for a long time I seemed to be merely spinning my wheels and getting nowhere. On several occasions I decided to abandon the entire project, but in each case, after several months of inactivity I thought of some other possibility that seemed worth investigating, and I returned to the task. Eventually it occurred to me that, when expressed in one particular form, the mathematical relation that I had formulated for the inter-atomic distance would have a simple and logical explanation if I merely assumed that there is a general reciprocal relation between space and time.

My first reaction to this thought was the same as that of a great many others. The idea of the reciprocal of space, I said to myself, is absurd. One might as well talk of the reciprocal of a pail of water, or the reciprocal of a fencepost. But on further consideration I could see that the idea is not so absurd after all. The only relation between space and time of which we have any actual knowledge is motion, and in motion space and time do have a reciprocal relation. If one airplane travels twice as fast as another, it makes no difference whether we say that it travels twice as far in the same time, or that it travels the same distance in half the time. This is not necessarily a general reciprocal relation, but the fact that it is a reciprocal relation gives the idea of a general relation a considerable degree of plausibility.
Inspired by the philosopher Samuel Alexander (author of the books Space, Time, and Deity Volume 1 and Volume 2), Dewey attempted to extend this idea as far as he could. To continue the above quote:
So I took the next step, and started considering what the consequences of a reciprocal relation of this nature might be. Much to my surprise, it was immediately obvious that such a relation leads directly to simple and logical answers to no less than a half dozen problems of long standing in widely separated physical fields. Those of you who have never had occasion to study the foundations of physical theory in depth probably do not realize what an extraordinary result this actually is. Every theory of present-day physical science has been formulated to apply specifically to some one physical field, and not a single one of these theories can provide answers to major questions in any other field. They may help to provide these answers but in no case can any of them arrive at such an answer unassisted. Yet here in the reciprocal postulate we find a theory of the relation between space and time that leads directly, without any assistance from any other theoretical assumptions or from empirical facts, to simple and logical answers to many different problems in many different fields. This is something completely unprecedented. A theory based on the reciprocal relation accomplishes on a wholesale scale what no other theory can do at all.
He eventually came to the conclusion that:
The physical universe, I find, is not a universe of matter existing in a framework provided by space and time, as seen by conventional science, but a universe of motion, in which space and time are simply the two reciprocal aspects of motion, and have no other significance.
An organization named The International Society of Unified Science (or ISUS) was set up to continue research into The Reciprocal System. Several groups (such as The Reciprocal System Research Society, The Larson Research Center, and The Reciprocal System Database) branched out, attempting to systematize or extend the theory in various ways. One of them states of the theory:
Larson did discover something quite remarkable: the precise, dimensional relationship between space and time. By using that relationship, he was able to build a theoretical universe based on two postulates that closely resembles the observed universe, at both small (subatomic) and large (galactic) scales. Larson predicted some events that must exist as a logical consequence of his postulates, which had not yet been discovered, from new forms of atomic disintegration to quasi-stellar objects.
The theory has been utilized to build devices as well. To paraphrase Hoyt Stearns Jr., electrical engineer and former president of ISUS:
The Reciprocal System model sets forth an explaination what a magnetic field really is. It led directly to my invention of a "reactionless thruster" based on the effect that the mass of a conductor decreases as the current through it increases due to the magnetic field created. (The magnetic field is the two dimensional residue of the three dimentional gravitional field due to the neutralization of it by the one dimensional electric current.) I think Peter Graneau has verified this principle with rail guns. What other theory can calculate the lifetime of the neutron, the properties of chemical elements, Planck's constant, and the gravitational constant G from basic premises without empirical data? Amazing!
Music & Math

As wild as it all might sound, there is some corroboration of these discoveries, both ancient and modern. We already noted how musical patterns are present throughout all of Nature. All waves (including sound) are measured in terms of their size (i.e.: "wavelength") and their speed (i.e.: "frequency"). These two properties are "inversely proportional" to one another. In other words, by increasing one, the other decreases. This is akin to the concept of space and time being reciprocal. However, the musical analogies do not end there. As the researcher Bruce Peret points out:
John Ernst Worrell Keely was a 19th century researcher whom developed a system now known as "vibratory physics". It is based on music theory, representing atomic structures as notes and chords in music. But what most people miss is that the "note" is a rational number... a ratio that is a subdivision of an octave (the ratio of 1:2). Larson's Reciprocal System is also based on ratios for its various atomic and subatomic structures, except Larson refers to them as "motions", not "notes", and "multi-dimensional motion" instead of "chords".
Thinking in terms of ratio and proportion, instead of absolute measurements, uncovers all sorts of archetypal patterns. In his paper, The Principle of Physical Proportions, the physicist A. K. T. Assis follows a similar line of reasoning. To quote the abstract:
We propose the principle of physical proportions, according to which all laws of physics can depend only on the ratio of known quantities of the same type. An alternative formulation is that no dimensional constants should appear in the laws of physics; or that all "constants" of physics (like the universal constant of gravitation, light velocity in vacuum, Planck's constant, Boltzmann's constant, etc.) must depend on cosmological or microscopic properties of the universe. With this generalization of Mach's principle we advocate doing away with all absolute quantities in physics. We present examples of laws satisfying this principle and of others which do not. These last examples suggest that the connected theories leading to these laws must be incomplete. We present applications of this principle in some fundamental equations of physics.
In engineering, there is a method referred to as "dimensional analysis" wherein one makes sure that the "units" that different measures are expressed in stay consistent when rearranging equations. This is a fairly common practice, to verify that equations are giving meaningful results. The engineer Xavier Borg has pointed out something less obvious though. All units can actually be reduced to measures of space and/or time! To quote his paper, Unified Theory Foundations - The ST system of units:
This paper shows that all measurable quantities we learn in physics can be represented as nothing more than a number of spatial dimensions differentiated by a number of temporal dimensions or vice versa. To convert between such space-time system of units and the conventional SI system, one simply multiplies the ST numerical values by dimensionless constants in order to convert between the natural space-time units and the 'historical' SI units. Once the ST system of units presented here is applied to any set of physics parameters, one is then able to derive all laws and equations without reference to the original theory which presented said relationship. In other words, all known principles and numerical constants which took hundreds of years to be discovered, like Ohm's Law, energy mass equivalence, Newton's Laws, etc., would simply follow naturally from the spatial and temporal dimensions themselves, and can be derived without any reference to standard theoretical background. Any relation between physical parameters one might think of, can be derived. Included is a step by step worked example showing how to derive any free space constant and quantum constant.

In summary, by looking at space and time in a different way, we can explain a lot about reality and how things interrelate. It is okay if none of the above makes any sense yet. We will continue to explore what it all means as we go deeper into The Reciprocal System...