iSoul In the beginning is reality.

Republican representation

This post builds on previous ones, such as here.

In the year 507 B.C., the Athenian leader Cleisthenes introduced a system of political reforms that he called demokratia, or “rule by the people.” This system was comprised of three separate institutions: the ekklesia, a sovereign governing body that wrote laws and dictated foreign policy; the boule, a council of representatives from the ten Athenian tribes; and the dikasteria, the popular courts in which citizens argued cases before a group of lottery-selected jurors. (reference)

The ancient Roman Senate was composed of patricians, members of the ruling families, who wielded varying amounts of influence and power in the Roman monarchy, republic, and empire. This aristocratic body is the forerunner of upper chambers of legislatures in the modern age.

Modern parliaments are descendants of the ancient ekklesia in single-chamber democracies. A legislative body of democratically-elected representatives is sufficient for this kind of democracy. A broader democracy includes two legislative chambers, with the lower chamber representing the people and an upper chamber representing tribes, ruling families, or key subdivisions of the country, that is, the land.

Representation of the traditional tribal, familial, or territorial alliances is important since they are the gluten than holds society together. While political principles and traditions are important, they alone cannot keep a society from separating, since they have no inherent attachment to a people or a place. There must be something so that a group of people are invested in the good of the country.

Hence a legislative body is needed that is tied to something tribal, familial, or territorial. In order to go beyond mere tribal or familial alliances, the territories of the people must be represented. A legislative body whose representation is not based on population will also mute the influence of gerrymandering.  The democratic approach to representation is through election so legislative divisions by territory are represented by the people who live in each territory.

One could go further and require that the electorate consist of those who live on land they own in the territory — or those who own their residence in the territory. These people are invested in the place. A republic includes both territorial-based representation and population-based representation. Hence a republic needs two legislative bodies with two different kinds of representation.

Dual calendar systems

The unit for all calendars is the day, the diurnal cycle of daylight and night. A lunar calendar is based on the monthly (synodic) cycle of the Moon’s phases. A solar calendar is based on the annual cycle of the Sun’s height above the horizon. A lunar-solar (lunisolar) calendar is based on the lunar month modified in order to match the solar (or sidereal) year. The solar-lunar calendar is based on the year but includes months similar to the lunar cycle.

“The lunisolar calendar, in which months are lunar but years are solar—that is, are brought into line with the course of the Sun—was used in the early civilizations of the whole Middle East, except Egypt, and in Greece. The formula was probably invented in Mesopotamia in the 3rd millennium bce.” (Encyclopedia Britannica)

The lunar and lunar-solar (lunisolar) calendars are the oldest calendar systems, and are still used in some traditional societies and religions. The Hebrew (Jewish) and Islamic calendars are examples of the lunar-solar calendar systems. Solar and solar-lunar calendar systems came from Egypt, Greece, and Rome. The solar-lunar month departs from the lunar month but combines to equal a year.

The question is why the Moon forms the primary cycle in some calendars, whereas the Sun forms the primary cycle in other calendars. The reason may well be that some societies think in terms of 3D time, whereas other societies think in terms of 3D space. The difference is that in 3D space the Earth revolves around the Sun and the Moon revolves around the Earth, whereas in 3D time the Earth revolves around the Moon and the Sun revolves around the Earth. In the former case the solar cycle is primary, whereas in the latter case the lunar cycle is primary.

When European societies considered the Earth to be the center of all celestial motion, their calendars were already established. So the correspondence between calendar systems and the dominant perspectives (spatial or temporal) applies to the original development of calendars.

Contraries as duals

Contrariety is a property of pairs of propositions, but it also applies to pairs of terms or concepts. “Two general terms are contraries if and only if, by virtue of their meaning alone, they apply to possible cases on opposite ends of a scale. Both terms cannot apply to the same possible case, but neither may apply.” (Aristotelian Logic, Parry and Hacker, p. 216) Opposite ends of a scale are also called extremes, which are contrasted with means between the extremes.

Every pair of contraries forms a duality by inverting the scale of which they are opposites. For example, quantitative contraries such as rich and poor become poor and rich when the scale is inverted. Every measurement scale can be inverted so in this sense a measurement and its inverse are a contrary pair that forms a self-duality. Every ratio or function of two variables, f(x, y), can be interchanged and form a duality, f(y, x). For example, the equation v = Δst can be interchanged to become u = v-1 = Δts.

The scale may be qualitative, too. For example, the qualitative contraries up and down become down and up, respectively, by looking upside-down. The contraries left and right become right and left when looked at facing the other way. Extension and intension are opposites that may be inverted by interchanging them with each other. Compare the duality of top-down and bottom-up perspectives.

“A pair of terms is contradictory if and only if by virtue of their meaning alone each and every entity in the universe must be names by one or the other but not both.” (Aristotelian Logic, Parry and Hacker, p. 216) May the terms X and not-X be made into duals? That depends. If not-X is the contradictory of X and means everything other than X, that includes things that are non-dual. But in some cases, not-X means the opposite of X, so that contraries are indicated.

Science, unity and duality

It is a Christian concept (or at least a theistic concept) that the world we inhabit is a universe. The existence of the universe requires there to be a perspective that encompasses the whole of the world, which is the perspective of a transcendent divinity. The universe is thus the whole of creation.

It is said that natural science studies the universe, but natural science today does not recognize a transcendent being, and so cannot genuinely recognize the universe. What can natural science recognize as the world that it investigates?

Natural science recognizes law and chance, the regular and the stochastic, but what determines the mix of law and chance? There are three possibilities: (1) the mix of law and chance is determined by law, in which case science investigates a cosmos; (2) the mix of law and chance is determined by chance, in which case science investigates a chaos; or (3) the mix of law and chance is determined by another mix of law and chance, which, if this duality continues at every level, indicates a dualism of law and chance as two independent principles for science to investigate.

Natural science seeks unity, so option (3) is distasteful. Option (2) is distasteful for aesthetic reasons, as well as for its lack of meaning. Option (1) is the least distasteful, and the science community increasingly states that they investigate a cosmos, a world of order that we inhabit. But mere law and order seems fatalistic, and the reality of chance keeps rearing its head, which undermines (1).

This pattern of seeking unity and finding duality occurs in other ways, too. Space and time are duals, but can they be unified by space or time? Either space alone is real (and time is unreal), or time alone is real (and space is unreal), or there is a duality of space and time that cannot be unified. Again, the first option is the most popular, though it has the same weaknesses as above.

The most satisfying answer for these dualities is that science investigates a universe, a unity that can be fully grasped only transcendently, but may be glimpsed by us. This gives us confidence that there is a unity, even if we haven’t yet found how that unity is shown by observation and experimentation. It is a qualified unity, which is not troubled by duality, and does not seek to force unity on a diverse universe.

Length and duration

Let us begin with (1) the motion of a body between two events and (2) two ways of measuring the extent of that motion: length and duration (or time). The measurement of length and duration is coordinated so that both measures are of the same motion. Length and duration are measured by a rigid rod and a stopwatch, respectively. A smooth manifold of length is called space (or 3D space), and a smooth manifold of duration is called time (or 3D time).

The length and duration of a motion are commonly measured along the trajectory (or arc) of the motion. The length along the trajectory of motion is the arc length (or proper length or simply length). The duration along this trajectory is the arc time (or proper time or simply time).

Once the length and duration are in hand, the next step is to form their ratio. The ratio with arc time as the independent variable and arc length as the dependent variable is the speed. Which is to say, speed is the time rate of arc length change.

Note that the ratio could just as well be formed in the opposite way, with the arc length as the independent variable and the arc time as the dependent variable. This ratio is called the pace from its use in racing, in which an arc length is first set and then the racer’s arc time is measured. As another way to state this, pace is the space rate of arc time change.

The reference trajectory for measuring the length of a motion is the minimum length trajectory between two event points. The length along this trajectory is the distance between the two event points, which forms the metric of space. Distance is represented as a straight line on a length-scale map.

The reference trajectory for measuring the duration of a motion is the minimum time trajectory between two event instants. The duration along this trajectory is the distime between the two event instants, which forms the metric of time. On a map, two isochrons are separated by a constant distime. Distime is represented as a straight line on an time-scale map.

Motion has direction as well as extent, and direction may also be measured in two ways. Consider the motion of rotation, which can be measured as a proportion of a circle and as a proportion of a cycle. For example, in an analogue clock a minute hand that moves the length of a right angle correspondingly moves a duration of 15 minutes and vice versa. The direction of motion may be measured by either length or duration.

A motion measured with length direction and distance comprises a vector displacement. A motion measured with time direction and distime comprises a vector dischronment. The ratio with time as the independent variable and displacement as the dependent variable is called the velocity. The magnitude of the velocity vector is the speed. The ratio with distance as the independent variable and dischronment as the dependent variable may be called the legerity. The magnitude of the legerity vector is the pace.

There are three dimensions of motion, and correspondingly three dimensions of length and duration. The three dimensions of length comprise space. The three dimensions of duration comprise time. The three dimensions of time come as a surprise, since the distime is often a parameter for ordering events. But the scalar distime should not be confused with the vector dischronment, which has three dimensions of motion measured by duration.

Historians and scientists

Historians establish the facts of history, of what happened in the past. They do this with a variety of sources, some documentary, some physical, and whatever else they find is relevant. Key particulars are more significant than universals in establishing the facts of history. Historians may consider scientific theory in doing this, but they may also conclude that some things happened that don’t fit well with current scientific theory. Whether or not there was an earthquake in 1755 that destroyed Lisbon is a matter of history, not science.

Scientists are dependent on historians for the facts of history. Scientists do not get to establish the facts of history, nor the limits of what could have happened in the past. The latter restriction is difficult for scientists to observe. If historians establish facts that don’t fit well with current scientific theory, then scientists are likely to react defensively rather than revise their theories.

Biblical (or creation) scientists consider the Bible as the key to history, and limit science to that which is consistent with biblical chronicles. As with all scientists, they depend on historians for facts about the past but not all historians have a high view of the biblical record. Disagreements among historians lead to variations in science, since they are working with different facts about the past.

The different rôles of historians and scientists are often confused. Astronomy is a case in point. Astronomical historians may work with documents produced by those who could be considered scientists from the distant past. But the interpretation of ancient or medieval scientific documents is not part of science. Astronomical historians deal with the particulars of history, in which universals play only an indirect rôle.

Astronomical scientists deal with universals, as all scientists do, and make use of the facts of history along with recent observations. Scientists may advise historians but science is dependent on history for facts about the past, not the other way around.

Space and time as opposites

A theme of this blog is that space and time are dual concepts, which means they are two ways of understanding the same thing. But in what ways are space and time opposite concepts?

Space is oriented toward its origin, the place that motion begins. Time is oriented toward its destination, the time that motion ends. Both length and duration are measured from an “origin,” a reference point, which is a zero point for each, but zero speed leaves a body in space at the beginning, whereas zero pace puts the body in time at its destination.

Length in the denominator of speed is a measure of the progress from the origin to the current location in space, whereas time in the denominator of pace is a measure of the lag from the destination to the current location in time. A body at zero speed will remain at its origin and never reach its destination, whereas a body at zero pace will arrive at its destination in literally no time. A body with a small speed will take a long time to reach its destination, whereas a body with a small pace will reach its destination quickly.

Large quantities in space correspond to small quantities in time. Large quantities in time correspond to small quantities in space. A high speed is fast, and a small speed is slow. A small pace is fast, and a large pace is slow. Mass and vass are inverses, as are energy and lethargy.

The origin in space corresponds to the destination in time. Time in space flows from the past toward the future. Space (or base) in time flows from the future toward the past.

Logical centrism

Other posts on centrism are here.

A moderate is one who takes two opposing positions and selects something in between. The opposing positions may be anything, so there are many people who call themselves moderate (or sometimes centrist). But moderation in this sense is dependent on the different positions one selects as the ends of a spectrum of positions. Thus anyone can call themselves a moderate.

A logical centrist is one who starts with positions that are contrary opposites, that is, they are opposites that pre-suppose one another. For example, one cannot have up without down, forward without backward, tall without short, etc., so these pairs are contrary opposites. Also included are functional contraries, such as libertarian and egalitarian, since generally speaking increasing one leads to decreasing the other.

Note that contrary opposites do not include the contradictory pairs true and false, good and evil, beautiful and ugly, etc. since they do not pre-suppose one another. That is, the true, the good, the beautiful, etc., stand on their own, whereas their contradictory opposites do not.

What is the contrary of a market economy? One says there is no market for something if either its demand is nil or its supply is nil. So, the contrary of a market economy is one without demand or supply. But that does not mean socialism, the state control of supply and demand, which is contradictory to a market economy.

A market economy tends to encourage greater demand and greater supply by stimulating demand through advertising and increasing production through capital investment. Its contrary opposite would encourage less demand and less supply by promoting conservation, frugality, and living simply. The centrist then selects something in between the contraries of an economy that encourages production and one that encourages conservation.


An arcloge (arc’-loje) is a continuous, independent measurement of length. That is, it measures an ever-increasing length, which is the base, similar to how a clock shows the time. The term is a combination of arc (as in arc length) and loge (as in horologe, a clock).

What does an arcloge look like? Start with a sector, which is a geometric figure fixed to the center of a circle that sweeps out an angle and a curved edge:

sector and arc of a circle Read more →

Basic definitions

Independent variable is a quantity that is not dependent on another quantity, which is either (a) a quantity chosen before an experiment or race, or (b) an ever-increasing quantity. Dependent variable is a quantity that whose value is a function of another variable.

Length is measured by a rigid rod. 3D length space is length measured in three directions of motion.

Duration is measured by a stopwatch, timer, or clock. 3D duration is duration measured in three directions of motion.

Length space is (1) 3D differentiable manifold of length; (2) the order of events on a baseline; (3) the base, the reading on an arcloge.

Duration space is (1) a 3D differentiable manifold of duration; (2) the order of events on a time line; (3) the time, the reading on a clock.

Length-duration is the 6D manifold formed from 3D length space and 3D duration space. Worldline is the path in length-duration traced out by an object in motion.

Displacement is the vector between two points (events) on a worldline. Distance is the magnitude of a displacement.

Dischronment is the vector between two points (events) on a worldline. Distime is the magnitude of a dischronment.

Reference frame (or frame) is an abstract coordinate system and set of reference points in 3D length space that uniquely fix the coordinate system and standardize measurements. Rest frame of a body is the reference frame in which the body is moving at zero speed, which is the time conversion pace.

Reference timeframe (or timeframe) is an abstract coordinate system and set of reference points in 3D duration space that uniquely fix the coordinate system and standardize measurements. Freeflow frame of a body is the reference timeframe in which the body is moving at zero pace, which is the base conversion speed.

Proper length is the length of a body measured by a rigid rod moving with it. Proper time is the time of a body measured by a clock moving with it.

Lorentz transformation is a set of equations that relate length space and duration space coordinates of reference frames moving at a constant velocity relative to each other.

Dual Lorentz transformation is a set of equations that relate length space and duration space coordinates of reference timeframes moving at a constant legerity relative to each other.