iSoul In the beginning is reality.

Places, spaces, and times

Time is like a river that flows on indefinitely, as observed from a place on its bank. The flow of time is downstream. Place does not change in this way but the time keeps changing.

Space is like a river that flows on indefinitely, as observed from a platform floating down the river. The flow of space is upstream, as places on the bank recede from view. Time does not change in this way but the place keeps changing.

Places have spaces between them. Spaces are distances measured as lengths (length of space). Places are also called stations, as in railroad stations, if they are places along a route (stance and station are related etymologically). Spaces are located by the places at their beginning and end points. “What station is it here?” could be asked by a passenger in a train at a stop.

Times have time intervals between them. Time intervals are distances measured as durations (length of time). Times are chronated (positioned) in 3D time. Time intervals are chronated by the times at their beginning and end instants. “What time is it now?” could be asked in many contexts.

Spacetime is a place-based metric. Timespace is a time-based metric.

In classical physics there is a conversion factor between space and time that is adopted as a convention by all observers and is measured by a uniform motion relative to each observer. In relativity physics there is a uniform motion that is absolute, that is, the same as measured by every observer, and functions as a conversion factor between space and time.

From spacetime to space and time

This relates to the post here.

There are three dimensions of motion with two measures of the extent of motion, which makes a total of six metric dimensions of motion. But these six metric dimensions collapse into two structures of one and three dimensions as the conversion factor approaches infinity.

The invariant proper length, , is:

dσ² = dr²dt²/ç² = dr1² + dr2² + dr3² – dt²/ç² = dr² – dt1²/ç² – dt2²/ç² – dt3²/ç² = dr1² + dr2² + dr3² – dt1²/ç² – dt2²/ç² – dt3²/ç².

As the conversion factor, ç, the pace of light, approaches infinity, this becomes

dσ² = dr² = dr1² + dr2² + dr3².

That is, the time coordinates separate from the invariant length, which becomes the Euclidean distance of three dimensional space. Time is left as an invariant scalar called the time.

The invariant proper time, , is:

dτ² = dσ²/c² = dr²/c² – dt² = (dr1² + dr2² + dr3²)/c² – dt² = dr²/c² – dt1² – dt2² – dt3² = (dr1² + dr2² + dr3²)/c² – dt1² – dt2² – dt3².

As the conversion factor, c, the speed of light, approaches infinity, this becomes

dτ² = – dt² = – dt² = – dt1² – dt2² – dt3².

That is, the length coordinates separate from the invariant time, which becomes the Euclidean distime of three dimensional time. Space is left as an invariant scalar called the stance.

The result is that six dimensional spacetime collapses into 3D space with scalar time or 3D time with scalar space.

Three kinds of empirical science

This post is related to an old post here.

Broadly speaking, there are three kinds of empirical science, which correspond to three views of nature.

(1) The ancient view of empirical science is represented by Aristotle, which includes the careful observation of undisturbed nature. Motion, for example, meant natural motion, not “violent” motion in which there is a change of the natural course of things. Experimentation was not considered a way to understand undisturbed nature.

(2) The early modern view of empirical science includes experimentation because nature is understood to include what happens after an intervention in the course of nature. These experiments allowed early modern scientists to isolate causal factors in nature. The human observer was not considered part of any experiment.

(3) The late modern view of empirical science includes the observer as part of nature. The distinction between natural and artificial is discarded. The origin and nature of humans is included in his view of nature. Empirical science covers all aspects of human beings that can be observed. The scientist has a double life in which they both are and are not the object of science.

The second kind of empirical science is superior because it goes beyond the undisturbed nature of the first kind and does not include the contradiction at the heart of the third kind.

Terminology contexts

This post continues the one here. While I avoid coining new terms or new definitions, some have been necessary. To have a consistent vocabulary, I try to imagine contexts in which they easily fit.

Some words are simply variations of words in use: distime is like distance; dischronment is like displacement; chronation is like location; etherance is like mass; levitation is the opposite of gravitation; and oldtons are the units for release, analogous to newtons for force. Metreloge is like horologe, which is a clock.

One context is racing. The term pace is used, particularly in running and (bi)cycling to mean the time interval per unit distance, which is the inverse of speed. The direction is ignored or assumed to follow the course of the race so a new term is needed to indicate the vector version of pace. A term that has been used is lenticity, from Latin lentus, slow. [Note: previously used legerity, which is an old literary term for lightness of movement.]

The second context is transport, such as package delivery. Consider an order to expedite a delivery. That means to reduce the time of transport, analogous to de-retardation. Release is analogous to a force applied. A package stamped with “RUSH” gets a greater effort to reduce the time of delivery, analogous to a negative release. Drawing means a release over a distance, analogous to a force applied over time (which is called impulse). Repose is a release applied over a dischronment, and is the inverse of work. Lethargy is the capacity for repose, which is analogous to energy.

Ratios of length and duration

This post relates to others such as this.

Consider Galileo’s figure (see his Dialogues Concerning Two New Sciences, tr. Crew & De Salvio p.249 Fig. 108 or Drake’s translation p.221):

Falling projectile

A projectile moves with uniform velocity horizontally to the left and begins to descend at point b. Galileo used the sequence a-b-c-d-e to represent time and the sequence b-o-g-l-n to represent the height of the projectile above the Earth. The sequence b-i-f-h represents the parabolic path of the falling projectile.

Any uniform motion can serve as a reference motion. There are two uses of a reference variable: (i) as a parametric variable, or (ii) as a measurement variable. A parametric variable is an independent variable that provides ordered input for any dependent variable. A measurement variable is a variable that is dependent on the independent variable being measured. In the figure above the parametric variable is the time (duration) of the uniform motion on the horizontal axis, and the measurement variable is the height (length) of the uniform acceleration on the vertical axis.

Combine this with the two measures of motion, length and duration, and there are four possible cases: (1) independent duration variable with dependent length variable; (2) independent length variable with dependent duration variable; (3) independent length variable with dependent length variable; and (4) independent duration variable with dependent duration variable.

The figure above is an example of case (1). Its complement is case (2). Cases (3) and (4) include only one measure, length or duration, and so cannot express a rate of motion. Galileo expresses case (1) as a proportion between ratios of the variables at different times: s1 : s2 :: t12 : t22, which avoids combining different units in a single ratio, consistent with Eudoxian proportionality.

Consider case (2) in which the independent variable is length. This variable is a stanceline for locating other motions, which is like a timeline except that it expresses an independent length as the order parameter. The dependent reference variable in this case is duration, which measures any independent variable, in this case projectile height. This could be expressed as a proportion between ratios of the variables at different times: t1 : t2 :: s12 : s22, avoiding different units in a single ratio.

Case (1) enables multiple length variables dependent on one independent variable, the timeline. Case (2) enables multiple duration variables dependent on one independent variable, the stanceline. Rates of motion in case (1) are in units of the independent timeline, which is duration. Rates of motion in case (2) are in units of the independent stanceline, which is length.

From length to duration and back

Let’s start with one-dimensional, i.e., scalar, functions, f, g, h, and k. Say there is the following functional relation:

s = f(t) = f(h(s)) ≡ g(s) = t,

t = g(s) = g(k(t)) ≡ f(t) = s,

in which s and t are parameters with different units. By implication the functions are either f or its inverse:

s = f(t) = f(f-1(s)) = t,

t = f-1(s) = f-1(f(t)) = s.

Function f takes t-units into s-units, and function f-1 takes s-units into t-units. The vector versions are as follows:

s = f(t) = f(f-1(s)) = t,

t = f-1(s) = f-1(f(t)) = s.

Motion space is an ordered pair of vectors s and t: (s, t), resulting in their direct sum vector space. Addition is conducted by components: (r, w) + (s, t) = (r + s, w + t). Scalar multiplication is also by component: (a, b) (s, t) = (as, bt). To multiply a scalar and only one component requires the other component to be unity. Thus additive unity is (0, 0) and multiplicative unity is (1, 1).

There are two ways to mask an ordered pair of vectors: left mask (s, t) = (s, t) and right mask (s, t) = (s, t), where s = |s| and t = |t|. What was described here as expansion and contraction may now be shown more clearly as masking and unmasking. A parametric length vector function is converted to a parametric duration vector function as follows:

r(t) = masked r(t) ↑ unmasked r(t) ↔ (inverted) = unmasked t(r) ↓ masked t(r) = t(r).

r(t) = [r(t), θ(t), φ(t)] ↑ [(t´, χ´, ψ´), θ´(t´, χ´, ψ´), φ´(t´, χ´, ψ´)] ↔ ((r´, θ´, φ´), χ´(r´, θ´, φ´), ψ´(r´, θ´, φ´)) ↓ [t(r), χ(r), ψ(r)] = t(r).

Intentional and extensional causes

This post continues previous posts on causes, especially the one here.

Final and formal causes constitute top-down causality, which may lead to efficient and material causes. Material and efficient (mechanism) causes constitute bottom-up causality, which may lead to formal and final causes. Top-down is intentional. Bottom-up is extensional.

The Inverse Causality Principle states that top-down causality is inverse of bottom-up causality.

The Inverse Correspondence Principle states that intentional motion is the inverse of extensional motion and experimentation is the inverse of observation. Similarly, transmission is the inverse of reception, developmental is the inverse of empirical, and time is the inverse of space.

The goal of science is empirical theory. The goal of engineering is development of something practical.

Goal and action go together like form and content or matter.

Consider Galileo dropping two balls, one wooden and one metal, from the tower of Pisa. One observer says it’s a race to the ground. Another observer says it’s an experiment. What is the nature of the balls? Or what does Nature do?

Final and formal causes are the inverse of efficient and material causes.

Science and history, part N

Science is inherently dualistic because it is based on distinctions, and cannot keep denying one side of a distinction without denying the distinction altogether.

Duality is as far as science can go. Unification is a temporary state, to be superseded by a more abstract duality.

Low-entropy science seeks fixed relations. High-entropy science seeks stochastic relations.

Science cannot properly speak of the universe because that ventures into metaphysics. Science can only speak of cosmos and chaos. Cosmos has low entropy. Chaos has high entropy. Also called law and chance.

Scientific history is potential history. Historical science is potential science.

Science boosters add metaphysics to science.

Life to a Darwinian is noise that happened to produce some harmonious sounds.

To a materialist chaos predominates. To an idealist cosmos predominates.

Science is a method, not a metaphysics. Science is the duality of induction and deduction.

Science is empirical mathematics. History is multi-experiential narrative.

Science is synchronic, so physics can replace time with a kind of length. History is diachronic, so history can replace space with a kind of duration.

The first scientist was Euclid. Classical geometry is the theory of length.

Duality as a convention

Is color an absorption phenomena or an emission phenomena? The answer is that it’s both. But absorption works subtractively whereas emission works additively. The question then is whether color is subtractive or additive. Again the answer is that it’s both. Color is a duality.

Does an artist work with subtractive colors or additive colors? Here the answer is one or the other. A painter works with pigments that are subtractive, whereas a glass artist works with stained glass that is additive. Even though absorption and emission are operating in both cases, working with color requires picking one or the other (except for mixed media).

A simultaneity convention can also be a duality. What has been called apparent simultaneity is the convention that the backward light cone is simultaneous. But it is possible to adopt a complementary convention in which the forward light cone is simultaneous (see here). Either of these is something of a combination of Newton’s and Einstein’s physics.

One could recover Newtonian physics by adopting a combination of the backward and forward light cone simultaneity conventions. For an absorption event the backward light cone is simultaneous. For an emission event the forward light cone is simultaneous. This is like half-duplex communication (push to talk, release to listen). Such a duality convention recovers Newtonian physics because it is as if the speed of light is instantaneous in all directions.

Newton and Einstein compared

Isaac Newton expanded on what is now called the Galilean transformation (GT). The GT encapsulates a whole approach to physics. Length and duration are independent variables, and accordingly are universal, and may be measured by any observer. The length of a body is a universal value. The duration of a motion is a universal value. These values are independent of the control or condition of an observer.

Albert Einstein expanded on what is now called the Lorentz transformation (LT). The LT encapsulates a whole approach to physics. There are two universal constants: the speed of light in a vacuum and the orientation of reference frames. These constants are independent of any observer, though the speed of light may be measured by any observer. The orientation of reference frames is assumed to be the same universally, as if all are aligned with the fixed stars according to a universal convention.

Galileo described the relativity of speed, so that inertial observers do not have a universal speed but have speeds relative to other inertial observers. There is no universal maximum one-way speed. The two-way speed of light is a universal constant, but one leg of its journey may be instantaneous by convention, consistent with common ways of speaking. The orientation of reference frames is also relative, so that two frames view each others’ velocities as having the same direction.

Einstein described the relativity of length and duration, depending on their relative speed, which is always less than the speed of light in a vacuum. By convention, the mean of the two-way speed of light is assigned to every leg of its journey. Since the orientation of reference frames is the same, two frames view each other’s velocities as opposite in direction.

The strength of Newton’s vision is his mechanics and its continuity with common ways of speaking. The strength of Einstein’s vision is its continuity with Maxwell’s equations of electromagnetism.

Note: The Galilean transformation is related to the Lorentz transformation in one of three ways: (1) as c → ∞, (2) as v → 0, or (3) as the simultaneity of the backward (or forward) light cone (i.e., c0 = ∞) [see here].