iSoul In the beginning is reality

General and special knowledge

General knowledge is based on common experience and is available to everyone. No special training or vocabulary are necessary for general knowledge. It is also called ‘general revelation’ and ‘common knowledge’. This is the knowledge that realist philosophy builds on.

General sciences are the areas of general knowledge. In philosophy these are ontology, epistemology, and ethics. Since the existence of God and creation may be demonstrated from general knowledge, there is a general science of theology. General creation is general knowledge of creation.

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Special knowledge is based on uncommon experience that is available only to those who make a special study of them and learn their special vocabulary. The special sciences such as chemistry and physics are forms of special knowledge. They begin with general knowledge but then add special studies of particular aspects of general knowledge. This is the knowledge that anti-realist philosophy builds on.

Special revelation is another form of special knowledge; it requires knowledge of revelatory texts and faith in their message. Special creation is special revelation or knowledge about creation such as the special status of humanity.

Special knowledge in the light of special revelation is different from special revelation in the light of special knowledge. Here is a diagram of their relationship:

General knowledge/revelation ⇒ special knowledge1 ⇒ special revelation2 vs.

General revelation/knowledge ⇒ special revelation1 ⇒ special knowledge2

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Examples of general revelation in the Bible:

In the beginning, God created the heavens and the earth. Genesis 1:1

The heavens declare the glory of God, and the sky above proclaims his handiwork. Psalm 19:1

Examples of special revelation in the Bible:

Genesis 1:2 – 3:24; Romans 16:25; I Corinthians 14; II Corinthians 5:19; Ephesians 3:3; Revelation 1:1

Terms for rates of motion

The scalar space of a motion is the arc length along the curve it traces out. The scalar time of a motion is the travel time along the route it traces out.

The time rate is “The rate at which something takes place over time.” The space rate is the rate at which something takes time over a route.

A quantity at an instant of time is instantaneous. A quantity at a point in space is punctaneous, from Latin punct(us) + (instant)aneous.

Speed is the time rate of motion, the scalar space per unit of scalar time. The speed at an instant of time is called the instantaneous speed, which equals the differential scalar space per differential scalar time or the magnitude of the instantaneous velocity.

Pace is the space rate of motion, the scalar time per unit of scalar space. The pace at a point of space is called the punctaneous pace, which equals the differential scalar space per differential scalar time or the magnitude of the punctaneous allegrity. A gradient is the space rate of change of a function or scalar field.

Displacement is the directed distance or vector difference between two points in three-dimensional space. Distimement is the directed duration or vector difference between two instants in three-dimensional time.

Velocity is the time rate of change of distimement, which consists of the speed and direction of motion. The average velocity is the displacement per scalar time of motion. The velocity at an instant of time is called the instantaneous velocity, and is the differential displacement per differential scalar time. The instantaneous velocity equals the time rate of change of the displacement.

Allegrity is the space rate of change of distimement, which consists of the pace and direction of motion. Allegrity is the rate of progress on a trajectory or path. The average allegrity is the distimement per scalar space of motion. The allegrity at a point of space is called the punctaneous allegrity, and is the differential distimement per differential scalar space. Allegrity is from allegr(o) + ity (cf. velocity).

Acceleration is the time rate of change of velocity. Modulation is the space rate of change of allegrity.

The first moment of mass is mass times distance. The momentum is the time rate of change of the first moment of mass. The first moment of vass is vass times duration. The space rate of change of the first moment of vass is the celentum, from Latin clim(a), slope + (mom)entum.

Power is the time rate of change of energy. Force is the space rate of change of energy.

Odologes

An odologe (o′∙do∙loje) a constant-rate length-measuring device symmacronized with a common waypoint. It is a new coinage from the Greek odo(s), way/path + (horo)loge, clock. In short, it is a clock that shows length or angle instead of time.

The simplest odologe takes time from a clock and multiplies it by a conversion speed to produce a length or angle. This is commonly done in relativity with c, the speed of light: ct equals time multiplied by the speed of light, resulting in a length. A device which output such a length would be an odologe.

Given a starting point the Moon could be considered an odologe that travels at the rate of 3,683 kilometers per hour, since that is its speed around the Earth. The Earth itself could be considered an odologe that travels at its orbital rate of 107,000 km/h. Another odologe is the distance of the Pioneer 10 spacecraft from the Earth and Sun, which is tracked here.

A circular analog clock is also an angular odologe of the angle made by each hand, as below:

Clock angles

Each minute is represented by 1/60 of a 360° circle, or 6° of arc. Each hour is represented by 1/12 of a circle, or 30° of arc.

There are 24*60 = 1440 minutes in a day, which equates to 360 = 1440/4 degrees, so the apparent mean speed of the Sun along the ecliptic is one degree every four minutes. The Sun provides an approximate angular odologe.

A kind of virtual odologe comes from using the typical speed for a vehicle in a metropolitan area to convert travel time into travel distance. So, for example, one might estimate that a traveler has progressed 20 kilometers since they have been gone a half hour and the typical speed is 40 km/h.

Another virtual odologe is an app that displays an odometer that increases at a constant rate, as illustrated below.

Why space and time are not different

Many differences are proposed between space and time. This post briefly indicates how all of them are a matter of convention, and so not real. For details, consult posts on this blog.

(1) There are three space dimensions but only one time dimension.

Directionality can be associated with either length (distance) or time (duration). 3D time is as legitimate as 3D space.

(2) The time is always changing (“flowing”) but space position need not change.

Time seems to “flow” because of its association with continual change, as of a river. But change can just as well be associated with length. Something floating down a river continually changes it length of travel. So a continual increase of length can be associated with change.

(3) There is an “arrow” of time, but not of space.

As in (2) above, if length is associated with change, then there is an “arrow” of length. Compare a vehicle’s odometer, which never decreases. An odologue shows length always increasing, like a clock.

(4) Time has a past, present, and future, but space does not.

Space includes where one was in the past, where one is now, and where one will be in the future.

(5) Travel takes place in space in all directions, but only in one direction in time.

Travel takes place in time in all directions since there is a travel time for each direction of travel. Space may be associated with the travel distance, which has one direction.

(6) Entropy grows with time, but not with space.

One can equally well define an entropy of space and show that it tends to increase with the distance of motion.

(7) Causality is ordered in time, not in space.

Causality is ordered in space as in time. What happens in one place is causally related to what happens in adjoining places, and on to other places.

(8) Causally connected events are timelike or lightlike, but cannot be spacelike.

In a 3D time and 1D space context, the properties of timelike and spacelike are interchanged.

Ten meanings of time

Carlo Rovelli’s “Analysis of the Distinct Meanings of the Notion of “Time” in Different Physical Theories” (Il Nuovo Cimento B, Jan 1995, Vol 110, No 1, pp 81–93) describes ten distinct versions of the concept of time, which he arranges hierarchically. Here are excerpts from his article:

We find ten distinct versions of the concept of time, all used in the natural sciences, characterized by different properties, or attributes, ascribed to time. We propose a general terminology to express these differences. p.81

… our aim is to emphasize the general fact that a single, pure and sacred notion of “Time” does not exist in physics. p.82

The real line is a traditional metaphor for the idea of time. Time is frequently represented by a variable t in R. The structure of R corresponds to an ensemble of attributes that we naturally associate to the notion of time. These are the following:
a) The existence of a topology on the set of the time instants, namely the existence of a notion of two time instants being close to each other, and the characteristic “one dimensionality” of time;
b) The existence of a metric. Namely the possibility of stating that two distinct time intervals are equal in magnitude. We denote this possibility as metricity of time.
c) The existence of an ordering relation between time instants. Namely, the possibility of distinguishing the past direction from the future direction;
d) The existence of a preferred time instant, namely the present, the “now”. p.83

In the natural language, when we use the concept of time we generally assume that time is one-dimensional, metrical, external, spatially global, temporally global, unique, directed, that it implies a present, and that it allows memory and expectations. The concept of time used in Newtonian physics is one-dimensional, metrical, external, spatially global, temporally global, unique, but it is not directed and it does not have a present. In thermodynamics, time has the additional property of being directed. Proper time along world line in general relativity is one-dimensional, metrical, temporally global but it is not external, not spatially global, not unique; on the other side, the time determined by a matter clock is one-dimensional, metrical, but not temporally global, an so on. p.87

… the notion of present, of the “now” is completely absent from the description of the world in physical terms. This notion of time can be described by the structure of an affine line A. p.88

… our list does not include the possibility of considering a non-metric but directional notion of time. p.89

Table I. [without the fourth column]

Time concept Attributes Example
time of natural language memory brain
time with a present present biology
thermodynamical time directional thermodynamics
Newtonian time uniqueness Newton mechanics
special relativistic time being external special relativity
cosmological time space global proper time in cosmology
proper time time global world line proper time
clock time metricity clocks in general relativity
parameter time 1-dimensional coordinate time
no time none quantum gravity

… our hypothesis concerning time is that the concepts of time with more attributes are higher-level concepts that have no meaning at lower levels. p.91

If this hypothesis is correct, then we should deduce from it that most features of time are genuinely meaningless for general systems. p.91

… we suggest that the very notion of time, with any minimal characterization, is likely to disappear in a consistent theory that includes relativistic quantum-gravitational systems. p.91

… the concept of time, with all its attributes, is not a fundamental concept in nature, but rather that time is a progressively more specialized concept that makes sense only for progressively more special systems. p.92

Space and time involution

J. C. C. McKinsey, A. C. Sugar and P. Suppes (hereafter MSS) wrote “Axiomatic foundations of classical particle mechanics”, (Journal of Rational Mechanics and Analysis, v.2 (1953) p.253-272), which is also described in Suppes’ Introduction to Logic (Van Nostrand, New York, 1957), pp.291-322 (see here). It is only a partial axiomatization of Newtonian mechanics but is sufficient to present an involution of mechanics below.

An involution in mathematics is a function that is its own inverse, which means if it is repeated the output is the input, that is, f(f(x)) = x. The involution here is the interchange of spatial and temporal quantities along with the inversion of mass. We start with MSS:

MSS system has six primitive notions: P, T, m, s, f, and g. P and T are sets, m is a real-valued unary function defined on P, s and g are vector-valued functions defined on the Cartesian product P × T, and f is a vector-valued function defined on the Cartesian product P × P × T. Intuitively, P corresponds to the set of particles and T is to be physically interpreted as a set of real numbers measuring elapsed times (in terms of some unit of time, and measured from some origin of time). m(p) is to be interpreted as the numerical value of the mass of p ∈ P. sp(t), where tT, is a 3-dimensional vector which is to be physically interpreted as the position of particle p at instant t. f (p, q, t), where p, qP, corresponds to the internal force that particle q exerts over p, at instant t. And finally, the function g(p, t) is to be understood as the external force acting on particle p at instant t. (Anna & Maia p,9)

We define MSS´ by the following involution: interchange P and Q; p and q; T and S; m and n=1/m; s and t; f and k; g and ; particle and moticle; instant and point; mass and vass. Then the explanation is:

MSS´ system has six primitive notions: Q, S, n, t, k, and . Q and S are sets, m is a real-valued unary function defined on Q, t and  are vector-valued functions defined on the Cartesian product Q × S, and k is a vector-valued function defined on the Cartesian product Q × Q × S. Intuitively, Q corresponds to the set of moticles and S is to be physically interpreted as a set of real numbers measuring scalar space (in terms of some unit of length, and measured from some origin point). n(q) is to be interpreted as the numerical value of the vass of qQ. tq(s), where sS, is a 3-dimensional vector which is to be physically interpreted as the position of moticle q at point s. k(q, p, s), where q, pQ, corresponds to the internal surge that moticle p exerts over q, at point s. And finally, the function (q, s) is to be understood as the external surge acting on moticle q at point s.

The corresponding axioms are as follows:

A1 Q is a non-empty, finite set.
A2 S is an interval of real numbers.
A3 If qQ and sS, then tq(s) is a 3-dimensional vector (tq(s) ∈ℜ³) such that d²tq(s)/ds² exists.
A4 If qQ, then n(q) is a positive real number.
A5 If p, qQ and sS, then k(p, q, s) = −k(q; p; s).
A6 If p, qQ and sS, then tq(s) × k(p, q, s) = –tp(s) × k(q, p, s).
A7 If p, qQ and sS, then n(q) d²tq(s)/dt² = ΣpQ k(p, q, s) + ℓ(q, s).

These axioms generate a dual to Newtonian mechanics. A5 corresponds to a weak dual version of Newton’s Third Law: to every surge there is always a countersurge. A6 and A5, correspond to the strong dual version of Newton’s Third Law. A6 establishes that the direction of surge and countersurge is the direction of the line defined by the coordinates of moticles p and q. A7 corresponds to the dual of Newton’s Second Law.

MSS show that mass is independent of the remaining primitive notions of their system. Because of this, its dual could be defined differently. It was thought best to take the inverse of mass, called vass, for the involution.

Centers of motion

Bodies in space-time orbit by gravitation around their barycenter, the center of mass. The word barycenter is from the Greek βαρύς, heavy + κέντρον, center. The barycenter is one of the foci of the elliptical orbit of each body.

For the two-body case let m and M be the two masses, and let r and R be vectors to m and M respectively. Then the center of mass or barycenter is

(mr + MR) / (m + M).

Define the reduced mass μ = mM/(m + M). Then the orbit is as if the orbiting body has reduced mass μ and there is a stationary central body with mass equal to the total mass (m + M). That is, the two bodies mutually orbit the center of mass.


Let’s reconsider the orbit in relation to the vasses, the mass inverses, orbiting by levitation. For the two-movement case let  and L be the two vasses, and let r and R be vectors from an origin to and L respectively. Then the center of vass is

(ℓr + LR)/( + L) = (Mr + mR) / (m + M).

Define the reduced vass Λ = ℓL/( + L). Then the orbit is as if the orbiting movement has reduced vass λ and there is a stationary central movement with vass equal to the total vass ( + L). That is, the two movements mutually orbit the center of vass.

The result for vass is the same except that the roles of the movements are reversed. One could call the center of vass the elaphracenter after ελαφρά, light (weight) + κέντρον, center.

Aristotle’s physics

Physicist Carlo Rovelli wrote the article “Aristotle’s Physics: A Physicist’s Look” published in the Journal of the American Philosophical Association, Volume 1, Issue 1, Spring 2015, pp. 23-40 with a free version available here. Luke Barnes summarizes the article here. For more on limited domains see here and here.

Below are some excerpts from the free version:

Aristotelian physics is a correct and non-intuitive approximation of Newtonian physics in the suitable domain (motion in fluids), in the same technical sense in which Newton’s theory is an approximation of Einstein’s theory. Aristotelian physics lasted long not because it became dogma, but because it is a very good empirically grounded theory. The observation suggests some general considerations on inter-theoretical relations. p.1

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Methodical Realism

Here are excerpts from Étienne Gilson’s Methodical Realism (Le réalisme méthodique), translated by Philip Trower (Christendom Press, 1990 / Ignatius Press, 2011):

The mathematician always proceeds from thought to being or things. Consequently, critical idealism was born the day Descartes decided that the mathematical method must henceforth be the method for metaphysics. p.11

Indeed, all idealism derives from Descartes, or from Kant, or from both together, and whatever other distinguishing features a system may have, it is idealist to the extent that, either in itself, or as far as we are concerned, it makes knowing the condition of being. p.12

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Handbook for Beginning Realists

From Étienne Gilson’s Methodical Realism (Le réalisme méthodique), Chapter V: A Handbook for Beginning Realists, Translated by Philip Trower (Christendom Press, 1990 / Ignatius Press, 2011). (See also here.)

1. The first step on the realist path is to recognize that one has always been a realist; the second is to recognize that, however hard one tries to think differently, one will never manage to; the third is to realize that those who claim they think differently, think as realists as soon as they forget to act a part. If one then asks oneself why, one’s conversion to realism is all but complete.

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