iSoul In the beginning is reality

Category Archives: Knowing

epistemology, science, kinds of knowledge, methodology

Reduced mass and vass

Here we take the reduced mass and show the parallel reduced vass.

In physics, the reduced mass is the “effective” inertial mass appearing in the two-body problem of Newtonian mechanics. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem.

Given two object bodies, one with mass m1 and the other with mass m2, the equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of mass:

where the force on this mass is given by the force between the two bodies.

Given two subject bodies, one with vass n1 and the other with vass n2, the equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of vass:

where the force on this vass is given by the surge between the two bodies.

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Distinguishing history and science

The post continues several posts on history and science such as here and here.

All histories are part of the humanities, which are separate from the sciences. There is no scientific history or historical science – that would be like a round square.

A purported scientific history or historical science is either science and not history or history and not science. A scientist who writes histories is to that extent an historian, not a scientist.

Histories are focused on significant dissimilarities, discontinuities, and particulars. Sciences are focused on significant similarities, continuities, and universals.

Histories are diachronic; sciences are synchronic. A history takes a region or subject and follows it over time. A science takes a period or object and explores it over space.

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Is Christianity a religion?

It’s not uncommon for evangelical Christians to say that Christianity is not a religion, it’s a relationship. Or to contrast works-based religion with faith-based Christianity, making that the difference between religion and non-religion.

But it’s a mistake to say that Christianity is not a religion. For one thing, that would mean religious freedom wouldn’t be important for Christians. But we dare not give up religious freedom. For another thing, it drops the question of which religion is true. And it promotes negativity about religion, which is bound to impact how people react to Christianity, too.

One problem is that the word religion is almost impossible to define since there is such a variety of religions. For example, not all religions are theistic. And where does irreligion fit in? Is atheism a religion? How about secularism as a way of life? There could be no end to what counts as religion.

The Oxford dictionary defines religion as “the belief in and worship of a superhuman controlling power, especially a personal God or gods.” Does that apply to Christians? Certainly it does. And it justifies the separation of the state from oversight of religion: a secular state has no competence or authority over what is beyond life in this world.

Christians would do better to adopt a positive attitude toward religion, since at least religion as defined includes “belief in and worship of” something or someone beyond us. That is a better place to begin than secularism, atheism, or irreligion. Christian apologetics could focus on making “the case for Christ” rather than having to convince materialists that transcendent reality exists.

Causes for subjects and objects

This continues posts such as the one here related to Aristotle’s four kinds of cause:

final cause formal cause
efficient cause material cause

A subject is a form with purposes. An object is a material with mechanisms. Objects exist in space-time. Subjects exist in time-space.

The upper causes apply to subjects, who have purposes and plans, destinations and routes. The lower causes apply to objects, which have mechanisms and materials, forces and masses. Though subjects can be considered as objects and objects as subjects.

why what
subjects: final cause formal cause
objects: efficient cause material cause

Dynamics is the study of why motion happens, whereas kinematics studies only what motion happens. Kinematics is the material for dynamics. The combination of kinematics and dynamics is called mechanics, but this implies that only objects are considered. If subjects are included, then an alternative term is needed, such as kinedynamics.

Mass and vass

In Isaac Newton’s Principia, Definition 1 states:

Quantity of matter is a measure of matter that arises from its density and volume jointly. (The Principia: The Authoritative Translation and Guide, Bernard Cohen, Anne Whitman, and Julia Budenz. University of California Press, 2016, p.403)

Today density is defined as mass per unit volume, which would make this definition circular. However, when Newton wrote, density was expressed as a relative quantity. (p.90) If we look at mass as the product of density and volume, a complementary measure arises: vass.

Density is a ratio, and ratios may be expressed as fractions in two ways: the ratio of nonzero quantities A:B is equivalent to either A/B or B/A. So instead of density as mass per unit volume we could just as well define its inverse, rarity, as volume per unit of mass. (See Max Jammer’s Concepts of Mass in Classical and Modern Physics, p.27.)

Then the rarity per unit of volume equals the vass, which is the inverse of mass. In SI units, that equates to (m³/kg) / m³ which equals 1/kg.

Mass is also defined as the ratio of force to acceleration, reflecting Newton’s second law. Force is the time rate of change of momentum. A complementary definition would be the space rate of change of fulmentum, which equals the vass.

Inertial mass is the resistance of an object to a change in its state of motion when a net force is applied. A complementary concept is the nonresistance of a subject to a change in its condition of movement when a net surge is applied.

If mass is the “quantity of matter,” what is vass the quantity of? Quantity of matter means how much of a material object there is. Vass answers how much of a material subject there is, which is measured inversely to the mass as subject and object are inverses.

Marriage as a sacrament

The dissertation When Two Become One: Reconsidering Marriage as a Sacrament in Protestant Theology by Adam Neal is online here. What follows are excerpts from the conclusion, pp. 304-310.

This study has set out to provide a coherent presentation for why Christian theology should consider marriage as explicitly sacred, and, in particular, advanced comprehensive argumentation for renewing its place as a sacrament in Protestant theology.

In addition to building a cohesive and comprehensive textual argument in favor of defining marriage as a divinely mandated sacred institution, this study has provided substantive historical research that challenges the sacramental theology established by the Scholastic tradition to which the Reformation reacted even while assuming certain untenable definitions.

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Physics and metaphysics

Physics and Metaphysics” is the English title of an essay by Pierre Duhem in Essays in the History and Philosophy of Science, translated by Roger Ariew and Peter Barker (Indianapolis: Hackett, 1996). It was originally published in 1893 as “Physique et métaphysique.” Below are some excerpts.

We have devoted ourselves above all to delineating the exact role of physical theories, which, in our view, are not more than a means of classifying and coordinating experimental laws. They are not metaphysical explanations that reveal to us the causes of phenomena. p.29

We regard the investigation of the essence of material tings, insofar as they are causes of physical phenomena, as a subdivision of metaphysics. This subdivision, together with the study of living matter, forms cosmology. This division does not correspond exactly to the peripatetic one. The study of the essence of things constitutes metaphysics in peripatetic philosophy. p.30

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Metaphysics and science

This post presents excerpts from Pierre Duhem’s The Aim and Structure of Physical Theory, first published (in French) in 1906, and translated into English in 1954 (Princeton University Press). See also the following post on Physics and metaphysics.

[I]f the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics. p.10

Now, to make physical theories depend on metaphysics is surely not the way to let them enjoy the privilege of universal consent. p.10

A physical theory reputed to be satisfactory by the sectarians of one metaphysical school will be rejected by the partisans of another school. p.10-11

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Speed of information

Nowadays, we say that the speed of information is the speed of light. That is justified by the rôle of the speed of light in relativity, in which it is the speed of causation. But it is also justified by the use of electromagnetic waves to transmit information between people.

It was not always so. It took much longer for information to travel in the past.

A day’s journey in pre-modern literature, including the Bible, ancient geographers and ethnographers such as Herodotus, is a measurement of distance. In the Bible, it is not precisely defined; the distance has been estimated from 32 to 40 kilometers (20–25 miles). Wikipedia

A critical fact in the world of 1801 was that nothing moved faster than the speed of a horse. No human being, no manufactured item, no bushel of wheat . . . no letter, no information, no idea, order, or instruction of any kind moved faster. Nothing ever had moved any faster.  Stephen E. Ambrose, Undaunted Courage (Simon & Schuster, 1996), p. 52.

The book A Farewell to Alms includes a table showing how long it took for news of sig­nif­i­cant events to reach London. Faster speeds resulted from the in­ven­tion and de­ploy­ment of the telegraph by 1880:

Speed of Information Travel to London, 1798-1914
Event Year Distance (miles) Days until report Speed (mph)
Battle of the Nile 1798 2073 62 1.4
Battle of Trafalgar 1805 1100 17 2.7
Earthquake, Kutch, India 1819 4118 153 1.1
Treaty of Nanking 1842 5597 84 2.8
Charge of the Light Brigade, Crimea 1854 1646 17 4.0
Indian Mutiny, Delhi Massacre 1857 4176 46 3.8
Treaty of TienSin (China) 1858 5140 82 2.6
Assassination of Lincoln 1865 3674 13 12
Assassination of Archduke Maximilian, Mexico 1867 5545 12 19
Assassination of Alexander II, St. Petersburg 1881 1309 0.46 119
Nobi Earthquake, Japan 1891 5916 1 246


6D invariant interval

Since one may associate either the arclength (travel length) or the arctime (travel time) with direction, one might think that the full coordinates for every event are of the form (s, t, ê), with arclength s, arctime t, and unit vector ê. Since the direction is a function of either the arclength or the arctime, the coordinates would be either (s, t, ê(s)) or (s, t, ê(t)).

However, since s = ∫ || r′(τ) || , where the integral is from 0 to t, and t = ∫ || w′(σ) || , where the integral is from 0 to s (see here), this reduces to either (t, r) or (s, w).

But science seeks unification and so must combine these forms into one. In that case, both s and t are redundant, and the full coordinates for every event are of the form [r, w]. That is, there are three dimensions of space and three dimensions of time. The arclength and arctime are implicit, and may be made explicit through integration.

The standard exposition of special relativity looks at one dimension of space and one dimension of time. This is convenient and makes Δs = Δx and Δt = Δw1. But in general Δs and Δt will either be measured directly or found through integration.

What is the distance-like invariant interval then between two events? The interval in length units (proper length) is (dσ)² = (cdw)² – (dr)²,  where c is the speed of light. The interval in time units (proper time) is (dτ)² = (dw)² – (dr/c)².

This appears different from special relativity because it substitutes the vector dw for the scalar dt. However, the scalar (dt)² = (dw1)² + (dw2)² + (dw3)² so there is no discrepancy.

In order to demonstrate that this interval is invariant for two observers traveling at different rates, one must either convert dw to dt or convert dr to ds, which reduces the six dimensions to four.

The intervals above may be generalized for general relativity with the relation L = cP √(–gμν dxμ dxν), where P is the path, gμν is the metric tensor, and there are six coordinates xμ and xν.