iSoul In the beginning is reality

Displacement vs. arc length

As pointed out here, average speed does not equal the magnitude of average velocity. But the instantaneous speed does equal the magnitude of instantaneous velocity. For example, the average velocity of one orbit is zero but the average speed is positive.

Consider a section of a curve as below:

The arc length of this section of the curve is Δs. The displacement is Δr. This with the horizontal and vertical differences Δx and Δy makes a triangle. The Pythagorean theorem gives the hypotenuse of the triangle:

(Δr)² = (Δx)² + (Δy)².

Clearly Δs is longer than Δr since the shortest path between two points is a straight line. Now consider a differential version of this:

Then (dr)² = (dx)² + (dy)². But in this case ds is not shorter than dr since they are both differentials, that is, infinitesimals.

So the differential ratios with denominator Δt as Δt → 0 equal dr/dt and ds/dt, which are equal. The instantaneous speed uses either the differential displacement or the differential arc length.

But determination of the arc length is much more difficult than determination of the hypotenuse. So the instantaneous speed, velocity, and acceleration are defined in terms of the hypotenuse, not the arc length. After all, arc length can be determined by integrating the differential hypotenuse.

So the displacement is used instead of the arc length.

Nominal breakthroughs

Modern science is quantitative, not qualitative. The top breakthroughs in modern science have broken through traditional distinctions of quality or kind. Consider the following:

(1) Newton’s theory of gravitation broke through the traditional distinction between the sublunar and supralunar universe (e.g., the earth and the heavens). All motion is subject to the same laws.

(2) The atomic theory of matter broke through the traditional distinctions between different kinds of matter (e.g., water, earth, air, and fire). All matter is merely a combinations of atoms (or subatomic particles).

(3) Darwin’s theory of evolution broke through the traditional distinctions between different kinds of organisms (e.g., humans and animals). All species are merely variations of life (or genes).

(4) Einstein’s theory of relativity broke through the traditional distinction between space and time. All dimensions are subject to the same laws.

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Hartford Appeal

The 1975 Hartford Appeal deserves to be better known. It may be viewed here. A book was written about it: Against the World for the World: The Hartford Appeal and the Future of American Religion by Peter L. Berger and Richard John Neuhaus (New York: Seabury Press, 1976). A 40th year anniversary reflection was written by Richard J. Mouw (see here). What follows are the 13 false themes identified:

Eighteen theologians and religious thinkers from nine denominations gathered at the Hartford Seminary Foundation, Hartford, Connecticut, January 24-26, to draft a declaration in response to themes in contemporary Christian thought which they viewed as “pervasive, false, and debilitating.”

Theme 1: Modern thought is superior to all past forms of understanding reality, and is therefore normative for Christian faith and life.

Theme 2: Religious statements are totally independent of reasonable discourse.

Theme 3: Religious language refers to human experience and nothing else, God being humanity’s noblest creation.

Theme 4: Jesus can only be understood in terms of contemporary models of humanity.

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Wise knowledge

Presuppositions are a priori suppositions, usually unstated. They are not inevitable. Presuppositions may be replaced with suppositions. That is, presuppositions may be made explicit.

For example, someone might say, “I will flip a coin. If it is heads, I will adopt presupposition A; if it is tails, I will adopt presupposition B.” In that case, neither A nor B are presuppositions; they are suppositions that are chosen a posteriori.

Mathematics is the discipline that is based entirely on suppositions. It is purely conditional. “If X is supposed (or given), then Y follows necessarily.” If X is rejected, then something else may follow.

The existence of mathematics shows it is possible to have knowledge that is truly universal. Science is the attempt to mathematize all knowledge and remove all subjectivity. That is the “view from nowhere”. See here for how induction works through formal definitions and conditions.

But is it wise to remove all subjectivity? No, for the simple reason that it would turn us into mere objects. The person in us cries out, “I am not a number; I am a free man” (The Prisoner). We are subjects and so want a “view from somewhere”.

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Middle ontologies

As the previous post noted here, nominalism seeks a minimal ontology, that is, a minimum of qualities. This qualitative parsimony leads toward the ultimate minimum ontology: an ontology of one. That is, the assertion that there is only one quality, one kind of stuff, whatever it may be called – matter, energy, or whatever.

This is a bias toward one extreme. Compare the opposite extreme: quantitative parsimony, which leads toward the ultimate of one member in each kind of thing so that each thing is unique. This has the advantage that it allows the individuality of every thing to be emphasized rather than obscured by being merely one member of a large class of things.

But either bias is a bias and so predisposes the search for knowledge toward a biased answer. It would be better to adopt a neutral ontology, or seek one, in order to avoid biasing the result. Such an ontology would be between these two extremes, somewhere in the middle. That allows a great deal of flexibility for research and discussion, contrary to the take-it-or-leave-it attitude that goes with an extreme ontology.

A middle ontology could be a common sense ontology, at least as a starting point, since common sense recognizes some qualitative distinctions. A middle ontology could be a mid-entropy ontology, with some notion of middle to select the best frequency or probability distribution. In any case, the search for knowledge should prefer middle ontologies, and only if all middle ontologies fail should an extreme ontology be considered.

Scientific nominalism

Nominalism has three senses:

  1. A denial of metaphysical universals.
  2. An emphasis on reducing one’s ontology to a bare minimum, on paring down the supply of fundamental ontological categories.
  3. A denial of “abstract” entities.

William of Ockham, the name most associated with nominalism, agreed with the first and second senses, and in a lesser way, the third sense. The scientific principle called “Ockham’s razor” (or “Occam’s razor”) focuses on the second sense.

Ockham’s “nominalism,” in both the first and the second of the above senses, is often viewed as derived from a common source: an underlying concern for ontological parsimony. This is summed up in the famous slogan known as “Ockham’s Razor,” often expressed as “Don’t multiply entities beyond necessity.” Although the sentiment is certainly Ockham’s, that particular formulation is nowhere to be found in his texts. Moreover, as usually stated, it is a sentiment that virtually all philosophers, medieval or otherwise, would accept; no one wants a needlessly bloated ontology. The question, of course, is which entities are needed and which are not.

What this means for science is not a vague simplicity but qualitative parsimony:

This distinction is between qualitative parsimony (roughly, the number of types (or kinds) of thing postulated) and quantitative parsimony (roughly, the number of individual things postulated). The default reading of Occam’s Razor in the bulk of the philosophical literature is as a principle of qualitative parsimony.

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Terminology discussion

In order to describe 3D time some new terms and new meanings for old terms have been introduced in this blog. The reasons for this are discussed in this post.

It would be possible to add a prefix to terms already in use but that over-emphasizes the similarities – or opposition if a negative prefix is used. In some cases, there are existing words that could be easily adopted. Most importantly, there is a need to emphasize that 3D time requires a different way of looking at the world than is commonly done.

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Problems in mechanics, part 3

This post continues a series of problems (part 1 here, part 2 here) based on the website Free Solved Physics Problems, this time concentrating on dynamics problems for time-space corresponding to problems in space-time.

Note: A newton is how much force is required to make a mass of one kilogram accelerate at a rate of one metre per second squared (1 N = 1 kg ⋅ m / s2 ). An oldton is how much rush is required to make a vass of 1 kilogram-1 expedite at a rate of one second per metre squared (1 O = 1 kg-1 ⋅ s / m2).

Problem 6.

A boy of mass 40 kg wishes to play on pivoted seesaw with his dog of mass 15 kg. When the dog sits at 3 m from the pivot, where must the boy sit if the 6.5 m long board is to be balanced horizontally? Solution here.

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Observation and transportation

Impossible objects such as the Necker cube above are drawings that appear as two different objects, in this case either a box standing out toward the lower left or toward the upper right. It can be seen as one or the other but not both simultaneously.

3D space and 3D time are like this. One can see either 3D space or 3D time but not both simultaneously. One may develop a unified 6D geometry for both of them but to measure rates either space or time must be reduced to a scalar or 1D quantity.

It is the same with observation and transportation. One can view a motion from the perspective of an observer (whether one is moving or on the sidelines) or from the perspective of a traveler (whether one is traveling or on the sidelines).

The observer sees motion taking place in 3D space ordered by scalar time. The traveler sees motion taking place in 3D time ordered by scalar space, that is, the stations.

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We the people

The preamble to the U.S. Constitution reads:

We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.

This founding document is written in the name of “we the people”. Who are “we the people”?

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