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Symmetric relativity

Although there are many experimental methods available to measure the speed of light, the underlying principle behind all methods [is] the simple kinematic relationship between constant velocity, distance and time given below:

c = D / t                     (1)

In all forms of the experiment, the objective is to measure the time required for the light to travel a given distance. (Ref.)

From the perspective of the experimenter, light is an object whose speed is to be determined. Even though the distance traversed is fixed, it is placed in the numerator because this speed is to be compared with the speeds of other objects. For the same reason the quantity to be measured, time, is placed in the denominator.

But if we take the perspective of the experiment, of what is measured, then the fixed distance is the independent variable, which is placed in the denominator. The dependent variable is the time, which is placed in the numerator, so the pace of light is measured:

= t / D                     (2)

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Reality and belief

Reality precedes us: we discover it rather than invent it. Belief precedes knowledge, and metaphysics precedes epistemology. That is realism. Nevertheless, experience and thought can lead to revision of belief, which is the way of science.

Anti-realists make the mistake of limiting reality to what they know, and so limiting belief to knowledge. But they ignore their own prior beliefs and wrongly think of themselves as neutral observers and unbiased participants. They may retreat to a position of nonbelief, as if that is possible.

There is no knowledge without prior belief, at least provisionally. Prior belief may be like common sense or like a postulate or hypothesis. It must first be asserted to find its implications for inductive exploration. The conclusion of induction is new belief, expressed in definitions and principles, which forms the basis for deductive exploration.

There is no society without prior loyalties, such as blood and soil, language and custom. There is no religion without prior revelation, such as from a prophet or shaman or charismatic leader. There is no economy without prior exchange, such as between neighbors, extended family, or tribes.

Christian marriage

I have written a number of times about marriage, especially about the oxymoron “same-sex marriage.” Do a search on the word “marriage” to find them.

Marriage is a social matter; societies formalize and recognize marriages within a society. There have been significant differences between societies, such as including polygamy or not. Modern societies have civil procedures to ensure the minimum qualifications are met: age, sex, and no other concurrent marriage. Recently this has been relaxed so that sex is no longer a requirement for civil marriage in many countries.

Christianity honors marriage and acknowledges that it was established by God for our first parents. But marriage remains primarily a social matter: it is society that decides who is married and who is not. While same-sex marriage expands the concept of marriage to an extreme, if that is what a society decides, then members of that society should accept that, though not necessarily approve of it.

What is most difficult about this is the misapplication of the language of marriage. It is like society deciding that parents are no longer mother and father but parent 1 and parent 2 — which is taking place in some birth certificates (see here and here). Will Mommy and Daddy be replaced by Oney and Twoey? The long tradition of marriage between a man and a woman cannot be jettisoned so easily; it will no doubt return someday.

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A demi-creator for science

Creationists reject what might be called the Deep Time Postulate (DTP): that long stretches of time existed before the earliest humans ever lived. The DTP enables uniformitarianism in geology, evolution of all species in biology, and evolution of the solar system in astronomy. DTP enables science to insert a kind of history before history, that is, before written records or human artifacts.

Without the DTP, less than ten thousand years have transpired in the universe, that is, the time since humans and other living kinds appeared on the earth as determined from human artifacts and records. Instead of the DTP, creationists accept what might be called the Demi-Creator Postulate (DCP): that a demi-creator exists (or existed) who formed the earth and celestial bodies as well as the kinds of organisms that originally populated the earth. The DCP enables large-scale catastrophism in geology and creation in biology and astronomy.

Why “demi-creator” instead of Creator? The answer is that science does not require the full range of characteristics that a Creator would have, such as in theology. For the purpose of science all that is necessary is a being like Plato’s demiurge*, who is like us but with much greater power and intelligence. I am calling this being a “demi-creator” since it is a partial creator. Whether it is the same being as the Creator of the monotheists is for them to decide. For science a creator-type being is like us, not creating from nothing but forming a product from something else.

From the existence of a demi-creator one may infer that the creation is intelligible by us and that it exhibits features that are recognizable by us as intelligently designed. From knowledge of some parts of the creation, we may be able to infer the character of other parts, since they would exhibit similar characteristics, as a design engineer implements an overall design in every part.

One consequence of the DCP is that the creation is finite because a demi-creator is only capable of what we could do given greater intelligence and power. Creationists take this as supporting the creation of a finite number of different kinds of organisms. Different kinds of organisms likely exhibit similar design features, in what those who accept the DTP would call convergent evolution.

* The demi in demiurge is not from demi, meaning half or partial, but from demos, common people; nevertheless, it suggests something less than divine.

Harmonic arithmetic

This post follows up on harmonic addition mentioned in the previous post here.

Harmonic arithmetic is an inverse arithmetic. It is based on an automorphism that interchanges the zero with the infinite and the greater-than-one with the less-than-one: 0 ↔ ∞ and x ↔ 1/x. So zero becomes the new inaccessible number and infinity becomes the new additive unit.

Harmonic addition was defined as a power operation:

Simple harmonic addition is thus defined as:

x\oplus y=\left ( \frac{1}{x}+\frac{1}{y} \right )^{-1} = \frac{xy}{x+y}.

The harmonic additive unit is infinity instead of zero. Harmonic adding one to infinity equals one. Incrementing one leads to one-half, and in general each increment leads to a smaller number:

x\oplus 1=\left ( \frac{1}{x}+1 \right )^{-1} = \frac{x}{x+1}.

Harmonic subtraction is defined as:

x\ominus y =x \oplus (-y) = \left ( \frac{1}{x}-\frac{1}{y} \right )^{-1} = \frac{xy}{y-x}.

Note the reverse of x and y in the denominator. Harmonic multiplication is defined from multiple harmonic additions as:

x \odot y = \frac{x}{y}

which is surprisingly non-commutative. Harmonic division is defined then as:

x \oslash y=xy

which is surprisingly commutative. Harmonic exponentiation is defined from multiple harmonic multiplications as:

x\, (\wedge )\, y=x^{^{1-y}}.

The harmonic square is the inverse:

Harmonic arithmetic is like counting down from infinity, in which an increment of one reduces the amount slightly.

Means and operations

The power means are defined for a set of real numbers, a1, a2, …, an:

The best-known of these are the arithmetic, geometric, and harmonic means, with p = 1, p → 0, and p = –1:

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Thoughts on science and history

History is diachronic. Science is synchronic.

History is a narrative of time. Science is a theory of space.

A scientist sees two things and notices their similarities. An historian sees two things and notices their differences.

A scientist seeks what is universal that explains. An historian seeks what is unique that explains.

For science the default inference is to a universal nature. For history the default inference is to a unique particular.

A history of science is not a science. A science of history is not a history.

Historical science universalizes recent history. Historicism particularizes universal science.

Scientific history, or a science of history, is pseudo-history because it devalues particulars and overvalues universals.

Evolution is a theory of history presented as a science. Whig history is a philosophy of science presented as a history.

Science and history posts

Posts on science and history:

10/17/2018 – Science and history once more

July 27, 2018 – Science or stories

3/13/2018 – Science and history again

2/19/2018 – Distinguishing history and science

January 17, 2017 – Combining history and science

September 19, 2016 – History and science once again

December 15, 2015 – From history to nature

August 8, 2015 – Science in history

February 21, 2015 – History and science

October 12, 2014 – Science and history again

January 21, 2014 – Science and history

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Church and ethnos

Most Christian congregations have an ethnos, a term from cultural anthropology for people with a common national or cultural tradition. Congregations are usually part of a larger network, denomination, or hierarchy, which has at least one ethnos. (Eastern) Orthodox autocephalous churches are national churches, which include the ethnos of their nation. The (Roman) Catholic church incorporates multiple national churches, each with its own ethnos. In places such as the U.S., a Catholic parish reflects the ethnic background of the parishioners, usually Italian, Spanish, Irish, or Polish.

Protestant denominations reflect their national origins. Lutherans have a Germanic or Scandinavian ethnos. Presbyterians have a Dutch, Scottish or Swiss ethnos. Anglicans have a strong British ethnos, which includes the Queen. Many denominations adopt the ethnos of the country they reside in, so for example American Baptists have an American ethnos. The Messianic congregations springing up have a Jewish ethnos.

A church ethnos reflects the way that Christianity is a universal religion that does not replace the ethnos of its adherents. The original Christian church had a Jewish ethnos but as Gentile believers became dominant, Christianity acquired the ethnos of the nations. The apostolic decision that Gentiles did not have to be circumcised or keep the Jewish law affirmed Gentile national customs and laws.

Some worry that a church ethnos may be excessive or even idolatrous. While that is possible, church and ethnos have been together for centuries without significant harm. The excesses that have been pointed out, such as the Russian Orthodox under the Czars or some Lutherans in Nazi Germany, have come and gone. And the Lutheran Confessing Church was a witness against an excessive ethnos in the church.

Doppler effect in spacetime and timespace

We follow the presentation of Guy Moore, formerly of McGill University, online here.

The Doppler effect is the phenomenon we have all noticed, that a sound produced by a moving source, or which you hear while you are moving, has its perceived frequency shifted.

Spacetime (3+1)

If a source of sound makes a sudden bang (pressure pulse) at time 0, then the location in space of the pressure pulse in relation to time will look like successive concentric circles. For a source moving to the right, letting out a series of “bangs,” the location of the successive pressure peaks will be closer together on the right and further apart on the left.

Now remember that a sound is just a series of pressure peaks, which are tightly separated in time, which is the period of the wave. Therefore, instead of thinking of the sound waves as due to “bangs,” you can think of them as pressure peaks in a periodic sound wave. In front of the moving object the peaks are closer together. That means that the wave length is shorter, which means it is a higher frequency wave. Behind, the peaks are farther apart, meaning that it is a longer wavelength sound, at a lower frequency. This is the gist of the Doppler effect.

Let us now actually calculate the size of the effect. Suppose a sound source is moving right at you, at velocity v. At time 0, it emits a pressure peak. At time Δt, it emits a second pressure peak. If its distance from you at time 0 was x, its distance from you at time Δt was xvΔt (it is nearer, since it is moving towards you).

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