iSoul In the beginning is reality.

Metric postulates for time geometry

January 17, 2020 4:02 pm ⋅

Geometry was developed by the ancient Greeks in the language of length, but it is an abstraction that may be applied to anything that conforms to its definitions and axioms. Here we apply it to duration. We will use Brossard’s “Metric Postulates for Space Geometry” [American Mathematical Monthly, Vol. 74, No. 7, Aug.-Sep., 1967, pp. 777-788], which generalizes the plane metric geometry of Birkhoff to three dimensions. First, Brossard:

Primitive notions. Points are abstract undefined objects. Primitive terms are: point, distance, line, ray or half-line, half-bundle of rays, and angular measure. The set of all points will be denoted by the letter S and some subsets of S are called lines. The plane as well as the three-dimensional space shall not be taken as primitive terms but will be constructed.

Axioms on points, lines, and distance. The axioms on the points and on the lines are:

E1. There exist at least two points in S.

E2. A line contains at least two points.

E3. Through two distinct points there is one and only one line.

E4. There exist points not all on the same line.

A set of points is said to be collinear if this set is a subset of a line. Two sets are collinear if the union of these sets is collinear. The axioms on distance are:

D1. If A and B are points, then d(AB) is a nonnegative real number.

D2. For points A and B, d(AB) = 0 if and only if A = B.

D3. If A and B are points, then d(AB) = d(BA).

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Posted in: Knowing, space & time ⋅ Tagged: ,

Length and duration in time and space

December 18, 2019 5:01 pm ⋅

Length and duration are defined by their measurement. Length is that which is measured by a rigid rod or its equivalent.

Length is “extension in space” (Dict. of Physics).

Duration is that which is measured by a clock or its equivalent.

Duration is “time measured by a clock or comparable mechanism” (Dict. of Physics).

Time and space and defined as concepts. Time is a local uniform motion that indicates the length or duration of local events by convention.

Time is “The dimension of the physical universe which, at a given place, orders the sequence of events.” (Dict. of Physics).

Space is a three-dimensional expanse whose extent is measured by length and duration.

“Space, a boundless, three-dimensional extent in which objects and events occur and have relative position and direction.” (Encyclopedia Britannica)

The difference between length and duration is the relation between the observed and the observed, the measurand. The question is, which one is the reference quantity and which one is the measured quantity. If the observer is (or has) the reference, and the observed is the measurand, then the value measured is length. If the observer is the measurand, and the observed is (or has) the reference, then the value measured is duration.

Time is derived from (1) three orthogonal uniform motions, or (2) one orthogonal uniform motion in which the three orthogonal uniform motions are components, or (3) the distance from the origin of the one orthogonal uniform motion in (2). In both (1) and (2) time is derived from three-dimensional, whereas in (3) time is one-dimensional or a scalar.

Space is derived from (1) three orthogonal uniform motions, or (2) one orthogonal uniform motion in which the three orthogonal uniform motions are components, or (3) the distance from the origin of the one orthogonal uniform motion in (2). In both (1) and (2) space is derived from three-dimensional, whereas in (3) time is one-dimensional or a scalar.

The difference between time and space is the relation between the observer and observed, or reference and measurand. If the reference motion is at rest in the observer’s frame, then what is measured is the length of motion of an observed body. If the reference motion is at rest in the observed frame, then what is measured is the duration of motion of an observed body.

Posted in: Knowing, space & time ⋅ Tagged: ,

Two forms of time and space

December 10, 2019 6:36 pm ⋅

The SI metric base unit of length is the metre. The SI base unit of duration is the second. Other units of length are the kilometre, millimetre, inch, foot, mile, etc. Other units of duration are the minute, hour, day (sidereal, solar, etc.), year, etc.

Duration time is also called time. Length time may be called stance. Length space is also called space. Duration space may be called chronotopy.

Time is an independent variable measured in units of length or duration. Space is a dependent geometry of positions measured in units of length or duration.

Time is indicated by a reference uniform motion, which in units of duration is called a clock and in units of length is called a metreloge. The reference rate of uniform motion is a convention that enables one to convert length to duration and vice versa. By appropriate choice of  units, this rate may equal one, in which case length and duration may be interchanged in calculations.

In uniform motion the spaces covered are proportional to the time elapsed. Independent space and time are two sides of the same coin.

The independence of time allows it to be selected independent of other variables, as in setting an appointment, a tempo for music, or the duration of a game. Its independence and its uniform motion allows time to change by some linear rule.

Posted in: Knowing, space & time ⋅ Tagged: ,

Kinds of rights

December 2, 2019 3:27 pm ⋅

Human rights are the political rights people have because they are human beings. They apply equally to all because of their common humanity. There are several statements of human, or natural, rights. The United Nations Universal Declaration of Human Rights issued in 1948 is a statement of human rights.

Developmental rights are the political rights people have because of their stage of development, notably, childhood or adulthood. The rights of children differ from the rights of adults because of the differences between children and adults. Children require adult parenting, whereas adults do not. Adults can marry, whereas children cannot.

Parenting is a developmental right because it concerns the stage of development. Adults parent children, not the other way around. In the confused times of today, developmental rights are confused with human rights and children are treated as adults.

Sexual rights are the political rights people have because of their sex, that is, male and female. Sex is also called gender, although gender is a grammatical term, whereas sex is a biological term. The rights of males differ from the rights of females because of the differences between males and females. An unmarried male adult has the right to marry any unmarried female adult. An unmarried female adult has the right to marry any unmarried male adult.

Marriage is a sexual right because it concerns a sexual relationship that naturally leads to the birth of offspring. In the confused times of today, sexual rights are confused with human rights and the sexes are treated as if they did not exist.

Woe to the society that confuses childhood with adulthood and male with female. That society will learn the hard way the importance of developmental and sexual differences.

Posted in: politics, Relating ⋅ Tagged:

Communitarianism

December 2, 2019 2:58 pm ⋅

This post is a parallel contrast to the previous post on Old style liberalism.

Communitarianism puts major emphasis on the freedom of communities to control their own destinies. Communitarianism is its creed; individualism and alienation its enemy. The state exists to protect communities from coercion by other communities or individuals and to widen the range within which communities can exercise their freedom; it is purely instrumental and has no significance in and of itself. Society is a collection of communities and the whole is no greater than the sum of its parts. The ultimate values are the values of the communities who form the society; there are no sub- or super-community values or ends. Nations are convenient social units; patriotism is a part of its creed.

In politics, communitarianism expresses itself as a reaction against individualistic regimes. Communitarians favored limiting the rights of individuals, establishing geocratic governing institutions, limiting the franchise, and moderating civil rights. They favor such measures both for their own sake, as a direct expression of essential political freedoms, and as a means of facilitating the adoption of communitarian economic measures.

In economic policy, communitarianism expresses itself as a reaction against individuals controlling economic affairs. Communitarians favor free cooperation at home and among nations. They regard the organization of economic activity through free private enterprise operating in a competitive market as a limited expression of essential economic freedoms and as unimportant in facilitating the preservation of political liberty. They regard cooperation among nations as a means of eliminating conflicts that might otherwise produce war. Just as within a country, communities following their own interests under the influence of cooperation indirectly promote the interests of the whole; so, between countries, communities following their own interests under conditions of cooperation, indirectly promote the interests of the world as a whole. By providing common access to goods, services, and resources on the same terms to all, cooperation would knit the world into a single economic community.

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Posted in: politics, Relating ⋅ Tagged:

Old style liberalism

November 29, 2019 12:11 pm ⋅

The following excerpt is from “Liberalism, Old Style” by Milton Friedman, published in the 1955 Collier’s Year Book, pp. 360-363. New York: P.F. Collier & Son, 1955. Reprinted in The Indispensable Milton Friedman, Essays on Politics and Economics, edited by Lanny Ebenstein, pp. 11-24. Washington, D. C.: Regnery Publishing, 2012 (see here).

Liberalism, as it developed in the seventeenth and eighteenth centuries and flowered in the nineteenth, puts major emphasis on the freedom of individuals to control their own destinies. Individualism is its creed; collectivism and tyranny its enemy. The state exists to protect individuals from coercion by other individuals or groups and to widen the range within which individuals can exercise their freedom; it is purely instrumental and has no significance in and of itself. Society is a collection of individuals and the whole is no greater than the sum of its parts. The ultimate values are the values of the individuals who form the society; there are no super-individual values or ends. Nations may be convenient administrative units; nationalism is an alien creed.

In politics, liberalism expressed itself as a reaction against authoritarian regimes. Liberals favored limiting the rights of hereditary rulers, establishing democratic parliamentary institutions, extending the franchise, and guaranteeing civil rights. They favored such measures both for their own sake, as a direct expression of essential political freedoms, and as a means of facilitating the adoption of liberal economic measures.

In economic policy, liberalism expressed itself as a reaction against government intervention in economic affairs. Liberals favored free competition at home and free trade among nations. They regarded the organization of economic activity through free private enterprise operating in a competitive market as a direct expression of essential economic freedoms and as important also in facilitating the preservation of political liberty. They regarded free trade among nations as a means of eliminating conflicts that might otherwise produce war. Just as within a country, individuals following their own interests under the pressures of competition indirectly promote the interests of the whole; so, between countries, individuals following their own interests under conditions of free trade, indirectly promote the interests of the world as a whole. By providing free access to goods, services, and resources on the same terms to all, free trade would knit the world into a single economic community.

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Posted in: politics, Relating ⋅ Tagged: ,

Combining equations

November 29, 2019 10:23 am ⋅

Given two equations with the same variable, how can they be combined? If the equations are consistent, they may be solved as simultaneous equations. But what if the equations are inconsistent? There are two ways to combine them in that case, one is OR, the other is AND.

Consider the equations x = a and x = b, where a ≠ b. If we multiply these equations together, we get

x² = ab,

in which the solution is x = √ab, so that x is the geometric mean of a and b.

If we make the equations homogeneous first, then multiply them together, we get: 0 = x − a and 0 = x − b, so that

0 = (x − a) (x − b) = x² − (a + b) x + ab.

The solution of the combined equation is either x = a or x = b. To combine equations with AND, multiply homogeneous equations together.

Another way to combine equations is to add them together. In this case, we get

x + x = 2x = a + b, or x = (a + b)/2,

so that x is the arithmetic mean of a and b. Homogeneous equations added produce the same result: 0 = x − a + x − b = 2x − (a + b), so that x = (a + b)/2.

Posted in: Knowing ⋅ Tagged: ,

Augsburg Confession briefly

November 24, 2019 12:45 pm ⋅

The Holy Bible is the final authority in all matters of faith and practice for Reformation Christians. The Augsburg Confession is the doctrinal confession of faith adopted by the Lutheran Church. It is part of the Book of Concord, which includes the three ancient ecumenical creeds: the Apostles’ Creed, the Nicene Creed, and the Athanasian Creed. It also contains the Apology of the Augsburg Confession, the Smalcald Articles, the Treatise on the Power and Primacy of the Pope, Luther’s Small and Large Catechisms, and the Formula of Concord. (reference)

Martin Luther wrote the Catechisms and the Smalcald Articles. Phillip Melanchthon wrote the Augsburg Confession, its Apology, and the Treatise. So, Melanchthon wrote more of the Lutheran doctrines than Martin Luther. Note that the other writings of Luther have no official status among Lutherans, although most of them make for sound reading.

The Augsburg Confession was written in a particular historical context in which the Lutheran movement attempted to explain and justify itself to the religious and civil authorities of the day, notably Emperor Charles V of the Holy Roman Empire, at the Diet of Augsburg on June 25, 1530. Although reconciliation did not happen, the Augsburg Confession provided the primary confession of the Lutheran movement.

The twenty-eight articles in the Augsburg Confession consist of twenty-one statements of doctrine and seven declarations about abuses, and demands for reforms. Although Melanchthon and his associates compiled the confession, Luther approved it as an accurate account of his doctrine.

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Posted in: Knowing, theology ⋅ Tagged: ,

Motion as a parade

November 22, 2019 9:31 pm ⋅

Have you ever seen a parade? Have you ever been in a parade?

parade

A parade is basically a linear (1D) motion. It begins at a point in space and time and ends at a point in space and time. It is planned to progress in a certain order.

The view from the side sees the parade pass by. The parade participants change in time but the location does not. The parade represents the diachronic perspective of motion in time.

The bird’s-eye view from above (as of a camera on a drone) sees the parade as a whole. The time keeps changing but the general location does not. The parade represents the synchronic perspective of motion in time.

The view from a parade participant sees the streetscape pass by. The parade watchers change in space but the chronation does not. The parade represents the diachoric perspective of motion in space.

The view from the plan for the parade sees the parade as a whole. The stance keeps changing but the chronology does not. The parade represents the synchoric perspective of motion in space.

Posted in: Knowing, space & time ⋅ Tagged: , ,

Prayers and benedictions

November 20, 2019 5:40 pm ⋅

Prayers from the New Testament (NET Bible)

Our Father in heaven, may your name be honored,
10 may your kingdom come,
may your will be done on earth as it is in heaven.
11 Give us today our daily bread,
12 and forgive us our debts, as we ourselves have forgiven our debtors.
13 And do not lead us into temptation, but deliver us from the evil one. Mt 6:9-13

22 Jesus said to them, “Have faith in God. 23 I tell you the truth, if someone says to this mountain, ‘Be lifted up and thrown into the sea,’ and does not doubt in his heart but believes that what he says will happen, it will be done for him. 24 For this reason I tell you, whatever you pray and ask for, believe that you have received it, and it will be yours. 25 Whenever you stand praying, if you have anything against anyone, forgive him, so that your Father in heaven will also forgive you your sins.” Mk 11:22-25

17 I pray that the God of our Lord Jesus Christ, the Father of glory, may give you spiritual wisdom and revelation in your growing knowledge of him, 18 —since the eyes of your heart have been enlightened—so that you may know what is the hope of his calling, what is the wealth of his glorious inheritance in the saints, 19 and what is the incomparable greatness of his power toward us who believe, as displayed in the exercise of his immense strength. 20 This power he exercised in Christ when he raised him from the dead and seated him at his right hand in the heavenly realms 21 far above every rule and authority and power and dominion and every name that is named, not only in this age but also in the one to come. 22 And God put all things under Christ’s feet, and he gave him to the church as head over all things. 23 Now the church is his body, the fullness of him who fills all in all. Eph 1:17-23

I kneel before the Father, 15 from whom every family in heaven and on the earth is named. 16 I pray that according to the wealth of his glory he may grant you to be strengthened with power through his Spirit in the inner person, 17 that Christ may dwell in your hearts through faith, so that, because you have been rooted and grounded in love, 18 you may be able to comprehend with all the saints what is the breadth and length and height and depth, 19 and thus to know the love of Christ that surpasses knowledge, so that you may be filled up to all the fullness of God. Eph 3:14b-19

9 And I pray this, that your love may abound even more and more in knowledge and every kind of insight 10 so that you can decide what is best, and thus be sincere and blameless for the day of Christ, 11 filled with the fruit of righteousness that comes through Jesus Christ to the glory and praise of God. Phil 1:9-11

6 Do not be anxious about anything. Instead, in every situation, through prayer and petition with thanksgiving, tell your requests to God. 7 And the peace of God that surpasses all understanding will guard your hearts and minds in Christ Jesus. Phil 4:6-7

9 For this reason we also, from the day we heard about you, have not ceased praying for you and asking God to fill you with the knowledge of his will in all spiritual wisdom and understanding, 10 so that you may live worthily of the Lord and please him in all respects—bearing fruit in every good deed, growing in the knowledge of God, 11 being strengthened with all power according to his glorious might for the display of all patience and steadfastness, joyfully 12 giving thanks to the Father who has qualified you to share in the saints’ inheritance in the light. 13 He delivered us from the power of darkness and transferred us to the kingdom of the Son he loves, 14 in whom we have redemption, the forgiveness of sins. Col 1:9-14

11 And in this regard we pray for you always, that our God will make you worthy of his calling and fulfill by his power your every desire for goodness and every work of faith, 12 that the name of our Lord Jesus may be glorified in you, and you in him, according to the grace of our God and the Lord Jesus Christ. 2 Th 1:11-12

4 I always thank my God as I remember you in my prayers, 5 because I hear of your faith in the Lord Jesus and your love for all the saints. 6 I pray that the faith you share with us may deepen your understanding of every blessing that belongs to you in Christ. 7 I have had great joy and encouragement because of your love, for the hearts of the saints have been refreshed through you, brother. Philemon 1:4-7

2 Dear friend, I pray that all may go well with you and that you may be in good health, just as it is well with your soul. 3 Jn 1:2

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Posted in: Knowing, theology ⋅ Tagged: ,