Equality and hierarchy

The state of nature was invented by Thomas Hobbes to support his idea of a social contract that was (or would have been) entered into by free individuals. In the natural state people would have been totally free but also lacking in security and other goods of society. So they voluntarily entered into a social

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Timelines and placelines

Events may be ordered in various ways (see here). Events ordered by time form a time line, or timeline, which is: 1. a linear representation of important events in the order in which they occurred. 2. a schedule; timetable. This may be generalized to the following definition: A time line is an ordering of events

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From 3D length to 3D duration

We observe the sun and the moon traversing the sky. We know that the moon is objectively orbiting the earth but the sun is not. Where then is the sun that is observed traversing the sky in daily and annual cycles? It is not in 3D length. It is in 3D duration. Binary stars orbit

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Ordering events

There are many ways to order events. One way is by time. Events happening at the same time are put in an equivalence class, which is then ordered from the earliest time to the latest time. History is usually ordered this way. With the advent of mechanical clocks and watches, modern people typically experience events

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3D time video series

I’ve posted a video series on 3D time (duration) online on Youtube. See the playlist 3D Time here: It’s also on Vimeo here. 3D Time: From Transportation to Physics Presentations: Introduction Part 1: Show Me Part 2: Objections Part 3: Kinematics I Part 4: Kinematics II Part 5: Dynamics Part 6: Orbits Part 7: Relativity

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Jesus’ brothers and sisters

The Gospel According to John, chapter 7:2-10 reads: 2 Now the Jews’ Feast of Booths was at hand. 3 So his brothers said to him, “Leave here and go to Judea, that your disciples also may see the works you are doing. 4 For no one works in secret if he seeks to be known openly. If you

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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

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