Spacetime 2: Orientation, an event charted

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Orientation in space and time on a rotating surface

We have found the four co-ordinates, and with them the basis of an individual spacetime continuum, and are now able to further investigate this specific event. For that purpose I shall try to visualize how space might look from such a specific place and time on earth. First we take a look at the relative movement of earth and sun inside the celestial sphere from some point in space.
The tilt of the earth's axis with respect to her orbit around the sun causes local differences between day and night, the seasons. Precisely because of this tilt it is hard to imagine the movement of objects in space such as the sun. Therefore I'll begin with the representation of the least complicated situation; the anti-clockwise movement of the earth in her daily rotation around her axis. The pictures in series 1 represent the situation on the northern side of the globe, where the zenith/nadir-axis coincides with the earth's axis, whereas the horizon (to be envisaged as a plane stretching out to the stars, as we have seen in ZZZ#9) coincides with the earth's and the celestial equator. At the North Pole, at the end of summer, the sun still remains day and night just above the horizon.
Clicking the picture will display twelve different situations and you can simulate the rotation. With respect to the precision I must ask you not to expect too much. The inclined ellipses were placed from view, which has consequences for the precision of the intersections.
 

  ^   1. The basic movement: the earth turning around her axis.
Local horizon: North Pole.
Date: about 4 September.
Interval: two hours.

Animation page

1. The basic movement: the earth turning around her axis
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Standing on the earth's axis both North and South are below your feet. At that place, both at the North and at the South Pole, all meridians meet and every direction around you is both East and West. With a single step you go to a definite meridian and the East and West directions then become apparent.
Let us take such a step and stand on the 0 meridian. Let's imagine that is at the left of the earth's axis. We will suddenly have the North at the right, the South at the left, while in front and behind us there are the West and the East respectively. If we would go to the right side at the 180 meridian, all directions would change places and we would find ourselves in a time zone with half a day's difference!
 
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Local horizon and directions from a 52 angle

The following series of pictures shows a situation at the 0 meridian somewhere near 52 North Latitude. We would be at Greenwich. The little figure continues to be turned toward us. Now he has the North at his left side, the South at the right, West is behind him and he looks at us in an Eastern direction. We want to know where the Ascendant is to be found (the horizon intersects with the sun's apparent path, the ecliptic, at two points: the eastern is called Ascendant, the western point of intersection is the Descendant).
 

  ^   2. The movement of the Ascendant along the Eastern horizon
Local horizon: 52 North, 0 longitude.
Date: about 4 September.
Interval: two hours.

Animation page

The point in the rotation of the earth which we choose to start with at the North Pole makes us, at this latitude, start in the dark.

2. The movement of the Ascendant along the Eastern horizon
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From the centre: setting up a more distinct map

Up until now we have looked at the motion from a distance. The data of the individual system of co-ordinates are available in Ascendant tables and ephemerides or we can use computer programs to calculate them. Right now I want to dwell a little longer on the question of how we can organize the information in a readable and serviceable form, for that is lacking in the above pictures. To make a well-defined map of an event we proceed as follows:

  1. The circle of the ecliptic (the path which the sun describes against the celestial sphere as seen from the earth) contains the information about its actual origin or point zero and about the sun;
  2. The co-ordinates of the event at the earth's surface, namely the South, the Ascendant and the zenith, can be projected on the ecliptic. In the same way, the other points of the compass, the Descendant and the Nadir, as they are derived from those, can also be added. In this way we transpose our standpoint from somewhere outside the celestial sphere to the specific place and time of that one event in which we are interested;
  3. The joint orbits of the Moon and of the planets form the Zodiac (a band against the celestial sphere on both sides of the ecliptic). The actual places of the Moon and the planets can be projected on the ecliptic. This adds just as many new co-ordinates and the most exact time;
  4. The star signs or signs of the zodiac (to be distinguished from the constellations which are spread over the whole celestial globe) can, starting at the origin at point zero, be added to the data on the circle;
  5. The information can be amplified by putting the twelve phases of the human process in the circle, starting from the Ascendant or from any other point to be studied;
  6. The connections between data on the circle can be drawn on the map.

In the following model I want to visualize the realization of such a map. We start from a relatively clear picture of the last series: number 12.
 

  ^   3. Rendering data and their relations on the circle of the ecliptic
Local horizon: 52 North, 0 longitude.
Date: 4 September 1952.
Time: 17:09 GMT.

The 7 pictures show:
0 - the local horizon seen from space,
1 - the ecliptic with point zero and the sun,
2 - with the co-ordinates of the event,
3 - with nine celestial bodies - time,
4 - with the signs of the zodiac,
5 - with the phases of the process,
6 - with the aspects put in the circle.

3. Rendering data and their relations on the circle of the ecliptic
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The charted movement of the Ascendant

For comparison with the visualization in the second series above, I'll show a series of twelve maps which represent the same steps of the daily movement. You'll see that the relations between the various parts are very clear in this rendition.
 

  ^   4. The maps with the moving Ascendant during one rotation
Local horizon: 52 North, 0 latitude.
Date: 3 and 4 September 1952.
Interval: two hours.

Animation page

The maps represent the same twelve situations as in the second series. The slanting line emphasizes the changing angle between Ascendant and Midheaven.

4. The maps with the moving Ascendant during one rotation
 
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Knowledge of space and time

It may seem as if I have strayed from my goal. I must admit, quietly studying the daily movement, which we can observe with the naked eye but of which the structure is not easily visualized, I enjoyed the interesting trail. I do believe, however, that I have construed a strong base for handling Einstein's idea. For me, in my search for insight into life, the importance of knowledge of space and time is a certain fact.

Take distance in space and time, shall we?
In ZZZ #9 we have, starting from the three spatial co-ordinates, searched for the co-ordinate which indicates time. For that we had to make a relation with outer space. The apparent path of the sun along the celestial sphere, the ecliptic, could be used for measuring after we decided on a point zero on the circle. By projecting the points of the compass and the zenith, the x-, y- and z-axes, on the circle, places on the meridians were related to space. By also projecting the point in the East, where the ecliptic intersects with the horizon, on the circle, every place on the globe was related in space. This point of orientation is called the Ascendant.
By doing so we also found a first instance of time. All four lines of projection on the ecliptic, in addition to a spatial location, also indicate time. Because of the rotation and tilt of the earth every location on the globe has its own set of four co-ordinates which indicate local time. By bringing the sun into the relation the knowledge of time is extended to one year. When we understand the meaning of the movement of the point zero on the circle, we can see the necessity of an extra day in leap-years. Thus our notion of time is extended to four years. More accurate mathematics would yield information about the movement of the earth's axis and extend the notion of time to a scale of thousands of years. Scholars in the far East and in vanished civilizations in the Americas, filled the gap between these notions by including the movements of the planets in their studies. Just realize that, for instance, Jupiter completes a full revolution in nearly 12 and Saturn in well over 29 earth years and it will be clear how that information contributed considerably to the range of chronology.
I think it necessary to notice that a stable civilization in need of a chronology and having the disposal of one cultivated language was a precondition to enable the maintenance of a system of registration of sufficient accuracy of measurement and knowledge over many ages. Some of the Greek thinkers about 500 BC took the earth to be a globe. That knowledge, coming from Babylon, got lost in the Western world. On the other hand, it is said that around the beginning of our era, Wise Men from the East still were capable of pinpointing not only the time when but also the place on the globe where, for instance, rare conjunctions could be observed. In the 15th century the science which concentrates on the study of the physical laws of space, called astronomy, started to evolve in the Western world. In the 16th century the earth as a sphere was rediscovered.

At this point I can close the subject. We now have the disposal of a spacetime map which shows characteristics of a certain point in space and time; as the map of an area refers to characteristics of an area and the hands of a clock refer to points in time in a continuous progress of time so the co-ordinates of our map refer to the characteristics of specific events. It is a map of the infrastructure of an event, of the interaction between an individual system with its surrounding systems, of a process in which the basic faculties of life, namely action, recollection, knowledge and emotion, are being co-ordinated in an individual manner by alternately initiating, applying and adapting them. The old astrologers would be proud if they had known how appropriate their method still is in throwing light on such a complicated matter as life, even in the present so much larger world.