Searching for the structure of human behaviour:
Spacetime 1: a unique system of co-ordinates
for the individual process.

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Introduction

A few years ago, while reading and rereading Albert Einstein's booklet about his theory of relativity, different spacetime-continua as a consequence of different systems of co-ordinates (systems like trains, the earth, rockets, et cetera), I wondered to what extent his findings have a bearing on humans [ note ].
My first reaction to that question was something like: of course they are, why would humans be an exception to the rule. In that case I would want to know whether it is at all possible to establish the four co-ordinates of a place on earth and I would need to know more about space and about time. Only then could I think about the question of what information such a system of co-ordinates could offer and, next, whether that information could be relevant to humans, could provide a better understanding of the ways in which they experience and behave themselves. I believe that I can do the first, go in search of the 4 co-ordinates, most distinctly with the help of pictures.
 

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About place and space

If there is going to be a search, we can best start with the familiar, with the three co-ordinates which mark the place and space of an object.
 

6ruimte0.gif flat surfaceThis first picture shows a piece of paper on which the footprints of a person can be seen.
6ruimte1.gif 2 co-ordinates: flat surface1. place and space

The area of the piece of paper can be described by means of two co-ordinates: x en y.
X stands for width and Y for length. When we refer to a spatial object, y can sometimes be named depth.

6ruimte2.gif 3 co-ordinates: 3D2. place and space

On this piece of paper stands a person. By choosing a point straight above the crossing of the co-ordinates X and Y, we find the co-ordinate Z which stands for height.
Z = zenith, the point straight above the object, in this case a human.

 
It would be nice and easy if we could determine time by just looking at the clock. But it's not as simple as that. For time on our clocks has been standardized. Around 1945 the globe was divided into time zones and, as a result, large areas of the globe have the same time in force. The actual time depends on the exact place on earth, where the object (the human being) is situated (strictly speaking it depends on the situation in space, but more of that later). First we shall have to relate the object to its place on the earth. We cannot get around that.
 
6ruimte3.gif 2 co-ordinates: flat surface3. place and space

The piece of paper lies somewhere on the earth's surface and we are now going to use the lines of longitude and latitude to determine the place thereon.
The parallels of latitude, which run from right to left across the globe, parallel with the equator which lies halfway between the poles, correspond with the X co-ordinate. The lines of longitude or meridians, which run from pole to pole, correspond with the Y co-ordinate.

6ruimte4.gif 2 co-ordinates: flat surface on globe4. place and space

Now the piece of paper, by means of two co-ordinates, has been related to an exact place on the surface of the earth.
A = axis of the earth
E = equator

6ruimte5.gif 3 co-ordinates: 3D on globe5. place and space

When linking the highest point, the zenith straight above the object, with the center of the earth, we connect the object spatially with the earth.
Z = zenith
A = axis of the earth
E = equator

 
For the moment this should be enough about place and space. Let us now direct our attention toward time.
 
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About time: the rhythm of day and night

We will now look for the fourth co-ordinate, time. Time on the earth depends in the first place on the rotation of the earth around its axis. In 24 hours the earth turns around its axis and day and night alternate.

Z = zenith     A = axis of the earth     E = equator


Rotating in 24 hours
In case this animation does not work...
  1. We start at midnight.
  2. The rotation is toward the east, to the right side of the picture. We see 'the sun rising in the east' and, later, set in the west.
  3. The earth has rotated to the point where the side with the little figure is turned fully toward the sun. It's day on this half of the globe and noon for the figure.
  4. It must be late afternoon at the place where our figure stands. The picture suggests that the figure can see the sun, which will soon set in the west.
  5. It is 24 hours since the first of these pictures. The earth has rotated a full circle and our little figure is back again at the night-side of the earth. The side with the figure is turned away from the sun.
 
With the help of the pictures, we have looked from the outside at the earth while it turned around. The axis has maintained the same angle in respect to the sun. Evidently time on earth is measured on the basis of the position of the earth and our place on the earth in respect to the sun. After all this it seems that we have to look outside the earth in order to find the place of the little figure in respect to the sun. To be honest, we also need to find out more about the three spatial co-ordinates.
 
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About time: the seasons

The earth not only rotates around its axis, but also moves in an orbit around the sun. You already knew that, but you will also notice that the proportions in the following pictures are even more awry than on the pictures above (we make a feature out of a fault). The slanting position of the earth's axis in its orbit around the sun proves to be of particular importance. The direction of the slanting position, as seen from a particular standpoint, always stays the same. This is how the seasons originate. I'd like to enter into that now.
I am going to use combinations of three pictures: on the left you'll find the earth in its orbit around the sun twice, as seen from above and sideways; on the right you'll find a map of the earth on which the line which divides day and night is clearly visible. A little red dot indicates the position of the sun (click on the picture to see it in the original format) [ note ].
 

1. the vernal equinox
6kal10.gif Sun on the equator: vernalequinox. On the northern hemisphere spring. beginsS = the sun -------- A = the axis of the earth

Approximately March 21: the sun is on the equator, moving in a northern direction (vernal equinox).

Day and night are equally long at any place on earth. As seen from the level of the orbit, the earth is hidden behind the sun.
In the northern hemisphere spring begins, in the southern hemisphere it's the beginning of autumn.Click on the picture for more details.

 
2. summer solstice on the Tropic of Cancer
6kal20.gif Sun on the Tropic of Cancer. On the northern hemisphere summer begins.Approximately June 22: the sun is at its most northerly point (the summer solstice on the Tropic of Cancer).

At this location of the earth in its orbit, the day is longest in the northern hemisphere.
As you can see on the pictures summer begins in the northern hemisphere, in the southern hemisphere however winter begins.
Click on the picture for more details.

 
3. the autumnal equinox
6kal30.gif Sun on the equator: autumnal equinox. On the northern hemisphere autumn begins.S = the sun -------- A = the axis of the earth

Approximately September 23: the sun is on the equator, moving in a southern direction (autumnal equinox).

Day and night are again equally long anywhere.
In the northern hemisphere summer ends and autumn begins, in the southern hemisphere the days get longer from now on and spring begins.
Click on the picture for more details.

 
4. winter solstice on the Tropic of Capricorn
6kal40.gif Sun on the Tropic of Capricorn. On the northern hemisphere winter begins.Approximately December 22: the sun is at its most southern point (the winter solstice on the Tropic of Capricorn).

Winter begins in the northern hemisphere with the shortest day, whereas in the southern hemisphere it's the longest day.
In the southern hemisphere, with the earth at this position in its orbit, summer begins.
Click on the picture for more details.

 
It is clear that the rotation of the earth around its axis and its slanting position in respect to its orbit around the sun determine both the rhythm of day and night as well as the seasons on earth. But still we have not found the co-ordinate we were looking for. We have made progress though (while we enter deeper and deeper into space). An individual spacetime relation has not emerged yet.
In the meantime we have established a relation between the earth and the sun. However, time is the time at a location on earth: the degree of latitude and the degree of longitude together mark the time of year and the time of the day. We have seasons but not a calendar. We don't yet know at which point in the orbit of the earth we are, we don't know exactly what date we have. We do not have a fixed point in time on the basis of which we could make appointments with other people.
What is the use of a clock when you can't make appointments because clocks register different times and you cannot agree upon the date?
 
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Projecting and relating in space

We can visualize the space around the earth and the sun, the heavens, as a sphere. In consequence we are inside that sphere. All around the inner side of that sphere we see stars and other heavenly bodies which hardly seem to move in respect to one another. Nor do they seem to differ in distance from the earth. The sun, the moon and the planets, however, clearly move against the starred background. We should now imagine a large circle lying in the same plane as the orbit of the earth around the sun. This circle is called the ecliptic.
 
A circle as a map of time

Relative positions of the sun seen from the earth at other dates.
Click here.
In order to determine where on a circle something is located, the circle needs a starting-point.
We draw a line from the center of the earth to a place on the circle in such a way that the line goes exactly through the center of the sun. We could do that every day and slowly go around the circle, but we choose the exact moment when the sun is just above the equator on its way from the tropic of Capricorn in the south to the tropic of Cancer in the north. This point is generally accepted as point zero on the circle.
For thousands of years this point of reference in space and time has been called 0 Aries [perforce since the time when it no longer coincided with the beginning of the constellation Aries, some 2200 years ago, and the distinction star sign or zodiacal sign Aries became necessary]. For purposes of correction because of shifts that occur, this point is regularly verified whereby the universal time (UT) is established, for instance to facilitate space programs.
 
the vernal equinox
the winter solstice, spring equinox and summer solstice

The little red dot on the three globes points directly toward the sun which you can imagine as opposite that point. The globe on the right indicates the beginning of winter, when the sun is at its most southern point, the Tropic of Capricorn. The globe in the middle gives a picture of the moment when the center of the sun travels from south to north across the equator, at the point of intersection of the earth's axis and the ecliptic. This moment, when day and night in any place on earth are equally long and spring begins in the northern hemisphere, is called the vernal or spring equinox. The globe on the left indicates the beginning of summer. The sun has arrived at its most northern point at the Tropic of Cancer.
The position of the little figure not only changes because of the rotation of the earth around its axis, which we saw earlier, but also because of this movement of the earth along its orbit.
 

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date and solar time on earth

Movement of the sun relative to the stars, as seen from the earth.D = date and time
Now we are actually going to relate the earth to its frame of reference in space, the circle of the ecliptic. We have put the earth in the center of the circle (on the plane of the ecliptic) for measuring purposes. We could hardly take the sun as the central point as its role when measuring date and time for the earth is only that of an expedient.

Seen from this angle, the sun is situated at approx. 142 degrees distance from 0 Aries on the ecliptic. On the earth's calendar it is approximately August 14th. The sun moves with an average velocity of one degree per day.

 
Now that we have found the time co-ordinate we have been looking for, we can combine space and time and try to draw a picture of the four co-ordinates for different places on the earth.
 
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A circle as a map of space and time.

The following examples show a number of possible places. I have chosen five locations on the Greenwich meridian, namely: Greenwich, the most northerly place, another location on the Tropic of Cancer, one on the Equator, one on the Tropic of Capricorn and one, the most southern of the five places, at the same latitude as Greenwich but in the southern hemisphere. When you click on the picture you can see the co-ordinates of the five locations in succession.
 

Notice the sun below, on and above the horizon...
Click here.
Data of the 5 charts on the left:
S = 27042', 22 December 2000;
Mc = 18112', 6:00 hour;
  1. Greenwich, 0 longitude, 5131' North
    Asc = 24413'; Z = 15413'.
  2. Tropic of Cancer, 0 longitude, 2327' North
    Asc = 26112', Z = 17112'.
  3. at the Equator, 0 longitude, 0 latitude:
    Asc = 27101', Z = 18101'.
  4. Tropic of Capricorn, 0 longitude, 2327' South
    Asc = 28046', Z = 19046'.
  5. more south, 0 longitude, 5131' South
    Asc = 29724', Z = 20724'.
..
S = date and solar time, the t co-ordinate
Mc = Midheaven, the south, indicates solar time on the local meridian, the Y co-ordinate
Asc = Ascendant, the eastern horizon of a specific place at the meridian, the X co-ordinate
Z = Zenith of that place, always at 90 from the Ascendant, the Z co-ordinate.
 
Now the 0 meridian lies at the other side of the globe...
Click here.
Data of these 5 charts:
S = 27026', 22 December 2000;
Mc = 9147', 00:00 hour;
  1. Greenwich, 0 longitude, 5131' North
    Asc = 18036'; Z = 9036'.
  2. Tropic of Cancer, 0 longitude, 2327' North
    Asc = 18047', Z = 9047'.
  3. at the Equator, 0 longitude, 0 latitude:
    Asc = 18056', Z = 9056'.
  4. Tropic of Capricorn, 0 longitude, 2327' South
    Asc = 18109', Z = 9109'.
  5. more south, 0 longitude, 5131' South
    Asc = 18203', Z = 9203'.
 
At other times than those at 6:00 h. in the first series, differences can be even greater. Around 12 and 0 hours however, differences are so slight that their relevance is not very obvious (see the second series). Nevertheless, it proved possible to determine the four co-ordinates of an object at a specific location and a specific date on earth. By relating this location both spatially and in time with the ecliptic, we have found the individual system of co-ordinates and the personal spacetime relation we have been looking for.
We have now also found that none of the four co-ordinates indicates either time or space exclusively.
 
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The notion of spacetime

Because spacetime is a continuum, because there is no interruption, we must by necessity conclude that we can only speak about apparent points of interruption on that continuum. How can we imagine such a moment and what then could be significant moments of interruption? Examples could be moments of beginning like: a birth, confirmation of a marriage, a formal proclamation or an official agreement, the launch of a rocket. Or moments of ending like: a death, the crash of an airplane, the adjudication of bankruptcy, the actual moment of arrival. In any case they should be moments and events which can be connected to a specific time and a location.

What point is there in establishing the fact that every object on the surface of the earth can be connected in its own way to the sun and space? The old astrologers have studied this matter and chronology within human memory. Ever since the 18th century, the Age of Enlightenment, scientists, engaged in the mechanics of movement of objects outside the earth, call themselves astronomers. Looking at the last pictures the method of econometricians came to my mind. They manipulate their many sources of information mathematically like they do co-ordinates or dimensions. A human's existence consists of more than four dimensions, more than four aspects are of importance. Our inner spacetime, our singularity, contains information in the form of our conditions and capacities, doesn't it? In order to chart a human's existence we would need to be able to handle information about more than four dimensions.

Link to
events co-ordinated and connected in space and time - structure #13/4.