Relativity of time

The following paragraph is from a new chapter, The Time Space Correlation, which doesn’t appear on Dr. Asher Eder’s book The Star of David, which was published in 1987 in English in Jerusalem by Rubin Mass Ltd.

Relativity of time 

In the previous chapter we reiterated the consensus about our notions of hours, days, and seasons. However, when looking closer, through a magnifying glass so-to-speak, we will notice that our time concept is somewhat rounded off, and subjective as well.

When someone in England or Scandinavia enjoys a nice summer day on the beach, he is hardly aware that it is winter on the southern hemisphere - at the same time. He would have to remind himself of that if he were to fly to Melbourne the other day, and to pack his winter clothes.
Everyone going, driving, or flying from say Moscow to Paris has to adjust his clock according to the local time. Usually this is done at the time of arrival. But how would he have to adjust his clock if for some reason he needs to know every minute, or after every kilometer of travel, the exact time?
Even this simple example can give us an idea about the intricate inter-relatedness between the calculation of the exact position in the three-dimensional space and its angle to the "two big lights which shall be [unto us] for signs and seasons and days" (and the hours, minutes, and seconds as fractions thereof). In addition to these four dimensions - the three conventional dimensions of space and the interrelated time - we have to take into account also the speed of the travelling body in relation to the movements of the other bodies (earth, sun, other airplanes, etc). This needs to be done e.g. for calculating the trajectories of missiles and of satellites. Based upon considerations like these, modern science developed the concept of space-time (in contrast to the conventional space and time) to indicate the inter-relatedness between these components.
Contemplating such thoughts, Albert Einstein developed his theories of relativity (in 1905), and the mathematician Herman Minkowski introduced (in 1908) the concept of the "union of space and time", or in brief, space-time.
Besides revolutionizing science, these new concepts settle the age-old philosophical dispute over objectivity or subjectivity: By nature, we are subject to the latter. For instance, we perceive the sun as a small ball although its diameter is more than a hundred times bigger than that of our globe. We also perceive the diameters of sun and moon as equal although the latter is even smaller than the earth. What is more, we derive all our measurements --meters, miles, furlongs; days, years; light-years, etc-- from subjective observations pertaining to our globe, standardize them conveniently, and take the results thereof for objectivity. There is nothing wrong with that as long as we are aware that they have no bearings on other planets (Mars, Jupiter, etc), not to speak of other solar systems, as said already.
Our hexagram with its straight lines depicts aptly these conditions we live in.
In the wake of the above mentioned modern considerations, the term absolute time became fashionable. However, this term is but one of the many examples for modern inflation and confusion of language. Time is by definition relative, relative to the position(s) of the body(ies) in view at a given moment. However, since no two bodies can at the very same instant be at the very same place, each of them has its own position and therefore its own time. The differences between them are usually so minute that they are of no tangible consequences for our daily lives, and so we can forget about them. But to speak of absolute time is more than exaggerated. Even viewing on TV a life broadcast lacks behind the actual event the time the electric waves need to cover the distance from there to the receiver (e.g. from one side of the globe to the other approximately 1/7 of a second).
There is no absolute time in the universe either as everything is moving relatively to everything else. Moreover, the velocities as well as the distances measured in light years are so huge that they don't allow to conceive of simultaneity.

The Meaning of the Hexagram For the Native American People

The following paragraph is from Dr. Asher Eder’s book The Star of David, which was published in 1987 in English in Jerusalem by Rubin Mass Ltd. The publication here is courtesy of Oren Mass
This version includes corrections and new materials that do not appear on the printed version

Excerpt from a letter received from the Sunray Meditation Society, Box 87, Huntington, Vermont 05462 (USA), dated May 20, 1983:

Thank you for your kind letter of 29 December.... The triangle is a basic concept and design element for the Native American people. The single triangle represents the building fires of Creation, and the double triangle represents a physical manifestation of those creative building energies which begin as an idea in the light or in the fire.... In our work, we understand the double triangle as expressing the wisdom: 'As it is above, so it is below'... the union of spirit and matter, Heaven and Earth. We experience this basic form as relating to a right relationship with Earth, devotion to the manifestation of an ideal form - knowing the abundance and harmony of the universe and choosing consciously to draw these qualities into the right manifestation in our lives on Earth. The double triangle also symbolizes the clan, the social form through which we know ourselves as a group working together for the good of all...

Jewish Leaders who were Against Using the Star of David

When the Star of David began to be used widely in the ninteenth and early twentieth centuries, it was strongly opposed by some Jewish prominent figures:

The poet Judah Leib Gordon, 1830 -1892, one of the most distinguished pioneers of Haskalah in Russia, claimed, it originally was used by pagan Druids.

Hungarian rabbi Leopold Löw, 1811- 1875, said it was derived from German myths.

• B. Vajda, in Zur Gesch. des Davidsschildes, in Magyar Zsidó Szemle, 1900, xvii. 310-322; thought that it is probable that it was the Cabala that derived the symbol from the Templars (see Vajda in "Magyar Zsidó Szemle," xvii. 314).

Joseph Gutmann ,The Jewish sanctuary,  ‏Brill,1983 Isbn 9004068937, 9789004068933 p. 21 

As late as the 19^th century, Rabbi Isaac Elhanan Spector [1817-1896], of Kovno, Lithuania, warned the local Reform congregation to remove the Magen David which graced the roof of their house of Worship

Moritz Güdemann, (1835-1918) wrote in 1916:

Men of Jewish learning cannot accept the fact that the Jewish people would dig out of their attic of superstition a symbol or emblem that it shares with stables

Hillel Roiter in Kountrass, April 2000, p. 54, quotes Gershon Sholem who wrote that Jacob Reifman, one of the leaders of the Haskalah movement, objected to the use of the Star of David, using the PSALM verse 106:35:

But were amingled among the heathen, and learned their works

Measure of Time

The following paragraph is from a new chapter, The Time Space Correlation, which doesn’t appear on Dr. Asher Eder’s book The Star of David, which was published in 1987 in English in Jerusalem by Rubin Mass Ltd.

35-5. Measure of time

The time measure we use in our daily lives (hours, years, etc) is depicted by the line h-i, i.e. that part of the line a-c which relates to us on our globe (cf. Gen.1:14,15). For an astronaut in his spaceship, or for a dweller on Mars or Venus - if there should be one - it would be different, not only since the days and years of the other planets are different timewise, but because the underlying forces and their combinations there, and consequently their effects, are different from those on our globe.
For the daily needs on our globe, our calculation (measurement) of time is based upon the following movements:
a) the earth's rotation. One revolution of the globe gives us the concept of one day (day and night together, that is, irrespective of longer and shorter periods of daylight in accordance with the seasons). The subdivision of a day into 24 hours (with 24 x 60 = 1440 minutes, or 1440 x 60 = 86400 seconds) is arbitrary, agreed upon for our conveniences. It derives from the sexagenary system developed by the Babylonians. As it is somewhat abstract, peoples in ancient times applied also other systems. For instance, the night was not subdivided into 12 hours but into 4 night watches. Before the invention of clocks, the watchman had to announce the times. Another example would be the duration of one inhale/exhale cycle of a man in rest which served as a measurement for smaller time units - it came up to approximately three and a half seconds.
b) the earth's orbit. A year is the time span our globe needs for one orbit. Our calendars render this time span as 365 days since the globe revolves approximately 365 times during one orbit. The western calendar balances the difference between orbit and rotation by introducing every 4 years a leap year with an additional day, the 29th of February.
When we say about someone that he is 60 years old, for example, we might say as well that he took part in 60 of the earth's orbits. However, such a saying would concentrate on the orbits and neglect many other forces which effect us during that period, too (as e.g. chemical, biological, spiritual forces). In fact, even for two people born at the very same minute, the 60 orbits or years have different meanings for each of them.
c) the earth's tilting. It makes up for the four seasons, with the equinoxes every 21.3. and 21.9. Perhaps Gen. 8:22 contains a hint that this tilting came about only after the Flood (it reads there: "summer and winter ... shall not cease...").
d) The waxing and the waning of the moon. The time span between one new moon and the next gave men the concept of one month. The earth rotates approximately 354 times during 12 moon months.
Most of the ancient cultures conceived the moon cycle as more important than the sun cycle, and consequently based their calendars upon the former. Islam whose followers comprise approximately 1/4 of the globe's population, follows the moon calendar. Because the moon year is shorter than the sun year, non-Muslim observers see the famous month of Ramadan (the month of fast) "wandering backwards" through the sun calendar, while the Muslim may look at the western calendar as "moving ahead" in comparison to the moon calendar he is accustomed to. Islam which originated in the hot desert of Saudi Arabia, inherited from ancient Babylon the moon calendar, obviously because the moon which governs the relatively cool nights is felt by the desert peoples as more beneficial than the burning sun. Besides, due to the climatic and geographical conditions there, they engage foremost in shepherding and trade, and not so much in agriculture which cannot be geared to the moon cycles only.
Focusing on the moon allows also for the concept that man should be like this heavenly body which reflects the light of the sun in purity. If man has waned for one reason or the other, he should, like the moon, always be ready to wax again in the light of the Divine.
The different calendars are not random choices. What we call western calendar, is in fact a northern calendar, i.e. it was developed and adopted by northern peoples who felt strongly the benefit of the light and the warmth of the sun. Moreover, the sun calendar allows for easier calculations of interest rates, salaries, etc: it is trimmed to the needs of industry and trade. Adhering to these needs, Christianity since the days of Emperor Constantine adapted to the sun calendar and conveniently depicts its founder as the sun of the universe. By doing so, it justified the continuation of observing the ancient pagan Sunday as day of worship.
In contrast, for ancient agricultural societies the moon cycles were of paramount importance as they give the times for seasonal sowings and plantings. It is for this reason that the festivals, most of them with an agricultural aspect, are tied to the moon (new moon or full moon).
Israel, located between north and south, and between desert and civilization, developed already in ancient times a combined sun-moon calendar (based upon Gen. 1:14-16 where we are told that both the big and the small light, i.e. sun and moon, shall be unto us for signs and seasons and days). In order to synchronize the moon and the sun cycles, the Hebrew calendar introduces seven leap years with a 13th moon month into each cycle of 19 sun years.
Everyone of these three calendars starts counting with a certain event: The Muslim's calendar commences with the Hejira, the day of Muhammed's escape from Mecca to Medinah; Christians count their calendar from the birth of Jesus; while the Jewish calendar begins with Adam, the father of all mankind (Gen. 5:1).
Other calendars base upon different observations and calculations. For instance, the ancient Persians tied their calendar to Sirius. Mathematically it was more accurate than the sun calendar, but it was also more abstract, and this may be a main reason why the cultures based on it did not prevail. - The Essenes of 2000 years ago tried to invent a more schematic calendar which, however, is not yet fully understood. - Modern physics invented for its needs a very precise atom clock, completely independent of the heavenly bodies and their movements. - Hypothetically, we could conjecture many other devices for measurement of time. For instance, the inhale-exhale cycle of a sleeping man served in ancient times as a time gauge, as mentioned already. Or, we could use the duration of a certain chemical process (as e.g. dissolving an iron ball of 1 c.c. in a given acid) as base for a time unit, and could build timepieces (watches) accordingly. While measurements taken from our bodies and its functions (as e.g. inhale-exhale cycle; cubit; foot; etc) differ from people to people and are not accurate enough for our modern needs, atomic or chemical processes, as accurate as they may be, have no tangible bearings in our daily lives, and do not match our sense of time. They have their own times, independent of the time we relate to.
e) This brief excursion into different calendars and other devices for measurement of time may demonstrate:
aa) time is not something independent, on its own. It is related to movements which are but changes of positions (not necessarily mechanical positions), and which have their bearings on us;
bb) our time concept, although based upon nature events, is very subjective, suiting best the daily needs of the respective individuals or groups. This holds true in view of the different calendars, but within them also in view of specific affairs.
An example may demonstrate this point: A venerable car factory, on occasion of clearing its yards, finds in 1991 in a corner a car built in 1928. After supplying it with a new battery and new tires, it works properly. In 1992 they manage to sell it as a unique piece, and the new owner applies for the license which he gets finally in 1994. He decides to exhibit it as a curiosity, and brings it only in 1995 on the road, brand new. How old is the car? Of course, its technical standard is that of 1928, i.e. in 1995 it is 67 years old, but according to the time of usage it is one year old. It is for this reason that we look in such cases at the wear and tear (mileage) not less than at the year of manufacture. That means to say we take different time bound impacts on the car into consideration.
f) In our context of measuring time, it might be of interest to ponder also on the question whether, and/or how, we would feel a change in the velocity of the globe's movements (rotation, orbit), if we had no clocks nor any other time piece which would show us the deviation from the present velocity? Suppose, the globe would slow down its rotation rate from 24 hours to, say, 30 hours of our present time concept. How would we notice it? Probably not immediately. Only within some length of time would we notice climatic changes, and would feel some unease, or disturbance, in our metabolisms which are attuned to the (present) 24 hours day. Provided the changes were not too severe, we would need some while to adjust to the new situation.
We may muse also about the question what kind of time concept we would have developed if our globe would have several moons (like Jupiter) instead of the one we know; or if our globe would orbit around a double sun (like Sirius)?
These hypothetical examples may show how much we made ourselves dependant on our clocks, even to such a degree that more often than not we delude ourselves by "thinking" the universe is geared to them.
g) We saw that time concepts are subjective, pertaining to our needs. Measurements which give these concepts their scientific touch, are worked out in the left brain which then translates it back to our consciousness. In our modern western world this leads to an over-emphasize of left brain attitudes. Children whose left brain is not functioning fully yet, have hardly any concept of measured time. Growing up into the world of the adults, they have to be trained to go by the clock. As our two brains, the right and the left, are anatomically balanced, our usage of their capacities --the analytical and the intuitional one-- should be balanced as well. Our graph which expresses many symbolic meanings, can serve as a symbol for such a balance, too.

Ferrara Cathedral

Hexagram on the Romanesque Cathedral of Ferrara, Emilia Romagna, Italy. Built in the 12th century.
Picture is courtesy of "padesig', who published it in Flickr and wrote the caption in Italian, which I don't understand; so I let Alta Vista Babel Fish do the job and here's what came up:

In the facade of the cathedral of Ferrara: what is one senz' other unusual one, but for me also much beautiful one... It seems is "an official" acknowledgment of the job and the contribution offered from the Jewish community of the time to the construction of the cathedral, but also an acknowledgment of the cultural and social importance that had the community in the period extensive

Time

The following paragraph is from a new chapter, The Time Space Correlation, which doesn’t appear on Dr. Asher Eder’s book The Star of David, which was published in 1987 in English in Jerusalem by Rubin Mass Ltd.

a) The peculiarity of time
"What is time?", is an ancient question. The Oxford Dictionary defines time as "duration; continued existence; progress of this viewed as affecting persons or things..., allotted or available portion of time...".We could also say that time is the conception of the changing succession of things one after the other. According to the Dictionary, the word time derives from the root of a Germanic word from which derives also the word tide. Often the words time and tide are interchangeable, while duration and time are not always identical.
How do we know about time, or continued existence? Obviously only if we can relate, or compare, it to something else.
Suppose the universe would consist of the sun and the earth only, and nothing else besides; and the earth would orbit the sun unceasingly in a perfect circle but would not rotate. This process could well be described as duration, continued existence (of sun and earth), but what about time/tide? Suppose, a human being would live on such an earth (if at all something could live there), and would be aware of a duration, but could he develop also a sense of time? Obviously, for doing so he would need a third point, and for that matter a fixed point, to which he could relate. Such a point could be a dark spot in the sun provided it stays always at the same place; or would move, or appear, in regular intervals. If such an earth would not orbit the sun, but would remain unmoving vis-a-vis the sun, or if such a sun and earth would move like a dancing couple, such a dark spot would allow for developing a sense of time only if it would change - or would appear as changing - position or density in regular intervals.
All this means to say that at least three points, or positions, moving in relation to one another, are needed for developing a sense of time, and for measuring it. This holds true in view of chemical and other processes, too, including the vibrations of an atom which provide the base for atom clocks. Also the latter case allows for a time concept only in relation to a third point.
The term developing a sense of time and measuring it, implies the conscious observation (by a human being) of such movements or changes in space. Atoms and minerals may change composition and/or form, each one in its own space, but the duration in which change(s) occur could be conceived by man as time only by putting the change in view in relation to other points or events.
It follows that any measurement of time has to "borrow" its components from spatial measurements. Any length of time can mathematically be rendered as spacial length. Theoretically, space could exist in duration, without time (tide, measurable intervals), but time cannot exist without space.
Sensing time is not given neither to plants nor to animals. In accordance with their inbuilt patterns, they react to changes in temperatures and/or quantities of light (and therefore get out of season in an unusual warm winter, for instance). The feeling of time, the ability to calculate it, and the capability to arrange our lives accordingly, or even independently thereof at least to some degree, are given to men only. This fundamental law is laid down in Gen. 1:14 where we read:
"And God said, Let there be lights in the firmament of the heavens to divide the day from the night; and let them be for signs, and for seasons, and for days, and years".
This whole idea is expressed in the word world. It is composed of two ancient Germanic words, "wer" meaning man, human being; and "aldh" (=old) meaning age, time: it describes our time-relatedness. Each individual is a world of its own ("whosoever has saved a human being from death has saved a whole world", is a famous saying of our sages) with his/her own time, but living in society urges each one to bring his/her time at least to some degree in line with its time table. It is left to us how we cope with it.
Similar the well-known Sanskrit word Maya. Composed of the syllables ma (derived from manu = man; and ya (derived from yuga = age, time, it describes our inclination to take time-bound, passing things for real, instead of yoking us (in yoga) to the eternal.

b) Time conditioned by movement(s(
No time awareness can be developed without movement(s), as we saw. Movement is an operational process the duration of which is conceived as time, namely the time needed for an object moving from place to place or from situation to situation.
While meter, mile, etc, are measurements of distances, we may say that time is a perception and/or measurement of the duration in which the changes in view occur - changes from one position to another due to physical movements as well as through chemical, biological, spiritual, etc processes.

c) Space without time
Time concepts are relevant to man upon earth, that is, upon the surface of our globe.
In coal mines, ore mines, etc several hundred feet below its surface, no time can be perceived (except by looking at a clock which was adjusted to our customary time measurements; or by feeling hungry, or tired, in accordance with the respective intervals our system got accustomed to). There are no changes of light, nor of temperature, nor are there other intervals which would allow for developing a sense of change, or time concept.
Our sun does not "know" time either: It is the source of light and heat, and its orbiting planets cannot provide any lead for time measurements, which would make sense. Each planet has its own specific orbit; its own specific "year" (=the time it needs for one orbit); and even its own speed - which decreases in ratio to its mass density and its distance from the sun. (This example shows, by the way, the inter-relatedness between time and matter; and sequaciously, between time and forces emanating from matter).
The crews in spaceships go either by clocks (similar to the miners), or by instructions sent from their stations upon earth.
There is definitely space in all these cases (mines; sun; spaceship) but they do not allow for developing a time concept.
This shows us that our time concept is ultimately founded upon the perception of intervals (tides, if you want) in light and/or heat intensities pertaining to the surface of our globe. We are children of light, at least in this respect.

d) Since the Creator is omnipresent, and therefore timeless, no measurement whatsoever can be applied to him. Revealingly enough, one of the epithets of God in Hebrew language is המקום, literally The Place but usually rendered as Divine Presence. This concept is one of the main reasons that Judaism does not know "holy places" (except for Mount Moriah), but stresses "holy times", foremost Shabbat. Another characteristic of the Hebrew language is its Wav conversive which changes the future tense of a verb into past, and vice versa the past tense into future. This indicates, amongst others, that there is no past nor future with the Omnipresent. These exist in our perspective only. Heeding the Halahah (Instruction for the Way of Life) entails organization of one's times. Together with the gift of the concept of time to man it is the sanctification of certain times as one of the means by which man raises above animals. All humans are entitled to share in this privilege.
We should note here that the observing the weekly Shabbat is not connected to nature’s seasons (except for the sunsets which mark the beginning and the end of the Shabbat days). It gives us a rhythm congenial to our specific human nature, and is therefore beneficial.
As the notion of a Creator seems incomprehensible to many scientists, let us consider the phenomenon of gravitation for illustration's sake. In contrast to other forces it has no speed and no movement, and therefore has no starting point. In our limited knowledge, we can at present only say that it exists. We feel it in our daily lives, and think we understand it as the force which makes an apple from the tree falling to the ground, and which keeps our solar system in its shape. But at present it is beyond our capacity of understanding to comprehend it as the force (or medium) which keeps huge galaxies with their immense extensions in their spiral forms. The question was put already before Job: "...can you loose the bonds of Orion?" (Job 38:31). Speaking of gravitation as a field, instead of a force, does not explain the phenomenon; it rather sidesteps it. How much less can we dare to comprehend or describe the Creator. One of his epithets is The Omnipresent. Omnipresence needs no movements, and therefore is timeless.
The line a-c in our graph may depict - if we wish to do so - the so-called "absolute" time of creation, including the "age" of the universe as perceived from our perspective, but foremost it depicts the relative times on our globe (see in the following par. 4 & 5) as perceived from our perspective.
Regarding the age of the universe, we would have to clarify first whether we could speak earnestly of some (supposed) gaseous clouds of hydrogen as universe before they (supposedly) condensed to stars and galaxies, etc.
Besides, speculations about the age of the universe are based upon observations which pertain to our relatively young solar system, and which we project to the rest of the much older and infinitely vast universe as we perceive it now. Applying the famous Zen saying: "What looked your face like before your father and mother were born?", we may ask: "What was time before our solar system came into existence"; and: "was time on our globe always the same; or were days, seasons, and years, different due to differences in the earth' rotation speed, tilting, and orbit, which might have occurred during its period of existence?"
While someone would be hard pressed to answer these questions, it is impossible for us to conceive of energy (אל, Power) before anything came into being. Let us mind that waves even in their shortest form are already something, that is, a thing(ness) in its utmost subtlety. What was before the (supposed) Big Bang? What caused the Bang? What banged? Why did it bang, and why did this bang turn out to become the universe? Thinking in theological terms, we would have to ask: What was God (the Creator) before creation came into being?"
Being honest with ourselves we will have to admit that due to ur own limitations we are not able to truly conceive a beginning of the universe; nor its end; nor its eternal existence without any beginning or end, notwithstanding the possibility that within such an absolute eternity it may change its form of appearance. Whatever the case may be, some might like to speak of its eternity (from our point of view) within the eternity of eternities.
Considering that question leads us to the conclusion that creation is as infinite and eternal as the Creator is infinite and eternal. Such a view is indeed held by the Indian cosmology which, accordingly, speaks of an endlessly ongoing process of expansion and contraction of the universe. It portrays it as a inhale-exhale process of Brahm, the absolute power before its manifestation as Brahma, the creative aspect. Our languages seem to support such a view. Both in Hebrew and in English, the word creation (בריאה) denotes even from the point of grammar an (eternally) ongoing process, - The usual translation of the first phrase of the Tanakh, “In the beginning God created the heavens and the earth…” is not quite congenial to the Hebrew text which should rather be understood as “With the beginning…”, this term meaning that with the beginning of time on our earth the heavens and the earth became destined to be partners in the unfolding process of that creation which pertains to man on earth – with the heavens being made manifest as the “Kingdom of Heavens” on earth.
Within this ongoing process many sub-creations so-to-speak, may take place. They range from those of our daily lives we call creations, as e.g. that of creating a book, or a new fashion, up to those recorded in the Tanakh (e..g. Ps.51:12; Jer. 31:21). Interestingly enough, the latter begins with the words: “…"בראשית ברא (“be’reshit bara…”, rendered as “In [or: with] the beginning created God…”). The fact that the Tanakh begins thus with the sign (letter) ב, beth, and not with the first sign (letter) of alphabet(h), א, aleph, is explained that that the latter stands for origin, God, while ב, beth, meaning house, indicates that the Tanakh is given to us for our lives in that “house”, our world, and not for speculations about the infinite creator and the rest of the universe.
Kabbalah, acknowledging our incompetence to answer questions about the eternal and infinite creator, states that beyond creation there was, and is, אין סוף, ain soph (translated as infinity; ∞ in the symbolic language of mathematics); and that everything is part of, and embedded in, אין, ain, a term which means "nothing", "no-thing-ness". We, created as limited beings, can only comprehend thing-ness (to some degree at least), i.e things in their contractions ((צמצום and limitations.
Consequently, those parts of the universe which we can perceive, are depicted in our graph by the sections h-i and k-l, with the resulting calculations shown by g-m. These observations and calculations are inaccurate for several reasons, the main one being due to the fact that the actual positions and movements, and probably also of the brightness of the heavenly bodies -stars and other galaxies- have changed from the moment they emitted thousands and even millions of light years ago the light waves we receive only now. Many of them may meantime even have ceased to exist yet with their light waves still traveling to us! While, on the other hand, new ones may have come into existence with their light waves still being on their way to us!. Moreover, our own position toward these far-away light-emitting bodies, as well as their positions one to the other, have probably changed, and we do not see them where they are now actually positioned.
If it is true that the universe expands, and that everything moves away from everything, we don't know in which direction the stars and galaxies move away (or, in other words, where they have been when they emitted the light we are receiving now).
Nearer to us than these speculations is the known fact that we perceive the rays of the sun which reach us, in a bent, or curved line. When we see the setting sun just touching the horizon, it is in fact already below it. Due to the rays' "travel time" of approximately minutes from there to our globe, our perception of the sun lags behind its real position. In fact, the rays of all the heavenly bodies, although they emit from them in straight lines, reach us in a bent, or curved way.
These facts as well as some others mentioned below may render our calculations rather inaccurate. The differences between the actual situation and our calculations are indicated in our graph by the difference between the straight lines h-i and k-l and the curved lines h'-i' and k'-l' (note: we even don't know the degree of their bend. See also below par. 9)

Cute Little Star of David Lantern

A cute little Magen David lantern at the entrance to a synagogue in Lion, France.
Picture is courtesy of "maria_noland" who published it on Flickr.