Update April 14, 2016 The Lascaux Sky Chart

NOTICE
April 28, 2016
The conclusions on this page may include minor errors that have been corrected with the most recent Cartes du Ciel software update.  The web page The Lascaux Sky Chart includes these changes. These changes are NOT yet reflected in the web pages Astronomy.html, Lascaux.html, and ZodiacClock.html. In particular, the animations need to be corrected. This notice will be removed from the updated pages as the corrections are completed.



In Celebration of Psalm Nineteen:
God's handiwork in Creation

ASTRONOMY:
Signs and Seasons, Days and Years
*
Comments on Genesis 1:14

And God said, “Let there be lights in the expanse of the heavens to separate the day from the night. And let them be for signs and for seasons, and for days and years."
Genesis 1:14, ESV


Prototype
The Silent Speech in Astronomy
as a Prototype for God's Silent Speech
    On Creation Day 4, God commissioned the starry heavens to be timekeepers. This is a prime example of Nature's built-in Silent Speech.  For stars to be timekeepers requires two things: First, God must ensure the stability of the starry hosts as timekeepers. This is the main task of Day 4. Second, humans must draw that speech out of the confusing array of heavenly bodies: order must come out of apparent random disorder, making astronomy one of the earliest formal scientific disciplines.

   Timekeeping doesn't come automatically without effort and skill, and so this is a prototype of how the silent speech of Psalm 19:4 works in practice.

  The silent speech in astronomy declares God's glory and handiwork in greater and greater detail as skilled craftsmen interpret the starry hosts as timekeepers. This skilled work has gone on since the beginning of civilization, and it continues today, always providing greater cause for wonder, as each major advance in astronomy leads to further evidence for God's handiwork, and its unfolding shows an unending increase in depth and complexity01.


The  Beginnings of Astronomy: Constellations and the Zodiac

Since prehistoric times -- long before the time of writing -- the stars have been used to mark off
"seasons and days and years", and the earliest historical records imply that the major constellations had already been long identified and named back in the mists of antiquity, many thousands of years ago.

Until very recently, one might have assumed that no written records meant no records at all. That all has changed with the discovery of astronomical sky charts in the Cave art at Lascaux Cave, dated to 17,800 BC. The cave art itself is the ancient writing -- the ancient method to record information about the skies (see the box).

    Constellations and Asterisms.

Faced with the sprinkling of stars throughout the heavens (in truth it looks anything but random
02), the mind looks for asterisms or patterns. Figure 1 is a map showing a number of the constellations recognized today.

This realization builds up over time:

The moon repeatedly waxes and wanes over the lunar months in a regular pattern.
• The sun follows a regular track, called the ecliptic, which can be traced on a rotating background of fixed stars. The sun retraces this track daily, but over the months the background appears to rotate, so that the stars that appear at dawn and dusk change, but repeat the same patterns every solar year.
• The duration of daylight changes over a year with the shortest day at the winter solstice (about December 21) and the longest day at the summer solstice (about June 21). Half-way between these are the spring and fall equinoxes (March 21 and September 21). It would take many years of systematic observation to realize and then determine these times, which have the practical use of signalling the year's seasons.
• Over many years, the stars show further slow changes which occur in some cases over thousands of years.

Pattern-finding is an automatic response of human contemplation. The mind cannot help it: one reason why people see patterns in gambling, the stock market and anything else that appears—or is in fact—random. This leads naturally to the identification and naming of the major constellations (Figure 1). Figure 2 shows the constellation Orion—here as an archer (one of several depictions of the constellation). The stars that form the belt and shoulders are quite prominent, and easily recognizable because they are among the brightest stars in the sky.


constellations
Figure 1
Map of Constellations
Galactic Coordinates
© Richard Powell
Creative Comons License



The Orion Constellation The Orion Constellation
Figure 2
Orion Constellation
The red giant star Betelgeuse is at Orion's shoulder


Early Evidence of the Constellations. By a remarkable providence there are literally hundreds of beautiful (and very fragile) cave paintings preserved in France and Spain composing what is called the Magdalenian culture, spanning from about 18,000 to 10,000 BP  (years before the present). In my view the preservation of these paintings is an example of a silent voice lovingly preserved by God for our benefit—see the box03. These paintings include the earliest known true sky charts—reaching back over 20,000 years.


The Silent Speech in Astronomy: Constellations and Sky Charts
A Sky Chart at Lascaux Cave

The prehistoric cave art of Western Europe is one of the most remarkable discoveries of modern times. Its preservation over tens of thousands of years is due entirely to God's providence. The unfortunate fact is that when the cave art is discovered, it rapidly degrades due to changes in moisture and atmosphere, and the introduction of fungus and various pathogens.

T
he discoveries were pure happenstance. They might—except for God's restraining hand—have been uncovered at any time in history. If they had come to light in the many thousands of years before the age of science, they would have been lost, and the memory would have at best been reduced to myth and folklore, and totally disregarded by modern science. As it is, all of the cave art discovered in the past 150 years is degraded from its original condition at the time of discovery. Only aggressive effort at preservation keeps it from further loss. See Dan Chure, The Tragedy of Lascaux for an account of this.

The silent speech preserved by God is the cave art itself which records the early beginnings of astronomical observation. The Lascaux cave includes a precise sky chart that maps several constellations in a single chart with remarkable accuracy, and is the earliest evidence to date that the constellation Taurus was already "named" (by a painted image of an aurochs, ancestor of the European bull) 15,000 years before the earliest mention in historical writing on clay tablets from Ur (see the Babylonian Zodiac below).

A cave painting at Lascaux cave in France (Figure 3) dated 17,300 BP appears to be the earliest known sky chart, as well as the earliest evidence for the naming of a specific constellation (Taurus)—named, that is, by the use of a bull image, since this is far earlier than the invention of writing. It is one of many images in a panorama in the Hall of Bulls that extends around the hall on the walls and wraps up into the ceiling. Some have asserted that the entire panorama depicts constellations in the sky, but I cannot verify that: some papers that say this seem to be more speculative than scientific04. See A Sky Chart at Lascaux Cave for further information.05.

Sky Chart
Figure 3a
Fall of Orion, 15,300 BC

Bull #18
Figure 3b
Lascaux Cave Bull #18
Source: animation (mp4, 487 Kb)
Expanded Animation (mp4,  1.5 Mb)

Whimsical or "Realistic"?
The cave paintings at Lascaux and other sites in France (a more recent find is Chauvet Cave, discovered in 1994 and dated to 30,000 BP) do not have obvious religious significance, being mostly scenes of the hunt, of nature and other similar subjects—despite many references to shamaans, rites and magic by the various "scholars" who comment on the work
06.

Another rich source of early artwork is found in the Egyptian temples, funeral crypts and coffins. These depictions—some very realistic, some fanciful, some whimsical—are simply that. Although Egyptian culture was rife with gods and godlets—that doesn't mean that the painters lack a sense of fantasy and humor. For example, consider the sky goddess Nut and earth god Shu that appear on many ancient Egyptian coffins and paintings (Figure 4). Did the Egyptians believe that these are literal gods literally forming sky and earth, or are the stories and depictions of these gods on the par with Kipling's Just-So stories? That is how I view such artistic work as this. Certainly the Egyptians did worship nature and had many nature gods, but they also used considerable artistic license in depicting them.

Sky goddess Nut and Earth god Shu
Figure 4
The Egyptian Sky goddess Nut and the Earth god Shu
depicted in many burial chambers and coffins

When the book of Job refers to the constellations Pleiades, Orion and the Bear (Big Dipper), he does not view them as gods. They are constellation patterns with widely accepted and imaginative names, selected for mnemonic association. The astrological and religious attributions to these constellations are almost certainly late additions layered onto the existing names.

    The Zodiac.

Given the year to year return of the same constellations, it is natural to mark the ones that lay along the the sun's path (the ecliptic) on its annual journey. T
he sun's "house" is the constellation that can be seen in the direction of the sunrise, just before dawn, and at sunset. These constellations form the zodiac (the word means "circle of animals"). Nobody knows precisely how this happened in the first instance, but it does seem to be a logical and fully reasonable process, use to mark time throughout the year. Today we commonly think of these constellations in terms of the mythical heroes of ancient Egyptian, Greek and Babylonian cosmologies, but their true value is not in the supposed influence over mankind narrated in these myths and in astrology, but in the use in time measurement—marking the seasons.

Some scientific facts fall out automatically—over a lifetime of careful observation—and would have been known in pre-history:

    (1) The Sun's path through the fixed star background07 is always precisely the same from year to year: this is called the ecliptic. The word literally means "line of eclipses" because lunar and solar eclipses occur when the Sun, Moon and Earth all lie in the Earth's orbital plane. Thus the ecliptic traces out the Earth's orbital plane in the background of fixed stars.

    (2)
In a Sidereal yearthe Sun returns to the same zodiac constellation at the same time each year. In particular the constellation at the spring  equinox is the same from year to year, and marks the beginning of the planting season for spring crops. The constellation that houses the Sun at the spring equinox usually heads the zodiac.

    (3) Most stars are fixed stars. F
ive planets or "wandering stars" and the Moon move relative to the fixed stars. They do not follow the same paths from year to year, but they do always move within about 8° of the ecliptic.

    (4) The field of stars appears to rotate about a fixed location—defining the North and South poles.

Here "fixed" is over a human lifetime. Some more subtle facts about the Zodiac have to wait for written records recorded over many lifetimes, when detailed star maps are made and observed over many years. But these facts are enough to make the beginnings of a starry timepiece.

The Babylonian Zodiac

The Babylonian Three Stars Each clay tablets are the earliest surviving record of the constellations and zodiac. They are dated to around 1200 BC. It can be inferred from this record that these constellations go back at least a thousand years earlier to the Sumerian Akkadian Empire period, 2270-2083 BC, the era of Sargon and the time of the Hebrew patriarch Abraham, when  Ur was a center of civilization. The inference comes about because many of the constellation names in the Babylonian list are Akkadian words. For example, the word "constellation" or "star" in the Babylonian text is  the Akkadian glyph MUL,MUL=Star.  Many current constellation names also trace back to Sumerian sources: Taurus, Leo, Scorpio, Capricorn, Gemini, Cancer. Presumably these records were written down, but they no longer exist. It is particularly interesting that the head of the Babylonian star list is Pleiades, the Akkadian glyph MUL.MUL,MUL.MUL = Star of Stars = Pleiades, or "star of stars". The name and head position imply that the Pleiades were the constellation at the Vernal equinox—nominally March 21—the beginning of the Spring planting season. This was the case around 2300 BC (see the Figure 5), and lends support to the thought that the entire star list may have originated around that time. Since the time of the later Bablylonian star tables, Pleiades and Orion have not been named as Zodiac signs, having been replaced by Aries, Taurus (which includes the Pleiades) and Gemini.

The book of Job mentions three constellations: Pleiades, Orion and the Bear (Big dipper). The mention of the Pleiades and Orion may hint at an early date for the book—when the Pleiades were considered the head of the zodiac, i.e. around 2000-2300 BC08. However, given the known fact that lists of zodiac signs tend to remain unchanged for very long periods of time, this would be rather crude evidence for dating.

Ecliptic and Orion-Pleiades
Figure 10
The Ecliptic showing Pleiades, Taurus and Orion

Precession of the Equinoxes.

Some of the more subtle facts about astronomy had to wait for records taken over many lifetimes, when detailed star maps could be compared over centuries. One of these facts is that the location of the sun at the vernal equinox moves along the ecliptic about one degree in 70 years, returning to its initial position after 25,800 years. This 25,800 interval is called the Great Year or Platonic Year09This is about five times longer than the entire span of recorded history, but it is long enough so that star catalogs prepared over thousands of years will show the change.

The movement of the equinox through the constellations is called "precession of the equinoxes" and is due to the fact that the Earth's axis precesses (much as a spinning top's axis circles around a  central  axis, only of course much slower—see the figure). The plane of the Earth's orbit doesn't change (so the Ecliptic and the constellations of the Zodiac are unchanged) but the time of the equinox does change. In addition the north star changes. Currently the earth's axis is aligned quite closely with the North star Polaris, but in ancient times that was not the case, and a few thousand years from now, the North star will change again. Even 500 years ago in the days of Chrstopher Columbus, Polaris was a degree further away from the north pole than it is today.
from http://www-istp.gsfc.nasa.gov/stargaze/Sprecess.htm
Precession

The earliest estimate of the great year was made by Hipparchus (190-130 BC)), based on small changes in the position of the vernal equinox since the 600 BC Babylonian star catalog.  He estimated that it takes about 30,000 years for the Vernal Equinox to cycle through the 12 signs of the zodiac.   This equates to 2,500 years for a Zodiac sign to move to the position of its neighbor.  The modern value for this parameter  is 25,771 years09a. Since none of Hipparchus' astronomical writings have survived, all of our information about his work come from Ptolemy, who wrote some 300 years later.

At present, the zodiac sign of the vernal equinox, which marks the beginning of Spring, is leaving Pisces and entering Aquarius. Figure 11 shows the precession between 4,000 BC and 2,000 AD.

Precession of the Equinoxes
Figure 11
Position of the Vernal Equinox
4000 BC to 2000 AD
Note: See Footnote 9a

Precession of the Perihelion.

In addition to precession of the Earth's axis, there is another precession that is important over longer timescales. This is the precession of Earth's perihelion, also called apsidal precession. Although the earth's orbit is nearly circular, it is not exactly so, and so the gravitational tug of the other planets cause it to precess with a period of about 110,000 years.

The Zodiac Clock. The zodiac clock records the net effect of these two precessions. Figure 12 shows the clock for 2,000 AD, which is part of a zodiac clock animation. See the web page Zodiac Clock for further details.

Zodiac - Calendar 2010
Figure 12
Constellations of the Zodiac with the calendar for 2010 AD


The Silent Speech of Astronomy in the Language of Mathematics

The constellations and the zodiac do not use the formality of mathematics. But to exploit the full value of the stars as timekeepers, it is necessary to study the heavens with its powerful logic. Thus mathematics becomes one of the particular languages in which the Silent Speech proclaims God's glory and handiwork. This is the language in which Einstein worked, leading to his famous remark, "The most incomprehensible thing about the world is that it is at all comprehensible."

Star catalogs and the Ptolemaic System.
The Greek civilization first introduced mathematical formality into the study of Astronomy. Hipparchus (~190 BC - 120 BC) "the father of trigonometry" was the first to develop and use constructions from spherical trigonomy, which he used to devise an effective measurement system to record star positions in space—similar to the present earth-coordinate system of latitudes and longitudes, which he expressed in degrees and minutes of arc.

By making extensive use of earlier Babylonian star catalogs (lost today), Hipparchus constructed a star catalog of some 850 stars visible in the night sky. That catalog is also lost, or rather it was merged by Ptolemy (c. 90 AD – c. 168 AD) into his own star catalog of 1025 stars (the Almagest). This star count compares favorably with an estimated 1,602 stars (worldwide) that are brighter than magnitude 5 and 4,800 stars brighter than magnitude 6—the faintest stars visible to the naked eye under good conditions.

Ptolemy appears to have incorporated the Hipparchus tables by adding 2°40' to the longitude of Hipparchus—1° per century for the 260 years lapse between the tables, which is quite accurate, taking into account the net effect of polar and absidal precession. This is absolute position error, not relative position error, which is generally on the order of one to ten arc-minutes (Ptolemy himself considered his tables to be accurate to 10 arc-minutes)
10.

Ptolemy's outstanding contribution was to develop a mathematical model of the Solar System which could be used to calculate planetary positions. In his model the sun and planets followed circular orbits centered on the earth with a system of Epicycles (Figure 13) superimposed. This was a mathematical fit to the star catalog data and a method  of calculating past and future positions of the planets and sun. Thus Ptolemy was the first to use mathematics to project accurately the positions into the past and future. Predictions of solar and lunar eclipses had been done since the Babylonian days, about 600 BC, but Ptolemy was the first to predict solar eclipses with good accuracy.

There is no evidence that Ptolemy actually believed his fairly complicated mathematical model—it was a mathematical fit to his star positions
11. It is likely that later scholars prior to Copernicus, who had an inaccurate concept of practical mathematics may have credited the Ptolemaic system with a reality that he didn't claim—much as many antiquarians today assume that the Egyptians accepted the "reality" of their depictions of cosmology.

The Ptolemaic System
Figure 13
Ptolemaic System of epicycles.
Click on the image for animation12.


The Copernican Revolution.  Nicholas Copernicus (1473-1543) replaced the Ptolemaic representation of the Solar System with one in which a rotating Earth and the planets follow circular orbits centered on the Sun (more precisely—each planet circled around a position centered near to but not exactly at the position of the Sun)—see Figure 14, which is an illustration from his book13. Copernicus could not dispense entirely with epicycles—although he used far fewer than Ptolemy.

Copernicus' Solar System
Figure 14
Copernicus' Solar System
,De Revolutionibus(1543)14
Book I, Folio 9 Verso.


Ideally any system—Ptolemy's or Copernicus'—had to explain the following data:
    • The positions (latitude, longitude) of the planets over time.
—These are the primary data of the star catalogs
    • The change in the planet's apparent speed along its orbit.
—All astronomers prior to Kepler assumed a constant speed of the planet along its path. Hence the need for epicycles, or orbits offset from the Sun and/or Earth.
    • The change in the planet's brightness
—This is a function of the distance to the planet and—for inner planets—the phase of the planet relative to the Sun (analogous to the phases of the Moon). The total Earth-planet-Sun distance should relate to brightness. The phases of Venus are only visible with a telescope, but the related changes in brightness could be observed with the naked eye.

Curiously, Copernicus still needed epicycles in his model, although fewer than in the Ptolemaic system. In his day the position of the Roman Catholic Church was that the Earth was the center of the universe. Copernicus avoided conflict with the religious authorities by presenting his calculations as a mathematical tool that was easier to compute than the method of Ptolemy, without (at least publicly) asserting that his model was to be equated with reality15. As an approximation to the planetary orbits, the Copernicus model was (somewhat) less accurate than Ptolemy's model, which by this time, had been tweaked and tested against astronomical observations for almost 1500 years. But computations using the Copernican model were much easier to do, and so his model was officially adopted by Pope Gregory XIII, as the basis for establishing the Gregorian Calendar, which replaced the Julian Calendar, and is still used today16.

Tycho Brahe and Johannes Kepler. Tycho Brahe's (1546-1601) life mission was to make more accurate star charts (Figure 15). Over many years of observation, he constructed accurate star catalogs with (relative) errors of 1 arc-minute or slightly less. These accurate tables showed that both Ptolemy's and Copernicus' models—even with Copernicus' epicycles and off-sets—had systematic errors. The worst case was the orbit of Mars.

Brahe Instrument
Figure 15
One of Tycho Brahe's Instruments
from his book.

Johannes Kepler (1571-1630) attempted to use Tycho Brahe's data to infer a more accurate model for the solar system. Regardless of his painstaking effort, Kepler could not avoid systematic errors of up to 3 arc-minutes—well beyond the accuracy of Brahe's tables. After years of effort Kepler solved the problem by using elliptical planetary orbits with the Sun located at one of the foci and on which the speed of the planet varied with distance from the Sun. He established the three laws of planetary motion that form the foundation for modern orbital calculations, and are known as Kepler's laws. He published these in his treatise Astronomia Nova in 1609, just one year before Galileo transformed astronomy with his telescopic observations, including the discovery of the Galilean moons orbiting Jupiter.

About 60 years later, Isaac Newton showed that Kepler's three laws are equivalent to his law of gravitational attraction which varies inversely with the square of the distance between the planet and the Sun. The remarkable thing is that Kepler did his work using only naked-eye observations. After he came up with his (correct) model for planetary orbits, he produced the Rudolphine star catalog in 1627. The calculations needed to produce this table were greatly simplified by the discovery and publication of logarithmic tables by John Napier in 1614, with improved tables by Henry Briggs in the following decade.


Kepler's methodology is good for projecting planetary movements into the distant past and future, and is especially useful for predicting lunar and solar eclipses. Modern astronomy programs are based on the Keplerian laws, with adjustments for the Earth's precession and other small variations, and have claimed accuracies of under 10 arc-seconds for projections several thousand years in the past or future17.

Astronomy in the Age of Science. Perhaps the most astonishing advance in Astronomy came with the publication of Isaac Newton's Principia, which laid the foundations of modern physics and wedded progress in physics with mathematics, particularly the calculus. In one fell swoop, physical science broke the shackles of earth-bound existence, because Newton's physics came to be seen (along with the addition of relativity and quantum mechanics) as applicable throughout the entire universe, and the universe itself was seen to follow precise natural laws, giving an unexpected new illumination to the concept of the universe as a precision timekeeper. The impact of these advances is further discussed as part of the Creation Narrative.

Summary: The Silent Speech in Astronomy. There are several instances of God's provision of Silent Speech in this short account.

    • The preservation of historical records is a gracious gift that God has granted to us so that we can learn details of the past that we have no a-priori right to expect. In some instances—such as the cave paintings—the full implications may still remain to be worked out.  It is clear that we had no right to expect such graphic details to be preserved for thousands of years, and have clear evidence of the tenuous and vanishing nature of the record, which requires special care to avoid complete loss. It is providential that these records were not recovered centuries ago—there is no logical reason, apart from God's providence, why they were not—and in that event they would have been lost and perhaps  been erased from our conscious knowledge, or relegated to fantastic folklore from the distant past.

    • The ability to express nature in mathematical terms that can be evaluated in closed form (using simple analytical equations), is another gift of God. This gets to Einstein's remark about the comprehensiblity of the universe. Any mathematician should know that very little of mathematics can be evaluated in terms of analytical expressions. The normal expectation would be that trajectories of planets and stars would require solution of the notoriously difficult many-body problem. Even Newton was puzzled by the stability of the Solar System, and conjectured that God had to intervene to preserve that stability18.

Until the very recent age of powerful computers, tackling such multi-body problems as the detailed trajectories of planets would have been utterly impossible. Would the computer age ever have dawned if not for the ability to make significant advances using simplified models of reality?


fractal.gif

FOOTNOTES

*
The background is an Armillary Sphere or spherical Astrolabe, used to measure positions of stars. This illustration is from Tycho Brahe, Astronomiae Instauratae Mechanica:

Brahe Instrument

For a discussion of Day Four of Creation, see my lecture A Haven for Life, Lecture Part One. This is the first of three lectures on the Genesis Creation Narrative. From that lecture: "The Task of Day Four is to ensure that the heavens as viewed from Earth provide a stable habitat for life. The value of the heavens as precision timepieces to mark the days, seasons and years, reflects this stability."

^n01 In contrast to this, consider Ernst Haeckel's claim that the explanation of the spontaneous origin of life (another grand theme of God's Silent Speech) is "no more difficult to us than the explanation of the physical properties of inorganic bodies." History of Creation (1876), Vol I. p. 406. See also his Riddle of the Universe and commentary on it by Sir Oliver Lodge, Life and matter : a criticism of Professor Haeckel's "Riddle of the Universe" (1900). Haeckel fell into the trap of assuming that the current understanding of science is accurate. To be fair, he changed his view when about twenty years later it was demonstrated that the protoplasm (the essence of the life-force in his view) is much more complex than he had asssumed.

^n02  The night sky show stars in patches, and many of the brightest stars form suggestive patterns. Even a stark amateur's eye is quickly attracted to the Big Dipper (Ursa Major), Orion's belt and the Pleiades—all of these are named in the Biblical book of Job—and with a little experience can identify many of the major constellations. True, some take a bit of imagination.  Figure 3 shows a 60°x45° region of the sky around Orion, Taurus (Hyades) and Pleiades (in the large circle). This region contains 115 stars of magnitude 4.8 and brighter. Most of these stars are concentrated in the constellations.

^n03 Having been preserved for thousands of years, since their first discovery in the late 19th and early 20th Century, many of the paintings have suffered severe and irreversable damage—not because of vandalism, but because of carbon dioxide, bacteria and other contaminents brought into the caves by visitors. For this reason many of the caves—Altamira (first discovered 1879, dated 18,500 to 14,000 BP) Lascaux (first discovered 1940, dated 20,000 to 10,000 BP), Chauvet (first discovered 1994, dated 32,000 to 20,000 BP)—have been closed to visitors, and even to most scientists. A video tour of the Lascaux cave is found here. In the Chauvet cave, carbon is used for black, so these paintings can be dated by radiometric means. In Lascaux cave, most of the black is manganexe dioxide, which is inorganic and cannot be carbon dated.


Preservation of Cave Art
I view this long preservation of the cave art, despite their fragility as a gracious gift from God so that we can see today the quality and evidence of supreme skill in this ancient art, and learn about our early human ancestors. It is providential that the paintings were not discovered in earlier centuries because they would undoubtedly have been lost to us today, and their significance would have been reduced to myth and folk tales. When the first cave paintings at Altamira were discovered, many detractors viewed them as frauds because of their evidence of very advanced artistic skill. The best examples show a high talent for perspective and realistic rendering, and even skill at abstract composition*—qualities that would otherwise be considered innovations of the renaissance and modern times.

* Picasso visited the Lascaux caves shortly after World War II. On leaving the caves he declared, "We have learned nothing in twelve thousand years."

^n04  Here are some observations regarding prior work that relates the Lascaux cave art to astronomy. Many of them seem to rely on sky chart programs that are considerably less capable than the excellent Cartes du Ciel (see note 5 below).

Dr. Michael Rappenglück's paper The Pleiades in the Grotto of Lascaux (1997) comments about Taurus and the Pleiades. I question some of his remarks on the Pleiades. He argues that internal evidence from the painting points to its execution around 17,000 BP and that the constellation refers to the equinoxes. He discusses the constellations separately and doesn't appear to view them as part of a single sky chart (I agree: they are not!). For the dating of the Lascaux paintings (17,800 BC ± 300y) see
The Lascaux Sky Chart.

Here's my calculation. All six stars of the Pleiades cluster are 380-405 ly away and all have similar proper motion (about 45-50
milli-arc second (mas) per year, in about the same direction). As a result it seems to me very unlikely that the proper motion or relative positions change enough in 17,000 years to be detectable in the art painting—as Dr. Rappenglück seems to claim. For reference, 10mas/year is 3 arc minutes in 17,000 years. Thus the constellation as a whole would move about 15 arc minutes—about the width of one of the painted spots—and virtually in tandem. Neither the relative movement within the constellation nor the proper motion would seem to be detectable in the painting, particularly as the Pleiades is NOT plotted in reference to Taurus (see below).

Regarding other assertions one can find on the  web, Lascaux Prehistoric Astronomers seems to
show sky charts, specifically this chart that concerns the region similar to Figure 3. Part of it is clearly bogus. Specifically, this "chart" fits in the 6 Pleiades spots with the bulls—that's impossible because of the orientation of the Pleiades in relation to the Bull's eye.  Also, the scale of the Pleiades is about 4x the scale of the overall Taurus constellation. It leads to the suspicion that the sky chart image is "fudged." Compare this with my image here.

One final web image is from a page titled Natal Charts for a Mother of all Living…. This purports to have a single map including various of the bulls from Lascaux cave. However it is fairly crude and I can't find the original source.

None of the above efforts appear to link in the painted Orion's Belt with the other constellations—as my image does.

One recent commentator is Gary D. Thompson, Astronomical Artifacts and Cuneiform Tablets, etc. The latest update is 2012 so I assume the contents reflects the author's current views. He reviews various web sites including submissions of Dr. Rappenglück. The typical remark is the non-committal "he believes…" and he summarizes by stating: "to date none of the arguments attempting to show the existence of some sort of Palaeolithic astronomy can be considered convincing. No research into prehistoric European cave art has led to the definitive identification of astronomical information  of any kind."

One common (and annoying) thread in some of this work is the constant reference to the religious significance of the art. In my view this is entirely gratuitous. There is no obvious evidence of religious ritual in connection with the art work. See note 6 below.

^n05 There are a number of free computer software programs that can show the appearance of the sky for thousands of years in the past and future. The program used for Figure 3 and the web page at lascaux.19thpsalm.org is Cartes du Ciel, also called Starry Night. The star charts it produces take into account the movements of the stars over time (generally very small), the precession (and wobble) of the Earth's North Pole, and precession of the Earth's orbit around the Sun. The star charts used by this program are based on the Hipparcos Catalog database (published in 1997) which includes proper motion to within 1 mili-arc second (mas) per year. This database was developed by the Hipparcos satellite in the early 1990s.

^n06 Paul Johnson in his book Art: A New History states, "There is nothing in these art works as such to suggest religious purpose." There is a modern prejudice (hubris?) that makes the default assumption that such artwork is based on religion and superstition, but that should be resisted unless there is positive evidence for that interpretation. This modern prejudice goes back to books such as James George Frazer's Golden Bough (1890) which has been called "a model of intriguing specificity wed to speculative imagination." Note that we use the term "Big Dipper" for the Bear (Ursa Major), as a mnemonic device with no religious significance.

^n07 Are the Fixed Stars Really Fixed? Almost all of the stars visible to the naked eye belong to our own Milky Way galaxy. In the Northern Hemisphere the only exception is the Andromeda galaxy which is a faint haze of stars in the Andromeda constellation. Perhaps very sharp vision can also see the Orion Cluster, a proto-galaxy (and the nearest birthplace of new stars) which appears in Orion's sword. In the Southern Hemisphere the Magellenic clouds are also galaxies outside the Milky Way.

This background of stars appears fixed because of the vast distances to even the nearest stars. In fact, the stars do move, just as our own Solar System moves, but the distances make the stars—particularly the constellations—appear to be virtually immobile over long periods of time—many times the entire span of recorded history. All of the apparent motion of the sun, moon and planets against this background of fixed stars is due to the motions of the earth, moon and planets, and the earth's spin around its axis. A few of the nearest stars have a parallax—the apparent change in position when viewed at opposite positions on the earth's orbit—but it is invisible to the naked eye.

As an example, Figure 12 shows the movements of the stars around the Big Dipper (Ursa Major) over 50,000 years. Clearly over this time the constellation is still recognizable. Over all of recorded history—even up to 30,000 years ago, if one includes the era of cave paintings, the big dipper has looked nearly the same. So, yes, star positions do change, but the vast majority of visible stars have barely changed their position over the entire extent of human history. See the Big Dipper animation spanning 200,000 years at the Ohio State University Website.

Precession of the Equinoxes
Figure 12
Motion of Stars near the Big Dipper

^n08 But perhaps not, since Zodiac lists tend to be fixed for long periods of time. Witness the fact that the astrological zodiac today still associates March with Aries. This was true around 500 BC, but currently the constellation for March is Pisces and will soon be Aquarius. Orion and the Bear are two of the most easily identified constellations in the winter night sky.

^n09 Technically, the use of the term "Platonic year" is a misnomer but is widely used. The "Platonic year" or "perfect year" as defined by Plato is the time for the planets to return to their original positions. The "Great Year"is the time for the constellations to return. But through history, these terms have been confused. The length of the Platonic year is about 16,000 years (?) compared with 25,600 years for the great year. The internet references are very confused about this distinction.

Plato's reference is found in
Timaeus 39d. Plato called  this the "perfect year" when the Sun, Moon and all of the planets return to their original alignment. "And God lighted a fire in the second orbit from the earth which is called the sun, to give light over the whole heaven, and to teach intelligent beings that knowledge of number which is derived from the revolution of the same.  Thus arose day and night, which are the periods of the most intelligent nature; a month is created by the revolution of the moon, a year by that of the sun.  Other periods of wonderful length and complexity are not observed by men in general; there is moreover a cycle or perfect year at the completion of which they all meet and coincide."

^n09a It appears that the precession line shown here does not include the effect of perihelion precession. See the web page on the Zodiac Clock for further information.


^n10  N.M. Swerdlow, "Astronomy in the Renaissance" in Christopher Walker, ed., Astronomy Before the Telescope, p.218

^n11 See the discussion at the SEDS website. Fourier analysis (harmonic analysis) is a modern mathematical equivalent to this—it expresses general functions as sums of trigonometric functions (sine waves of various frequencies), without any assertion that the approximations have an actual underlying reality. A point on the rim of a circle (or a planet on an epicycle) moving along a line traces out a Sine wave. so there is an intimite connection between Fourier analysis and the approximation of planetary motion via epicycles. The approximation of elliptic paths (as Kepler will show planetary orbits to follow) by Ptolemy's method of epicycles can, as can Fourier methods, match the actual positional data with remarkable accuracy—and can be made arbitrarily accurate by adding more epicycles.

^n12 If the animation doesn't work note that Java is required. Go to the Wikipedia article on epicycles and click on the  "Java simulation of the Ptolemaic System" under the heading "Animated Simulations" at the bottom of the page. The simulation is from at Paul Stoddard's Animated Virtual Planetarium, Northern Illinois University.

^n13 This is an oversimplification: a thorough discussion of Copernicus' model is in Swerdlow, op cit.

^n14 This diagram does not show the epicycles that Copernicus used to adjust for the apparent speed change over an orbit.

^n15 Despite the general condemnation of Copernicus for doing this, in fact it is a completely reasonable thing to do. The objections indicate, in my view, a lack of mathematical perception, if one's purpose is to approximate the planetary orbits without claiming to explain their precise mathematical nature (see also footnote 11). The purpose of the star tables is to predict the positions of the stars and planets in the past and future. This is a remarkable achievement in its own right. There was no a-priori reason at this time to assume that the actual planetary orbits could be described mathematically, or that it is even possible to understand the physics of their motion, so the aim to approximate the orbits was a worthy effort in itself.

^n16 See Owen Gingerich, The Book Nobody Read (2004), p. 144, discussion about the Church's use of Copernicus' calculations (forty years after his death).  See also biography of Nicolaus Copernicus: "As early as 1514 the Lateral Council, convoked by Leo X, asked through Bishop Paul of Fossombrone, for his [Copernicus' - dcb] opinion on the reform of the ecclesiastical calendar. His answer was, that the length of the year and of the months and the motions of the sun and moon were not yet sufficiently known to attempt a reform. The incident, however, spurred him on ... to make more accurate observations; and these actually served, seventy years later, as a basis for the working out of the Gregorian calendar." The Pope's interest in a correct calendar is based in part on the desire to calculate the date of Easter, which is based on the date of the Passover in the Hebrew lunar calendar, which is based in turn on the time of the Vernal equinox. By the time of Gregory, the Julian calendar mis-calculated the vernal equinox by about 10 days.

^n17  The following is a table of positional accuracy in star measurements up to the present time.

Accuracy of Positional Measurements recorded in Star Catalogs
  
Star Catalog
Time Period
Accuracy
Remarks
Lascaux Cave Hall of Bulls
17,800 BC
10-30 arc-minute
Sky chart of Orion's Belt, Taurus and the Pleiades. Painting traces out lines of stars that form the constellation outlines.
Ptolemy (naked eye)
Almagest
c. 200 AD
3-8 arc-minute
some systematic errors due in part to adjustments from Hipparches' sky catalogs. Ptolemy considered the (relative) accuracy of his tables at 10 arc-minutes.
Copernicus (naked eye)
De Revolutionibus (1543) 
1543 AD
3-8 arc-minute
Used Ptolemy's tables, corrected and updated in the intervening years by many (mostly moslem) scientists.
Tycho Brahe (naked eye)
Astronomiae Instauratae; Mechanica (1602)
1590 AD
0.5 to 1 arc-minute
naked-eye measurements.
Circular approximation to Mercury's orbit had maximum systematic errors of up to 3 minutes.
Johannes Kepler
Opera omnia (1858)
Harmonices Mundi
De Stella Nova (1606) and
Astronomia nova (1609)
1609 AD
0.5 to 1 arc-minute Discovery of the Elliptical orbits of the planets removed systematic errors. Prior to this discovery,  Fitting the Mars data with the Brahe/Copernican models showed errors up to 8 arc-minute.
Galileo Galilei
Two New Sciences
(1638)
1610 AD
3 arc-seconds
Galileo's early telescope was able to resolve satellites of Jupiter that were separated by about 10 arc-seconds.
Planet diameters are: Jupiter - 20 to 40 arc-sec; Venus - 10 to 60 arc-sec; see T. Pope,  Jupiter Through the Galilean Telescope.
Friedrich Bessel (First parallax msmt of 61 Cygni)
1838

First star parallax measured—0.3 arc-seconds for star 61 Cygni (distance 11.43 ly). Required a precision timepiece such as John Harrison's regulator clock (1761).
Atmospheric smearing


Atmospheric smearing of starlight is about 0.5 arc-second.
Twinkling (scintillation) can be 0.4 arc-second at clear, high altitude. Overall, a 1 arc-second smearing is considered good.  This affects spectral analysis of starlight as well as pointing.
Hubble Space Telescope (1990-2009),
Hipparcos satellite (1989)


Present day accuracy 0.001 arc-second.
Very Long Baseline Interferometer (VLBI) radio astronomy
2010?
10-6 arc-second Direct geometric distance measurements for certain classes of galaxies, out to 25 million light-years
(2009 Measurement of Galaxy NGC 4258 at 23.5x106 light-years ± 7%)

NOTES

1. The width of the Moon is about 29.5 to 33.5 arc-minutes. The width of the Sun is about 31.6 to 32.7 arc-minutes. If a full solar eclipse occurs while the Moon is at its perigee, the Sun's corona is visible over the entire perimeter. It remains complete for only a few seconds.
2.
Earth's rotation will cause a star on the Ecliptic to move about 1 arc-minute in 4 seconds, so precise measurements of absolute position required accurate and reliable clocks, which did not exist until after Harrison's invention of the regulator clock. Tycho Brahe achieved accuracies of 0.5 arc-minutes in relative (star to star) position measurements averaged over a number of observations.
3. Parallax measurements using large baselines require very precise clocks. Cesium atomic clocks have an accuracy of 10−9 seconds per day.
4. The Modern Tycho-2 star catalog includes over 2.5 million stars up to magnitude 11 based primarily on the Hipparcos satellite observations. Advertised proper motion accuracy is .0025 arc-seconds/year.

Direct measurement of Astronomical Distances by Parallax.  Parallax is the direct geometric measurement of changes in the direction of a stellar object when viewed at the extremes of a very long baseline. The first parallax measurements were done in the 1800s to measure the distance to the nearest stars. The accuracy and practical maximum distance that can be measured in this way depends on the length of the baseline and the precision of the angular measurement. The most accurate positioning at present is done in radio frequency astronomy using the Very Long Baseline Interferometer (VLBI) antenna arrays which receive signals from widely separated locations on the Earth. Of course the measurements depend on stellar objects that have suitable coherent radiations in these frequencies. The potential accuracy of current and planned VLBA precision is 10-6 arcseconds which equates to direct distance measurements out to 25 million lightyears. Recently, the galaxy NGC 4258 was measured at  23.5x 106 lightyears ± 7%, based on direct geometric triangulation. According to NASA, VLBI Radio Interferometry is hundreds of times more detailed than the Hubble Space Telescope and the dedicated Hipparcos parallax-measuring satellite.

The Goddard Space Flight Center  VLBI Summary says "VLBI is a geometric technique: it measures the time difference between the arrival at two Earth-based antennas of a radio wavefront emitted by a distant quasar. Using large numbers of time difference measurements from many quasars observed with a global network of antennas, VLBI determines the inertial reference frame defined by the quasars and simultaneously the precise positions of the antennas. Because the time difference measurements are precise to a few picoseconds, VLBI determines the relative positions of the antennas to a few millimeters and the quasar positions to fractions of a milliarcsecond. Since the antennas are fixed to the Earth, their locations track the instantaneous orientation of the Earth in the inertial reference frame."


Reference on various cosmological models and computer simulations.


^n18 Newton was puzzled at the apparent long-term stability of the planetary orbits. In effect, Newton concluded that God had to intervene occasionally to preserve the stability of the planetary orbits. About a century after Newton's remarks, the mathematician Laplace (Pierre-Simon Marquis de LaPlace) thought that he had proved that the planetary orbits are stable. When he presented a copy of his Celestial Mechanics to Napoleon, Napoleon asked whether God entered into his calculations. He replied, "I have no need for that hypothesis." In fact, LaPlace was in error in his "proof" of the stability of the planetary orbits. The orbits are not mathematically stable. The modern view is that all of the planetary orbits are inherently unstable – a consequence of modern chaos theory. LaPlace's reply is often cited as a triumph of mathematical reasoning over religion, such as at the website Positive Atheism. In fact, it is no such thing.

Wikipedia on Earth's Orbit: "In 1989, Jacques Laskar's work showed that the Earth's orbit (as well as the orbits of all the inner planets) is chaotic and that an error as small as 15 metres in measuring the initial position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years' time. Modeling the solar system is subject to the n-body problem." Jacques Laskar (1989), "A numerical experiment on the chaotic behaviour of the solar system."

Another author explains: “the basic ellipse of the Earth's orbit is not fixed in space:it gradually rotates or precesses, at a current rate of 0.3 degrees per century due to perturbations by the other planets,most notably Jupiter.” “The study of chaos has revealed that even completely deterministic systems, such as those involving gravitational interactions, can be chaotic and that Laplace's world-view was wrong. For example, the motion of the ball in a spinning roulette wheel is, in principle, a deterministic system. Although the ball and wheel are subject to known forces, trying to predict the final outcome is unlikely to be a rewarding experience. We now know that, except for special cases, the general motion of many (n) bodies interacting through gravity, the "n-body problem", is not integrable.” J.A.Jacobs, Deep Interior of the Earth


19   ^n19  n

20   ^n20  n


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REFERENCES

Dan Chure, The Tragedy of Lascaux (Feb. 2012).

C. M. Linton, From Eudoxus to Einstein: A History of Mathematical Astronomy, Cambridge (2004).
p52 "The work of Hipparchus, based as it was on a merging of Greek and Babylonian approaches, marks the transition between qualitative and quantitative mathematicaal astronomy."

E. Walter Maunder, Astronomy in the Bible (1922). An annotated version with updates to the present is available as an Amazon ebook. A further update is in preparation for posting at ibri.org.

Mario Ruspoli The Cave of Lascaux: The Final Photographs (1986).

Christopher Walker, Ed. Astronomy before the Telescope, St. Martin's Press (1996).
Lascaux Cave {GET REFERENCE}

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Update April 14, 2016 The Lascaux Sky Chart