1. Before writing

Long before anyone wrote, people watched the sky. They saw the Sun's rising point creep along the horizon and turn back, the Moon fill and empty, and the same stars come back each year. They left marks: notches on bone, pits in a Scottish field, a tomb in Ireland that lets in the midwinter sunrise, a platform in China with slots for the Sun, a line of towers in the Peruvian desert, a ring of stones in Australia, a bronze disc in Germany. This chapter visits them and asks the question that runs through the whole book: how do we know what these people knew? Some of the evidence is strong, some is a guess, and some famous claims have not held up. Each one is marked.

In this chapter

You will learn:

• what anyone can see in the sky with no instruments, and which cycles people could count
• how archaeologists study the astronomy of people who wrote nothing down, and the three traps they must avoid
• why the famous notched bones of Africa are weak evidence for counting Moons
• how Warren Field, Newgrange, Stonehenge, Nabta Playa, Taosi, Chankillo and Wurdi Youang faced the Sun
• the Emu in the Sky, a constellation made of dark clouds, and the Nebra sky disc, the oldest known picture of the sky
• how to work out where the Sun rises on a solstice from the latitude alone
• how to test whether an alignment could be chance

You need: nothing. For the sky itself, the physics lessons The Sun in the sky, The Moon and stars and Days, years and seasons are a gentle start.

Levels: 1.1 to 1.3 are beginner; 1.4 to 1.10 are beginner to intermediate; 1.11 is advanced; 1.12 is expert.

1.1 The sky anyone can see

Go outside at the same time every day for a year and you will find three clocks running in the sky.

The day. The Sun rises, crosses the sky and sets. At night the stars turn round a point in the sky, near the Pole Star in the north. That is the Earth spinning.

The month. The Moon goes from new (invisible, close to the Sun) through full and back to new in about 29.5 days. Its shape on any night tells you roughly how far through the month you are.

The year. Watch where the Sun rises. In the northern hemisphere, in June it rises well north of east. Each morning after that it rises a little further south, until in December it rises well south of east; then it turns back. The two turning points are the solstices, from the Latin for "the Sun stands still", because near them the rising point hardly moves for days. Halfway between, at the equinoxes in March and September, the Sun rises close to due east. South of the equator the same thing happens with the seasons swapped: the June solstice is the shortest day.

The stars. The stars rise about four minutes earlier each night (a day divided by 365), so the stars you see at dawn change through the year. When a bright star appears again just before sunrise, after weeks lost in the Sun's glare, it marks the season. Many peoples used such a star as a sign; in Egypt it was Sirius (chapter 3).

These clocks do not fit together:

Cycle	Length	What you see
Day	24 hours	the Sun rises and sets
Lunar month	about 29.53 days	full Moon to full Moon
Year	about 365.24 days	the Sun's rising point goes from one solstice to the other and back
Twelve lunar months	about 354.4 days	eleven days short of a year

A calendar of twelve Moons runs eleven days short every year. After three years it is a whole month out, and "the month of the harvest" comes before the harvest is ready. Anyone who counted Moons and also cared about the seasons needed a way to put the count right: a fixed point in the year, such as the solstice sunrise, from which to start again. Keep this problem in mind. Several monuments in this chapter may be answers to it, and in chapter 2 the Babylonians solve it with arithmetic.

Sources

• Lunar month (synodic period, 29.53 days): NASA, Moon fact sheet.
• Year (tropical orbit period, 365.242 days): NASA, Earth fact sheet.
• The horizon drawing uses the method of section 1.11, for Stonehenge's latitude and the Earth's tilt in 2500 BC.

1.2 How do we know, with nothing written?

When there is no writing, there are three kinds of evidence.

1. Objects: marks on bone, pictures on a disc, things buried with the dead.
2. Buildings and landscapes: which way a tomb, a stone row or a doorway faces, and what is on the horizon in that direction.
3. Living knowledge: what peoples who still keep their own sky traditions say the sky means. In Australia, the Pacific and the Americas this knowledge is alive today and is the best evidence of all, because it can tell us why as well as which way.

The study of ancient sky knowledge is called archaeoastronomy. It is a young subject, and it has learned the hard way that three traps catch the unwary.

Trap 1: chance. A site with many stones offers many lines between them, and some of those lines will point at something in the sky by luck. Clive Ruggles, a leading archaeoastronomer, warns that in many cases it is not clear that a claimed alignment was intended at all, especially when modern investigators picked it out from many possibilities. Section 1.12 puts numbers on this.

Trap 2: dating. A monument is dated by what is dug up with it, often by radiocarbon. But the sky has changed since. The Earth's tilt, which sets how far north and south the Sun rises, was about 24.0° in 3000 BC and is 23.44° today, so a sunrise line that was exact then is now a little off. And the stars shift slowly against the seasons, so a "star alignment" can be made to fit almost any monument if one is free to choose both the star and the date.

Trap 3: meaning. A tomb that faces the midwinter sunrise tells us the builders cared about that sunrise. It does not tell us they were keeping a calendar, still less doing science. Ruggles points out that the word "observatory" can mislead, because watching the sky always had wider social purposes: ritual, power, the timing of feasts and farming.

What makes a case strong? A feature built only to let the Sun in (Newgrange's roof-box, section 1.5). A complete set of markers covering the Sun's whole range (Chankillo, section 1.8). Two independent sets of markers pointing the same way (Wurdi Youang, section 1.9). And best of all, people who can still tell us what the sky figures mean (the Emu in the Sky, section 1.9).

Sources

• Clive Ruggles, Observing space 2,200 years ago, University of Leicester, 16 September 2021: on the word "observatory" and on alignments picked from many possibilities.
• The Earth's tilt: J. Laskar, "Secular terms of classical planetary theories using the results of general theory", Astronomy and Astrophysics 157 (1986), 59–70; today's value from NASA's Earth fact sheet.

1.3 Counting Moons on bone?

Two small bones from Africa are often called the oldest calendars in the world. Both are real, both are carefully notched, and both are much weaker evidence for Moon-counting than the books that repeat the claim suggest.

The Border Cave bone, South Africa

At Border Cave in South Africa, in a layer dated to about 43,000 to 42,000 years ago, lay a piece of a baboon's leg bone (a fibula) with a row of 29 notches. Popular books call it the Lebombo bone, after the mountains the cave is in, and since 29 is close to the number of days in a lunar month, it is often described as a Moon counter.

In 2012 Francesco d'Errico and his colleagues looked at it under the microscope. They found that the 29 notches are an incomplete sequence, because the bone is broken, and that they were cut in four separate sets, each with a different tool. Three sets are complete and one stops where the bone broke; the last set, of three widely spaced notches, was added after the others. The team concluded that the people of Border Cave used notched bones to record something, as San hunter-gatherers of southern Africa later used notched sticks for counting. That is a remarkable finding: notation 43,000 years old. But nothing in it points to the Moon. The number 29 is only the number that happens to survive, and four batches cut with four tools is not what a single tally of nights would look like.

The Ishango bone, Democratic Republic of the Congo

The Ishango bone was found in 1950 on a terrace by Lake Edward (Lake Rutanzige), where the Semliki River flows out, in what is now Virunga National Park. People there fished and gathered. The bone is again a baboon's fibula, about 10 cm long, with a small piece of quartz fixed in one end as a blade. Its notches run in three columns:

Column	Groups of notches	Total
G	11, 13, 17, 19	60
M	3, 6, 4, 8, 10, 5, 5, 7	48
D	11, 21, 19, 9	60

A later review of the dating puts the bone between about 25,000 and 16,000 years ago. It was first read as early mathematics in 1962: column G holds the four prime numbers between 10 and 20, columns G and D both add to 60, and column M has pairs that look like doubling (3 and 6, 4 and 8, 5 and 10). Others have read it as a calendar of Moon phases, and Vladimir Pletser as a tool for counting in twelves.

The patterns are real, but each reading picks the patterns that suit it. Primes may be chance: column D contains 9 and 21, which are not prime. What the bone shows for certain is that someone took great care over groups of marks.

Verdict. People in Africa were keeping counts on bone more than 40,000 years ago. What they counted we do not know. Moons are one guess among several, and not the best supported.

Sources

• Border Cave: F. d'Errico and others, "Early evidence of San material culture represented by organic artifacts from Border Cave, South Africa", PNAS 109 (2012), 13214–13219: the layer dates, the 29 notches, the four sets and four tools, notched bones "for notational purposes".
• The name "Lebombo bone", from a weaker source: Wikipedia, Lebombo bone.
• Ishango: C. Ruggles and M. Cotte (eds.), ICOMOS–IAU Thematic Study on Astronomical Heritage (2010), case study 1.3, The Ishango Bone: the find in 1950, the place, the size, the three columns and their counts, the dating, the first reading in 1962.
• V. Pletser, Does the Ishango bone indicate knowledge of the base 12? (2012), which also names the earlier "arithmetic" and "calendar" readings.

1.4 Warren Field, Scotland: twelve pits and a gap in the hills

Warren Field lies near Crathes, in the valley of the River Dee in Aberdeenshire. Marks in the ground there were first spotted from the air in the hot, dry summer of 1976, and the National Trust for Scotland dug them from 2004. They are 12 pits in a gentle arc about 50 m long, first dug by hunter-gatherers around 8000 BC and fully formed by about 7800 BC, nearly 4,000 years before Britain's first farmers. The pits held burnt material and stones brought from some distance, and some were dug out again about four thousand years later.

In 2013 a team led by Vincent Gaffney of the University of Birmingham proposed what the pits were for:

• the twelve pits mimic the phases of the Moon and could stand for the months of a year;
• the arc faces south-east, and a line through its middle points at the Slug Road pass, a clear notch in the hills;
• around 8000 BC, the midwinter Sun rose in that notch.

If so, the monument held its own reset button. Count Moons along the pits; each midwinter, when the Sun comes up in the pass, start again. That is exactly the answer to the problem at the end of section 1.1, and if the reading is right, Warren Field is the oldest known calendar by thousands of years, older than the first known formal calendars of the Near East by nearly 5,000 years.

How sure is it? Gaffney himself said, of one detail, "we can't prove it". The team checked the midwinter alignment against a model of the landscape and the sky of 8000 BC. The Moon reading is harder: twelve is the number of months, but it is also simply the number of pits that were dug, and there is no writing or living tradition to tell us what they meant. In a note to the paper, Clive Ruggles worked out what a watcher at the site would actually see of moonrises through the year, a reminder that the Moon's rising point wanders in a more complicated way than the Sun's. Treat Warren Field as a strong proposal: a monument built and kept up by hunter-gatherers for thousands of years, facing a midwinter sunrise, and possibly a calendar.

Sources

• V. Gaffney and others, "Time and a Place: A luni-solar 'time-reckoner' from 8th millennium BC Scotland", Internet Archaeology 34 (2013), with the conclusions (the pits recut four thousand years later) and Clive Ruggles's note on moonrises.
• University of Birmingham, The Beginning of Time?, 15 July 2013: about 8000 BC, dug by the National Trust for Scotland in 2004, nearly 5,000 years before the first time-measuring devices of the Near East.
• Current Archaeology, Mesolithic Timelords, 5 September 2013: found from the air in 1976, 12 pits in an arc about 50 m long, fully formed about 7800 BC, the Slug Road pass and the midwinter sunrise, Gaffney's words.

1.5 Newgrange and Stonehenge: buildings that face the solstice

Newgrange, Ireland

Newgrange is one of about forty passage tombs at Brú na Bóinne, in a bend of the River Boyne in County Meath. Radiocarbon dates put the passage tombs at about 3200 BC, centuries before the Great Pyramid. A long stone passage runs into the mound to a chamber, and above the entrance is a separate opening, the roof-box.

People living nearby had long said that the sun filled the tomb at midwinter, but no one had seen it. Michael O'Kelly, who dug the site from 1962 to 1975, found the roof-box and saw that the passage faced south-east. On 21 December 1967 he and his team waited inside, and became the first people since prehistoric times to see the sunrise light travel up the passage and into the chamber. It happens for two or three days around 21 December.

This is about as strong as evidence gets without writing. The roof-box has no other use: it is a slot built to let in the Sun on a few mornings of the year, and it works. What the builders believed about that light we can only guess; one idea is that it opened the way for the dead.

Stonehenge, England

Stonehenge was built and rebuilt for over 1,500 years. About 3000 BC a circular ditch and bank about 100 m across was dug, with 56 pits just inside it. About 2500 BC, the time of the Great Pyramid, the great stones went up: the big sarsens, brought from West Woods about 25 km to the north, and the smaller bluestones, brought from the Preseli Hills in Wales, over 250 km away.

Its main axis runs along the solstice line: from the midwinter sunset in the south-west to the midsummer sunrise in the north-east. Other monuments nearby are built on the same line or on the opposite one (midsummer sunset to midwinter sunrise). English Heritage notes that more theories have been put forward about Stonehenge than about any other prehistoric monument; the one most generally accepted is that it was a temple aligned with the movements of the Sun.

Sources

• Newgrange: National Museum of Ireland, The winter solstice at Newgrange: forty passage tombs, the roof-box, O'Kelly's excavation and his observation on 21 December 1967, two or three days around the solstice, the date of about 3200 BC.
• Stonehenge: English Heritage, History of Stonehenge (the ditch of about 3000 BC, the 56 Aubrey Holes, the stones of about 2500 BC) and Significance of Stonehenge (the Great Pyramid, the stones' sources, the solstice alignments, over 1,500 years of building).
• The solstice axis: ICOMOS–IAU Thematic Study on Astronomical Heritage, case study 2.1, Stonehenge.

1.6 Nabta Playa, Egypt: stones by a lost lake

West of the Nile in southern Egypt, in what is now bare desert, lie the stones of Nabta Playa. About 11,000 years ago the summer monsoon moved north and filled a lake here. Herders came each year with their cattle, and buried some of the cattle with great care. Some 6,500 to 6,000 years ago they set up large stone slabs, some nearly 3 m tall, dragged from a mile (1.6 km) or more away. The lake dried up for good about 4,800 years ago.

Fred Wendorf's team came to the site in 1973, led there, by one account, by the Bedouin guide Eide Mariff. In 1998 Wendorf, the astronomer J. McKim Malville and their colleagues described:

• a small stone circle under 4 m across with four pairs of upright slabs: two pairs on a north–south line, and a pair giving a line of sight to the summer solstice sunrise;
• five lines of standing and fallen stones running out from a central group, one of them east–west.

Nabta lies near the Tropic of Cancer, so for about three weeks before and after the summer solstice the noon Sun stands straight overhead and upright stones cast no shadow. That time also brought the rains that filled the lake, which may be why the solstice mattered here.

How sure is it? The north–south and solstice lines in the small circle are simple and plausible. Later, the same team argued that some stones lined up with the bright stars Arcturus, Sirius and Alpha Centauri, and with Orion, around 4800 BC. Those claims walk straight into the second trap of section 1.2: they need a chosen date and chosen stones. Treat the solstice line as likely and the star lines as unproven.

Sources

• University of Colorado, Oldest astronomical megalith alignment discovered in southern Egypt, 30 March 1998, on the paper by J. M. Malville, F. Wendorf, A. A. Mazar and R. Schild, "Megaliths and Neolithic astronomy in southern Egypt", Nature 392 (1998), 488–491: the dates, the circle, the five lines, the east–west line, the zenith Sun, the lake, the cattle burials.
• Astronomy magazine, Nabta Playa: The world's first astronomical site, 20 June 2020: the find in 1973 and Eide Mariff, the later star claims, the monsoon.

1.7 Taosi, China: slots for the sunrise

Taosi, in Xiangfen county in Shanxi province, was a large walled town of the late Neolithic. Old histories and local tradition make this area the heartland of the Xia, the first dynasty in Chinese history. Ten kilometres to the east rises the long ridge of Ta'er Mountain.

In 2003 and 2004 a team led by He Nu dug a half-circle platform against the town's southern wall, about 60 m across, built in three levels like an altar. On the top level, a curved bank of rammed earth facing east-south-east is cut by twelve slots, each about 25 cm wide and about 1.4 m apart, with the stumps of earth pillars between them. It was built about 2100 BC.

The team guessed the slots were for watching the sunrise over the ridge, and they tested the idea the direct way. In 2004 and 2005 they put up an iron frame the size of a slot, one slot after another, and watched the Sun come up through it. Only afterwards did they find a small round platform of rammed earth at the centre of the arc: the spot where the original watchers stood.

David Pankenier, Liu Ciyuan and Salvo De Meis then worked through the survey with the sky of 2100 BC. Numbering the slots E1 to E12 from south to north:

• E2 and E12 frame the winter and summer solstice sunrises, to within a few minutes of arc, and better in 2100 BC than today. In fact the summer sunrise can no longer be seen in E12 at all, because the Earth's tilt has shrunk since: trap 2 of section 1.2, caught in the act.
• E7 catches the sunrise three days from each equinox.
• E1 points too far south for the Sun ever to rise in it. It has been suggested it marked the Moon's southernmost rising, but the authors found that the full Moon at its southern limit rose at least two Moon-widths further south. So E1 remains a puzzle.

The slots are evenly spaced, but the Sun's rising point moves fast along the horizon near the equinoxes and slowly near the solstices, so the periods between slots were very unequal: not neat fortnights. The building is also rough: the arc is not a true circle, and some slots do not point exactly at the watching spot. The authors suggest the builders set out the winter solstice slot first and then stepped the others northwards at a fixed spacing. The platform stood next to the graves of the town's elite, and access to it was through the town wall, which suggests the sunrise watch was in the hands of a ruling few.

Nothing written survives from Taosi. Pankenier and his colleagues call the find unprecedented in China, and its slots show the same idea as Chankillo in Peru, two thousand years and an ocean apart.

Sources

• D. W. Pankenier, Liu Ciyuan and S. De Meis, "The Xiangfen, Taosi site: a Chinese Neolithic 'observatory'?", Archaeologia Baltica 10 (2008), 141–148: the place, the Xia tradition, the excavation by He Nu's team, the platform's size and slots, the date, the sunrise tests, the observing point, the slot-by-slot analysis, the comparison with Chankillo.

1.8 Chankillo, Peru: thirteen towers on a ridge

In the desert of the Casma valley on the coast of Peru, at a ceremonial centre built between 250 and 200 BC, a row of thirteen stone towers runs north–south along the top of a low hill. They stand 2 to 6 m tall and about 10 m on a side, and enough survives of 51 of their 52 corners to fix where each stood.

The towers had been noted for decades. In 2005 the Peruvian archaeologist Iván Ghezzi and Clive Ruggles surveyed them. Ghezzi had already dug round a doorway in a building to the west of the towers and found offerings left there. From that doorway the towers make a toothed skyline, and Ghezzi and Ruggles found within two days that the towers cover exactly the stretch of horizon where the Sun rises during the year, from the June solstice at one end to the December solstice at the other. A second, mostly destroyed building on the far side was placed to watch sunsets across the towers in the same way.

From the western point, the Sun rises behind a different gap between towers as the year goes on, each gap about ten days' movement, slower near the solstices. A watcher there could tell the date to within a day or two. The spot had room for only one or two people, presumably a ruler or priest. Ghezzi and Ruggles published the finding in Science in 2007, and in July 2021 UNESCO made the Chankillo archaeoastronomical complex a World Heritage Site.

Chankillo is more than 1,500 years older than the Inca, whose rulers, early chroniclers wrote, timed farming and festivals by the sun rising or setting behind pillars on the horizon near Cusco (chapter 11).

How sure is it? As sure as anything in this chapter. Ruggles, who has spent his career warning against weak "observatory" claims, says Chankillo is not one of them. The reasons: the towers cover the Sun's range exactly, there are two purpose-built viewing points with offerings, and the set is complete. That is evidence by design, not by a line picked out afterwards.

Sources

• Clive Ruggles, Observing space 2,200 years ago, University of Leicester, 16 September 2021: the date of 250 to 200 BC, the towers' size and corners, the survey of 2005, the doorway and offerings, the sunset building, about ten days a gap, the date to a day or two, the Inca pillars, the World Heritage listing of 27 July 2021, "Chankillo is not one of them".
• I. Ghezzi and C. Ruggles, "Chankillo: A 2300-year-old solar observatory in coastal Peru", Science 315 (2007), 1239–1243, summarised in the Earthwatch press release.
• The plan is a sketch, with the two solstice directions for Chankillo's latitude worked out as in section 1.11.

1.9 Australia: Wurdi Youang and the Emu in the Sky

Aboriginal Australians reached what is now New South Wales by 40,000 BC and kept a continuous culture, with little outside contact, until the British arrived in 1788. That makes Aboriginal sky knowledge some of the oldest in the world, and it is not "before writing" in the sense of being over: it is held and taught today. Some of it is sacred and not shared with outsiders, and this book does not try to reach behind that. Chapter 12 tells more; here are two pieces that bear on the questions of this chapter.

Wurdi Youang, Victoria

Near Little River in Victoria, the Wathaurung people built an egg-shaped ring of basalt stones about 50 m long, its long axis running almost exactly east–west. At the western end stand three prominent stones about 0.8 m high, with smaller stones, "outliers", beyond them.

In 2003 Morieson suggested that lines from a gap between the two largest stones over the outliers mark where the Sun sets at the solstices and equinoxes. A survey by Ray Norris and colleagues, published in 2013, confirmed this, and found more: the straight sides of the ring point to the same solstice directions, and the three big stones, seen from the eastern end, mark the equinox sunset. Two independent sets of markers agree, which, as section 1.12 shows, is very hard to get by chance; the team's computer test agreed. Wurdi Youang is the only Aboriginal site known so far that marks horizon points other than north, south, east and west.

The Emu in the Sky

Look along the Milky Way on a dark night in the southern hemisphere, and instead of the stars look at the dark clouds of dust between them. Many Aboriginal peoples across Australia see an emu there. Its head is the dark Coalsack beside the Southern Cross, and its neck and body stretch along the Milky Way through Scorpius and Sagittarius, about 90° of sky, larger than any European constellation. A constellation made of darkness is a different way of reading the sky from the dot-to-dot star figures of chapter 7.

The Emu also keeps time. Its shape and position change through the year, and so does the way it is read. The Wardaman people time initiation ceremonies for when "the Emu comes down to drink", as its head nears the horizon; initiation is linked with emus because the male emu, not the female, raises the chicks. In Kuring-gai Chase National Park, north of Sydney, near the Elvina Track, a finely engraved emu lies on the rock with its legs trailing behind it, as the Emu in the Sky's do and a real emu's never do. Hugh Cairns proposed that it shows the sky emu. Ray and Barnaby Norris then found that the engraving matches the Emu in the Sky's orientation above it in the evening at the time of year when emus lay their eggs. While photographing it with low lamps, they also found an egg engraved inside the emu, which archaeologists had missed.

Half a world away, some Indigenous peoples of Brazil see the same dark clouds, from the Southern Cross to Scorpius, as a rhea, the South American cousin of the emu.

Sources

• R. P. Norris, "Dawes Review 5: Australian Aboriginal Astronomy and Navigation", Publications of the Astronomical Society of Australia, 2016 (arXiv:1607.02215): arrival by 40,000 BC and a continuous culture to 1788; sacred stories not discussed; Wurdi Youang (section 7.3.1) with Morieson's idea, the 2013 survey and the test against chance; the Emu in the Sky (section 3.6), its size, the engraving, the egg, the emu and initiation, the rhea in Brazil.
• R. P. Norris and others, "Wurdi Youang: an Australian Aboriginal stone arrangement with possible solar indications", Rock Art Research, 2013 (arXiv:1210.7000).

1.10 The Nebra sky disc

In the summer of 1999, detectorists dug up a hoard near the top of the Mittelberg, a hill near Nebra in central Germany, and sold it illegally. In February 2002 police in Basel, working with the German authorities, recovered it. It is now in the State Museum of Prehistory in Halle, and in June 2013 it joined UNESCO's Memory of the World register.

The hoard held swords, axes, a chisel and arm spirals, and a bronze disc 32 cm across inlaid with gold. The museum calls it the oldest known concrete picture of the sky. Close study shows it was changed several times:

1. First it showed a night sky: a large gold circle (full Moon or Sun), a crescent Moon, and 32 small gold stars. The stars are scattered so as to make no constellation, except one tight cluster: the Pleiades.
2. Then two gold arcs were added at the edges, covering two stars. The arcs span 82°. Seen from the Mittelberg, the setting Sun moves about 82° along the horizon between midsummer and midwinter. The museum adds that, with the disc lined up on the hill, the end of one arc points to the Brocken, the highest peak of the Harz mountains, where the Sun sets at midsummer.
3. A third, feathered arc, of a different gold, was squeezed in between the stars: it is read as a boat crossing the sky.
4. Holes were punched round the rim, perhaps to carry it on a pole.
5. One horizon arc was taken off before it was buried.

Section 1.11 shows how to check the 82°: on a flat horizon at the Mittelberg's latitude the answer comes out at about 81°.

The argument over its age. The museum dates the disc by the objects found with it: the axes and chisel are of a type used around 1600 BC, and birch bark in the sword hilts gives radiocarbon dates in the 16th to 15th centuries BC. In 2020 two archaeologists, Rupert Gebhard and Rüdiger Krause, argued that the hoard is not a reliable closed find, that the disc may not come from the place stated, and that its style fits the Iron Age, about a thousand years later. Ernst Pernicka, Harald Meller and colleagues replied the same year that the court testimony, the soil on the objects and the chemistry of the metals tie the disc to the hoard and the hoard to the Early Bronze Age. The museum keeps the Bronze Age date, but this is a live argument, and a good example of how much depends on knowing exactly where and with what an object was found.

Sources

• State Museum of Prehistory, Halle: The Nebra Sky Disc (the find, the recovery in Basel, Memory of the World), The phases of the Sky Disc (the five phases, 32 stars, burial around 1600 BC), The universe of the Sky Disc (the Pleiades), Scientific research (32 cm), The place of discovery (the Brocken) and Dating (the axes, the birch bark).
• The 82°, measured by Wolfhard Schlosser: World History Encyclopedia, The Nebra Sky Disk.
• The dispute: R. Gebhard and R. Krause, "Critical comments on the find complex of the so-called Nebra Sky Disc", Archäologische Informationen 43 (2020); E. Pernicka and others, "Why the Nebra Sky Disc dates to the Early Bronze Age", Archaeologia Austriaca 104 (2020).

1.11 Working it out: where does the Sun rise?

Every alignment in this chapter rests on one calculation: in which direction does the Sun rise on a given day, at a given place? Here it is.

Measure directions on the horizon as an azimuth \(A\): degrees from north, turning through east, so east is 90° and south is 180°. Let \(\varphi\) be the latitude, and \(\delta\) the Sun's declination, its angle north or south of the sky's equator. At the June solstice \(\delta = +\varepsilon\) and at the December solstice \(\delta = -\varepsilon\), where \(\varepsilon\) is the tilt of the Earth's axis. When the centre of the Sun is on a flat horizon,

\[\cos A = \frac{\sin \delta}{\cos \varphi}.\]

Why. Set up arrows of length 1 at the watcher: \(x\) to the east, \(y\) to the north, \(z\) straight up. The Sun on the horizon at azimuth \(A\) is in the direction \((\sin A,\ \cos A,\ 0)\). The sky's north pole is due north, raised by the latitude: \((0,\ \cos\varphi,\ \sin\varphi)\). The declination is 90° minus the angle between the Sun and the pole, so \(\sin\delta\) is the dot product of the two arrows: \(\sin\delta = \cos A \cos\varphi\). Divide by \(\cos\varphi\).

The tilt then. The tilt changes slowly. From Laskar's formula it was about 24.04° in 3200 BC, 23.97° in 2500 BC, 23.93° in 2100 BC, 23.88° in 1600 BC and 23.73° in 250 BC; it is 23.44° today.

Example 1: Stonehenge, 2500 BC. \(\varphi = 51.18°\), \(\varepsilon = 23.97°\). \(\cos A = \sin 23.97° / \cos 51.18° = 0.4063 / 0.6268 = 0.6483\), so \(A = 49.6°\). The midsummer Sun rose at 49.6°, north-east, and the midwinter Sun at \(180° - 49.6° = 130.4°\). The spread between them is 80.8°.

Example 2: Taosi, 2100 BC. \(\varphi = 35.88°\), \(\varepsilon = 23.93°\). \(\cos A = 0.4056 / 0.8102 = 0.5006\), so \(A = 60.0°\): the solstice sunrises are at 60.0° and 120.0°, a spread of 60.1°. That is the range the twelve slots had to cover.

Example 3: Chankillo, 250 BC. \(\varphi = -9.56°\), \(\varepsilon = 23.73°\). Near the equator \(\cos\varphi\) is close to 1, so \(\cos A = 0.4024 / 0.9861 = 0.4081\) and \(A = 65.9°\). The spread is only 48.2°: the closer to the equator, the narrower the Sun's range. At the equator itself, \(\cos A = \sin\varepsilon\) gives \(A = 90° - \varepsilon\) and the spread is exactly \(2\varepsilon\).

Example 4: Nebra, 1600 BC. \(\varphi = 51.28°\), \(\varepsilon = 23.88°\): \(A = 49.7°\) and the spread is 80.7°, about a degree short of the disc's 82°. Hills on the horizon, which change where the Sun first or last shows, can easily make up that degree.

The curve is for the Earth's tilt in 2500 BC; each site's dot uses its own date. Beyond about 66.6° today, inside the Arctic or Antarctic circle, \(\sin\varepsilon / \cos\varphi\) is larger than 1 and there is no solstice sunrise at all: the midsummer Sun never sets and the midwinter Sun never rises.

Two corrections. Real sunrise is not the moment the Sun's centre touches the horizon. The air bends light near the horizon by about 34′ (just over half a degree), lifting the Sun into view early, and the first gleam is the top edge, 16′ above the centre. Together that is 50′. Put \(h = -50′\) into the fuller formula \(\sin\delta = \sin\varphi \sin h + \cos\varphi \cos h \cos A\) and Stonehenge's midsummer sunrise moves from 49.6° to 48.2°, about 1.4° further north. Hills do the opposite, holding the Sun back. Good archaeoastronomy measures the real horizon at each site.

On Mars. A Stonehenge on Mars would see a wider swing, because Mars is tilted more:

At latitude 51.18°	Mars	Earth
Tilt of the axis	25.19°	23.44°
Midsummer sunrise azimuth	47.2°	50.6°
Spread between the solstice sunrises	85.5°	78.8°
Length of the year (Earth days)	686.97	365.24

Sources

• The tilt in past years: from J. Laskar's formula, Astronomy and Astrophysics 157 (1986), 59–70.
• Refraction of 34′ and the Sun's radius of 16′: US Naval Observatory, Rise, set, and twilight definitions.
• Tilt and year: NASA, Mars fact sheet and Earth fact sheet.
• Latitudes: Taosi from Pankenier and others (2008); the others from published maps of the sites.
• For angles in the sky and how light bends, the physics lessons Angles in the sky and Refraction and Snell's law.

1.12 Could it be chance?

Suppose a site has some lines (a wall, a row of stones, a doorway), each pointing in a direction that has nothing to do with the sky. How likely is it that at least one of them points at something astronomical anyway?

Count the targets: the sunrise and sunset at each solstice (4), sunrise and sunset at the equinoxes (2), and north and south (2). That is 8. Allow each line to miss by up to 1° and still "count". A random direction hits one of the targets with probability

\[p = \frac{8 \times 2°}{360°} \approx 0.044.\]

With \(n\) independent lines, the chance that none hits is \((1-p)^n\), so the chance that at least one does is

\[P = 1 - (1-p)^n.\]

For \(n = 10\), \(P = 1 - 0.956^{10} \approx 0.37\). For \(n = 20\), \(P \approx 0.60\). A large site with twenty possible lines will more likely than not have "an astronomical alignment" by luck alone. Add the Moon's four extreme rising and setting points, or a few bright stars at a date of your choice, and \(P\) climbs towards certainty. This is trap 1 of section 1.2, in numbers.

What beats chance?

• Choosing the line before looking. The main axis of a building, or the one doorway of a tomb, is a single line chosen by the builders. Here \(n = 1\) and \(p = 0.044\): a hit is unlikely to be luck.
• Several independent hits. If three separate features each hit a target, and each had only a 4.4% chance, the chance that all three are luck is about \(0.044^3 \approx 0.00009\). This is the logic behind Wurdi Youang, where the outliers and the straight sides of the ring point the same way. (The real test is subtler, because features are rarely fully independent; Norris's team used a computer simulation, a Monte Carlo test.)
• A complete set. Chankillo's thirteen towers do not just hit a target; they fill the Sun's whole range from end to end, seen from two marked viewing points. Getting that by chance is far less likely again.
• A feature with no other use. Newgrange's roof-box is not one line among many. It exists only to let light in.

None of this tells us what the builders meant: that is trap 3, and only other evidence, or living tradition, can help with it.

Sources

• This is a simple version of the reasoning used in archaeoastronomy; for the real tests, see Norris and others (2013), Wurdi Youang, and Clive Ruggles, Astronomy in Prehistoric Britain and Ireland (Yale University Press, 1999).

Check yourself

1. (beginner) Why does a calendar of twelve lunar months drift against the seasons, and by how much each year?

Answer

Twelve lunar months are \(12 \times 29.53 \approx 354.4\) days, but the year is about 365.24 days. The calendar runs about 11 days short each year, so after three years it is a whole month early.

2. (beginner) What is a solstice, and why is the solstice sunrise a good mark for a calendar?

Answer

It is one of the two days in the year when the Sun's rising point stops moving north (or south) along the horizon and turns back. It is a fixed, repeating point in the solar year, and at a place with a clear horizon anyone can see it. Its one drawback is that near the solstice the rising point barely moves for several days, so pinning the exact day takes care, as at Chankillo.

3. (beginner) Name the three kinds of evidence for sky knowledge without writing, with one example of each from this chapter.

Answer

Objects (the Ishango bone, the Nebra disc); buildings and landscapes (Newgrange, Chankillo, Taosi); living knowledge (the Emu in the Sky in Aboriginal tradition).

4. (intermediate) Give two reasons why the Border Cave bone is weak evidence of counting Moons.

Answer

The bone is broken, so 29 is only the number of notches that survive. And the notches were cut in four separate sets with four different tools, which does not look like one tally of the nights of a month. The bone shows that people were recording something, not what.

5. (intermediate) Why can the summer solstice sunrise no longer be seen through slot E12 at Taosi?

Answer

The Earth's tilt has shrunk from about 23.93° in 2100 BC to 23.44° today, so the summer Sun now rises a little further south than it did. The slot was set for the sky of 4,100 years ago.

6. (advanced) Newgrange is at latitude 53.69° N. In 3200 BC the Earth's tilt was 24.04°. In what direction did the midwinter Sun rise there, on a flat horizon?

Answer

\(\cos A = \sin 24.04° / \cos 53.69° = 0.4074 / 0.5922 = 0.6879\), so the midsummer Sun rose at \(A = 46.5°\). The midwinter Sun rose at \(180° - 46.5° = 133.5°\), south-east, the direction the passage faces.

7. (advanced) Show that on the equator the two solstice sunrises are exactly \(2\varepsilon\) apart.

Answer

At \(\varphi = 0\), \(\cos\varphi = 1\), so \(\cos A = \sin\varepsilon = \cos(90° - \varepsilon)\) and \(A = 90° - \varepsilon\). The other solstice gives \(180° - A = 90° + \varepsilon\). The difference is \(2\varepsilon\): about 47° today.

8. (expert) A site has 15 lines between its stones. Using 8 targets and a 1° allowance, how likely is it that at least one line points at a target by chance? What would make you believe an alignment there was meant?

Answer

\(p = 16/360 \approx 0.044\) and \(P = 1 - 0.956^{15} \approx 0.49\): about an even chance. To believe it, look for a line chosen before looking (the main axis, an entrance), several independent features pointing the same way, a feature with no other purpose, or a living tradition or later record that says what the line was for.

Summary

• The sky offers three clocks, the day, the lunar month and the year, and they do not fit: twelve Moons are 11 days short of a year. A fixed point such as the solstice sunrise lets a Moon count be put right.
• Without writing, the evidence is objects, buildings and landscapes, and living knowledge. The traps are chance, dating and meaning.
• The notched bones of Border Cave and Ishango show counting more than 40,000 years ago in Africa, but not that Moons were counted.
• Warren Field (about 8000 BC) may be a Moon calendar reset by the midwinter sunrise: a strong proposal.
• Newgrange (about 3200 BC) lets the midwinter sunrise into its chamber through a purpose-built roof-box. Stonehenge (about 3000 to 2500 BC) is built on the solstice line. Nabta Playa (about 4500 to 4000 BC) has a likely solstice line; its star lines are unproven.
• Taosi in China (about 2100 BC) and Chankillo in Peru (250 to 200 BC) are horizon calendars, the second as convincing as any ancient site.
• Aboriginal Australians read dark clouds as the Emu in the Sky and built Wurdi Youang on the solstice and equinox sunsets; their knowledge is living.
• The Nebra disc (buried about 1600 BC, though some argue it is later) shows the Moon, the Pleiades and arcs that match the Sun's 82° swing on its hill.
• \(\cos A = \sin\delta / \cos\varphi\) gives the sunrise direction; the spread of solstice sunrises grows from \(2\varepsilon\) at the equator to nearly 100° in Scotland.

Next: chapter 2, Mesopotamia, where the sky is written down for the first time, night after night, for centuries.

Further reading

• Clive Ruggles, Ancient Astronomy: An Encyclopedia of Cosmologies and Myth, ABC-CLIO, 2005. Short entries on sites and claims worldwide, with careful verdicts.
• Clive Ruggles (ed.), Handbook of Archaeoastronomy and Ethnoastronomy, Springer, 2015. Three volumes, every region.
• Clive Ruggles, Astronomy in Prehistoric Britain and Ireland, Yale University Press, 1999.
• Ray Norris and Cilla Norris, Emu Dreaming: An Introduction to Australian Aboriginal Astronomy, Emu Dreaming, 2009.
• C. Ruggles and M. Cotte (eds.), Heritage Sites of Astronomy and Archaeoastronomy in the Context of the UNESCO World Heritage Convention, ICOMOS and IAU, 2010: the thematic study, with a case study for each great site.