Given the arrival of the summer solstice and this post on the EarthSky website, I decided to write a little bit about what prehistoric monuments (like Stonehenge) suggest to me about some of the roots of mathematics.
With a photograph to support the claim, the EarthSky post tells us:
If you stood inside the Stonehenge monument at sunrise on the day of the summer solstice, you would see the sun rise above the famous Heel Stone.
This Stonehenge monument – built in 3,000 to 2,000 BC – shows how carefully our ancestors watched the sun.
In their photo, the slightly pointed top of the Heel Stone seems to direct your attention to the center of the rising sun. There is disagreement, however, about the significance of this alignment. Evidence that there was once a stone neighboring the Heel Stone has challenged the idea that the Heel Stone is a solstice sunrise marker. Some scholars now even believe that prehistoric people visited the site only during the winter solstice.
Stonehenge’s construction (over the course of at least 1500 years) began as early as 3100 BC. Although many of claims about its astronomical alignments have also been disputed, there does seem to be an astronomical aspect to the structure, and one that it shares with other prehistoric monuments. At Stonehenge, on the day of the northern winter solstice, the setting sun lines up with the narrow space created by three stones known as the Trilithon – two large vertical stones that support a third horizontal stone across the top.
Newgrange, a monument located on the eastern side of Ireland, is primarily a large mound within which was built a chambered passage. Newgrange dates back to 3200 BC and has the striking feature that, on the day of the winter solstice, the rising sun floods the stone room within the mound with light. Their website describes it this way:
At dawn, from December 19th to 23rd, a narrow beam of light penetrates the roof-box and reaches the floor of the chamber, gradually extending to the rear of the chamber. As the sun rises higher, the beam widens within the chamber so that the whole room becomes dramatically illuminated. This event lasts for 17 minutes, beginning around 9am.
The accuracy of Newgrange as a time-telling device is remarkable when one considers that it was built 500 years before the Great Pyramids and more than 1,000 years before Stonehenge. The intent of its builders was undoubtedly to mark the beginning of the new year. In addition, it may have served as a powerful symbol of the victory of life over death.
Newgrange also has some abstract rock art that includes circles, spirals, dot-in-circles, and parallel lines.
Exploring some of the prehistoric monuments that are known to have astrological significance led me to read a bit about the relatively new area of study called Archaeoastronomy. Wikipedia describes it as the study of how people in the past have understood the sky, how they used what they understood, and what role the sky played in their culture. Inevitably this kind of investigation crosses paths with archaeology, anthropology, the history of science, and cognitive science. There’s a nice collection of relevant sites at a website called Ancient Wisdom that includes discoveries in the Americas – like the ‘sun-dagger’ in Chaco Canyon, New Mexico, the Bighorn Medicine Wheel in Wyoming, and Chichen Itza in Mexico. The alignments of the Bighorn Medicine Wheel are particularly clear and described here.
On top of the Bighorn Range in Wyoming, a desolate 9,642 feet high and only reachable during the warm summer months, lies an ancient Native American construction — an 80′ diameter wheel-like pattern made of stones. At the center of the circle is a doughnut-shaped pile of stones, a cairn, connected to the rim by 28 spoke-like lines of stones. Six more stone cairns are arranged around the circle, most large enough to hold a sitting human. The central cairn is about 12 feet in diameter and 2′ high.
If you stand or sit at one cairn looking towards another, you will be pointed to certain places on the distant horizon. These points indicate where the Sun rises or sets on summer solstice and where certain important stars rise heliacally, that is, first rise at dawn after being behind the Sun. The dawn stars helped foretell when the Sun ceremonial days would be coming. The area is free of snow only for 2 months — around the summer solstice. The wheel has 28 spokes, the same number used in the roofs of ceremonial buildings such as the Lakota Sundance lodge. These always includes an entrance to the east, facing the rising Sun, and include 28 rafters for the 28 days in the lunar cycle. The number 28 is sacred to some of the Indian tribes because of its significance as the lunar month. In Bighorn’s case, could the special number 28 also refer to the helicial or dawn rising of Rigel 28 days past the Solstice, and Sirius another 28 past that?
For me, a glimpse of these ancient constructions gives me a chance to muffle the voice of scientific objectivity in favor of a more participatory cosmic experience. The consistency of the human desire to mark the summer and winter solstices is impressive. These ancient feats also tell me something about how our attention was directed, how determined we were to look out at the distant horizon. Our ancestors began early to live within observed patterns and cycles. Their monuments give us the chance to see something about how they were inclined to mark what they saw, and re-present it to themselves, in patterns of their own making. Building the alignments that are contained in these structures is an analysis of space as well as pattern and often also involves a count of some kind, with ourselves at the very center of the action. These are really the elements of measurement, that abstract arrangement of sensory facts that we so often make. This most certainly leads to what we later call a mathematical intuition. But they emerge through the kinship of the earth, the sky and the organism, and use the strength of the whole organism, the whole body. In this light, another look at these ancient accomplishments could contribute something new to what we think about the nature of science and mathematics. These are things that the body is doing, and we may not fully understand why.
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Thank you Gregor for all of your thoughts. They have made a substantial contribution to the subject of this post and I do enjoy that. You may have never looked (back at your math books), but you have kept your eye on some of the insights the subject can help bring.
Thanks again.
Sentience, language, and mathematics makes us what we are. Everything else in Nature has some degree of the first two attributes, but the latter defines our humanity and, through our perception of pattern, allows us to contemplate sacred divinity real or imagined.
Thanks for your considered clarification Joselle, as well as the original provocative post. I think I was trying also to take issue with peoples of this modern epoch objectifying facts (and reality itself as well) so I like how you’re attempting to say (without meaning to put words in your mouth) how much you enjoy “feeling the mathematics in your body through the contemplation of such physical structures.” Freeman claims the key for unlocking the sidereal secrets of that perpetual time machine out there on the open Canadian Prairie was his recognition that the landscape itself is part of the artefact.
And one of Freeman’s themes throughout his book is how, during the decades spent pursuing his “hobby” (ie, spending weeks at a time enduring inhospitable climate and wild animals at ungodly hours over the course of years surveying stones in an apparently bleak and barren landscape) it makes the hair on the back of his neck tingle every time he confirms the stunning accuracy of a suspected sightline…
“I feel a direct mental connection with the people who designed and built the place thousands of years ago each time I see the Sun’s first or last flash along an anciently marked line. In fact, any time I now happen to see the first or last flash of the Sun on the horizon, I feel pleasure a bit like the flutter I get any time I unexpectedly see Phyl [his wife and accomplice] these last fifty-eight years” (pp 109).
I failed math in Grade 10 and never locked back, but I am a pretty proficient finger picker and singer songwriter on a guitar. I know music is mathematical, but mathematics does not make music – at least the kind that can make your soul bleed. And don’t get me started on academic “scholars” as I had my fill of them, especially in my History faculty, when I quit university halfway through my MA thesis entitled “Goethe’s critique of Newtonian optics and colour theory.”
I am interested in what he revealed and will look into it. But I think you are misunderstanding what I mean by participatory cosmic experience, and I can see how what I said can sound like something very different from what I mean. I’m married to a high energy physicist and have a passion for modern mathematics. I don’t want to muffle what has been perceived, and I marvel, with everyone else, at its precision. The contrast I was trying to make was between a culture (like ours) that completely objectifies facts and information about a world ‘out there’ somewhere,and one where the individuals explore their relationship to the facts – in these cases building the facts and information into structures that surround them, by moving the very ground on which they live. In this experience, the individual is more a part of what they see.
I also feel strongly that these structures demonstrate a mathematical sense, or a mathematical way about us, that is more natural than we sometimes believe.
Why would you want to “muffle the voice of scientific objectivity in favor of a more participatory cosmic experience”? Instead, perhaps you could actually apply scientific objectivity to your participatory cosmic experience like a right and proper Natural Philosopher.
Like Canadian theoretical chemical physicist Gordon Freeman did with his discovery of a 5,000 year old astronomical calendar on the Canadian Prairie in the province of Alberta that had been in continuous use until we “displaced” the First Nation Peoples who built it a mere couple of hundred years ago.
The problem with squabbling “scholars” is so few of them get off their academic butts and actually go out and apply the science!!! That is to say, acquire the precise mathematical measurements required to make an intelligent argument in the first place. And so, instead, they take such umbrage from the possibility that “primitive” folks might have been more brilliant as well as cosmically participatory than they themselves ever will be.
After Freeman measured the Canadian Sun Temple, he applied his rather precise mathematical measurements to Stonehenge and various other potential astronomically significant sites in Britain and Wales. You might be interested in what he revealed:
http://canadastonehenge.com/