Sunday, May 24, 2015

How the Discredited Geocentric Cosmos Was a Critical Component of the Scientific Revolution

How Ptolemy's Geocentric Astronomy
Helped Build the Modern World

(all images are from

If you took the standard required western history course in college as I did, you learned that about 400 years ago astronomers Copernicus,  Galileo and Kepler along with Isaac Newton were key players in the scientific revolution that overturned the cumbersome system of geocentric astronomy. In this outdated system the Sun, moon and stars went around the stationary Earth. Instead these early scientists proved that the Earth and the planets went around the Sun. Known as the Copernican Revolution, it is considered the beginning of the scientific revolution, a new way of thinking which continues to this day and has created our modern world and our modern hi-tech marvels.

Well, that story is sort of true, but in hindsight it greatly simplifies the complex path that the scientific revolution took, the path that ultimately led to today's scientific and technological wonders. Specifically it leaves out the fact that the geometry of a geocentric universe and its foremost astronomer, Ptolemy, who perfected the geocentric system, were key players in this new scientific outlook. In fact the discredited geocentric theory was, oddly, essential for building our new scientific/technological world.


Over hundreds of years the early ancient Greeks put together a concept of the Solar System as a coherent system of concentric circles -- which was a major advance for Western thought. Later in the 4th century BCE, Plato and then Aristotle decided that the Earth was stationary and at the center of the universe, while the Sun, moon, planets and stars moved in perfect circles -- thought of as concentric spheres -- around the Earth. In the ancient Greek view of the cosmos, the orbits had to be perfect circles since all things in Heaven were considered 'perfect'. Each heavenly object moved with its own uniform motion.

However, "the geocentric model of Plato could not explain the retrograde motion of the planets. Around 140 A.D. Ptolemy proposed his refined geocentric model. In the Ptolemaic universe, a planet moves in a small circle called an epicycle, and the center of the epicycle moves along a larger circle around the Earth."

"A simple illustration showing the basic elements of Ptolemaic astronomy.
It shows a planet rotating on an epicycle which is itself rotating around
a deferent inside a crystalline sphere." Quoted from:

Claudius Ptolemy in his book the Almagest (published around 150 CE) laid out his refined geometry for the movement of the heavenly bodies, based on earlier Greek science and the work of the Greek astronomer Hipparchus. His revised system was quite accurate and this view of the universe lasted for almost 1500 years.

Ptolemaic Model Of The Solar System
From NASA's Cosmos: By selecting suitable radii and speeds of motion, Ptolemy could use this system of uniform motion around two [ED: perfect] circles to reproduce the apparent motions of the planets with remarkable accuracy. He succeeded so well that his model was still being used to predict the locations of the planets in the sky more than a thousand years after his death.
The problem people had with Ptolemy's cosmology was that it was complicated:The resultant system...seems unwieldy to modern astronomers; each planet required an epicycle revolving on a deferent, offset by an equant which was different for each planet.
Eventually the new heliocentric science advanced by Copernicus, observed by Galileo, perfected by Kepler and then explained by Newton was easier to calculate. It was accepted in part because it was a more elegant and simpler mathematical solution and once refined was more accurate than the predictions of Ptolemy's system.

So what is my argument with all of this you might ask?


Ptolemy's system had a large but hidden benefit. The perfect circles that were the key component of his system meant that man-made machines -- first clocks and later engines -- could be easily constructed with circular gears.

Ptolemy's system mapped out how mechanical models could be made of the solar system and these machines eventually led to the building of clocks. Yet even before the first astronomical clock was made, the idea of a mechanical universe based on Ptolemy's ideas was widely known.

Page from De sphaera mundi
The Sphere of the Cosmos (De sphaera mundi) is a medieval introduction to the basic elements of astronomy written by Johannes de Sacrobosco (John of Holywood) [ED: publication date] c. 1230. Based heavily on Ptolemy's Almagest, and drawing additional ideas from Islamic astronomy, it was one of the most influential works of pre-Copernican astronomy in Europe. Sacrobosco's De sphaera mundi was the most successful of several competing thirteenth-century textbooks on this topic. It was used in universities for hundreds of years. Sacrobosco spoke of the universe as the machina mundi, the machine of the world... This concept is similar to the clockwork universe analogy that became very popular centuries later, during the Enlightenment. [ED: my emphasis]
Around 1264 Campanus of Novara, an Italian astronomer, "wrote a Theorica Planetarum [which] ... included instructions on building a planetary equatorium as well as its geometrical description. The data on planets are drawn from the Almagest [by Ptolemy] and the Toledan Tables of the Arab astronomer Arzachel. Campanus gave precise instructions on using the tables, and made detailed calculations of the distances to the planets and their sizes."
The Theorica Planetarum has been called "the first detailed account of the Ptolemaic astronomical system... to be written in the Latin-speaking West."
Benjamin, Francis Seymour; Toomer, G. J. (1971). Campanus of Novara and medieval planetary theory: Theorica planetarum. 
Thus, the ancestors of Western clocks were early planetaria, and forerunners of what later became known as astronomical clocks.
Fraser, J.T. (1978). Time as Conflict: A Scientific and Humanistic Study.
In the middle ages starting in 1364 CE, many astronomical clocks were made throughout Europe. They were both timekeeping instruments and devices that showed the movement of the Sun, moon, planets and the zodiac.
See a list here:
Most of the first clocks were not so much chronometers as exhibitions of the pattern of the cosmos ... Clearly the origins of the mechanical clock lie in a complex realm of monumental planetariums...   
White, Lynn Jr. (1966). Medieval Technology and Social Change.
The first documented astrarium clock was completed in 1364 by Giovanni de' Dondi (1318–1388)... The original clock, consisting of 107 wheels and pinions, was lost..., but de' Dondi left detailed descriptions which have survived, enabling the reconstruction of the clock. It displays the mean time, sidereal, or star, time and the motions of the Sun, moon and the five then known planets Venus, Mars, Saturn, Mercury, and Jupiter. It was conceived according to a Ptolemaic conception of the solar system.[ED: my emphasis]

"The Prague astronomical clock [above] was installed in 1410...and is the oldest functioning Astronomical clock in the world." Quoted from:

The Prague clock was built more than 130 years before Copernicus published On the Revolutions of the Celestial Spheres in 1543. The publication of Copernicus' book is considered by some to be the beginning of the modern age, yet was preceded by astronomical clocks starting in 1364 (see above) -- almost 180 years earlier.

Explanation of the information on the Prague astronomical clock.

The design of these mechanical clocks, a huge technological advance for the age, was largely based on Ptolemy's geometry. Clocks eventually became the symbol for the Newtonian age -- the age of the scientific revolution. They helped spawn the idea that God was the great watchmaker.
In the history of science, the clockwork universe compares the universe to a mechanical clock. It continues ticking along, as a perfect machine, with its gears governed by the laws of physics, making every aspect of the machine predictable.
René Descartes saw "the cosmos as a great time machine operating according to fixed laws, a watch created and wound up by the great watchmaker."

Gears in a pocket watch.

So the idea of a mechanical universe -- a central idea to this new scientific revolution -- was derived from the discredited geocentric astronomy. In addition the building of geared clockwork machines was also due to the geocentric model, showing the importance of this system to the manufacture of practical technological devices.
Clocks were the "key machine of the modern industrial age."
Strandh, Sigvard (1979). A History of the Machine.
This was the ultimate irony: The central image for the new scientific mechanical age was a watch which was created with the discredited geometry and physics that the scientific revolution had overturned.


Yet the story does not end here -- it continues today. In fact you probably use geocentric physics everyday. For example, much of the gearing in automatic transmissions in cars and other vehicles is based on a geocentric design. Let me explain.

What Ptolemy achieved with his circles within circles was an advanced design of gears and gearing -- gearing that worked well and was quite reliable -- as had been shown in the creation of clocks. The ability to create such gears was not only critical to the construction of clocks but later to the design of engines and machines such as the early Watt steam engine -- the mechanical device that kick started the industrial age and the Industrial Revolution.

About the Watt steam engine in 1785:
"The firm's [ED: Watt's company] fourth innovation [was] Sun and planet gearing...
As Boulton and Watt engines were prime movers in the Industrial Revolution, this very significant engine represents not just invention and entrepreneurship, but also wealth creation, mass consumerism, great changes in working life, a massive shift in the use of resources, and consequent damage to the natural environment."
While it was called a Sun and planet gear with the Sun in the middle, in fact the gearing was based on the geocentric geometry of Ptolemy with his understanding of perfect circles, epicycles and uniform motion.

"This particular [Watt steam] engine was installed in
Whitbread's brewery in 1785, 
and clocked up 102 years' work." Quoted from:

Early locomotive gearing due in part to the geocentric system of interrelated circles.

Today epicycle gears, also known as planetary gears, are used in a wide range of machines including automatic transmissions for automobiles and bicycle gearing.

About modern epicycle gears from Wikipedia:
Epicyclic gears get their name from their earliest application, which was the modeling of the movements of the planets in the heavens. Believing the planets, as everything in the heavens, to be perfect, they could only travel in perfect circles, but their motions as viewed from Earth could not be reconciled with circular motion. At around 500 BC, the Greeks invented the idea of epicycles, of circles traveling on the circular orbits.With this theory Claudius Ptolemy in the Almagest in 148 AD was able to predict planetary orbital paths.

 A modern epicycle gear train or planetary gear train.


One of the reasons Ptolemy's science has gotten such bad press and even been labeled bad astronomy was due to the trial of Galileo by the Catholic Church which prevented him from criticizing this geocentric system. This was seen later as a huge impediment to the advance of science, when the new ideas of Copernicus, Kepler and Newton won out. As a result the Ptolemaic system itself took part of the blame for standing in the way of scientific investigation. Yet it is important to note that the cosmology of Copernicus was initially not as accurate as that of Ptolemy and even more complicated -- although it did solve a number of nagging problems.
However, Copernicus, like Ptolemy, also used circular orbits and had to resort to epicycles and deferents to explain retrograde motions. In fact, Copernicus was forced to use more epicycles than Ptolemy, i.e. a more complicated system of circles on circles. Thus, Copernicus' model would have failed our modern criteria that a scientific model be as simple as possible.
Yet, as we know, history is written by the victors and in this case, the science of Newton et al was the victor, so the previous science was discredited.

Stephan Jay Gould in his book Time's Arrow And Time's Cycle pointed out that something of a similar nature occurred in the science of geology. It would seem that this attitude of denigrating and distorting past thinkers is also true in just about every branch of science.
Gould, Stephan Jay (1987). Time's Arrow, Time's Cycle: Myth and Metaphor in the Discovery of Geological Time.

Perhaps Albert Einstein understood the process of theorizing better than anyone and understood how one theory builds on another -- which does not mean that the earlier theory was in error, but rather that it was a necessary step in the process.
Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism...But he certainly believes that, as his knowledge increases, his picture of reality will become simpler and simpler and will explain a wider and wider range of his sensuous impressions.
Albert Einstein

Tuesday, April 28, 2015

The Development of Consciousness & the Origins of Religion

Once homo sapiens had evolved biologically, I believe modern humans acquired full consciousness perhaps 50,000 years ago. This is when there was an explosion of new more powerful tools, and an increased understanding of how to make tools.

Definition (Google):
The fact of awareness by the mind of itself and the world.
The English word "conscious" originally derived from the Latin conscius (con- "together" and scio "to know"), but the Latin word did not have the same meaning as our word -- it meant "knowing with", in other words "having joint or common knowledge with another". There were, however, many occurrences in Latin writings of the phrase conscius sibi, which translates literally as "knowing with oneself", or in other words "sharing knowledge with oneself about something". This phrase had the figurative meaning of "knowing that one knows", as the modern English word "conscious" does.

In addition to making more powerful and effective hunting tools, humans now made certain tools that were specifically designed to assist in the making of these hunting tools, or to put it another way they made tools to make the tools. In a sense, they had stepped back and carefully considered the needs of the hunt. Then they crafted tools that would help them make these more sophisticated tools. And this, I believe, was a critical step; I call it meta-thinking because this meant their consciousness had now risen to a new level, a meta-level. (Meta is defined as: denoting something of a higher or second-order kind. Google dictionary)

LEFT: "About 45,000 years ago Cro Magnon developed blades and spear-throwers with a considerably greater range, velocity and penetration. Hunters could now kill large animals from a longer, much safer, distance."RIGHT: "Over this period our ancestors invented burins to help make tools from antlers, such as bone spears and harpoons that were often beautifully engraved and carved."Burin: a type of stone tool used for carving or engraving on wood or bone."  (

Beginning around the same time, there was also an explosion of sculptures and symbols.

"Löwenmensch - a lion-headed figurine found in Germany and dating to the Upper Paleolithic, about 40,000 BCE"

"The Venus of a fragmentary ivory figurine from the Upper Paleolithic. It was discovered in a cave at Brassempouy, France in 1892. About 25,000 years old, it is one of the earliest known realistic representations of a human face."

My guess is that consciousness was both something that developed in each individual and also in the tribe as a whole. This relates to the Latin meaning of consciousness as "having joint or common knowledge with another." It came about as a result of shared gestures, signs/symbols, song/ music/dance and language plus concepts and abstractions along with a sophisticated shared sense of time. This sense of time meant they understood the concept of 'when', i.e., when in the past,  when in the present and when in the future along with the ability to imagine 'what if?' which allowed them to plan. As I have written, I believe the key difference between humans and other animals is the ability to understand time in terms of 'when' and this ability is a central part of human consciousness.

Because consciousness created a meta-world, a virtual world within the mind of each member of the tribe -- but a world that was also shared as a common ground -- it took perhaps a hundred thousand years or more to build this man-made internal landscape and to learn how to navigate through it and to share common thoughts.

Exactly how this happened or developed is lost to us in prehistory. But the sudden birth of consciousness in the blind/deaf Helen Keller might give us some hints about the process the human race went through to develop its conscious thinking and that a sense of time was critical. In the following passage written by Helen, she describes her sudden breakthrough into consciousness.
My inner life, then, [ED: before consciousness] was...without past, present, or futureSince I had no power of thought, I did not compare one mental state with another.When I learned the meaning of "I" and "me" and found that I was something, I began to think. Then consciousness first existed for me.  Helen Keller, The World I Live In, 1908
See my blog: Time & Consciousness

The development of consciousness gave humans a power that allowed them to imagine the future and the past, to plan, to coordinate, to 'time travel' in their mind's virtual time. We now had a virtual tool that made us the most powerful beings on the Earth.

See my blog: Virtual Human Meta-Time

I have been writing about the human experience of time now for three years in my blog: -- I believe the human ability to measure time, determine 'when' in time and to plan is the reason humans became the dominant species on the Earth. See my blog: Animal Senses Compared to the Human Sense of Time

And while we cannot know the process that humans went through to obtain consciousness, nevertheless, we do know for certain that consciousness did develop and that once it had a foothold, it  there was no turning back.

See my blog: The Human Revolution: Symbolic Culture

"Man is distinguished above all animals by his self-consciousness, by which he is a 'rational animal'."   
Immanuel Kant, Critique of Pure Reason

But the cost was also quite high. Before consciousness humans had been part of nature, now they were aware they were removed and separated from nature.

And while the power of consciousness, shared symbols and culture allowed a rapid development of shared knowledge and added skills that could be passed down from generation to generation, it also opened the door to imaginings that were too painful to withstand. Because with the ability to imagine the future, humans now had a concept of death. This meant that they could be certain they would die and also their family would die -- and that early death was an ever present threat.
Unlike animals, humans understand the inevitability of their own death and in fact can imagine a world in which we are no longer alive. To Death & Back, PBS

We know that in human history there was a distinct change about 100,000 years ago when humans began to be buried in a ceremonial fashion. Burial practices are particularly important to our modern understanding of the past because when people were buried with pottery, jewelry and other artifacts it signaled an awareness of death and that a collective consciousness had reached a high level of sophistication.
The first undisputed deliberate human burial is:"About 100,000 years ago at Qafzeh, Israel, the remains of as many as 15 individuals were found in a cave, along with 71 pieces of red ocher and ocher-stained stone tools. The ocher was found near the bones, suggesting it was used in a ritual."  NOTE: Red ocher comes from iron embedded in stone and is part of the lore and skills of old stone age cultures.


The focus of this article is not so much about consciousness but rather its consequences, as the price for acquiring consciousness was quite high. I believe the roots of religion are directly attributable to the emergence of consciousness -- as consciousness created a separation from nature and also an awareness of death.

People in just about every culture, both in the past and in the present, have held a set of religious beliefs. Anthropologists include religious beliefs as one of the common traits of all cultures and civilizations. So it would seem that religion, from the earliest times to the present, is a fundamental need of human beings. For more about this see:

Perhaps the best evidence for the connection between consciousness and religion comes from the story of Adam and Eve. This story is found in Genesis, a book of the Torah, the first of the first five books of the twenty-four books of the Tanakh, the canon of the Hebrew Bible (the first book of the Old Testament for Christians) -- which is considered a sacred text by Christians, Jews and Muslims, i.e., more than half the people on this Earth.
NOTE: When the 'tree of knowledge' is mentioned, the word 'knowledge' in Hebrew can also mean awareness. This also ties in with the notion of consciousness, since consciousness from the Latin means 'with knowledge' and after all what is knowledge but awareness. With this interpretation, then, eating the fruit from the 'tree of awareness' caused a separation from the original state of oneness with nature -- and created an awareness of death. For more about this please see:   ALSO NOTE: "The phrase in Hebrew ... translatable as 'good and evil', may be an example of the type of figure of speech known as merism. This literary device pairs opposite terms together, in order to create a general meaning; so that the phrase "good and evil" would simply imply "everything"."

Genesis 2
And the Lord God commanded the man, “You are free to eat from any tree in the garden;
but you must not eat from the tree of the knowledge of good and evil, for when you eat from it you will certainly die.” [ED : My emphasis]
Adam and his wife were both naked, and they felt no shame.

Genesis 3
When the woman saw that the fruit of the tree was good for food and pleasing to the eye, and also desirable for gaining wisdom, she took some and ate it. She also gave some to her husband, who was with her, and he ate it.
Then the eyes of both of them were opened, and they realized they were naked; so they sewed fig leaves together and made coverings for themselves.
Then the man and his wife heard the sound of the Lord God as he was walking in the garden in the cool of the day, and they hid from the Lord God among the trees of the garden.
But the Lord God called to the man, “Where are you?”
He answered, “I heard you in the garden, and I was afraid because I was naked; so I hid.”
And he said, “Who told you that you were naked? Have you eaten from the tree that I commanded you not to eat from?”
 To Adam he said, “Because you listened to your wife and ate fruit from the tree about which I commanded you, ‘You must not eat from it,’
“Cursed is the ground because of you;
    through painful toil you will eat food from it
    all the days of your life.
It will produce thorns and thistles for you,
    and you will eat the plants of the field.
By the sweat of your brow
    you will eat your food
until you return to the ground,
    since from it you were taken;
for dust you are
    and to dust you will return.”
So the Lord God sent him away from the garden of Eden to work the ground from which he was taken.

In another ancient passage from sacred texts, Enoch, the great-grandfather of Noah, writes of his perception of the tree of knowledge.
NOTE: Although the Books of Enoch have been verified as being quite old, they are generally considered part of the Apocrypha. The text quoted here is from the Book of Watchers -- dated to about 300 BCE -- and considered part of the holy cannon by some Jews and Christians, but not by most others although "most Christian denominations and traditions may accept the Books of Enoch as having some historical or theological interest or significance..." For more about this see: 
From the Books of Enoch: And I came to the Garden of Righteousness, and from afar off trees more numerous than these trees and great -- two trees there, very great, beautiful, and glorious, and magnificent, and the tree of knowledge, whose holy fruit they eat and know great wisdom.
That tree is in height like the fir, and its leaves are like (those of) the Carob tree: and its fruit is like the clusters of the vine, very beautiful: and the fragrance of the tree penetrates afar. Then I said: ' How  beautiful is the tree, and how attractive is its look!' Then Raphael the holy angel, who was with me, answered me and said: 'This is the tree of wisdom, of which thy father old (in years) and thy aged mother, who were before thee, have eaten, and they learnt wisdom and their eyes were opened, and they knew that they were naked and they were driven out of the garden.'  Enoch's Journeys through the Earth and Sheol, Chapter XXXII,
In this text, it is clear that eating the fruit from the inviting, beautiful, fragrant tree of knowledge would give a person great wisdom -- but at a terrible cost.

My interpretation is that eating the fruit of 'knowledge and awareness' had turned Adam and Eve's original innocent oneness with nature into a self-consciousness separation from nature -- being naked (what is more natural?) was now something they were ashamed of and gaining knowledge meant that they now knew they were mortal.
The object of the myth evidently was to explain the origin of death,C. Staniland Wake, Influence Of The Phallic Idea In The Religions Of Antiquity, 1870.
These simple allegories [ED: the fall of man in Genesis] ... are condensed explanations, stripped of minor details, of the great underlying laws of existence.Charles Fillmore, Mysteries of Genesis, 1936.
Thus man eats "of the fruit of the tree of the knowledge of good and evil." In these few words is summed up the fall of man from an Edenic a consciousness of matter and the desperate struggle of personality for existence.Charles Fillmore, Mysteries of John, 1946.
This story with many variations appears in a number of other cultures as detailed in the following chapter:
Heathen Fables Illustrative Of The Fall Of Man in the book: The Worship of the Serpent by John Bathurst Deane, 1833.
In most hunter-gatherer cultures:"There are invariably two temporal orders of existence, with an Early mythical or 'dreamtime' preceding the present. In the former, nature and culture are not yet fully separated. Out of this existence...crystallizes the distinction between humans and animals, even mortality itself, and virtually everything of cultural significance."  Introduction: The Cambridge Encyclopedia of HUNTERS AND GATHERERS
The above quotes point to the two principle themes in religion: the fear of death and a separation from nature and the cosmos. Religion offers a solution by providing a connection to nature, by helping humans find their “place in the universe” as Carl Jung once said, along with a promise of an afterlife and/or an understanding of death.


Based on what we know about contemporary hunter-gatherer cultures, early religious beliefs in the Paleolithic or Mesolithic eras were nothing like modern day organized religion. It was not until Neolithic times that formal observances with priests, buildings and rituals would appear.

It seems safe to assume, from the study of modern hunters and gatherers, that religion originally took the form of shamanism. Virtually every modern hunter-gatherer people today, for example, engage in shamanism or did in the recent past. 
(The Cambridge Encyclopedia of HUNTERS AND GATHERERSIntroduction)

This early division, this first separation from nature, required that within the tribe's symbolic culture there had to be a way to connect, to understand, to communicate, to relate to the world of nature. And from this basic need, I believe religion, or what I prefer to call 'spiritual beliefs' at this state, was born. Because of the certainty of death and the desire to be in touch with nature, early humans needed to find a way maintain a relationship with the natural world that they believed was made of spirits. These beliefs meant that there was a "hovering closeness of the world of myth to the actual world" (Robert Bellah, quoted in the The Cambridge Encyclopedia of HUNTERS AND GATHERERSIntroduction).

In this early stage, shaman, who were part-time religious practitioners, were able to travel the gap between humans and nature and communicate with spirits and with the dead due to their ability to alter their consciousness. Shamanism was widespread and common among hunter-gatherers. They were not so much priests but people with special powers who could help people in the tribe -- especially those with concerns relating to spiritual matters. While shaman were revered, their cultures were generally egalitarian (contemporary ones are according to The Cambridge Encyclopedia of HUNTERS AND GATHERERS) and they did not have the same authority that priests would have in later forms of religion.

Definition: Shamanism:  Shamanism is a practice that involves a practitioner reaching ALTERED STATES OF CONSCIOUSNESS [ED: my emphasis] in order to encounter and interact with the spirit world and channel these transcendental energies into this world.

Shamanism is another major practice common to the great majority of hunting and gathering peoples. The word originates in eastern Siberia, from the Evenki/Tungus word saman meaning "one who is excited or raised."  The Cambridge Encyclopedia of HUNTERS AND GATHERERS, Introduction

I find it telling that a key element of shamanism at this beginning stage of religious belief is an 'altered state of consciousness', since I believe that the emergence of normal human consciousness is what caused the need for religious practices. An altered state of consciousness would bridge the gap and allow the shaman to have a relationship with the spirit world. The shaman could then try to heal, if you will, the rift with nature that normal consciousness had created.

A shaman is a person regarded as having access to, and influence in, the world of benevolent and malevolent spirits, who typically enters into a trance state during a ritual, and practices divination and healing.Shamanism encompasses the premise that shamans are intermediaries or messengers between the human world and the spirit worlds.---Shamans act as mediators in their culture. The shaman communicates with the spirits on behalf of the community, including the spirits of the deceased. The shaman communicates with both living and dead to alleviate unrest, unsettled issues, and to deliver gifts to the spirits.

The Sámi’s believed “that the living and the departed were regarded as two halves of the same family.” ...their belief was not just a religion, but a living dialog with their ancestors

Primitive religions are on the whole oriented to a single cosmos...The distance between man and mythical being, which was at best slight, disappears altogether in the moment of ritual when 'everywhen' [ED: a term coined by anthropologist W. E. H. Stanner] becomes now. All present are involved in the ritual action itself and have become one with the myth.Primitive religious action is identification, participation, acting out. Just as the primitive symbol system is myth par excellence, so primitive religious action is ritual par excellence. In the ritual the participants become identified with the mythical beings they represent.In primitive ritual the individual is put in harmony with the natural divine cosmos.Robert N. Bellah, Religious Evolution

Of course, it is hard to determine when the emergence of consciousness caused the break with nature that was irredeemable. The most likely scenario is that as consciousness slowly developed, hunter-gatherers were able to keep and continue a sense of oneness with nature. Their survival depended on their ability to read the flow, the signs of nature -- when fish ran, animals migrated, plants bloomed, and when certain stars such as the Pleiades appeared. Hunter-gatherers lived off the land as they found it; they lived spontaneously. They lived in harmony with nature.

Tim Ingold stated: "Hunter-gatherers do not, as a rule, approach their environment as an external world of nature that has to be 'grasped' intellectually ... indeed the separation of mind and nature has no place in their thought and practice." Willerslev extends the argument by noting...that the animist self identifies with the world, "feeling at once within and apart from it so that the two glide ceaselessly in and out of each other in a sealed circuit."

Adam tilling the ground after his expulsion from Eden, from The Story of Adam and Eve by Boucicaut Master circa 1400.

It seems likely that the break with nature came as farming and sedentary Neolithic thinking encroached on the earlier nomadic way of life. The Neolithic point of view required planning, control and a new sense of time which separated it from the earlier hunter-gatherer lifestyle.

The arrival of the new stone age, the Neolithic, was the single most momentous shift in all of our history. It was the moment we stopped being hunter-gatherers roaming from place to place and became farmers tied to the land and to the seasons. Everything we consider part of the modern world...all of that has its roots in the Neolithic.It was also to profoundly alter our sense of ourselves as human beings, as part of the natural world...It would change the land, the things we ate. It would change our relationship with time.  Neil Oliver, Archaeologist, A History of Ancient Britain, BBC Two

Rather than being part of the environment, Neolithic people made their own environment on their farms. The areas beyond the fields and houses of the Neolithic villages began to be seen as wild and untamed. This division created "a wound of awareness" or the "pain of consciousness" [my phrases], a break with their earlier sense of belonging in which they were a part of nature -- which was perhaps a romanticized memory of a former Garden of Eden.

A new kind of religion in Neolithic cultures provided a way for that wound to heal -- but like a broken leg or arm, the point where the break occurred would mend, yet it would always be scarred.

It is sometimes said that animist worldviews are unitary, totalized, and seamless...Animist worldviews neither recognize nor use a series of dichotomies that we tend to take for granted and which are prevalent, if not dominant, in modernist worldviews. These dichotomies include (but are not limited to):Nature/SupernaturePhysical/MetaphysicalMatter/SpiritMaterial/Ethereal....It is my contention that these conceptual dualisms arose in conjunction with and as a consequence of the Neolithic transition. [ED: My emphasis] The process, I surmise, began with the newly built environment featuring the settlement and house. From this materiality flows ideas about inner/outer and private/public. In these seemingly innocent dualisms we find conceptual seeds that will eventually sprout into ideas about property, ownership, wealth, and distinction.  UNITARY ANIMIST WORLDVIEWS

During this [Neolithic] period it does seem that for the first time we began to think of ourselves as separate from the natural world which is sometimes in opposition to us and which we need to control. From now on it becomes important to appease the enormous communal effort was required to impress these invisible beings, an effort that shaped the beginnings of organized religion, and created the first divine beings or gods. Now magic and ritual are shared among thousands to invoke “Cosmic Maintenance.” The collaboration from the unknown worlds to ensure and improve survival in the known world becomes the new way to understand and think about solutions to problems of survival

In this stage of human culture, in this Neolithic age of sedentary farming, it appears that over time the powers of nature became personified as gods and spirits. It also seems likely that an upper caste of divine priests developed. These officials with high authority were a reflection of the more complex farming culture, new stone age technology and increasing specialization as well as the fact that now much larger communities shared the religion.

BTW I find it interesting that quite learned Biblical scholars, such as Isaac Newton, James Ussher, Johannes Kepler in the 17th century, made an effort to determine the age of the Earth based on the Bible. They made careful calculations using the information in Genesis and came to the conclusion that according to the Old Testament the world was created about 4000 BCE or around the start of the Neolithic Era -- just when many scholars believe religion as we now know it, such as Judaism, began.

With the arrival of city-states and empires, the gods became more stratified and hierarchical, reflecting the structure of the civilizations -- such as the religions and gods of Babylon, Egypt, Greece and Rome.

This Greek pottery depicts a dead hero being carried by the Greek god of Death, Thanatos, while being helped by Hypnos (Sleep) as Hermes looks on.

During the last 400 years with the emergence of science and technology, the inner world of humans has grown, civilization has expanded and our store of conscious scientific knowledge greatly increased. As a result the outer world of nature -- we even speak of it as 'outside' -- has become even more remote. People, in a sense, now live inside their virtual man-made worlds and often see the forces of nature as things to be subdued or controlled.

Yet from the beginning, there has always been a deep felt need to belong, to be a part of something larger, to feel a oneness with the cosmos, to find a “place in the universe” as Carl Jung said. Religion through its symbols and rituals satisfies that need -- and by connecting people to a spiritual divine world that is timeless and boundless, religion is comforting and for most people, essential.

In this brief transit where the dreams cross
The dreamcrossed twilight between birth and dying...
This is the time of tension between dying and birth
The place of solitude where three dreams cross...
Suffer me not to be separated
And let my cry come unto Thee.
TS Eliot, Ash Wednesday 

     Diagram of the conscious mind by Robert Fludd, died 1637.

Please Note: All pictures are from

Tuesday, March 17, 2015

Computing the Winter Solstice at Newgrange: Was Neolithic Science Equal To or Better Than Ancient Greek or Roman Science?

Measure what is measurable, and make measurable what is not so.
Galileo Galilei
The purpose of this article is to compare the scientific accuracy and precision of two methods of determining the day of the winter solstice: that of the Neolithic builders of the Newgrange passage tomb in Ireland around 3000 BCE and that of the Roman Empire 3000 years later around 0 CE. It is my contention that the Neolithic method of capturing light in a massive 'spot dial' was equal to or superior to the Roman method of sighting the sun at noon over a period of days and then interpolating the time of the solstice. I believe I can support this argument with available research.


But before I make my argument, I would like to give my readers a bit of background and a personal story.

Once when I was teaching an advanced photography workshop, my class went on a field trip to the Duke greenhouse in Durham, NC in the winter. As we walked in, a student saw a flower in perfect light, lit by a shaft of sunlight coming down through the leaves of vegetation above it. He reached for his camera but then realized he was at the end of a roll of film, so he quickly rewound the exposed roll and put in a new one. But when he turned around about a minute later the flower was in shadow and the shaft of light had moved onto a leaf next to it. It was then that I realized how quickly the sun moves and how precisely moving light from the sun could be marked.

As a professional photographer for 40 years and the author of 3 books about the craft and art of photography along with a MA in Media, I understand how light works. Photography (literally meaning 'light drawing' from the Greek) is the medium of light. Photographers are craftsmen and artists who work with light and because of this, I believe photographers are more sensitive to light and its effects than non-photographers. So it is with this background I approach the subject of the remarkable 'light instrument' at the Newgrange passage tomb.

See my resume at:


The sun's declination during a year viewed from the side. (

The sun's declination during a year viewed head on. (

The Duration Of The Winter Solstice

...the sun appears to halt in its incremental journey across the sky and change little in position during this time.
National Geographic
It is important to note that at the winter solstice the sun barely moves (i.e., the sun's declination). In fact the word solstice means just that. It comes from the Latin 'solstitium' meaning "point at which the sun seems to stand still" ( While modern scientific explanations assert this happens only on one particular day and after that the days get longer -- this is not quite true. The length of the shortest day and longest night can remain almost the same (within a few seconds) for about week.

Because the sun 'stands still' for a number of days with very little movement,
it is hard to determine the precise day that the solstice occurs. 
The changes in Solar declination become smaller as the sun gets closer to its maximum/minimum declination. The days before and after the solstice, the declination speed is less than 30 arcseconds per day which is less than 1/60 of the angular size of the sun...This difference is ... impossible [ED: to detect] with more traditional tools like a gnomon or an astrolabe [ED: ancient tools the Romans and Greeks would have used]. It is also hard to detect the changes on sunrise/sunset azimuth due to the atmospheric refraction changes. Those accuracy issues render it impossible to determine the solstice day based on observations made within the 3 (or even 5) days surrounding the solstice...


Measuring the difference in the sun's movement at the time of the solstice was impossible with Greek and Roman tools and is barely "detectable with indirect viewing based devices like a sextant equipped with a vernier" which were not available until the 18th century. (

The following was the method almost certainly used by the ancient Romans & Greeks:
It is most likely, then, that equinoxes and solstices were determined by observing noon solar altitudes for a series of days before and after the events. [ED: my emphasis] When the Sun is crossing the meridian at noon, it is relatively easy to measure its altitude, and then knowing the geographical latitude, to compute the declination. From the declination, it is easy to compute the Sun’s position on the ecliptic (the longitude), and we know that Hipparchus knew how to do it. But it is only at noon that such an easy determination is possible. It is then fairly straightforward to estimate the time that the Sun’s declination reaches some specific targeted value: 0° for an equinox, and maximum or minimum for a solstice.That series of daily altitude measurements were used to determine the time of cardinal events can hardly be doubted, even though no surviving ancient source has documented such an episode. Especially for the solstices, it is essentially the only viable option... [ED: my emphasis]
Dr. Dennis Duke, Four Lost Episodes in Ancient Solar Theory, Journal for the History of Astronomy, (2008)


The Newgrange winter solstice alignment was first observed by renowned archaeologist, Professor Michael O'Kelly about 50 years ago:
Over the course of the early excavation, some of the many local visitors would often tell the O'Kelly's of a tradition, that the rising sun, at some unspecified time, would light up the triple spiral stone in the end recess of the chamber at Newgrange. 
Some minutes before sunrise on the 21st of December 1967, Professor O'Kelly stood alone in the darkness of the chamber at Newgrange, wondering what, if anything, would happen. To his amazement, minute by minute, the chamber grew steadily lighter and a beam of sunlight began to enter the passage and to travel inwards, "lighting up everything as it came until the whole chamber – side recesses, floor and roof six metres above the floor – were all clearly illuminated".

Entrance to Newgrange -- the critical roof-box is above the entrance. (

Overhead diagram of Newgrange passage and solstice light. (Irish Art History Section, Professional Development Service for Teachers, P.D.S.T., Ireland)
Diagram of Newgrange passage and solstice light from the side. (Irish Art History Section, Professional Development Service for Teachers, P.D.S.T., Ireland)

After about 50 years since it was first discovered, there is now general agreement that the passage and chamber at the Newgrange passage tomb in Ireland is aligned with the winter solstice and that around the time of the solstice and only then, light falls down the long passageway to the farthest part of the chamber.
Once a year, at the winter solstice [the sun] shines directly along the long passage into the chamber for about 17 minutes and illuminates the chamber floor. This alignment is too precise to be widely considered to be formed by chance...Today the first light enters about four minutes after sunrise, but calculations based on the precession of the Earth show that 5,000 years ago, first light would have entered exactly at sunrise.
Document of the US space agency NASA.
The key piece of the Newgrange design was a 'roof-box' or 'light-box' which controlled the way light came into the passage. It was built with carefully crafted baffles that restricted the entry of light to the time of the winter solstice and also so that the light only came in at sunrise.
For 17 minutes, therefore, at sunrise on the shortest day of the year, direct sunlight can enter Newgrange, not through the doorway, but through the specially contrived slit that lies under the roof-box at the outer end of the passage roof.
O'Kelly, Michael J., and Claire O'Kelly. Newgrange: Archaeology, Art, and Legend.
Roof-box that controls the light coming into the passage during the solstice.  (

Shaft of light going into the passage. Used with permission: photo by Anthony Murphy,

Triple spiral carved in a stone in the chamber at the end of the passage. According to legend, the light from the sun illuminated these triple spirals on the day of the solstice. Used with permission: photo by Anthony Murphy,


As a photographer it struck me, that the setup at Newgrange is very much like a camera: there is an opening with a lens or aperture, there is a dark chamber (the word camera is derived from the Latin, camera obscura, meaning ‘dark chamber’), there is an exposure (a period of time that light is allowed into the camera and then shut off), i.e., the 17 minutes that the light shines down the hallway each morning and only during the time of the winter solstice. Plus, like a camera there is a point of focus, i.e., the day of the solstice when legend has it that the light shines down to the furthest chamber and illuminates the stone with triple spirals.

In fact, the Newgrange instrument has many similarities to a pinhole camera whose origins go back into prehistory. For example, it was already a well known phenomena when it was examined by Aristotle in the fourth century BC. The discovery of the pinhole effect is based on a common occurrence:
The camera obscura [ED: pinhole camera] works on a naturally occurring phenomenon...and can, for example, often be observed when sunlight filters through dense leaves.
Because of Newgrange's striking similarity to a camera, I dug a bit deeper on the Internet and found the following by Martin Brennan, a respected researcher, who discovered the following about a Neolithic structure related to and not far from Newgrange:
In 1980 Irish-American researcher Martin Brennan discovered that Cairn T in Carnbane East is directed to receive the beams of the rising sun on the spring and autumnal equinox - the light shining down the passage and illuminating the art on the backstone. The Cairn T alignment is similar to the well-known illumination at the passage tomb at Brú na Bóinne (Newgrange), which is aligned to catch the rays of the winter solstice sunrise.
Here is what Martin Brennan said about his discovery:
Suddenly, I stared in amazement as this beam of light began to register against a stone bearing measured inscriptions. As the day progressed, the beam of light slowly moved from west to east across the stone, the sequence being measured by the inscriptions. This observation provoked a chain reaction of intriguing thoughts. First of all, if there was any sundialling, it was advanced sundialling. They were using a ray of light. This is called a "spot" dial and it is a considerable advance over using a shadow. Secondly, a gnomon, which is simply a stick used to cast a shadow, is thought to be the first scientific instrument and its earliest uses can be placed over twenty thousand years ago, back in the Ice Age. A progressive development of this leading to the use of a spot dial could exploit the full potential of the instrument and its astronomical implications.
A spot dial is, in a sense, the opposite or negative of a traditional sundial, i.e., it is the reverse of a sundial that casts a shadow. Instead of capturing a shadow that is cast by the sun, a thin beam of light from the sun is captured in a dark chamber where it can be closely studied.


The spot dial at Newgrange magnified the movement of the sun at the winter solstice when the sun's movement was particularly hard to detect. With the right construction the movement of the sun can be magnified significantly. Here is O'Kelly's description of the movement.
...minute by minute, the chamber grew steadily lighter and a beam of sunlight began to enter the passage and to travel inwards, "lighting up everything as it came until the whole chamber – side recesses, floor and roof six metres above the floor – were all clearly illuminated"
In addition O'Kelly also stated that in 17 minutes the 'first pencil' of direct sunlight widened to a 17cm band and then narrowed before disappearing entirely. (O'Kelly, Michael J., and Claire O'Kelly, Newgrange: Archaeology, Art, and Legend)

However, J. Partrick, who investigated the alignment, at the request of Professor O'Kelly, found that originally the maximum width of the light would have been 40cm. The beam of light is now only 17cm because "...some of the stones are now leaning inwards, thus trimming down the width of the beam of light." (J. Patrick, Midwinter sunrise at Newgrange, Nature, 1974)


At exactly 8.54 hours GMT the top edge of the ball of the sun appeared above the local horizon and at 8.58 hours, the first pencil of direct sunlight shone through the roof-box and along the passage to reach across the tomb chamber floor as far as the front edge of the basin stone in the end recess. As the thin line of light widened to a 17 cm-band and swung across the chamber floor, the tomb was dramatically illuminated and various details of the side and end recesses could be clearly seen in the light reflected from the floor. At 9.09 hours, the 17 cm-band of light began to narrow again and at exactly 9.15 hours, the direct beam was cut off from the tomb. For 17 minutes, therefore, at sunrise on the shortest day of the year, direct sunlight can enter Newgrange...
O'Kelly, Michael J., and Claire O'Kelly. Newgrange: Archaeology, Art, and Legend. 
I would like to have very exact figures, such as the width of the beam of light every 5 seconds, as well as the position of the light on the walls and floor. But these figures are not available. However, with the figures we do have, we can do a rough estimate of the rate of the sunlight's movement.

I am guessing that the light spread from an original 4cm to 40cm at its maximum (the estimated original maximum as computed by J. Partick). Then according to O'Kelly, it took 11 minutes from the first pencil of light to reach the maximum width.

So:  Widening of light = 40cm - 4cm = 36cm or 360mm
Time it took to widen = 11 minutes = 660 seconds
So the movement of the light grew at this rate: 360mm/660 sec. = or about .5mm every second or about 3cm per minute (a little more than 1 inch per minute).

This means that the movement of the light was significantly magnified, enough to study it and to use that information to make a determination about the day of the winter solstice.

The above refers only to the widening of the light and not the movement of the band of light from one side of the passage to the other -- which I do not have any data for, but which would be an additional indicator for this instrument.

I believe that with this kind of magnification, it would be possible to make fine distinctions that could pinpoint the actual day of the solstice in real-time -- if the sky was clear.

A magnified display of the sun's movement is possible with large structures and the figure of .5mm per second is consistent with another large sundial, the Giant Sundial of Jantar Mantar in Jaipur, India.

"The Giant Sundial of Jantar Mantar in Jaipur, India, also known as the Samrat Yantra (The Supreme Instrument), stands 27m tall. Its shadow moves visibly at 1 mm per second, or roughly a hand's breadth (6 cm) every minute."


One supposition that emerges from these studies of monuments incorporating astronomical alignments is that many of them became “special” when the astronomical body in question appeared at the appointed place. At these times, their sacred power was surely reinforced. Another way in which a similar effect could be achieved -- creating a very considerable visual impact at certain special times -- was through the interplay of sunlight and shadow.. A famous example occurs at the passage tomb of NEWGRANGE in Ireland.
What was the purpose and meaning of such hierophanies (ED: meaning "to bring to light the sacred" from the Greek]?  By carefully placing rock art designs, sunlight could be made to play across them at certain times, with impressive effect. The Luiseño [ED: a California Indian tribe], for example, had an intense ceremonialism, a rich sky lore, and a calendar regulated by various astronomical observations. Although their seasonal calendar was lunarbased, they observed and celebrated the solstices, attaching particular importance to the winter solstice, which they regarded as a time of cosmological crisis.
Dr. Clive Ruggles, (Professor of Archaeoastronomy), Ancient Astronomy: An Encyclopedia of Cosmologies and Myth


"Today the first light enters about four minutes after sunrise, but calculations based on the precession of the Earth show that 5,000 years ago, first light would have entered exactly at sunrise."
Document of the US space agency NASA.
Detailed drawing of Newgrange passage showing the precise placement of stones and the shaft of solstice light. Used with permission: 
First, the roof-box is an anomalous feature without any obvious function in utilitarian terms (as it seems to us). Second, if the gap in the roof-box were merely 20 cm [8 inches] lower or higher, or the [lower] passage a few metres [10 feet] shorter or longer, then sunlight would never have entered the chamber.
Dr. Clive Ruggles, Astronomy in Prehistoric Britain and Ireland Astronomy in Prehistoric Britain and Ireland
Speaking of the original alignment 5000 years ago:
Originally, the beam would have struck the rear chamber orthostat (C8) and, possibly, would have been reflected onto another chamber stone, C10, which contains the famous triple spiral. 
Anthony Murphy, quoted from a lecture to Astronomy Ireland in January 2002
The Ancient-Wisdom website in the UK made this comment:
The Light-box/Roof-box - Above the entrance passage is a 'light-box', which precisely aligns with the rising sun at the winter solstice of 21st  December, so that the rays touch the ground at the very centre of the tomb... Many of the upright stones along the walls of the 19m (62ft) passage, which follows the rise of the hill, are richly decorated.
A researcher who took photographs at Newgrange over a number of days surrounding the winter solstice has this to say:
I noticed from my photographs that it [ED: the shaft of light] was in a different position each day. As the solstice approached the beam of light seemed to penetrate further each day, beginning on the left and ending on the right. However after the solstice the beam withdrew from the furthest point of entry and penetrated the central chamber less each day until it eventually failed to enter the central chamber at all.
Tim O'Brien
Tim O'Brien also said:
"The construction features of Newgrange provide the ideal environment in which to study the minute movement of the sun when it is at visual standstill." 
Writing about another but related Loughcrew Neolithic passage tomb in Ireland:
"As the sun shines directly onto the symbols engraved on the backstone they act not just as primitive representations of the sun, but as devices precisely positioned to measure solar movement."
Dr. Kate Prendergast made this point about its precision:
Further research has demonstrated just how precise this alignment is. Patrick (1974) has proved that the winter solstice orientation was operative when Newgrange was constructed, and therefore is an original, central and permanent feature of the monument. O’ Brien (1988) has shown that the chamber and passage are sophisticated and complex constructions, designed to maximize the accuracy and length of the beam of light coming into the chamber. His research indicates that at the time of construction, the beam of light entering the passage at Newgrange was so precisely framed by the roof-box that it could be used to calculate the day of the solstice itself. In short, Newgrange was precisely aligned on the winter solstice rising sun in such a way it could be used as a ‘clock’ to calculate the exact moment of the solstice. [ED: My emphasis]
Dr. Kate Prendergast, The Neolithic Monument of Newgrange in Ireland: A Cosmic Womb? 


I believe this device could have determined the day of the solstice even during cloudy periods, and when the sky was clear, it might have been able to pinpoint the day of the solstice in real-time.

Since the weather in Ireland is unpredictable, the Neolithic Newgrange astronomers, nevertheless, would have been able to determine the specific day of the winter solstice even if it was cloudy or rainy. They could do this by noticing the pattern of light on clear days before and after the solstice when the light was advancing and receding. Then they could make a determination by interpolating, a method very similar to that of the Romans who, as I have said, calculated the actual day of the solstice after the fact by making a number of observations followed by interpolation.

O'Kelly has remarked that in the years since he discovered the Newgrange solstice alignment, there has always been at least one clear day during the period surrounding the solstice. (O'Kelly, Michael J., and Claire O'Kelly. Newgrange: Archaeology, Art, and Legend)

However, when the sun was out and the days were clear, I believe that it was possible for the astronomers at Newgrange to determine the day of the solstice in real-time, something which was not possible for the Romans or the Greeks.

If we can view the Newgrange structure and winter solstice alignment as an instrument, then we can say the following:
Light at sunrise near the time of the solstice was at first restricted to a narrow beam that went down a narrow hallway where it spread out, but in a controlled manner. This 'device' was very much like a magnifier that could enlarge and exaggerate the movement of the sun at a time when detecting movement was particularly difficult. Everyday the angle of the light changed along the walls and floor, and the light advanced further or retreated.

It is, therefore, possible that Neolithic astronomers could have made a determination about the day of the solstice with the following data their instrument had gathered: the entry point of the light, the length of time the light shown, the angle and amount of the light on the walls and floor, the width of the light, the rate at which the beam of light widened and contracted and possibly the quality of the light and shadows on the deeply grooved triple spiral stone and other stone carvings.


This Neolithic instrument at the Newgrange passage tomb in Ireland, that was designed to measure the sun's movement around the time of the winter solstice, was possibly equal to or superior to ancient Greek or Roman methods of measuring the day of the winter solstice.

It seems possible that the Newgrange instrument could determine the exact day of the solstice:
  •  If The Weather Was Cloudy: by measuring a one or more days near the time of the solstice and then calculating with interpolation the precise day of the solstice -- similar to what the ancient Romans and Greeks did but possibly requiring fewer days of observation to make a correct calculation
  • When The Sky Was Clear: on the exact day of the solstice by observing the character of the band of light -- something which the ancient Romans and Greeks could not do
Today it might be possible with computer simulations to test out these hypotheses. Hopefully in the future, this will be done.


These sundials demonstrate that with the right construction and design, sundials can be extremely accurate.

A precise modern sundial that is correct within 30 seconds all year long -- showing that sundials can be quite accurate when constructed properly.  (

"Precision Sundial at the Carl Zeiss Planetarium in Stuttgart. Martin Bernhardt created a special gnomon for an equatorial sundial which adjusts for the equation of time and that allows one to read the time without knowing the date, to a precision of less than a minute."