Tuesday, February 7, 2012

How big is the Universe?

Mankind has always had a drive to see what is on the other side of the hill. “To go where no man has gone before” (Roddenberry, 1964). How we perceive the Universe tells us as much about ourselves as the Universe. Our desire to explore, to know, and to understand is at the core of us as a species. Why study questions about the Earth, the Sun, and the Universe? What good does does it do for us? Hans Reichenbach explored these questions on the first few pages of his book, From Copernicus to Einstein. “We do not want to go blindly through the world. We desire more than a mere existence. We need these cosmic perspectives in order to be able to experience a feeling for our place in the world. The ultimate questions as to the meaning of our actions and as to the meaning of life in general tend to involve astronomical problems” (Reichbach, 1970, p. 11).

As we study the Universe, we study ourselves. This was talked about in Eugen Herringel’s book “Zen and the Art of Archery” where he said "In the case of archery, the hitter and the hit are no longer two opposing objects, but are one reality” (Herringel, 1971).

Literally, the biggest question we can ask is just how big is the Universe? As our understanding of the world we live in has grown, the scope of our ideas about the size of the Universe has grown. This paper will explore the ideas of the ancients, the Greeks, the Renaissance, and the modern era to try to come to some context of how the ideas of how  the Universe is has changed over time, and why those changes have been important.

Ancient people didn’t have books to read, or television to watch. They lived outside all day and night long. Once it got dark, they had nothing else to do but watch the skies. As the Sun set, the stars appeared to replace the blue sky, brightest stars first. These stars appeared to also rise in the east and set in the west. The Moon rose in the east and sat in the west. The evidence of their senses says that they were standing still, and that the sky holding the Sun and the stars wheeled overhead (Reichenbach, 1970, p. 13).  The circular motions and appearance of the heavens inspired the idea that the circle was the perfect shape.  This idea would be fundamental to astronomy for thousands of years.

The ancients decided, based on what they could see, that the entire Universe was a dome over a small piece of land. A blue dome and a clear dome with holes in it that allowed the heavens to shine through. The Sun, Moon, and planets all rested when you couldn’t see them. Everything had a spirit inside it that animated it and directed the object’s motion.  They thought that the Universe was small enough to walk to the edge, and unless you were very careful, you could fall off the edge into nothingness.

They noticed patterns in the sky repeating every day, every month, every year. They noticed patterns that repeated every 18 to 19 years when the Earth, the Moon, and the Sun came back into almost the same alignment (Armitage, 1947, p. 14-17). People used these patterns to know when to plant food, when to harvest, and how to travel across the expanses of wilderness that surrounded them. The civilizations that allowed people to study and learn about the Universe were more successful than civilizations that did not. With this knowledge came mastery over the physical world. Such knowledge became concentrated in a priest class of philosophers. “Egyptian astronomers had discovered that when the bright star Sirius could just be seen rising in the east before the Sun, the flooding of the Nile was imminent. Such knowledge gave tremendous power to the priesthood and inevitably involved its members closely with the state” (Shawl, Ashman, & Hufnagel, 2006, p. 84).

The Sumerians, and later the Babylonians, recorded very accurate observations about the positions and appearance of the stars, moon, Sun and planets. This information was transferred to the Greeks as scholars moved from the ruins of the Babylonian empire to the thriving Greek empire.

“They [the Babylonians] also took over the Sumerian number-system, a fact of great scientific importance, since this used a place-value notation, just as does our own system (unlike that of Roman numerals). The difference is that where we work to a scale of 10, they took a scale of 60” (Norton, 1995, p. 21).

This base 60 system is still in use today, in degrees of a circle, the minutes, hours, and seconds of the day, and the minutes and seconds of latitude and longitude (Norton, 1995, p. 21). Base 60 is convenient because it can be divided into 2,3,4,5,6, 10, 12, 15, 20, and 30 even sections. But the concept of a placeholder would be further developed in the middle east and come back to us at the end of the middle ages.

The Greeks added their own observations to the centuries of accumulated data and came up with the theory that the entire Universe spun in large spheres with the Earth the center of everything.   They calculated the distance to the Sun at greater than ten million miles and thought that the sphere containing the stars was even further away.   Twenty million miles across was the size of their Universe, a figure too vast to really understand.

This Geocentric view of the world was brought to major prominence in the world of a scholar named Ptolemy. His master work called “The Almagest” was the standard astronomy book from around 200 ad until the 14th century (Ptolemy, 160ad). The Ancient Greeks had a good idea that the world was round, even calculating its radius amazingly accurately with the tools they had at hand.  But even to the Greeks the thought that the Earth was moving was totally against reason.   Ptolemy argued against the Earth moving because the air and the birds would be stripped away from the Earth if the Earth were moving (Reihenbach, 1970, p. 15-16).

In 1901 an amazing device was found in the shallow waters of the Mediterranean. The finding was so incredible that it took almost a hundred years to be completely understood. It was a geared mechanism for predicting the motions of the Sun, moon, stars, and planets and could even predict the possibility of the occurrence of eclipses. “This finding is forcing historians to rethink a crucial period in the development of astronomy. It may well be that geared devices such as the Antikythera mechanism did not model the Greeks' geometric view of the cosmos after all. They inspired it” (Marchant, 2010).

The Greek clockwork view of the Sun, moon, and planetary motions were influenced by the devices they used to calculate the motions. If everything had a circular orbit around the Earth, then just simple gears could explain the motions. But they had to add extra gears to accurately model the motions of the planets and the Moon. These extra gears were called epicycles to explain the retrograde motions of some of the planets when the Earth was between the Sun and that planet. This clockwork view of the Universe would persist for over eighteen hundred years, only recently being overturned recently by fundamental quantum mechanical theories about how atoms work.

The knowledge to build such complicated devices faded from human ken, not to be rediscovered until the 18th century.  Any remaining devices were melted down for their metal during this time, destroying all evidence of the knowledge.  No significant advances in astronomy would be made for the next 13 centuries. The Greeks declined and the Romans took over the Mediterranean. Progress in science slowed until it was almost stopped and much accumulated knowledge was lost (Shawl et al., 2006, p. 84).

This was a period of time characterized by a failure of economic systems, combined with a complete certainty that those in power not only knew what was right, but that they were infallibly correct. To question the official policies on anything was to risk facing the Inquisition, where one could be made to see reason with the rack, or with burning hot iron implements.

After hundreds of years some areas began to do better and this growth in economics fueled a new interest in science and astronomy. There were “new worlds” full of gold and new amazing foods and spices that had been discovered; whoever could chart a course to these distant locations, in the largest ships the world had seen to this time, could be assured of wealth beyond the dreams of avarice. This was the Renaissance.

A researcher we call Copernicus began to promote what is called the Heliocentric view of the Universe. This was where all the planets and the Earth rotated around the Sun. He was not the first to have this view, but the way he chose to ask the question led many others to consider his ideas (Armitage, 1947, p. 10). The very name of Copernicus now means a turning point in history. The work of Copernicus moved Earth from the center of the Universe, but it also moved man from the center of Earth. Man went from the center to being a speck on a speck (Reichenbach, 1970, p. 12). Copernicus required great independence of thought and great scientific knowledge to persuade his peers to accept his world view as true. Only and insight into a deeper understanding of nature lead him to discern these new approaches to reaching the truth (Reichenbach, 1970, p. 17).

At this time, a new number system came from the middle east, sweeping Europe and converting everyone over from Roman numerals to Arabic numerals. Astronomers led this change, because they had found the collected astronomical knowledge of the Sumerians, Babylonians, Greeks and Arabs preserved by the scholars in the Middle East. The knowledge of this superior system came with the information and was quickly adopted.  The Arabic number system is the number system we use to this very day.

Astronomy was useful in navigation, and navigation was very important to this resurgence of wealth and power. So astronomers lead this resurgence of science. Rich patrons built large, accurate devices capable of measuring the stars in one minute of arc, whereas the previous best was in degrees, a two order of magnitude improvement in the measuring of the locations of the stars and planets. One of these observatories was built and ran by a man named Brahe. His observations are at the limit that a human with superior eyesight can make with the naked eye. Kepler associated with Brahe in order to get access to the detailed, accurate observations the man had made over decades of painstaking work. After Brahe’s death Kepler took the work from Brahe’s heirs and used it for his own purposes (Shawl et al., 2006, p. 94).

Kepler tried again and again to match the predicted location with the actual observed data. But the measurements didn’t agree with the predicted values based on science that was known to be absolutely true at that time. This was not only bad from a theoretical standpoint, but the books of tables used for navigation were going out of date, and ships were ending up lost. This was costing wealthy men money.

Convinced that he was wrong, Kepler rechecked his calculations and tried to add in more and more epicycles to make the observations of the orbits match the predicted values. They always diverged. Finally, almost in desperation, convinced that he was wrong, Kepler threw away centuries of accumulated knowledge about epicenters and the celestial sphere and tried to calculate the orbits of the planets as if they occurred around the Sun. But the math was still wrong, the perfectly circular orbits around the Sun also did not agree with the predicted values. Circular orbits were based on the previous work of Copernicus. Even more desperate, Kepler took the step of assuming that the orbits were not circular. Instead they would be elliptical orbits around the Sun, with one focus at the Sun. An elliptical orbit is like a circle, but with two foci, instead of a single center like a circle. A circle can be thought of a special case of an ellipse with both foci at the center. I can’t emphasize enough about how huge a step this was. “At last after 8 years Kepler boldly rejected the hallowed idea that planetary motion must take place on circular paths, thus ending two millenia of tradition. He describes in his diaries the fear and trembling he suffered in his mind when he took this step” (Reichbach, 1970, p. 22).

The math finally worked out and the values that Kepler predicted matched with the accurate observations he had at his disposal. Kepler wrote letters to various people and his ideas spread to those in the small community of astronomers of his day, including Galileo.

The major problem with Kepler was that he was a mystic and many of his ideas were very far out and tended to drive people away from the truths he was pointing out, because he was also pointing out some wacky things that were obviously not real. A few of his many numerological ideas had merit and were called Kepler’s Three Laws. These formulas are still in use to this day and are taught in every introduction to Physics and Astronomy class. Later in his life Kepler wrote of his Three Laws: “At last I have found it, and my hopes and expectations are proven to be true that natural harmonies are present in the heavenly movements, both in their totality and in detail -- though not in a manner which I previously imagined, but in another, more perfect manner” (Reichenbach, 1970, p. 21).

Kepler and Galileo corresponded with each other and many other astronomers of their day and the basic consensus was that the Earth was a planet and all the planets orbited the Sun. Galileo was the first to point a telescope at Jupiter and had seen four moons orbiting the planet. This small system seemed to mirror the ideas of Copernicus, and Galileo supported the view that the planets went around the Sun in circular orbits (Drake, 1980, p. 43). Galileo did not invent the telescope, but he was the first to pioneer its use in astronomy. The telescope brought even more precision to astronomy than any previous method of observation, especially of the planets, and is the method we use to this very day (Reichenbach, 1970, p. 22). Galileo wrote to Kepler, “You would laugh if you could hear some of our most respected university philosophers trying to argue the new planets out of existence by mere logical arguments as if those were magical charms” (Reichenbach, 1970, p. 22).

Many people assume that Galileo got in trouble with the Inquisition because of his beliefs, but this was not true. What got him in trouble was the mocking attitude present in the letter to Kepler; an attitude apparent in a popular satirical book Galileo had published that mocked the established scientific views that the church held. Galileo had been told once before by the Inquisition not to publish such a book. The book was too much for the Inquisition and they called Galileo before them again. After being show the hot coals and pokers for his eyes if he should ever make a mistake again, Galileo was placed under house arrest for the rest of his life. He was going blind because of his research on Sun spots. He was able to correspond with some of his astronomy friends, but he never published another book.

But the damage had already been done. The book Galileo had published, as well as the books several others also published, changed the public perception of Earth’s place in the Universe. We went from being the center of the Universe to just one of many planets circling the Sun.  This meant that the stars were now a vast distance away, so far away that even the distance of a half a year of Earth’s orbit would show a parallax shift.

Galileo once said “What has philosophy got to do with measuring anything?” (Drake, 1980, p. vi).  This shift from philosophy to science driving our view of the world was as huge a perceptual switch as the dethroning of our place in the Universe. More shifts were at hand in the lifetime of Galileo, less dramatic, but no less important. Newton was considered a great unifier because he pulled together all the theories of the day into a single set of basic laws. He extended the works of Kepler, Galileo and others, invented even better telescopes, and changed our world view of how gravity and momentum worked. He created three laws of motion that defined exactly how motion works and described the math that models how the planets circle the Sun and interact with each other. It was no longer magic, or spirits that moved things, but the force of gravity (Shawl et al., 2006, p. 99-105).

One of the many fields that Newton studied was light. He never succeeded in explaining how light worked, but he did set the stage for others to expand on his work. One of the reasons he invented the reflecting telescope was to compensate for the color fringes that occur in refracting telescopes.  These color fringes are actually caused by photons of light moving in waves and slowing down in the denser media at different rates depending on their frequency.  For several hundred years after Newton, people tried to understand how light worked.  This was not discovered for decades later when people began researching the rainbow that a prism makes.

Many people added bits and pieces and many theories were disproved. Ironically, the next level of understanding about our Universe came from looking at how the smallest parts of the atoms work: the electrons, protons, and neutrons. Everyone knows about Einstein's formula “E=mc squared”, but this was not the work he was recognized for with a Nobel prize. Einstein performed fundamental work to understand the photoelectric effect. This is the effect that allows solar cells to make electricity. This basic understanding is what allowed others to build on Einstein’s work to create the quantum mechanical theories. The atom bomb was built using the same theories that underlie solar panels (Niaz, Klassen, McMillan & Metz, 2010).

Around this time, astronomers were calculating the distance to the nearest stars and their speed. In 1929, a man named Edwin Hubble calculated the redshift and speed relative to the Earth of many stars, over a decade of observations. When he plotted the graphs out, he found that the further away something was, the faster it was moving away from us, or us away from it (Shawl et al., 2006, p. 615). If you calculate backwards, this means that everything would meet at a single point sometime in the past. This led to the development of the Big Bang theory, where we all came out of a single point (a singularity) and have been moving away every since. This set the age of the Universe to 10 Billion years and our distance from the center (Shawl et al., 2006, p. 617).

At this time we were also realizing that we were part of a larger collection of stars called a galaxy. Just like many of the galaxies we could see in the distance with our telescopes. And not the center of the galaxy even. Just a nondescript star circling out along one of the many arms.  We could see to the edge of our own galactic core around 30,000 light years away.  There were bright objects that appeared even further out.  Like a man in a foggy street, how far we could see appeared to be how big the Universe was.

Currently theory is racing ahead of popular beliefs about the world.  String theory and quantum mechanics is not easy to describe or understand. There are no simple formulas and no easy definitions. Instead of there just being three subatomic particles, suddenly there are dozens, each named strangely and with strange properties associated with them. Worse, these particles don’t move or appear like normal every objects seem to operate.  If you know where the object is, you don’t know how it is moving.  If you know how it is moving, you don’t know where it is.  Because of the confusion surrounding this new science and the esoteric research being done in this area nobody is famously associated with the development of the science. Einstein denied quantum theory to the end of his life, despite his work with its development, saying “God does not play dice” (Hawking, 2001, p. 24-26).

We know that we are currently in an expanding Universe based on Hubble’s red shift research. But would we eventually slow down and begin to fall back onto ourselves, ending in fire, in another big bang as we thought the Universe started? Or would we continue to expand forever, slowly drifting off, everything getting colder and slower and the Universe ending in ice? As we built better instruments and looked further away, we saw more and more galaxies, as many galaxies in the sky as stars in our galaxy. The better instruments we built, the further we could see and the further something is, the faster it is moving away from us. And the rate increases the further away we are. So it appears that we are accelerating faster and faster.   Given enough time the Universe is effectively infinite in size, according to the current theories.

But from where is this acceleration coming? Acceleration is caused by force being applied to mass, according to Newton’s Second Law. A search began for the source of this extra force that appeared to be accelerating everything away from everything else at an ever increasing rate. In checking their numbers it appeared that everything we saw weighed much more than we thought it should. There appeared to be a lot of “dark matter” that we cannot see. For every 17 kilograms of matter we can observe, there appeared to be 83 kilograms of dark matter that we cannot see. Nobody knows what this dark matter is, or where it is hiding. Theories abound. Any future theories about the size and shape of the Universe will have to account for this hidden mass ( Cho 2011).

Aristotle said, “Knowing yourself is the beginning of all wisdom.” The more we know about ourselves, the more it tells us about the Universe. The more we know about the Universe, the more it tells us about ourselves. Socrates said, “The more I learn, the less I know that I know.” Right now, we are unsure about many things in the Universe. Just as we are unsure about our future on this planet. It seems that our culture is in just as much upheaval as our theories about the Universe.

I wish I could tell you that the Universe is a certain size. It seems that instead of making things simpler this paper has managed to just ask more difficult questions. Over the course of recorded history, lead by the breakthroughs of a handful of brilliant, determined people, we are finally in the position to at least know what questions to ask. It is a great time to be alive. Revolutionary work is going to be done in the most basic of sciences, changing our view of our place in the world several more times. Changing even the most basic understanding of the world, and of the stuff from which it is made. Everyone studying science is part of this great endeavor. Anyone of us could be the one that looks at some small discrepancy in a measurement and realize some new basic truth that changes humanities perception of the Universe.

A revolutionary understanding about the Universe and our place in it would give a new determination in going forth and beginning to finally live in this Universe that we have passively observed for so long. Just as the Wild West was settled by those that believed they had a manifest destiny, so would having a firm belief in ourselves finally allow us “To boldly go where no man has gone before” (Roddenberry, 1964).


Armitage, A. (1947) The World of Copernicus. Signet Science Library.
Cho, A. (2011) Curious Cosmic Speed-Up Nabs Nobel Prize. Science [serial online]. 7 October 2011;334(6052):30.
Drake, S. (1980) Galileo. Hill and Wang.
Hawking, S.W. (2001) The Universe in a nutshell. New York : Bantam Books.
Herringel, E. (1953) Zen in the Art of Archery. Pantheon Books.
Marchant, J. (2010) Ancient Astronomy: Mechanical Inspiration. Nature, 25 Nov 2010.
Niaz M., Klassen S., McMillan B. & Metz D. (2010). Reconstruction of the history of the photoelectric effect and its implications for general physics textbooks. Science Education [serial online]. September 2010;94(5):903-931.
Norton, J. D. (1995) The Norton History of Astronomy and Cosmology. New York, New York.
Reichenbach, H. (1970) From Copernicus to Einstein. Dover Publications Inc.
Roddenberry, G. (1964) The Cage, Star Trek Pilot. NBC.
Shawl, S. J., Ashman, K. M., & Hufnagel, B. (2006) Discovering Astronomy. Kendal/Hunt Publishing Company.

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