Cosmos #3 Harmony of the Worlds

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of Wisconsin - Green Bay

In my opinion (and many others'), the best episode. The attention to historical detail and production values are amazing.

Astrology

Science or Pseudoscience?

Sagan distinguishes sharply between Astrology and Astronomy. Johannes Kepler was the first astrophysicist (someone who attempts to describe the heavens in exact physical terms) and the last scientific astrologer (someone who attempts to use the motions of heavenly bodies to predict human affairs). Kepler is the "last scientific astrologer" because after Kepler it started to become clear than natural forces governed the heavens.

Sagan uses the term "pseudoscience" to describe astrology. Pseudoscience is any belief system that attempts to gain credibility by falsely claiming to use the methods of science, or falsely claims to have scientific support. The conflict between science and pseudoscience is one of the recurring themes in Cosmos

Believers in astrology, of course, hotly deny that they are pseudoscientists, and accuse orthodox scientists of not having an open mind on the subject. Without getting sidetracked by the details of the conflict, here's a simple test. It's easy to picture what might convince scientists of the reality of astrology: repeated and reliable accurate predictions of events. Now, where is the astrologer who is willing to state what might disprove the validity of astrology? Just who in this conflict has the closed mind?

Falsification is one of the most widely applicable tests of whether a concept is really scientific. One of the most reliable indicators of the pseudoscientist is a reluctance to put his belief on the line and state what might prove it wrong.

The song "Age of Aquarius" from the 1960's musical Hair refers to the astrological belief that astrological signs pointed to an impending age of harmony and peace. The 1960's were a mixed time of real intellectual vitality and a tremendous boom in crank theories of all sorts. The binge of crank thinking continued through the 70's, abated somewhat in the '80's, and then resurged in the mid 90's.

Tracking the lunatic fringe is one of my major research interests and I have plans to put many of my findings on line, but have not done so yet.

Chinese astrologers and records

The stories of Chinese astrologers being executed for inaccurate predictions are of dubious historical accuracy. What is of undeniable historical value are the Chinese records themselves. Much of what we know about ancient visits of Halley's Comet, slowing of the Earth's rotation as deduced from ancient eclipse records, and historical supernova explosions comes from Chinese records.

Sagan's Counterarguments Against Astrology

Sagan criticizes astrology by pointing out that the gravity of the obstetrician when a baby is born is a lot greater than that of Mars: "Mars is a lot bigger, but the obstetrician is a lot closer." That's not entirely true. Imagine the obstetrician weighs 80 kg and is a meter away. Mars weighs 6.4 x 10^23 kg and is 200 million kilometers away on the average (2 x 10^11 meters). The gravitational pulls are proportional to mass divided by distance squared. For the obstetrician that figure is 80/1 or 80. For Mars it's 6.4x10^23/(2x10^11 x 2x10^11) = 16. It's actually surprising that Mars exerts fully one-fifth the gravitational pull of the obstetrician! At Mars' closest, 50 million kilometers (5 x 10^10 meters), Mars' gravitational pull is 256 - three times that of the obstetrician!

A more subtle point is that the Earth, moving through space, is in free fall, exactly the way astronauts in orbit are. The gravity of Mars, or any other body, affects everything on Earth exactly the same. Mars cannot say, move atoms around to cause genetic changes, because it pulls on every atom in your body with the same force. And if the planets exert physical changes, wouldn't conception rather than birth be the most likely time for them to be effective?

The criticism "How could it work?" has to be applied with caution. It is a valid criticism when some alleged phenomenon requires wholly unknown laws of nature, when we have fairly complete knowledge, and the evidence for the phenomenon is weak. In this case it's a strong criticism, because no known law of physics could do what astrology is claimed to do and there does not appear to be any evidence for radical new undiscovered laws of physics. However, the same criticism was once applied to continental drift, and it was a much weaker argument because our understanding of processes in the Earth's interior was much less complete and the evidence for continental drift was far stronger.

Constellations and Culture

Sagan points out that we live in "an in-between world" with the right mix of simplicity and complexity so that phenomena are interesting but understandable. Isaac Asimov's classic short story Nightfall is a good example of how science might have evolved on a different world. In that world, science develops on a world in a multiple star system. The movements of the six suns are very complex and provide perpetual daylight, so that the inhabitants never (almost never! - the whole point of the story!) see the stars or other planets. Their technology is in many ways Twentieth Century, but their astronomy and mathematics have only recently reached the level of Newton.

Sagan notes that in our world, "We can do science and with it we can improve our lives". This is a direct challenge to a lot of writers in the 1960's and 1970's who were extremely hostile to science. Here again, Sagan calls them as he sees them.

What we call the Big Dipper was a plow in medieval England and a wagon in Germany. It's an interesting coincidence that both the Greeks and many native Americans saw this group as a bear. The Greek word for bear, Arktos, is the origin of our word "arctic", denoting the region where the bear is high in the sky.

In ancient times constellations were pictures and patterns. Renaissance astronomers named new constellations for the sake of filling blank areas, honoring patrons, and getting into the history books. Stars not part of a constellation were termed "unformed" and once included about a quarter of all stars visible from the Northern hemisphere. Some stars, on the other hand, were part of two overlapping constellations. Modern astronomers have defined the constellations to cover the entire sky. There are 89 constellations; every star is included in one, and only one, constellation.

To see how true it is, as Sagan claims, that we put pictures in the sky, it is only necessary to look at star lore from other times and cultures. Some star groups like Orion and the Big Dipper are widely recognized; others are seen radically differently by other cultures. A few examples:

Many peoples have constructed observatories. The Anasazi observatories in the video are excellent examples. The stone spiral calendrical device, called the "Sun Dagger", was only discovered in 1978, just as Cosmos was being produced. An apparently natural settling of one of the boulders a few years ago has damaged the precision of the device. The locale is Chaco Culture National Monument in New Mexico.

Claudius Ptolemy; the Undeserving Villain

The treatment of Claudius Ptolemy in histories of science is one of the real scandals of academia. Ptolemy is somehow made a villain for coming up with a system so good that nobody could improve on it for 1500 years! One extreme work, The Crime of Claudius Ptolemy, even went so far as to allege that Ptolemy could invent such a system using faked data.

In reality, Ptolemy's system was more accurate and a lot less clumsy than often alleged. It accounted for the varying speed of the Sun's apparent motion in the sky, for example. From surviving copies of the Alfonsine Tables, we know that Ptolemy's system included only a few circles for each planet, not the 20 or more that have often been alleged.

The basic problem in planetary motion is that the planets don't move smoothly eastward among the stars. Instead they appear to stop periodically, reverse direction for a few months (called retrograde motion), then stop and resume their normal motion. Ptolemy imagined that the principal planetary motion was due to the planet moving in a large circle around the Earth (the deferent) and the looping motion was due to the planet moving on a smaller circle, the epicycle.

Medieval Astronomy

Ptolemy's works were discovered by the Arabs, and the Arabic title, the Almagest, has come down into English. It means "the great work" and is a corruption of the Greek title. The "mag" part is related to the Greek root "mega", as in "megaphone" or "megaton". By 1100 the Almagest was known in Europe. King Alfonso the Wise of Castile ordered astronomical tables to be created from Ptolemy's work. These tables, the Alfonsine Tables, were compiled in the late 1200's and were the standard in Europe for 200 years. (It is a myth that Alfonso said he could have come up with a simpler way to organize the Solar System) By the 1400's, however, they were out of date and no longer accurate. Orbital data for the planets simply wasn't accurate enough to allow accurate predictions over a span of centuries. Part of the stimulus for the work of Copernicus and others was the need to improve on the Alfonsine Tables.

Another problem was calendar reform. Julius Caesar reformed the Roman calendar, instituting Leap Year. He also set January 1 as the date of New Years'. The year had begun in March - September was originally the seventh month. He renamed the month of Quintilis after himself and took a day off February to make "his" month longer. His successor Augustus (see where this is going?) did the same to the month Sextilis. You can thank the Caesars for "thirty days has September..."

The reformed (Julian) calendar was good but still not perfect and by the 1500's the accumulated errors added up to 10 days. This was important to the Church because the date of Easter is determined astronomically. Christ was crucified just before Passover, which is the first full moon after the spring equinox. Hence Easter is the first Sunday after that. To predict the date of Easter it is necessary to be able to predict the motions of both the Sun and the Moon.

Pope Gregory XIII convened a panel of astronomers, who recommended dropping 10 days from October 1582 to bring the calendar back in line with the seasons (if you think people were upset over paying a full month's rent for a 21-day month, you're right. There were riots.) They also added a slight refinement: century years would not be leap years unless they were divisible by 400. Thus 1700, 1800 and 1900 were not leap years but 2000 will be - the rarest scheduled event in history.

Despite the problems between the Church and Galileo, the Church was solidly ahead of the curve on this point, and Protestant countries grudgingly fell into line over the years. England gave in in 1752. George Washington was born on February 11 in the old calendar, not February 22 (and definitely not on the third Monday in February!) Greece and Russia didn't adopt the revised, or Gregorian calendar until this century.

Sagan and the Middle Ages

Consider the following quotes from this video:

Reality check: the main events in the video took place around 1600-1620. This is:

This video takes place solidly in the Renaissance, not the Middle Ages.

Nicolas Copernicus 1473-1543

Nicolas Copernicus was the first modern astronomer to propose that the Earth revolves around the Sun. Sagan claims Copenicus' system worked "at least as well as Ptolemy's", but that's not true. How could it be? Copernicus had no new observational data; he was using the same data as the Ptolemaic System, plus his system lacked all the refinements of Ptolemy's system. What Copernicus did achieve was a great conceptual improvement. His system did so many of the same things as Ptolemy's, so much more simply, that it was clearly worth trying to improve.

The reactions of the Church and Luther are instructive. The Catholic Church, of course, was suspicious of anything that threatened orthodoxy. The stereotype of Galileo and the Inquisition is so deeply ingrained that most people are not aware that Protestants were equally hostile.

How did Copernicus find the sizes of the planets' orbits? The retrograde or looping motion of planets was attributed by Ptolemy to a small circle (the epicycle, or circle-on-a-circle) that moved on a larger circle (the deferent, meaning "carrying around"). Once Copernicus realized the retrograde motion was actually due to the Earth moving in its orbit, it's obvious that the epicycle corresponds to the Earth's orbit and the deferent corresponds to the planet's orbit. Thus the relative sizes of the planets' orbits could be deduced from Ptolemy (though not their true sizes).

The life and times of Johannes Kepler

Kepler was a thoroughgoing medieval mystic

Why doesn't this video deal with the life of Copernicus? First of all, we don't know much about how Copernicus developed his ideas. Second, he died just as his book was being published, so there is nothing to say about how he and his ideas interacted with the world. It was Kepler, not Copernicus, who made the leap to an exact quantitative theory. And Kepler is just a much more interesting individual.

Kepler was fundamentally driven by his religious convictions, but in a deep sense. Kepler saw God in the order and harmony of the Universe: "Geometry is God himself", and Kepler's religion seems to have revolved about the numinous rather than around doctrine. He became convinced that the five perfect solids of Pythagoras were the framework of the spheres of the six known planets.


Shown here are the five perfect or Platonic solids, the shapes that have identical regular polygon faces and identical vertices. The same number of polygons meet at each vertex. It's not hard to reason out that these are the only possibilities.

Kepler's fascination with the perfect solids led him to do some innovative work in geometry and some pioneering work in crystallography. He discovered these two lovely shapes, which can also be considered regular solids if you allow edges and faces to penetrate through one another. Every face (all five-pointed stars; each star is separately colored) has identical vertices, all with the same angle, and every vertex has identical faces meeting at it. In this context only the endpoints of lines are considered vertices; intersections in the middles of the lines are just crossing points.

Shown here is Kepler's vision of the Solar System. Each sphere was circumscribed around one of the perfect solids (shown on the right from outermost at the top to innermost at the bottom). The next sphere in just touched the faces of the solid on the inside. The actual ratios of the spheres for the different solids can be arranged to correspond to the ratios of the planets' orbits, but only crudely.

Kepler's remark that "Geometry is God himself" has echoes in some famous statements by Albert Einstein. Reacting to some of the strange ideas of quantum mechanics, Einstein said "God does not play dice with the Universe" and "God may be subtle, but he is not malicious." Scientists of all religious persuasions have a deep and well-grounded belief that the universe is fundamentally orderly

Kepler's Stormy Personal Life

Kepler's mother sold drugs which could have included home remedies, love potions, poisons, or perhaps "recreational" items. Purity, effectiveness and safety were pretty much optional in those days. She was a lot closer in many ways (both in activities and personality) to the medieval concept of a witch than many other victims of the witchcraft craze. Except note the time: the early 1600's. Most witchcraft trials took place in the Renaissance, not the Middle Ages. The trials at Salem, Massachusetts, in 1692, were only 30 years before the birth of George Washington!

In discussing Kepler's upbringing, Sagan pictures Kepler wondering if some adverse conjunction of the planets caused his father to abandon his family. It seems much more likely, given what we learn about his mother's personality, that we don't need to look to the stars for an explanation!

Strange Start - Good Finish

Kepler started off with the mystical idea that the orbits of the planets were linked to the perfect solids, and ended up correctly describing the motions of the planets. How could that be? Science often proceeds by a process of successive approximation: make an assumption, see how it fits reality, modify it (junk it if necessary) and try again. This differs profoundly from circular reasoning, where you start off with an assumption, modify observations to fit the assumption, then use the results as proof of the assumption. The difference is that in successive approximation, there is always the option to leave the loop. People who engage in circular reasoning almost never scrap or modify their initial hypothesis - the whole point of circular reasoning is to justify the initial hypothesis at all costs. After a few iterations of successive approximation you can be very far from your starting point, and even fairly strange initial assuptions can lead to correct results.

How Did Kepler Do It?

Kepler's technique for finding the true shape of the orbit of Mars reveals the man's true brilliance. He reasoned that every 687 days Mars was at the same position in its orbit. On the other hand, 687 days is 43 days shy of two Earth years. Thus, we would see Mars at a different position in the sky. If we plot our lines of sight to Mars 687 days apart, they should intersect at Mars' true position. He triangulated, except that the point he was trying to locate was moving. He solved this problem by realizing that Mars returned to the same point in space.

Kepler's Laws

  1. Planets travel around the Sun in elliptical orbits with the Sun at one focus.
  2. A line from the planet to the Sun sweeps out equal areas in equal times.
  3. The square of a planet's period in years and its distance cubed are proportional. Mercury's period is 0.241 years. The square of 0.241 is 0.058. Its distance is 0.387 that of Earth; 0.387 cubed is also 0.058. Verify the law for Pluto (period 248 years, distance 39.6 times Earth's)

Tycho Brahe

Tycho really did live the outrageous lifestyle shown in the video and really did have a gold nosepiece. He died the way he lived. He was hitting up some noble personage for patronage and support and, fearing that somebody else might upstage him, refused to leave to go to the bathroom. He developed a bladder infection and died. And you think you're a party animal!

There's a coincidence involving Tycho and Shakespeare that is so neat it really is no coincidence. Hamlet's two student acquaintances are named Rosenkranz and Guildenstern. (The play Rosenkranz and Guildenstern are Dead is a black comedy that tells the story of Hamlet from their perspective. The joke is that one expects deep new insights into Hamlet, and they stumble around without a clue.) Tycho, modest unassuming chap that he was, published a book whose frontispiece showed his portrait and 16 crests showing his illustrious lineage going back four generations. And guess what two of the names on the crests are: Rosenkranz and Guildenstern. Hamlet was Danish. Tycho lived in Prague, but was Danish by birth, and in fact his family estate looks right across the strait to Elsinore Castle where Hamlet takes place. Tycho and Shakespeare had a mutual acquaintance in an English astronomer named Thomas Digges. Clearly, Shakespeare worked an inside joke into Hamlet that sharp members of his audience were expected to catch.

The error between Kepler's best circular orbit and Tycho's data was tiny. It's a tribute to Tycho's accuracy that Kepler was convinced enough to scrap an idea he deeply wanted to believe in. As Sagan notes, Kepler "Preferred the hard truth to his dearest illusion"

So Who's Galileo?

Galileo (1564-1642) did not invent the idea of the Earth going around the Sun, nor did he invent the telescope. His scientific innovations included being the first person to publish astronomical observations made with the telescope, and helping to clarify concepts in physics and mechanics.

Galileo's great historical role was as a popularizer of the Copernican model, and that was what got him into trouble. However, the story is (as usual) far more interesting and complex than the stereotypes. Galileo's abrasive and argumentative personality made him enemies that eventually worked to undo him.

In Galileo we see a brilliant and original scientist, but one who is better known to most people for his popular writings on science. He was also very blunt and alienated quite a few people. In short, he comes across very much as a 17th century Carl Sagan.

Isaac Newton (1642-1727)

Isaac Newton discovered the physical and mathematical basis for Kepler's Laws. He discovered Newton's Laws of Motion, gravity, and calculus, and was able to prove mathematically that orbits of the planets were indeed ellipses. He also corrected a minor discrepancy in Kepler's Third Law and proved that objects travelling fast enough to escape the Sun's gravity would travel orbits that are parabolas or hyperbolas.

Comets were shown to have orbits that were nearly parabolas, but Edmund Halley found that several comet apparitions 76 years apart seemed to have the same orbit. He guessed that the orbit was actually a very long ellipse and that the comet would return. It did, and ever since has carried Halley's name. This was the first new object orbiting the Sun to be discovered, and since the outermost planet then known was Saturn, it tripled the size of the Solar System.

Essential Points

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Created 13 January 1998, Last Update 20 May 2020