Wednesday, September 06, 2006

Galileo and the Ptolemaic System

The Galileo Project

Ptolemaic System

In his Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican of 1632, Galileo attacked the world system based on the cosmology of Aristotle (384-322 BCE) and the technical astronomy of Ptolemy (ca. 150 CE).

In his books On the Heavens, and Physics, Aristotle put forward his notion of an ordered universe or cosmos. It was governed by the concept of place , as opposed to space, and was divided into two distinct parts, the earthly or sublunary region, and the heavens. The former was the abode of change and corruption, where things came into being, grew, matured, decayed, and died; the latter was the region of perfection, where there was no change. In the sublunary region, substances were made up of the four elements, earth, water, air, and fire. Earth was the heaviest, and its natural place was the center of the cosmos; for that reason the Earth was situated in the center of the cosmos. The natural places of water, air, and fire, were concentric spherical shells around the sphere of earth. Things were not arranged perfectly, and therefore areas of land protruded above the water. Objects sought the natural place of the element that predominated in them. Thus stones, in which earth predominated, move down to the center of the cosmos, and fire moves straight up. Natural motions were, then, radial, either down or up. The four elements differed from each other only in their qualities. Thus, earth was cold and dry while air was warm and moist. Changing one or both of its qualities, transmuted one element into another. Such transmutations were going on constantly, adding to the constant change in this sublunary region.

The heavens, on the other hand, were made up of an entirely different substance, the aether [1] or quintessence (fifth element), an immutable substance. Heavenly bodies were part of spherical shells of aether. These spherical shells fit tightly around each other, without any spaces between them, in the following order: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, fixed stars. Each spherical shell (hereafter, simply, sphere) had its particular rotation, that accounted for the motion of the heavenly body contained in it. Outside the sphere of the fixed stars, there was the prime mover (himself unmoved), who imparted motion from the outside inward. All motions in the cosmos came ultimately from this prime mover. The natural motions of heavenly bodies and their spheres was perfectly circular, that is, circular and neither speeding up nor slowing down.

It is to be noted about this universe that everything had its natural place, a privileged location for bodies with a particular makeup, and that the laws of nature were not the same in the heavenly and the earthly regions. Further, there were no empty places or vacua anywhere. Finally, it was finite: beyond the sphere of the fixed stars and the prime mover, there was nothing, not even space. The cosmos encompassed all existence.

Christian Aristotelian Cosmos. From Peter Apian, Cosmographia [click for larger image]
Now, ingenious as this cosmology was, it turned out to be unsatisfactory for astronomy. Heavenly bodies did, in fact, not move with perfect circular motions: they speeded up, slowed down, and in the cases of the planets even stopped and reversed their motions. Although Aristotle and his contemporaries tried to account for these variations by splitting individual planetary spheres into component spheres, each with a component of the composite motion, these constructions were very complex and ultimately doomed to failure. Furthermore, no matter how complex a system of spheres for an individual planet became, these spheres were still centered on the Earth. The distance of a planet from the Earth could therefore not be varied in this system, but planets vary in brightness, a variation especially noticeable for Venus, Mars, and Jupiter. Since in an unchangeable heaven variations in intrinsic brightness were ruled out, and since spheres did not allow for a variation in planetary distances from the Earth, variations in brightness could not be accounted for in this system.

Thus, although Aristotle's spherical cosmology had a very long life, mathematicians who wished to make geometrical models to account for the actual motions of heavenly bodies began using different constructions within a century of Aristotle's death. These constructions violated Aristotle's physical and cosmological principles somewhat, but they were ultimately successful in accounting for the motions of heavenly bodies. It is in the work of Claudius Ptolemy, who lived in the second century CE, that we see the culmination of these efforts. In his great astronomical work, Almagest, [2] Ptolemy presented a complete system of mathematical constructions that accounted successfully for the observed motion of each heavenly body.

Ptolemy used three basic constructions, the eccentric, the epicycle, and the equant. An eccentric construction is one in which the Earth is placed outside the center of the geometrical construction. Here, the Earth, E, is displaced slightly from the center, C, of the path of the planet. Although this construction violated the rule that the Earth was the center of the cosmos and all planetary motions, the displacement was minimal and was considered a slight bending of the rule rather than a violation. The eccentric in the figure below is fixed; it could also be made movable. In this case the center of the large circle was a point that rotated around the Earth in a small circle centered on the Earth. In some constructions this little circle was not centered in the Earth.

The second construction, the epicycle, is geometrically equivalent to the simple movable eccentric. In this case, the planet moved on a little circle the center of which rotated on the circumference of the large circle centered on the on theEarth. When the directions and speeds of rotation of the epicycle and large circle were chosen appropriately, the planet, as seen from the Earth, would stop, reverse its course, and then move forward again. Thus the annual retrograde motion of the planets (caused, in heliocentric terms by the addition of the Earth's annual motion to the motion of the planet) could roughly be accounted for.

But these two constructions did not quite bring the resulting planetary motions within close agreement with the observed motions. Ptolemy therefore added yet a third construction, the equant. In this case, the center of construction of the large circle was separated from the center of motion of a point on its circumference, as shown below, where C is the geometrical center of the large circle (usually called in these constructions the excentric circle) but the motion of the center of the epicycle, P (middle figure), is uniform about Q, the equant point.

Ptolemy combined all three constructions in the models of the planets, Sun, and Moon. A typical construction might thus be as in the picture below, where E is the Earth, C the geometric center of the eccentric circle, Q the equant point, F the center of the epicycle, and P the planet. As mentioned before, the eccentric was often not fixed but moved in a circle about the Earth or another point between the Earth and the equant point.

With such combinations of constructions, Ptolemy was able to account for the motions of heavenly bodies within the standards of observational accuracy of his day. The idea was to break down the complex observed planetary motion into components with perfect circular motions. In doing so, however, Ptolemy violated the cosmological and physical rules of Aristotle. The excentric and epicycle meant that planetary motions were not exactly centered on the Earth, the center of the cosmos. This was, however, a "fudge" that few objected to. The equant violated the stricture of perfect circular motion, and this violation bothered thinkers a good deal more. Thus, in De Revolutionibus (see Copernican System), Copernicus tells the reader that it was his aim to rid the models of heavenly motions of this monstrous construction.

Aristotelian cosmology and Ptolemaic astronomy entered the West, in the twelfth and thirteenth centuries, as distinct textual traditions. The former in Aristotle's Physics and On the Heavens and the many commentaries on these works; the latter in the Almagest and the technical astronomical literature that had grown around it, especially the work of Islamic astronomers working in the Ptolemaic paradigm. In the world of learning in the Christian West (settled in the universities founded around 1200 CE), Aristotle's cosmology figured in all questions concerned with the nature of the universe and impinged on many philosophical and theological questions. Ptolemy's astronomy was taught as part of the undergraduate mathematical curriculum only and impinged only on technical questions of calendrics, positional predictions, and astrology.
Copernicus's innovations was therefore not only putting the Sun in the center of the universe and working out a complete astronomical system on this basis of this premise, but also trying to erase the disciplinary boundary between the textual traditions of physical cosmology and technical astronomy.

Notes:[1] The traditional English spelling, aether, is used here to distinguish Aristotle's heavenly substance from the modern chemical substance, ether.[2] The title is one given to this book by Islamic translators in the ninth century. Its original Greek title is Mathematical Syntaxis.
Sources: The Aristotelian cosmos is described in his Physics and On the Heavens, see The Complete Works of Aristotle: The Revised Oxford Translation, ed. Jonathan Barnes, 2 vols. (Princeton: Princeton University Press, 1984). On the relationship between Greek cosmology and astronomy, see B. R. Goldstein and A. C. Bowen, "A New View of Early Greek Astronomy," Isis 74 (1983):330-40, and Thomas S. Kuhn, The Copernican Revolution (Cambridge: HArvard University Press, 1957. The best translation of the Almagest is Ptolemy's Almagest, tr. G. J. Toomer (London: Duckworth; New York: Springer Verlag, 1984). Godd expositions of the technical details of the Ptolemaic System can be found in Olaf Pedersen, A Survey of the Almagest (Odense: Odense University Press, 1974); Michael J. Crowe, Theories of the World from Antiquity to the Copernican Revolution (New York: Dover, 1990); and Olaf Pedersen and Mogens Pihl, Early physics and astronomy : a historical introduction (London : MacDonald and Janes ; New York : American Elsevier, 1974; 2nd ed. Cambridge: Cambridge University Press, 1993). On Medieval cosmology and astronomy, see Edward Grant, "Cosmology," in Science in the Middle Ages, ed. David C. Lindberg (Chicago: University of Chicago Press, 1984), pp. 265-302; and Olaf Pedersen, "Astronomy," ibid, pp. 303-37. For an account of Aristotelian cosmology and Ptolemaic astronomy in the period leading up to Galileo's discoveries, see James M. Lattis, Between Copernicus and Galileo: Christoph Clavius and the Collapse of Ptolemaic Cosmology (Chicago: University of Chicago Press, 1994).


Blogger AimerVoyage said...

I think that this article is about one of the very things that led to the “Enlightenment”. Pre-Ptolemaic era consisted of a world where people relied solely upon the word of God. They relied upon the words in the bible to tell them what to believe, what to have faith in, what to distrust, and how to live their lives. However, the bible says nothing of the earth revolving around the sun or of the other planets. So why shouldn’t they believe that Earth was the center of everything? But the implementation of Ptolemy’s ideas that it wasn’t the center of everything, and that the universe didn’t move in perfect circles (since this is the perfect shape, and God is perfect, therefore everything he creates must BE perfect) caused doubt and even distrust. When the realization hit that what Ptolemy said was true, people began to wonder if what the text said or if what science said was correct. This led to many believing science AS WELL AS what was in the bible. This was the beginning of modern science and possibly the reason why we trust science today.

6:23 PM  
Blogger pinkismyfavoritecolor said...

I found this article very interesting in a historical point of view. Living in a world full of technology and scientific advances, it's hard to imagine living in a world when falsehood is the closest to truth you can get. No wonder so many people belived Galileo's work; it was all the knew. And even though it was prooved to be wrong later, the ideas and concepts behind it are still amazing in that there is such a complexity of thoughts. People such as Galileo, Aristotle, Di Vinci, and Ptolemy had a vast amount of intelligence and an amazing amount of wonder to be able to devote the time and energy they did into coming up with their ideas. Math, today, is a completely different subject that mathmatics were in that time. Also, science is completely different too. We no longer have to have the outlook that some things will never be known (though some won't). Today, we have the ability and advantages to actually seek out our hypotheses and discover things that, even twenty years ago, were never thought to be discovered.

4:34 PM  
Blogger The Filthy Titan said...

Water, earth, air, fire. If I have to read those things in a fantasy novel one more time, I'll go mad.

But that's not the point.

The most interesting thing about this post is how scientific the whole process is. I'm not saying it's right- that's obvious to everybody. But with this, Aristotle really tried to make something that was "logical"- his pretenses are wrong, but there's only so much one can do with the tools he had at the time. And, after all, much of his stuff is, surprisingly, correct, though not for the reasons he thinks.

A good example is stones. They fall "down" (and you would assume it was down in Aristotle's day- no knowledge of Earth's round, spherical nature). This is because of gravity, but lacking such ideals, why not claim that it was its "nature"?

Likewise, fire does rise- ask anybody who rides in hot-air balloons.

And technically, the continents we live on *are* just pieces of land sticking up out of water.

So he's right, but for the wrong reasons. Strange.

4:48 PM  
Blogger The Filthy Titan said...

To Aimervoyage:

I agree with the basic premise, but I see one thing as more important: reliance on what was old. The Bible was relied upon, not because the vast majority of people had read it (they hadn't) or even because they truly cared (somebody would kill you if you didn't believe- a catch-22). They believed it because it was old.

This led to some hilarious and slightly ridiculous blendings of both Biblical accounts and Roman classicalism- references to demigods, who are very much a no-no in Christianity (there is only one God, after all), are referenced constantly by writers of the time, sometimes in the less than metaphorical sense.

Science did not destroy people's faith- look at the Christians we have today, who are more widespread than ever before (at 40% of the planet, the world's biggest single religion). But it did stop the fanatical belief in anything "old" that was rampant at the time we are studying. Perhaps as an aftereffect of the fall of Rome, people longed to return to past days...

Science, by giving them something of their own, let them move on with their lives after the destruction of Rome. Science and Christianity met, shook hands, parted.

It was Science and Tradition that got into the big, knock-down, drag-out fight.

4:59 PM  
Blogger pinkismyfavoritecolor said...

--to gf--

I disagree with the whole science vs. christianity bit. Just look at the rediculous conflicts people are still having today about evolution (which is by the way, a very uneducated, pointless argument) Christians aren't widespead today...they're all a bunch of fakes. Of all the people who claim to be Christians (which is quite a lot since people love to have the security of saying they believe in God however do absolutely nothing to prove it in their lives), probably only about 10% actually live the Christian life. I think that science pushed out christianity for the simple reason that people no longer had to believe in something they couldn't see or feel. They now had something that had actual proof. If modren day people could just stop being so close minded and realize that evolution actually does happen and there is more than enough scientific proof, then maybe we would have a slightly more intelligent society. And yes, science and tradition were the ones who got into the fight but what is christianity other than a big tradition?

4:23 PM  
Blogger Beatrice Baudelaire said...

Math and Physics are two fields in which concepts are proven with reason from within. Everyone can envision a perfect circle with a constant radius spinning 360 degrees around a single foci but accurately representing it on a chalk board is impossible. In instances such as these, math and physics must be defined through principles generated from preexisting knowledge or instinct rather than deduced from experiences and senses from the outside world. Although explanations provided by classical physics about things such as projectile motion roughly match what happens in nature, the basic principles were perfect-world models first, before experimentation had to occur.
In the case of Copernicus, he was able to break down a very complex phenomenon into component parts based on reasonable math. He ignored the traditional paradigms of his field in order to construct a model that was sound in reason as well as observable phenomenon. Divinity and perfection was removed from the model in order for the math to work. Many would interpret this as a more cut and dried method of removing God from the equation as Shakespeare removed him to allow his plots to progress. Others would view this as a form of practicality.

7:31 PM  
Blogger swiffer_mop1234 said...

As pinkismyfavoritecolor basically said, these first "scientists", I suppose you would call them, opened up the door for everything we know today about science. I cannot even imagine not knowing some of the things they know, not just about the planets. It's just common knowledge anymore to know that the planets orbit around the sun and even the order of the planets. I think many people take for granted everything that we know because of what the early scientists found out, and the curiosities they sparked. I am sure that Galileo would love to live in today's times and to know the things that we know.

7:44 PM  
Blogger AubergineClementine said...

This all reminds me of a Dan Brown novel.
Anyway... gf, I like your comment to aimervoyage. But I do think that your distinction between science v. tradition and science v. christianity is flawed. Tradition has largely been based upon religion throughout history (think praying before meals and going to church every Sunday). This includes Christianity. And so to me, Christianity would go ahead and be categorized with tradition. People, as you say, after the fall of Rome relied heavily on new ideas of science and that battled the tag team of Christianity and Tradition. And, as you say, Christianity has not faltered majorly (still 40%?), but I guess there's no telling what that percentage could be had it not been for that fight with science.

7:55 PM  
Blogger Larogoth said...

I agree with gf in that I also feel that the most interesting part of this article is the thought process that went into it. It made me think back at all the historical things that I had learned thus far in life pertaining to Aristotle, Galileo, and the like. I know that it is not accurate, but the way in which these people went about coming up with their theories of the universe is what intrigues me. The logic behind the Earth and the different parts of it (Earth, water, air, etc.) also intrigues me in how he went about explaining them.

9:14 PM  
Blogger thisismyname said...

I enjoyed reading this entry, too. However, I probably should have read this one before the “Galileo, Astronomy and Physics” entry. Anyway, science has certainly come a long way. I have to agree with gf that when I first read about the earth, wind, fire, and water theory, I naturally thought of some fantasy book or video game. If you think about it, how else would an ordinary person without the technology we have today explain the way our world works? If I had no concept of the earth revolving around the sun, I would probably think, with practically everybody else, that the earth, full of heavy rocks, was the center of the solar system. Heck, I’ll throw in believing the world was flat for good measure, too. Science has to start somewhere! As I said with the other article, I’m amazed at how people like Galileo thought outside the box and came up with these ‘outrageous’ theories that would still be used today. It blows my mind!

9:58 PM  
Blogger bob_barker_is_my_hero said...

Evolution and Christianity don't necessarily have to be kept separate. According to Tennant it makes sense that there is an intelligent being out there who fine-tuned the world as it was to produce human beings. He saw it as everything is set up so perfectly for life that it must have had a designer with a plan. On the other hand the world could have just evolved to where life was possible with no link to an intelligent designer. I think it’s a neat idea the pinkismyfavorite color may want to look into. I myself am no Christian and still believe that the idea deserves some merit.

9:40 AM  
Blogger Esrever said...

I agree that there are many more people who call themselves Christian than people who live their lives in such a manner, but I disagree with pinkismyfavoritecolor’s statement that science pushed Christianity out of the way. To this day many people of the Christian faith question newly found scientific proofs and discoveries, even if they don’t “live the Christian life.” The only reason they come to accept these facts are because they’re, well, facts. Because of this, I don’t see science as pushing Christianity away, but, rather, as the main cause of the adaptation of the Christian faith. Astronomical discoveries such as those of Galileo have caused Christians to move from “God created a perfect universe” to “God chose for the planets to revolve around the sun in elliptical motions.” Similarly, evolution is causing Christians to change their views toward mankind’s creation. Humankind wasn’t just created from scrap? Well, um, that’s because God put evolution into motion…duh! After all, it’s not like there’s a story in the Bible that specifically states that God directly created humankind. Oh wait…

8:46 PM  

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