Program 08 - "Hellenistic Greece and the Ptolemaic System"

Music Ah, I finally got it figured out.The earth moves around the sun.That's the only way to explain the reason why the stars move.Yeah, sure, and I suppose next you're going to tell me thatthe moon is falling from the sky, and the sun holds on to the earthwith a leash to keep it from flying into the space.Well, actually, I had thought about that but I wasn'treally sure that my two friends...Get serious.Everyone knows the earth doesn't move.What about the wind?Or if you jumped up, a tree would come up from behindand knock you over, and we'd all be flown off he surface of the earth like, like rocks from a sling.Tsk, you know, you've got to use some common senseor you're never going to get ahead in the world.Tsk, moving earth.The odd ball theories that people come up with.Why can't they'd just kept things the way are, rather than causing trouble, tsk.MusicWe're back with Science 122, the telecourse that asks reallyimportant questions, like why is the Hellenistic culturecalled Greek when it was in Egypt?

Before we're done with this program, we will have seenhow Aristotle's paradigm influenced the Greek culturein the city of Alexandria and eventually became forgedinto the Ptolemaic system through the contributionsof the Hellenistic scientists with names like Aristarchus,Eratosthenes, Euclid, Hipparchus, and Ptolemy.We'll see how the Ptolemaic system became the astronomyof choice, and how it differed from the cosmology of Aristotle.Be sure to read these objectivesin the Study Guide and refer to them as you study the lesson.Focussing on the Learning Objectives will help youto study and understand the important concepts.Compare the objectives with the study questions for this lessonto be sure that you have the concepts under control.With the death of Alexander the Macedonian Empire literally fell apart.

The Greek city states had lost their magic and no longer heldthe allure of the intellectual or the political or the economic forces.With the decline of the Greek city states, a new centerof civilization began in the city of Alexandria, which was builtby Alexander in honor of himself to be the city of the future.Alexandria was actually part of Alexander's idea of spreadingthe Greek culture throughout the world that he had conquered.You know, who can really explain the details of social conditionsthat cause the decline of one region while another region flourishes.But history is full of such happenings, and it is not ourpurpose to try to trace their detailed demises and developments.It is important for this course, though, to see how the culturalvalues of these different cultures took the ancient ideas and modified them.Only then can we really understand the importanceof the great revolution in science, the topicof the seven program in the section, Section 2.So, it's easy to say that the essence of Athenian culturedied with Alexander in 323 B.C., and with the deathof Aristotle the following year in 322 B.C.

The death of the political glue and the philosophical strengthof an empire can have devastating effects, especially whenin the case of Alexander and Aristotle they were so closelylinked, and ended practically at the same time.Just for a minute, consider the effect that the death of JFKhad on the United States as a small scale parallel.What happened after the death of JFK in this country?Social unrest, dissent, threat of revolution, ethnic issues,all of these things come to the forefront in this sort of chaosthat follows this, a major event like this.So, think of the same effect, some 2300 years ago when aninvading army of Macedonians accomplished what threegenerations of war with Sparta had not been able to do;that is, to basically conquer Athens and destroy thepolitical structure of the city states.Ravaged by war, and torn by social dissent, the Greek culture wasundermined by the new dominion of Phillip of Macedon.In fact, there was little left of it by the time Alexander died.Without his leadership, which wasn't that goodto begin with, it never made a comeback.So, the center of Greek culture shifted to Alexandria.This is a seaport on the Nile delta.In fact, on the opposite side of the delta from where the city of Cairo is today.

The Hellenistic civilization was named after a characterin Greek mythology, strangely enough called, Helen,and it grew from Alexander's efforts to spread the Greekculture as he conquered the world.Alexander had a good idea.I mean, conquering people is not necessarily the best wayto spread your ideas, but Alexander recognized thatthe Greek culture was a very good culture, and wantedto spread it amongst the world.After Alexander's death dynasties were established that broughtback some of the political disunity in the empire.By disunity I mean the separate city states decentralized thegovernment and allowed these various places to goon their own way from there on.But it did promote the Greek unity of trade and learning.That is, it kept the ideals of the Greek culture going.In fact, in Alexandria, a new culture developed in art, letters and science.The same sort of thing happened in some of Alexander's othercities, but it was in Alexandria where it really flourished.In Alexandria the standard of living was high,especially for the well to do.Like here in our country, the well to do are generallywell educated, and have lots of money.Literature was abundant and the concept of learning, as distinctfrom the concept of knowledge and philosophy, came into being.

We'll explore in the next program a little bit the idea of learningversus knowledge, and for now, just keepin your mind that they are two separate things.The Alexandrians were great builders.In fact, they built libraries, but they also compiled anthologiesof literature, they developed the art of sculptureand studied mathematics and science.Like any place, when life is good, there's a lot more timefor curiosity, and people have a lot more time to spend studyingthings that are not directly related to making a living or to survival.So successful were they at spreading the Greek culture,in fact, that the triumph of Rome, the next major power to arisein the Mediterranean, was due mostly to the fact that Romewas able to absorb the culture of the Hellenistic Greek ratherthan to try to overpower it like they did in many other places.Had the Romans tried to overpower the Greek culture,they probably would not have been successful.Alexandria was home of two of the most famous scientists.These were Archimedes, whose understandingof buoyancy saved his king a fortune.This would be a good topic for you to researchif you wanted to have a nice story.And Euclid.Euclid's geometry, in fact, was so precise that it's still taughttoday almost exactly as Euclid presented it nearly 2000 years ago.

In Alexandria the atmosphere was much more practical and muchless metaphysical than it was in Athens.In Athens there had been a lot of concernabout knowledge for the sake of knowledge.Alexandria relied upon engineering mathematical problems, and so forth.Also, in Alexandria mechanical arts like painting and sculpturebecame more popular as the disapproval of manual work disappeared.Remember, I mentioned last time that part of Aristotle's problemwas that manual labor had been dishonored in Athens, so that itwas not thought to be the proper thing to do,to build instruments and to collect data.This was all changing in Alexandria.In fact, the making of instruments and maps had advanced to a veryhigh level of sophistication by the first century A.D.So that now, the planetary observationsand the locations of the planets could be recorded.Also, at the same time, a new interest in understanding theworld, and this is part of the key, and in doing experimentsand taking measurements began to grow.In Alexandria was a library.In fact, the Library of Alexandria was the greatest repositoryof knowledge anywhere in the world until the 19th century.

The Library was a spectacular place.It was a huge and elegant building in the classical Greek stylewith large columns, you know, the kinds like you seein Washington, D.C. and all over Europe--these majestic buildings.Among other things, the Library contained most of,if not all of, Aristotle's writings.Some of them were original and only copies.There simply just weren't enough copies of them to make copies for everyone.Silico: "Excuse me.Didn't they have copying machines and faxes and other things?I cannot imagine a world without electronics."Yeah, that's pretty funny.Just like I can't imagine a world without brain cells.Hey, wait a minute.You're a computer.You're not supposed to imagine things.Well, anyway, the sad part about the Library was that it wasdestroyed in a series of raids over a 350 year period--350 year period.And, just so we don't have any ethnic preferences here,I want to point out that it was destroyed first of allby Septemia Zenobia in 269 A.D.Wow, Septemia Zenobia.I really like that name, you know.Sounds like somebody you meet in the StarlightCafe, or a chat room on the intergalactic internet.

I wonder what a little research on her would reveal.Silico: "I will work on it."Yeah, good, you do that.Well, just so, again, so that we don't have any ethnicpreferences here, the Library was sacked again in A.D. 415by a mob of orthodox Christians who werefighting against heresy and pagan learning.In fact, this group was led by a bishop who was concerned thatthere were non-Christian documents being held herewhich, you know, glorified such things as Aristotle and Plato and things like this.So they did a pretty good job of burning it.Aristotle's writings, no doubt, were among the things thatwere destroyed, although we have really know wayof knowing which things were destroyed.And again, just to keep our ethnicity broad based here,the Library was finally destroyed for good by Moslems in A.D. 640.Many of the documents, however, this time were salvagedby the troops and made their way eastward wherea new center of civilization was developing.But that's another story, and one we'll get to in the next program.

One of the earliest of the Hellenistic scientists was a fellow named Aristarchus.His main value as far as our following this river of timewas the contribution that he made in questioningAristotle's geocentric system.Remember that Aristotle had adapted thisgeocentric system from Plato and from Exodus.Aristarchus considered the possibility of a rotatingearth revolving around the sun.In other words, the heliocentric theory.He asked what kinds of effects would you observe if the sunwas the center and the earth was actually going around it.It was a wonderful unbiased account on his part,although he still considered only circular motionto be the only true motion for the heavens--a Platonic view.Aristarchus did not collect data, he simply considered what theuniverse would look like from earth, if the sun was the centerand the earth was going around it.So, the heliocentric universe of Aristarchus was discountedby the Greeks of his time for several reasons, but three main reasons.

More than anything else, Aristarchus started a debatethat really had the effect of strengthening the geocentrictheory, because by being able to look at the heliocentric theoryand say, "Well, this doesn't seem like this works,"it gave the geocentric theory a lot of weight.So, there are three reasons.The first reason was that it was a qualitative system.A qualitative system simply means there were nocalculations of planetary paths.There was no observation of where the planets actuallywere, and he offered no system of calculating it.It's like saying, "on amerry-go-round it appearsas if the earth is spinning around you," but youreally can't tell the difference, right?You can say either the way and there's really no waythat you can tell, although on a rotating platformlike a merry-go-round there might be other clues thatwill tell you whether or not who's moving,like for example, if you let go, you'll fall off.These three methods we, I don't want to go into them in greatdeal right now, but we'll explore this idea somewhat later whenwe get down to Aristotle's theories of motion.

So for now, let's just note that the Greeks also looked for somesigns of evidence for one theory over the other, geocentricversus heliocentric, but simply couldn't find it.Let me detail this a little bit, right now.For one thing, one of the things that you would expect to findif the earth was moving around the sun, is something called parallax.Everybody knows what parallax is, right?If you don't think you know it, you probably do.Parallax is what happens when you pointat something with one eye closed and then switch eyes.

OK, come on, try it.It's OK to point, it's for science.If your family or friends think you're weird, just tell themit's for science, and they'll understand.So, what happens is that when the finger that you're pointing withcan't line up with both eyes at the same time.It's geometry.OK, so, here's what you do.Point with one eye and like this, OK, keep your hand stilland move head from side to side, like this.Come on try it.Come on, I know, I can see you, you're not trying, come on, point at me.Put your finger up, move your head from side to side, and see thatyour hand or your finger no longer points at the same thing.Again, the finger and the object can't line upwith both sides at the same time.In other words, you're seeing things from a different perspective.If it's the earth that's moving in a circular orbit, the earth's goingaround the sun like this, then as you look from the earth outat the star background, the stars should appear to be like yourfinger, goes around the earth, moving around in the orbit likethis, then you should expect things not to line up.It's important because, first of all, you can't seeparallax of stars without a telescope.

Secondly, we know today that the stars are so far apart from usthat the parallax is too small to be seenwithout sensitive telescopes and tracking.In fact, the stellar parallax was not observed until the 19thcentury, long after we had given up the geocentricidea and accepted the heliocentric model.OK.There are several types of parallax.There are two kinds of parallax that I want to note here.One of these is called alignment parallax.This is where two objects line up at one time and not another as motion occurs.To see this, hold up both of your index fingerson both hands and line them up like this,

OK.Close one eye, line up your fingers like this and then switch eyes.You'll see that the two fingers are no longer lined up.And so, if you have two stars which are close together,what effect would you expect to see from thosestars as the earth moves around?OK, try it.Put your fingers up like this, close one eye, move your head backand forth, and you'll see that the two fingers don't line up, again.In fact, the greater the distance apart the fingers are,and the greater the distance of your eye from those fingers,the greater the movement you appear to see.This is fairly easy to demonstrate with the two fingers.The concept of angular parallax is a little bit harder, but it's similar.You can see the picture on the screen what it is.I won't try to demonstrate this for you.I'll let you figure this one out as a wayto demonstrate this with your fingers, if you want to try it.

So the idea with angular parallax is that angular parallax doesn'trequire that the two objects ever line up because whether or notthey're lined up, the apparent angle between them will appearto change even if they're the same distance from us.What I mean by that is like, I hold my two fingers up like this,and if I move over to the side like this and look at themfrom a different angle, then the apparent distance between themappears to shrink, and in art we would say they've become foreshortened.

OK, so those two reasons, right?The heliocentric theory of Aristarchus was qualitativeand you couldn't observe the stellar parallax.The third thing has to do with simply the paradigm.The heliocentric paradigm simply would not fit inwith Aristotle's System of the World, which requiredhomocentric and geocentric spheres to explain the motions of the planets.The whole cosmology of the system, remember,and Aristotle's system, depended on the fact that planetarymotion was as Aristotle described it.Silico: "A message just flashed through my circuits that said 'A chainis no stronger than it's weakest link.'What does that mean?"Not having ideas are you?You're not supposed to have ideas.You only have a 0.40 chip and no floating point unit.I dunno what it is with this computer having ideas like this.Well, OK, you have the idea, let's ask then, "What does it mean?"What does it mean that a chain is only as strong as its weakest link?What is a chain and what is the link here, in this analogy?Hmm.That's a good topic to explore in an exposition.Oh, that means you might want to write about it.

OK.You see, to get back to Aristotle and the heliocentric theory,the whole idea of heliocentrism would violate the obviousdistinction between the earth and the heavenly realm.Right?Although in Aristarchus time it's doubtful that most people evenknew where that connection came from.It had been 300 years since Aristotle.It's really funny because Aristarchus in his time was criticized.In fact, one of his detractors said, "Howdare this man put in motion the hearth of the universe."Hearth of the universe, the earth?It's violating the sacred principle, like you know, barbecuing thesacred cow or something, and this goes backto the idea of how strong the paradigm can be.Right?So his ideas, Aristarchus, were largely rejectedon the basis of these three criticisms.I want to note here something that here we have a caseof the absence of something being used to prove something else.In other words, if the Greeks or anybody had been able to see astellar parallax, there would have been no question thatheliocentricism was the correct view.But, because they could not see stellar parallax, they rejectedthe heliocentric idea and adopted the only otheralternative of geocentrism.

One of the most influential and probably one of the mostintelligent and certainly the most prolific of all of theseAlexandrian period Greek scientists was a fellow whosename is almost impossible to pronounce.His name is Eratosthenes, and lucky for you, you don't have to say it.I'm the only one who has to say it.What Eratosthenes did was to measure the size of the earth.Now, this requires a little background.We learned in school, or at least I learned in school backin the last century when I went to school, that everybody thought,until Christopher Columbus sailed across the seain 1492, that the earth was flat.This is really not true at all.In fact, even in Columbus' time very few people, at leasteducated people, considered that the earth was flat.The ancient Greeks knew that the earth was roundand Eratosthenes figured out a way using geometryand with a couple of assumptions, to measure the circumferenceof the earth to within a few miles of what we know it to be today.

Let me show you how he did this.It worked something like this.Here's a flat surface.Suppose that there's a stick that's vertical on this flat surfaceand suppose that the sun's rays are coming inat some angle to the stick, like this.So the sun's rays are coming in at an angle like this.What would happen with the stick?The stick would cast a shadow.So, the shadow, the length of the shadow here would be dependentupon the length of the stick and the angle of the sun's rays.In fact, this angle, here, is the same angle as the angle of the sun.So, from the length of the shadow we should be ableto calculate the angle of the sun.What would happen to another stick someplace else?Suppose, over here there's another stick?What's the angle to the sun from that point?Here's where an assumption is involved.

If the angle to the, if the distance to the sun is very great,then Eratosthenes reasoned that the angle between, of the sunbetween those two points, would be pretty much the same.In other words, over here the angle of the sun will become,with the sun will becoming from about the same angle,so if the earth was flat, he said, then the length of the shadowover here at point "A" should be length same as the shadowat point "B," if you could somehow measure themat the same time on the same day.So, how did he use this to figure out the circumference of the earth?That's the question you're probably asking.Well, what he did was this.He noticed that on a particular dayin Alexandria a vertical well saw the shadow of the sun.In other words, here's well, and here's the surface, and the sunon that particular day in Alexandria shown straight down into the well.In other words, the sun was directly overhead.So, the angle of the sun is like this.Eratosthenes put a stick to make sure.So he puts a stick like this.You can make the stick vertical by letting it hang,and he noticed that the stick cast no shadow.He had to wait a whole year to do this again.But, he had a friend the next year in a different citythat's about 500 miles away.

Now, they didn't use miles in these times.About 500 miles away, had a friend measure the angleof the sun at a different city 500 miles away on the same day at the same time.So, what would happen, or what would you assume, if anotherstick in a different place on that same day had adifferent angle with the sun?So, suppose, for example, then in this place the sun comesin an angle like this and the stick actually forms the shadow.This is what Eratosthenes observed--that the stick 500miles away from Alexandria on the same dayat the same time had a different angle to the sun.So, what's the assumption?Well, very simple assumption, actually.The assumption is that it's not a flat surface at all.There might be other ways to explain it,but Eratosthenes looked at it this way.He said, "

OK, suppose that the earth is curved."Here's a curved surface and over here is a stick at Alexandria.The sun's rays are coming in directly on top of that stick.In other words, it's coming in directly vertically like this.And since the sun is far enough away, an assumption thatEratosthenes made, then the direction to the sun is the same everywhere.Right, so all of these red lines are parallel.Right?All pointing in the same direction.So, a stick that's vertical over here will have the sun's rayscoming in at some angle other than vertical.So, this stick will cast a shadow.The sun's coming in like this.This stick will cast a shadow.How do you use that now to determinethe circumference of the earth?What is done here is to make an assumption first of all that thedirection to the sun would be the same no matter where you areon earth, and it's the surface of the earth that's curving and not the sun.You see how to turn this into a measurement?Well, here's what Eratosthenes did.He measured the angle of the sun here and found it to be about 7.1 degrees.I'll write this down here, 7.1 degrees.So how do you turn that now into a circumference?\dWell, it's geometry.Remember geometry?Geometry.By the way, geometry means "geo," earth; "metry," measure.

The word, geometry, comes from measuring the earth.So, do it like this.You say, draw this line down here, draw this line down here, right?This represents the vertical stick and the two locations,the angle 7.1 degrees, that's up here, must be the same angleas this one which must also be 7.1 degrees.If you don't know geometry and you're not following the detailsof the geometry, don't get concerned.Our purpose here is not for you to be able to reproduce this,but simply to see how advanced science had become so thatEratosthenes was able to do this.So, we know that this angle, 7.1 degrees and this distance is,in modern measurement, 500 miles.So, can you see from that how to turn it into the circumference?Well, let me go to another page here and I think we can see one final time.

This time I want to draw a little smaller scale of the earth.So, here we have Alexandria.Here we have the other city.We have a 7.1 degree angle.7.1 degrees.We have 500 miles here.OK, everybody, quick, how many degrees are there in a circle?360, right?So, all the way around the circle here is 360 degrees.So, this fraction 7.1 divided by 360, right, must be in the sameratio as this number 500 is to the circumference of the earth.Right?Same fraction, same ratio.Well, if you do the arithmetic, you come out with a nice numberfor the circumference, the distance all the way round the earth.It's about 25,352 miles.Now, again, your job is not necessarily to know how to do this.I'm not going to ask you to reproduce this.The idea is, look at the way geometry is used,and how sophisticated the ideas in the geometry have come.

Now, even though Eratosthenes was able to measure thecircumference of the earth, he didn't prove that the earth was round.Because there is that assumption that the direction of the sunwill be the same--that the sun's rays are never parallel.We know this to be true today because the sun is nearlya million miles across and the earth's only a few thousand miles across.So, we know this to be true.So, he didn't prove anything, what he did was to say, if this is thecase, then the earth must be curved and circularand we can figure out the circumference.The fact that it's so close to the modern measurement,I think it's a testament of the accuracy and the good sciencethat these people were doing back here, almost 1800 years ago.Probably the most influentialof the residents of Alexandria was Euclid, the father of geometry.

Euclid basically collected the entire Greekknowledge of geometry and formalized it.Formalized means that he wrote down rules for doing it.He stated axioms, he developed methods of proof,methods of relating, of constructing geometric figuresof all kinds, analyzing the properties of different shapes,calculating their perimeters and areas, just to name a few things.His book, entitled simply "Elements of Geometry," hasprobably had more influence on more people than anyother book except maybe the Bible.It's been used in schools for more than 2300 yearsand still the best overall reference for so-called planegeometry or the geometry of flat surfaces, or two dimensional geometry.The logic that he used, in fact, the use of logic in analysisin problem solving is just as important to our modernscience and our study of science as is the geometry.But solving mathematical problems of any kind can oftenbe made easier if there's a model, problem solving model, to follow.Several of these types of problems will rear their headsduring our studies and we'll deal with them when they pop up.But sort of keep this floating around in the back of your mind.

Constructing geometric figures is more than just drawing lines.There's a very precise methods for bisecting a line segment,for example, or drawing equilateral figures like triangles and squares.Equilateral means the sides are all the same lengthlike the polygons of Pythagoras.There are very specific rules for constructing right angles.We've already seen how the Pythagorean triples can be used to do that.There are also rules of proportion for triangleswhich contain angles of the same measure.And so on, the list goes on endlessly.So, we will not undertake a detailed study of these rules,but some of them will return to haunt us later.Like the problem solving, we'll deal with these when we getto them, so sort of put this in a back drawer of your mental filecabinet and we'll come back to it a little bit later on.There are several words that are good to know.

We'll see them again with Newton who relied heavily on Euclid'smethods when he analyzed the motions of the planets while hewas formulating his discription of gravity.So, let's take a look at some of these words.First of these is "axiom."An axiom is a statement of assumed fact.It's a hypothesis that's not subject to proof, but which seems to be true.Here's an example of an axiom.On a flat surface, parallel lines never cross or converge.This is one of Euclid's axioms about the nature of lines on a flat surface.On a flat surface, parallel lines never cross or converge.This does two things, it states a property of the flat surface;at the same time it defines the concept of parallel lines.

OK, "theorem."A theorem is a statement which is subject to proof using formalmethods of logic and mixed with previously proved statements.So you're getting the picture here.You start with these axioms and you then throughlogical methods derive theorems and proof.What do we mean by "proof," exactly?We all use the word, like you know, "Hey, prove it to me."A mathematical proof involves some method of logical stepswhich shows that a statement such as a theorem is true for allsituations, not just one case or two cases, but all situations.Such a statement, for example, might be thatsimilar triangles have proportional size.That's a theorem.A "corollary" is a statement which follows from a proven theorem.

Once a theorem is proved, then there are, and you know thatto be true, then the theorem behaves like and axiom,and you can from there develop other statements which rely upon that.An example might be the ratio of the sidesof a triangle depend on the angles in the triangle.Once we've shown that triangles have proportional sides.So we'll leave Euclid behind for now, but he will resurface againand we'll see how his method works when westudy Newton in a later program.Hipparchus easily ranks among the greatest astronomers of all time.His contributions and inventions took astronomy to a level neverbefore obtained, and not even matched until Tycho Brahein the late 16th century, nearly 1500 years later.A list of accomplishments of Hipparchus is impressive.

Using instruments such as the astrolabe which he designedand constructed, he made very careful observationsand published the first detailed star catalog.Hipparchus also invented the system of latitude and longitudethat we use even today for location on the earth as well asthe location of stars in the heavens.The many modifications that he made to the Aristotle Systemreached their culmination with Ptolemy's publicationof the Almagest which became the standardastronomical reference until the time of Copernicus.In fact, it's easy to say that Ptolemy owes very much of his work to Hipparchus.We need to take a minute to see the relationship between theaccuracy of measurements and the predictions of the motions of the planets.For one thing, you see, the more accurate the measurement is,the more you know whether or not the model is working.In fact, the more accurate the measurement is, the moredifficult it is to find the model that reproducedthem to a sufficient level of accuracy.It's sort of like saying, OK, if the planet Mars, if I predict it'sgoing to be over here in this part of the sky tonight, and you lookin that part of the sky and you see Mars is definitely overin that part of the sky, then you say, "Oh, that's a good theory."But, if I can make a good measurement of the locationof Mars, if I can say, for example, I have this instrument,I'm going to sight, I'm going to say, OK,

I'll start from northand I'm going to go 23 degrees to the east and then I'm goingto go up 16 1/2 degrees and that's where Mars is.That's a very different qualitative precise kindof measurement than simply saying, it's over in that part of the sky someplace.So, if I say it's going to be 23 1/2 degrees and 16 1/2 degrees up,and you look in that exact spot, and it's not there,then you're going to say that my predictions are not accurate.So, the astrolabe is like a surveyor's transit.But, the important difference is that it hasa sighting tube instead of a telescope.A sighting tube is just like a long tube that you canlook through to find the location of a star.The telescope, remember, would not be invented for another1750 years, so the astrolabe was the high tech instrumentat the time, and there was nothing like it anywhere elsein the world, not just in Alexandria, but nowhere else in the world.Using these instruments Hipparchus made very carefuland very many accurate measurements of the stars and planets.In fact, they were the most detailed observations ever made up to that time.And as a result, they showed that previous calculationsof the planetary motions did not really predict themotions of the planets very well at all.Hipparchus was a remarkable guy.He was able, for example, to calculate the moon and sundistances from solar eclipse using the times and durations of the eclipse.In fact, he found a method for measuring thedistance both of the sun and the moon.

Now, think about this.This is really remarkable.How many of us could figure out how to do that?Suppose it's your job tonight to out and figure out how far it is to the sun.So what, you take a piece of string and you tie it to a treeand you go all the way up to the sun and you measure how long the string is?Well, that doesn't work very well.In order to this from eclipses, it first of all requires anunderstanding of what causes eclipses.And that's, if you think about it, a fairly sophisticated notion.In fact, it's one which escapes many people hereat the end of the 20th century.Well, although Hipparchus did this quite well, the distance that hemeasured to the sun was incorrect.This kind of threw people off for many years thereafter.The method was sound, although his measurement was incorrect.Partly this is due to the fact that time measurements are very difficult.Remember, there were no clocks in Hipparchus' time.In fact, there were no clocks until around the 15th century.This is another 1400 years after Hipparchus,and there was no decimal number system.In fact, there was no decimal number system in useuntil the Arabs modified the Hindu decimal systemsomewhere between 400 and 800 A.D.So, this is still another 650 years or so after Hipparchus' time.

Hipparchus did make a very detailed star catalog.There are only about 3000 stars visible to the naked eye,not counting those which are spread across the Milky Way.Locating each one of these stars and recording its coordinates,if you think about it, it's an awesome job.Now, 3000 isn't a lot, but it's too many to count and it's too manyto keep track of without some sort of system.The star catalog of Hipparchus contained about 500 stars;that's about one sixth of the total stars in the heavens.That's a pretty amazing thing.If you don't think so, go out tonight and try to findthe detailed locations of 500 stars,and those that you don't know what to call them,invent names for them at the same time.

OK.The idea of a grid system for describing location on a sphereis one we take for granted today because all of our maps of boththe earth and the sky has these numbers already on them.But, who thought of it for the first time?Could you have done this?I don't know, I probably wouldn't have.And once again, here we see the power of the inventionof genius which helps propel us into a different kindof understanding of our world.This is important because once a grid system isin place, it's a simple concept.But once it's in place it becomes much easier to record thelocations of the stars and also, of course, to keeptrack of where you are on earth.That's important in navigation, right?A seafaring economy like Alexandria's, those people whodidn't get lost get the good ships and get the business.Those who did get lost, got lost and didn't get the business.So, it's a pretty important thing.It's also important to note here that Hipparchus was amongthe chief detractors of the heliocentrism of Aristarchuslargely because of lack of parallax which we alreadymentioned, but also for the other reasons.If you've forgotten these, you might want to go backto Aristarchus now and review this rejection of his heliocentric theory.

Another important thing that Hipparchus pointed out is thefailure to observe the crescent of Venus.Venus is a planet, but it's closer to the earth than the sun.That means that in a geocentric system, Venusmust always be between the earth and the sun.So, it should never exhibit a full range of phases like the moon.You may remember that in order to see a full moon, the moon hasto be on the opposite side of earth from the sun.We'll see when we look at the Ptolemaic system a little lateron that one of the requirementsof a geocentric system is that theVenus always be between the earth and the sun, therefore,you should never expect to see anything other thanGibbus, I'm sorry, crescent phases.The phases of Venus can't be seen with the naked eye.Why not?It's too small.Venus is very far away.In fact, you can only see these with a fairly powerful telescope.You might be able to resolve them with a pairof low power binoculars, but probably not.They weren't seen until Galileo pointed his telescopeto the heavens in 1609, 1500 years after Hipparchus,and was able to then to see the phases of Venus.I'm getting a little ahead of things here, but it's importantto understand that Galileo, upon seeing the phases of Venusthrough the telescope, first time anybody had ever seen them,immediately and instantly knew that 2500 yearsof thought and paradigm was wrong.

You might want to think about you being in that positionof recognizing something that important and that big waswrong and what you would do about it.We'll cover this when we get to Galileo.The system of Hipparchus was a little bit different.In fact, he, instead of using the homocentric spheres of Euxodusand Aristotle, Hipparchus found the calculations easier,if he thought of the motions as circles, still keepingthe circular paradigm, but circles were to not have the same centers.What he did was to add something which he called epicycles and eccentrics.This we'll look at in detail when we look at Ptolemy here in a little while.But, see in abandoning the homocentric model of Exodusand Aristotle, you still have to account for the retrograde motions.Retrograde motions, after all, is the whole reason for this complicated system.And this is after all where the system of, the concept of circles originated.To visualize an epicycle, imagine a small wheel.Imagine a wheel like a, small wheel like a wheel on a shopping cart.Paint a white dot on it.

Now, if you spin the wheel around and hold it in oneplace, the white dot describes the circle.If you roll the wheel along a flat surface, what kindof pattern would the white dot show you?Yeah, it would be sort of a looping thing, wouldn't it?It would be like a circle that's being rolled along a flat surface.So, what happens if the wheel's rolled around the outside of a larger circle?Such as around the outside of a large can, like a trash can?What shape does the white dot make then?Well, let's think about this.When it's stationary it makes a circle, when it's rolling itmakes a loop, so what does it do it you rolled around the outside of the drum?It makes loops like this.In other words, sometimes the white dot reverses its directionand moves backwards just like a planet does during retrograde.So, the modifications that were made by Hipparchusto Aristotle's system of the world did reach culmination with Ptolemy.But before we get to Ptolemy, I want to point out thatby the time these ideas got to Ptolemy, it had verylittle in common with the original ideas.In fact, about the only thing that Ptolemy's system had incommon with Aristotle's was it was geocentric, and, oh yeah, it was circular.

Claudius Ptolemy was a mathematician, astronomer, and geographer.He systematized, recorded, and added the data and doctrinesknown to the Alexandrian scientists.He was systhesist.His book called the "Almagest," which was widely translatedand influential in Europe, in the Middle East and even into India,until the 16th century, presented Ptolemaic system of astronomywhich was based largely on the concepts and data of Hipparchus.Ptolemy is kind of an interesting character,although we know little of his life.There a few personal records, so we know next to nothing abouthim, except through his publications.In fact, even the dates of his birth and death are approximations.He's one of those guys who wrote books, published several majorworks, but really didn't make much of a stir otherwise.Mostly his books were textbooks on a varietyof astronomical and geographic topics.They were quite mathematical and his skill as a mathematicianwas quite good, although he did make a lot of mistakes.Oh, well, what do you expect, he still didn't have any numbers to work with.All of his calculations were done from truth tables, like when youfind the distance between two cities on a road map.

It took a long time to do these calculations and they were not very precise.Because remember the concept of decimalsand things hadn't been invented yet in Western thought.His geography text, in fact, was the most comprehensive of all time.It had detailed maps of the entire Mediterranean region, lattitudeand longitude, and was used as the navigationalstandard for the Alexandrian sailors.Ptolemy's greatest work, on top of all these others, was the "Almagest."It was a combination textbook, encyclopedia, and astronomical almanac.It was a remarkable piece of work, despite the errors.The Greek title was the "Great Syntaxis," or the"Great Compilation", or even, you might think of it as the "Great Synthesis."But the European title that was passed down to us comesfrom the Arabic word, "Al Majisti," the same root wordas majestic and majesty,essentially, the "Greatest" book.It gives you a clue that the folks thereabouts thought quite highly of it. In fact, I think it would be pretty much of an honor to write abook which somebody translated it as the greatest book ever written.If I can ever write one like that I'd be very happy, I think.

The book was essentially a compilation and collectionof data, calculations and methods of observation as well as thecalculations and tables of planetary locations.Basically, it was a compendium of 600 years of Greek astronomyas well as new results that Ptolemy had addedof his own work on planetary motion.It also contained an update star catalog, with several hundrednew stars some of which discovered by himself and someof which discovered by others since Hipparchus'stime nearly 250 years before.It's important to keep the perspective here that althoughwe're jumping from Hipparchus to Ptolemy,that 250 years lapsed between these two guys.And again, I remind you that's longer than theUnited States has been in existence as a country.So, the book was such a good book and it had so much informationin it that it defined the basis of mathematical astronomy,and remained the best and simplest book availableuntil Copernicus described his heliocentric methodsin the 16th century 1500 years later.So, not surprisingly, this system of Ptolemy which was put forthin the "Almagest" has come to be known as the Ptolemaic system.

So, let's take a look at the Ptolemaic system.It became the standard because it was the best at the time.And Western civilization, as we'll learn later, went into a veryrapid decline as the unity of the Roman Empire weakenedbefore anyone could come up with a better system.Ptolemy, in fact, marks the last of the greatAlexandrian tradition in science and learning.Since Ptolemy's system had such a strong and lasting influenceon the Western world, we should take a few minutes to look at its structure.What we're going to do is analyze what Ptolemy had synthesized,and if those words are confusing, you'll be hearing them manytimes and you might want to go back and lookat definition of synthesis and analysis.There are several important differences between Ptolemy'ssystem and Aristotle's system, and these will turn out to besignificant because when the works of these two guysreemerge in Europe a thousand years later, they turn out to saydifferent things and people were kind of confused about who they should believe.So one of the most important differences between Ptolemy'ssystem and that of Aristotle is the linkage of motions.You may remember that Aristotle had linked the motions togetherand in Aristotle's universe nothing, nothing happenedwithout cause and nothing happened independently from the whole system.

By Ptolemy's time, this cosmology had been lost, completely.Never mind what caused the planets to turn, it was hardenough figuring out how to describe how they did turnand calculating where they were going to be.So, what Ptolemy did really was keep the mathematics,the calculation, without concern for what causes the planets to move.This might have been fine for the growth of science, but therewas the Church, who would surely become greatly concernedwith cause, but would remain ignorant of much of Aristotle's work until the 12th century.Well, there I go getting ahead of things again, but the Church,basically, had a thousand years to work on its own causesbefore the works of Aristotle reemerged.

I'd like to say that Ptolemy saved the appearances very elegantlyin a masterpiece of mathematic artistry.You may not like to say it that way,but what he did, anyway, was very Platonic.He used mathematics to turn the perfect circular motionsof the heavens into the observed paths of the planets, retrogrademotion and all, very consistently and very accurately.In fact, the calculations that he had for planetary tablesand navigation were the most accurate of the timeand at least as accurate as anybody could make observations for.He used this to describe the motions of the five planets, the sun and the moon.This system accounted for the retrograded motion of the planets.It accounted for the changing speeds against the backgroundof fixed stars, it accounted for the changing brightnessand size of the planets during the retrograde phases.This is something that Aristotle's model failed to do, and you mayremember this is some of the weaknessesof Aristotle's system we listed.

One of the tools Ptolemy developed was really a gift from Hipparchus.He elaborated on it and refined it, but he called these tools, "devices."Think about this for a minute.What is the word, device, bring to mind?How is a device different from a tool?It would be a good idea here to take some time to lookup the two words in the dictionary.Silico: "This would make a great topic for a short essay."It would make a topic for an essay.It's already in the study questions.Didn't you read them?So, take a look at the devices here.You can see from the pictures that the basic device is the epicycleand deferent which was borrowed from Hipparchus.This is the idea of a smaller circle rolling around the outside of a large circle.The problem was that in Ptolemy's system, he still couldn't quitemake the planetary motions work out this way.There were still inaccuracies.So, he discovered that he could still maintain the Platonicintegrity of this perfect circle if he kept the motionsof the planets circular, but, and this is really funny, he decidedthat the earth didn't have to be the center of the circle.That the planets could still move in a circle, but earth is nolonger the center of circle which is offset to one side a little bit.The effect that this has is that it allows the planets to still moveat a constant speed around the circle, but the apparent angularspeed of the planets through the sky changes dependingon which part of the orbit they're in.Very clever, very clever solution of the devices.

The other device was one called an equant.An equant was simply that the circle itself became offsetfrom, the motion, I should say, became offset from the circle.Now, again, if we're looking at these pictures and panicking,saying, "Oh, do I have to know this stuff?"And again, the answer is, no.You're not expected to know the details of the devices.The idea is the device, itself, not necessarily what the device,or I should say, how to use the device.The concept of the device is the important one.So, the reason why it's important to us is becausePtolemy used the devices inconsistently.In other words, sometimes it was necessary to usethe device and then for a while not use it.I mean, so, for example, you're trying to calculate the motionsof the planet Mars today, and you want to project this into twoweeks from now, and so you use the device and it really worksreally fine, and then after a couple of weeks it doesn't work anymore.

So you say, "OK, I'm not going to use the device anymore."In fact, sometimes Ptolemy would allow the eccentric to change locations.In some cases he'd allow the eccentric of the equant to movearound the circle with the planets.You know, it was really quite difficult to do the calculationsto begin with, and even harder to know when to do what kind of calculations.You see the problem.With our modern mathematics,if we're going to do a calculation, we do it all in the same way.We solve a problem, we use the same kinds of equation.What Ptolemy was doing here basically was using the formula,if it worked and not using it, if it didn't.Let me say that in a different way.If the formula gave the correct results, then it was thecorrect formula whether or not it made any sense,or whether or not it was consistent.So, you see, even though it was mathematics, there was reallyno underlying structures of the mathematics.

The philosophy, methaphysics and physics of how and why thissystem worked were simply not important to Ptolemyand the people who read his book.What was important was that it could be used to predictthe locations of planets to within the degree of accuracy thatanybody could actually see them.Ptolemy did, in addition to the calculations go to some lengthto justify the fact that the earth was stationary.Just so we don't forget, remember that we thought we learned thatColumbus thought the earth was flat.But Eratosthenes recognized its roundness in calculating the circumference.So, it's not too surprising that they would think of a roundearth or a spherical earth, but Ptolemy's argumentsfor a stationary earth were quite convincing and reliedspecifically on Aristotle's theories of motion,even as he was ignoring or was unaware of the cause of planetary motion.So, it's kind of interesting that he keeps the platonic circles,and keeps Aristotle's idea of motion but completely throwsout the concept of the cosmosand the intergalactic spheres and all that.Ptolemy's system also, by the way, allowed him to calculateeclipse times, something that none of the earliertheories could do very well.Ptolemy also was one of the first peopleto specifically state the idea of parsimony.

Parsimony, remember, is simplification.He did this in his justification for notincluding a discussion on the cause of motion.He simply said that the simplest system was the one that workedbest with the smallest number of complications.His model was very reductionistic, having removedfrom it all that was not necessary to make it work.All this stuff about the connections between thespheres did not affect whether it works or not, so dump it.Now, it's difficult for us today to go back and criticize Ptolemyor any of those who adopted his system.It was, in fact, a really good system.It's just that it didn't have the cosmology.It was later in the Middle Ages that astronomers triedto integrate this into a coherent physical system.In fact, it wasn't long after Ptolemy's deatharound 140 A.D., that the metaphysics began to creep back into this theory.Later astronomers tried to integrate a coherent physical system.They asked questions like, "OK, if I got all these spheresand epicycles and things, what's between them, what's thematter, what's the space made out of between them?"And these are not all the questions or some of the questions.As we'll see in the next program, Medieval philosophers had littleluck in providing answers to these questions.

On this program we've learned how Aristotle's systemof the world became corrupted as Hellenistic Greek culturecontinued in Alexandria after the deathof Alexander and Aristotle, late in the 3rd century, B.C.We followed the river of thought through contributionsby Aristarchus, Euclid, and Hipparchus.Then we saw the major tributary of Ptolemy's grand synthesisadding the best of Greek astronomy to the streamof history, where it would soon replace the lost cosmologyof Aristotle with the fresh view of Christianity.Well, I guess that's it.The time has run out again on the Nature of PhysicalScience, but we will be back.Remember, when it comes to science, get physical.Bye.So, you have anything to add before we go?Silico: "Yes, thank you.I would like to say that I now have a much better understandingof the role of Greek philosophy in our modern science.For one thing, I thought only computers had truly Platonic relationships.I especially liked the continued use of the river metaphor."Music