Wisconsin Public Television University Place UW Space Place  Jim Lattis, "Constellations, Signs and the Zodiac: Are there 13 Now?"  February 8, 2011 UP550      cc >> Jim Lattis: I'd like to welcome you to Space Place tonight. Our presentation tonight is on a topic that's been of interest just lately, in the news a lot just lately, and that is this business about a 13th sign of the zodiac. So what's all this about a 13th sign of the zodiac? Turns out there's been a lot of discussion about this, a lot of which fails to actually define even the language that's it's using, and so I have found that the explanations of this have been lacking everywhere. So I've tried to take us through it here. We talk a lot about, along the way, well a bit about, astrology. And so this is not a talk about the validity of astrology, but just for the record astrology is nonsense and we can have a talk about it some other time. [LAUGHTER] But that's not what we're going to talk about tonight. But these things do come into the foundations of astrology, which is certainly important in the history of our culture, but also, and just as much, in the history of astronomy. And we'll see that as we go along. So what's all this about a 13th sign of the zodiac? The claim that we've been hearing, as I refer to these news stories that we hear, is that the precession of the equinoxes has caused there to be a 13th sign of the zodiac. 

And then we also hear that the new sign is the constellation Ophiuchus, or is named Ophiuchus, which is the constellation that few enough people have heard of that just the very mention of it often causes giggles and mirth. But it's a perfectly good constellation. It's easily as old as all the rest of them that we've all heard of, and we'll talk about it just a little bit, too. But we need to get a little bit of background, which is exactly where many of the news stories have been failing. We need to get a little bit of background, and so to do that, I'm going to use this software that I like to use and recommend called Stellarium, so that we can look at the parts of the sky that we need to talk about here in order to understand the basic ideas. Sign of the zodiac suggests that we need to know about the zodiac and we do. Here we have the sky, shown actually in the daytime but with the atmosphere turned off so that we can see the sun right there and planets and the stars all conveniently the way we never see them unless we live on the moon or something. During the course of the year as the earth orbits the sun, the sun appears to move through the sky, makes a complete track through the sky, 360 degrees all the way around during the course of the year. And not related to this particularly is that changes in latitude in the sky cause our seasons and that kind of thing. But for our purposes, what's important is if you could see the sun moving through the sky, as well as the planets, which of course we can see moving through the sky, against the background of stars, if you tracked it during the course of the year you would find that it follows this path. 

Here we're only seeing, of course, a section of it which goes all the way around the sky. And the path of the sun during the course of the year is, as it's labeled there, the ecliptic. That's the path of the sun. We always find the planets, for example Mercury and Venus, but all the planets and, all the visible planets, and the moon always in the general vicinity of the ecliptic. You can see they're not perfectly on the ecliptic. Mercury and Venus are off a little bit. So the ecliptic defines this region of the sky that is where we always find all the solar system activity, the motion of the sun, moon, and planets. The ecliptic passes through, we say, or in front of if you like, constellations. And so the set of constellations across which the ecliptic passes, so the background of stars here, that set of constellations is called the zodiac. But now I just used the term that we actually have to talk about just a little bit and that is a constellation. 

So what is a constellation? Most everybody has an idea of what we mean by a constellation, and most of us probably think of a constellation, when you first mention the word, as a star picture. And Stellarium is perfectly good at that. Stellarium will fill-in these star pictures for us, which are generally pretty closely related to the name of the constellation. The way most of us learn to see them, though, is by connecting the stars together with dots, or using the stars as dots to connect together lines to make star pictures and little characteristic shapes that we can remember. The star picture idea of a constellation is quite ancient. It's probably the original idea of what a constellation is, although not necessarily, it might be that people thought of regions of the sky as dedicated to one concept or another and only later put together a picture. I don't know. But right now, our idea is usually that there's some kind of thing represented up there. For example, right over here is the constellation of Scorpius, the scorpion, and right above Scorpius was our friend that we've already been talking about, Ophiuchus right up here. And I'll just turn the constellation art back on for a moment. 

I'll turn on the star labels too. So now you Ophiuchus and there you see Scorpius. In the oldest star catalog that we have, we have a star catalog that's a couple thousand years old, the astronomer Ptolemy, who's going to come up again, the ancient Greek astronomer Ptolemy, compiled a star catalog based on earlier star catalogs but we don't have those. Ptolemy star catalog uses the star picture idea as the basis of its organization. In the star catalog it's the star constellation Ophiuchus for example. Then he'll say the star in the head. That's actually how this star which we have a name for, Rasalhague, an Arabic name, we can also call it alpha --, that star in Ptolemy's star catalog is the head. It just says the head, meaning within Ophiuchus. And then he gives the coordinates of it and estimates its magnitude. And that's how the whole star catalog works. 

So then there'll be the right hand under Ophiuchus, or the left hand, the right leg, the left leg, whatever. All the constellations are identified that way. The head of the eagle, the tail of the eagle and so on. So the star picture idea is intrinsic to this organization that comes down to us from antiquity, and that's what a constellation has meant for most of astronomical history. However, there is another way of thinking about them that you'll find more often in star catalogs and things these days than the artwork. When somebody says a star belongs to one constellation or another these days, they're usually referring to these boundary lines that you can see, the red lines. I hope they're standing out enough for you to see them. These are the constellation boundaries that were identified, set up to find, I guess is the word, by the International Astronomical Union in 1922. And sort of like setting up where Utah ends and Nevada begins or whatever, the boundary lines are the places where the constellations bud up against each other, and they don't leave any unmapped space in the sky. So unlike the star pictures where there can be gaps and where if Ptolemy doesn't mention a particular star you don't know where it's intended to go, as far as a constellation, the boundary lines don't have that problem. 

The boundary lines map the entire sky, and so it's unambiguous whether a given star is part of Scorpius or part of Ophiuchus. So down here, for example, is Ophiuchus which kind of extends down in that direction. You can sort of see the boundary lines. I hope you can see that the boundary lines can extend down there, and Ophiuchus ends and Scorpius begins. And these stars right here, which are sort of in between Scorpius and Sagittarius right here, those stars are designed to be part of Ophiuchus by the modern definition. But that's only since 1922. That's the modern idea of what it means to be a constellation. We're going to talk mostly about the star picture because that's how people have seen them for a long time. So let's turn the star pictures back on, and you might be able to notice here a little bit better that there's Scorpius, once again, and there's Sagittarius, the well-known teapot asterism right there, and here is Ophiuchus, and here is kind of a straggling bit of stars which, it turns out by the modern definition, fall on the Ophiuchus side of the line, some of them up here and then some of them fall wherever the line actually falls, some of them fall in Scorpius. They're kind of right in there in the middle, and, as it happens, the ecliptic runs right through there. 

So by both the modern definition of the constellations and by Ptolemy's ancient definition, it's possible that the ecliptic moves through the constellation Ophiuchus. If you decide that that's part of Ophiuchus. By the star picture idea it depends on whether you want the star picture's leg to extend that far down into that part of the sky. By the modern boundaries it definitely passes right through there. Well, one of the things that's been asserted is that precession of the equinoxes causes this to be a relatively new thing. We're going to see that that's not the case. In fact, the ecliptic runs right through Ophiuchus there, or at least what might be a part of Ophiuchus. By the way, in Ptolemy's star catalog, when he gets to those stars down there in that sort of, this end, I guess it's the end of Ophiuchus' leg or something, the star picture kind of trails off, when Ptolemy's star catalog in modern editions gets down there you'll find that the modern editors put asterisks by all of those stars because they're not actually sure which stars Ptolemy is talking about. There's some ambiguity in, we get this ultimately out of manuscripts that are many, many centuries old, there's some ambiguity about just which stars Ptolemy is talking about. So it's possible that Ptolemy thought of Ophiuchus as ending considerably farther north there. 

But that's all a little bit fuzzy, fuzzy enough that we'll just have to say that it's possible that Ptolemy understood the ecliptic to run through Ophiuchus as well. Okay, so that's constellations, that's the zodiac, why are there 12 of them? There are 12, as you know, signs of the zodiac. Why isn't Ophiuchus a sign of the zodiac? Well maybe because ancients didn't consider those stars to be part of Ophiuchus, but maybe it's because 12 is a convenient number and a 13th one would be unwelcome and inconvenient. There are 12 full moons during the course of the year, for example. 12 is a very convenient number to divide into 360, and the idea of dividing a circle into 360 parts is a very old idea. 12 would have been a much more convenient number if you wanted to divide up the ecliptic. And there's good reason to think that actually that's what people wanted to do. They wanted a good scheme to divide up the ecliptic. And I say that because now we're going to talk about the idea of a sign. What is a sign of the zodiac? Since antiquity, let's just slide this over a little bit, since antiquity, astronomers and astrologers both have divided up the zodiac, I should the ecliptic really, have divided up the ecliptic into 12 equal divisions of 30 degrees each, adding up then to 360 degrees all the way around. 

You don't have to look very long at the constellations here to see that they don't all occupy the same angular width. Only a short bit of the ecliptic passes through Scorpius here. More of it passes through Capricornus here and Aquarius. Pisces actually sprawls quite a ways depending on where you would decide to draw the boundaries. Aries is where the coordinate system has always started, either in name or in actuality, but those aren't always the same thing. Aries is where the system of signs traditionally started. So the first sign was said to be Aries, and then you just divide it up into 36, I'm sorry, into 30, I'm sorry, into 12 equal divisions into 30 degrees each all the way around the zodiac. And the precise reference point was the vernal equinox, which is the point where the sun crosses the celestial equator. So here we are, this has shifted over the years and we'll talk about precession, this is where it is now because we're set for 2011 here. This is the celestial equator, what divides the northern sky from the southern sky, and this is the path of the sun. 

And when the sun crosses the celestial equator headed northwards, that is the vernal equinox, which happens around March 21st, and it's that point in the sky which was considered to be the origin of the system of signs. So the sign of Aries started there and then went for 30 degrees and then the next sign after Aries and so on all the way around until you'd done all 12. So already using a system like that it's not really very important whether you're talking about the stars of Aries because what you're really talking about is the position of an object in the sky and how many degrees past the vernal equinox it is. That's what the coordinate system of signs was designed to do. And astronomers and astrologers both use that system for quite a long time. So the signs are not necessarily, in fact the signs are really not the same as the constellations. You could think of them as a series of 30-degree segments that are named after the constellations which were nearby at the time that this system was defined, whenever that was. Well, so I mentioned that this point has moved, and what I'd like to do is talk about why this point, the vernal equinox, has moved. This, what we call, precession of the equinoxes. I'm going to switch back over to the other screen here and talk a little bit about the history of precession. 

Actually, this has been known for quite a while. The precession of the equinoxes was discovered by a guy who lived around 150 BC, the Greek astronomer Hipparchus. Hipparchus was looking at records of positions of stars that were already quite a bit older than him, at least a couple hundred years old at the time that he was studying them, and he compared the positions of the stars in those records to the positions of the stars in his day and found that the stars had shifted eastward with respect to the vernal equinox. I'm going to go back to Stellarium and show you this in just a minute. He found that the stars had drifted eastward with respect to the vernal equinox. He estimated that they had shifted approximately one degree in 100 years. So it's 360 degrees all the way around, so one degree during a hundred years is not something, certainly, that a casual observer would notice. And unless you were making high precision measurements, not something that you would care about even over generations. But over a number of generations Hipparchus was able to establish that they had shifted. He thought of this as a motion of the stars. 

He thought of the equinox as the fixed thing because he was, like most people, a geocentrist. The earth was stationary and central in the cosmos, and so it was the stars that were shifting. The stars were doing a shift eastward little by little, one degree per one hundred years. Hipparchus' astronomical work was continued, I'm skipping over lots of other astronomers, it's not like these were the only two guys in antiquity, although they were sparse, but Hipparchus' work on precession was continued by Ptolemy, the guy I mentioned a little while earlier. Notice he lives about 300 years later than Hipparchus, so this was not an ongoing research program or something. But Ptolemy came to gather up Hipparchus' work, redo Hipparchus' star catalog into the one that we have inherited, and Ptolemy's star catalog, the one in the Almagest, is the reason why he had to deal with precession because he knew the stars were shifting because of Hipparchus' work, he had to figure how much they had shifted during that time in order to put their coordinates into his star catalog. He wanted to correct for this precession. He decided, on the basis of observations going back to Hipparchus and perhaps even before, that Hipparchus had had the right number of about one degree per century, which means that the whole cycle of precession would take 36,000 years. During that amount of time, the stars, which were imagined as fixed to a sphere out at the outer edge of the universe, and we'll see some diagrams of that in a minute too, would rotate around the earth one complete revolution in 36,000 years. Now, that's not the way we see it now. 

So just to make sure that we are talking about modern physics for a minute, the way we understand precession of the equinox is not that the earth is central and stationary, of course, but rather that the earth, which orbits the sun annually and rotates on its axis daily, the axis of the earth also has another motion. Usually we will think from day-to-day because we don't think too much about precession, it takes a long time to affect us, we think about the earth's axis here as always pointing in the same direction in space which is basically up to the north and south celestial poles. In the northern hemisphere, we get to look up to Polaris. So from directly above the pole here you would find the star Polaris up there. But, in fact, the earth's axis has a slow wobble to it. So it's carried around in a circle just the way a gyroscope, if set on a table, or a top will precess. It spins very rapidly, wobbles more slowly. Its axis makes a conical motion which is called precession, the earth does that as well. And the modern a rate, modern measurements put that rate about one degree in 72 years. So a little faster than Hipparchus and Ptolemy thought. 

That comes out to about 26,000 years that it takes the earth's axis to make one swing around here and come back to pointing, in this case, at Polaris. So 26,000 years from now, the earth will have done one complete wobble and be pointing back up there at Polaris, if Polaris is still there. Polaris could have wandered over that amount of time, but if Polaris didn't, then we have Polaris as the north star again but only after 26,000 years. All right, let's go back to Stellarium.  All right. So what is this precession, what did this precession look like to Hipparchus? One of the great things about this software is that we can find that we can set Stellarium back to dates long past. Here we are in 2011, but Hipparchus lived, as we just said, around 150 BC. So let's put in negative 150. Oops.  There we go. 

159 will do. Here we are and we're looking at the sky as Hipparchus would have seen it. And when we look to see where the vernal equinox is, so here's the ecliptic and where it crosses the equator headed northward, that's the vernal equinox, and here we see the vernal equinox and it's east of the middle of Pisces. Here's the constellation Pisces right here. If we go back further, let's go back another thousand years or so just to make the effect even more clear. There we are. We'll go back about a thousand years, and now about 1,000 BC here's the vernal equinox occurring clearly in the vicinity of the constellation of Aries. Now it would make sense to start your coordinate system in Aries. You'd say, oh, okay I'm going to start at the vernal equinox, and I'm going to call that 30 degrees Aries, and the next one is going to be Taurus and so on around there. By Hipparchus' time, where we just were a minute ago, go a thousand years ahead of time, the vernal equinox had moved this far. 

By Ptolemy's time, the vernal equinox had moved from over here to over there. So you see what's happening. The equinox seems to be going westward or, the way they were thinking of it, the stars are going eastward. The stars are drifting eastward kind of slowly. Let's go a thousand years after Ptolemy. So I'll just slip in a zero here. You see that the vernal equinox is now over on this side of Pisces. So at 1,000 BC it was over here, and then it was over about here for Hipparchus and then Ptolemy and a thousand years later it's drifted this far, and if we come back to today, or close enough, we'll find the vernal equinox down here. So look how far it's gone. It started out over here about 3,000 years ago, and in that amount of time it's gone from Aries and most of the way across Pisces and headed for Aquarius, and you've all heard about how great things are going to be when the equinox gets there into Aquarius. 

That's what that's all about, the vernal equinox moving into Aquarius. And that's, sure enough, where precession is taking the vernal equinox. So let's just take a quick look at what this, so this is what Hipparchus saw because the vernal equinox was something that he could measure. But what we were just talking about was looking at the pole, up at the north celestial pole. So if we go up here to get a look at the north celestial pole, we'll turn on some coordinate lines. Here's the north celestial pole right there, and if we go backwards in time, we'll go back, the easiest thing for me to do is just slip a negative sign in there and we'll jump back 4,000 years. All right, there's Polaris right there. And there is the north celestial pole. So if you go out tonight and look up, look for the Big Dipper right over there and look for the Little Dipper right there, 4,000 years ago when the pyramids were brand new, the north celestial pole was sort of halfway in between these two stars and the Little Dipper and the bowl and handle of the Big Dipper right out there near a star in Draco called Thuban. And if we creep forward in time a thousand years, oops, there, a thousand years, we'll see that the pole, our pole star seems to have moved closer. 

What's actually happening is the pole of the earth is swinging around because of precession and coming this direction, but what we're seeing, again, is the motion of the stars because Stellarium wants to keep the coordinate system centered there. If we go a thousand years again, here's the pole star. It's approaching right here, or you can think of it as the pole approaching the pole star. And then we'll go another thousand years, and then we'll just do the other thousand years. Oops, I better take out that negative sign, sorry. The other thousand years and here we are back to the familiar looking situation where the pole is very close to Polaris right there. So that's the same motion, the very same motion that's moving the equinox is moving the direction that the pole points. It's just that we tend to think, in the modern idea, we tend to think about where the pole points. That's sort of the Newtonian mechanics idea because we think about the earth as a gyroscope, but the astronomical idea, the same motion, the astronomical idea was the precession of the equinoxes away from their ancient, their older positions. All right, now we want to go back here to the area of the vernal equinox and go back to our slides here. 

 All right, so what's this got to do now with the astrological signs and the astronomical signs? Well, about 3,000 years ago the astronomical/astrological sign system started in Aries, and astronomers used that as a way to specify where they saw things in the sky, at least we presume that they did. But that sign system, at that point, was pretty much independent of stars. It doesn't matter anymore whether they're attached to the constellations or not. And the sign system always started at the vernal equinox, and we've seen that the vernal equinox was shifting. This is just a generalized idea, a generalized graphic to show that the signs here, this is from the 16th century astronomy textbook, this was how the author illustrated the idea of the signs. This is an astronomy book, and the signs are these equal 30-degree segments that divide up the entire sky around the ecliptic. Notice that the stars are shown here, but they're not constellations, it's just that's how we divide up the stars. The signs always started at the vernal equinox, 30-degrees each, named after the constellations, but they were not coincident with, in fact steadily farther and farther away from them. Always begin with Aries, that's the conventional place. And the precession moves it in such a way that the signs, for astronomers' purposes, are completely arbitrary. 

How is that different from astrological signs? Well not very. In fact, the astrological signs were almost the same. This slide is intended to show you the precession from about the same period, a different textbook, but this slide is intended to show the precession of the equinoxes. Here's the earth at the center and stationary, and we're not going to talk about all the planets, but there are all the planets orbiting the earth including the sun and moon, and out here, you get out to the outer edge and here is the sphere of the stars, what was then called the eighth sphere. That was considered the to be the last visible part of the universe out here or the firmament where the stars are stuck. And you see that the stars here are represented by the signs. There are the symbols for the signs, and what I really wanted to point out here and I'm going to talk about how they imagined this working in just a minute, I wanted show that there's another set of signs out here. These are in the ninth heaven. The ninth heaven doesn't have any stars. That sphere is invisible but it's out there, and it has what were thought of as the real signs back in the background with the stars shifting in front. 

So these are not, although they look like the stars, they're really intended, sorry, these look like signs here but they're actually intended to represent the real constellations because they've shifted. See that shift? That's the precession. That shift, that distinction between the stars in the firmament and the signs back there in the celestial sphere that start with Aries. Now they had really practical uses, the signs, even though they don't match up with the stars, and here's just an example. This is a replica, astrolabe, but you would always find on the back of an astrolabe, this is just convenient maybe for obvious reasons, on the back of an astrolabe there's a scale that allows you to convert dates into signs of the zodiac. So, for example, today, February 8th there, ends up, if you draw a line from the center out, it tells you that the sun on that date is in about the 19th degree of Aquarius. That's what that's telling you. So the sun is in the 19th degree of Aquarius, and Aquarius doesn't mean the constellation, it means the sign. And so you would add up 30 degrees for every constellation along the way. So from Aries, Taurus and so on, 30 degrees for every one of these constellations, plus the 19 that had been used up in Aquarius, and that's how many degrees away from the vernal equinox the sun had moved. 

We, today, call that celestial longitude, and we just give you a number for God's sake. It's 272 degrees or whatever it is. But the way it was traditionally expressed was 19th degree of Aquarius. So it's a very practical thing. This is not unique to astrology in any way. So the astrological signs, how are they different from the astronomical signs? Well actually not at all. They're just exactly the same. Always start at the vernal equinox, always have 30 degrees all the way around. The only difference is that astrologers attach significance to the signs. So Pisces, because the constellation Pisces is a watery constellation, astrologers can tell you what that means, don't ask me, but it means something to the astrologers. 

That's the only difference. They're the same. It's the same set of signs, they start the same way. They divide up the sky in the same way. So, the question then really is, is there anything to talk about in terms of a new sign? I'm going to go back to Stellarium for a minute here. Let's see I have to click over here. All right. So with that background, let's look back over at the situation with Scorpius, Sagittarius, and Ophiuchus right here, and let's ask ourselves whether the precession of the equinoxes has changed anything over here. We're going to do the same experiment that we did with the vernal equinox and with the pole except we're going to be looking in this part of the sky to see whether the ecliptic has changed its relationship to Ophiuchus in the last 4,000 years. So I'm just going to slip in a minus sign in front of there. 

Now the angle has tipped a little bit, but there's Scorpius. There it is passing through Ophiuchus, and there is Sagittarius. 4,000 years ago the ecliptic went right through Ophiuchus, modern Ophiuchus at any rate, just the way it does today. And if I went back a thousand years at a time, you wouldn't see any significant difference at all. So the claim that the precession of the equinoxes has caused Ophiuchus to be different somehow today than it was 4,000 years ago is clearly not the case. There have been shifts in where the pole points, shifts in the location of the vernal equinox, but the path of that red line through the sky is defined by the plane of the earth's orbit which is much more stable than most of those other things. And the background of the stars, although there is a slight variation, but the background of the stars has remained essentially the same. So Ophiuchus is not new to this game. Ophiuchus was just never included from the beginning for whatever reason. Either because those stars weren't considered to be part of Ophiuchus or, more likely, because 12 was a really convenient number and who needs a little chunk thrown in there. 

Whatever the reason was, Ophiuchus was never in the game, and things haven't changed right now. So to talk about a change is wrong and to suggest that we need to introduce Ophiuchus in there is really off the mark because the signs have been divorced from the constellations for millennia anyway. Well, what I think is interesting about this, so my answer is I can't see what all the fuss is about, there's no need for is 13th sign, nobody uses the signs anyway except astrologers, and the signs weren't connected to the real constellations even in antiquity. Let's go back to the slides because I think there's actually something more interesting to talk about. And I'd like to close with that. What's interesting here is the way people have tried to understand the precession of the equinoxes. Let's go back to this slide here from Peter Apian. If you go back and look at the sphere of the stars, the eighth sphere here, and I mentioned the little deviation here, the displacement between the visible stars and this invisible sphere out here, the ninth sphere, what you'll see if you come around here, what are these funny little wheels right there, what's that? And there's another one. And they're right there. That's Aries. 

This funny little wheel is stuck right here at the beginning of Aries. Those are in there because in the middle ages astronomers have a different idea of precession than Hipparchus and Ptolemy did. During the 9th century, the astronomer al-Battani was checking Ptolemy's numbers, and he decided, and of course he would have had to make the connection for precession just as Ptolemy did before him, he decided that precession seemed to have gone faster since Ptolemy's day than it had from Hipparchus' day to Ptolemy's. He measured the precession during his day and thought that it was approximately one degree in 66 years, which would give you a full cycle of a little bit less than 24,000. Quite a bit faster than the 36,000 years that Ptolemy had talked about. So al-Battani had thought that precession had speeded up, not a steady rate the way Hipparchus and Ptolemy had both imagined it. And in order to explain this, his contemporary, Thabit ibn Qurra, created a theory called trepidation, which is also sometimes called variable precession or sometimes also, in Latin texts they'll call it the kind of awkwardly named access and recess of the stars. It really means that that eighth sphere was not just creeping around but was going back and forth over a long period of time so that its rate varied. Al-Battani thought that's what he had seen was the varying of the speed. This actually became the standard picture in the west. 

It's interesting that oriental astronomers, successors of these guys, of Thabit and al-Battani, didn't really pick up on the idea. They didn't like it for whatever reason. We don't see it in star tables that were composed in the east, but it became popular in the west, in particular in Muslim Spain, and became the standard way of calculating precession in some astronomical tables that were very influential. The Toledan tables from Toledo around the year 1,000 have trepidation built into them. And the later ones, the Alfonsine tables also created in Spain around the mid-13th century also have trepidation built into them. But by the time we get to the Alfonsine tables, the precession correction was so much, just the observable precession correction, that they had to add another motion. So what you end up with is a fairly complicated picture here. So in order to simplify it I've gotten rid of everything from the stars in, and we're looking on the outside and this solid sphere here is the sphere of the stars from the outside. Since we're on the outside you can't see the stars, of course. This is the thing which is trepidating, is that the word, is accessing and recessing. 

The way that works is the eighth sphere here is connected to two little circles, those are those little gears, two little circles here and here which are embedded in the surface of the ninth sphere, and they rotate around in such a way that the eighth sphere, where the stars are, wobbles. In effect, it goes forward and back. It actually does a little bit of this, too, which is one of the reasons it was later rejected, but it goes ahead and back. Those circles carry the vernal equinox up and back and up and back. And then the ninth sphere here is embedded in a tenth sphere. And with respect to the tenth sphere, the whole ninth sphere creeps steadily ahead. So there's a steady motion, and superimposed on that is the trepidation. So it's gotten fairly complicated, one might say fairly sophisticated, by this time. Now, this idea was really influential, so influential that even Copernicus took it for granted. In Copernicus' de revolutionibus the thing that he does is say, well clearly it's not the stars doing all this motion, because in Copernicus' picture the stars are fixed out there and it's the earth doing all the moving, earth and planets. 

So the earth is orbiting the sun. It's spinning on its axis. It's doing this precession, and as it's precessing, it's speeding up and slowing down and also doing what we call today mutation, bobbling up and down during its precession motion. So he actually gave the earth two independent motions. The earth's axis had two independent motions here that were superimposed upon all the others ones, and that's because he needed to account for trepidation which was accepted as a phenomenon in his time. Of course, as you know, Copernicus' ideas were not immediately taken up as a great cause by the world. It took a little while for people to assimilate this. And even a half century later people still didn't like Copernicus' idea, at least some didn't, but some of the foremost astronomers of that period decided that Copernicus' solution was really good, that it actually worked better than the traditional medieval trepidation, and so they adapted Copernicus' mechanisms but they believed that the earth was central and stationary. But you could get those motions built into the celestial sphere if you just introduced another sphere. So here is this latest development here where once again we have the firmament right here, and it's doing C to D, and it's mounted, this is the eighth sphere, the firmament is mounted inside the ninth sphere, which is doing this A to B motion, and then it's being, sorry I lost count of the spheres. 

The eighth spheres is on the inside of there. It's on the inside. The ninth sphere is doing one of those. The tenth sphere is doing another, and the 11th is doing the steady, what they thought was about 49,000 years by that time, the steady precessional motion. So this is actually Copernican astronomy then adapted to the geocentric idea still trying to make sure that they've got trepidation built in there, variable precession built in there. Now, we don't teach trepidation today in astronomy classes, and that is because Tycho Brahe, the famous astronomer Tycho Brahe, was the one who got rid of it. Tycho Brahe compiled and published the first original star catalog since Ptolemy. Isn't that astounding? Ptolemy in 150 AD published a star catalog, and the next original one was published in the early 1600s, about 1601. Obviously, like everybody before him, if you're going to do a star catalog, you have to deal with precession. What Tycho brought to the problem that others did not, and Tycho was not a Copernican at all, Tycho was a geocentrist, what Tycho brought to this was an appreciation for what happens when you make measurements. 

He is really the first guy that we see who deals with what we today call observational error. Whenever you see data these days, if it's responsibly presented, they tell you how well-known the data is. That's the error bars on some measurement. Well we know the temperature today to be plus or minus however many tenths of a degree our thermometer allows us to measure. That idea that there's an uncertainty in a measurement is what Ptolemy brought to this, a concept which was relatively, well was new as far as I know. New with Tycho. Al-Battani had looked at Ptolemy's numbers and had no idea how accurate they actually were. It turns out these were difficult measurements to make, the longitude of stars. Al-Battani didn't know how to estimate the uncertainty of his own measurements, so he could only take these numbers and not realize that the accuracy would have allowed you to draw many lines through the rate of precession, and so instead of changing, you could draw multiple lines through them, the average number, which Tycho came up with, was about one degree per 71 years or very, very close to the modern number. He did that just by averaging all the historical numbers but not treating each one as a very precise number that indicated a change in the rate of precession. 

And I have just a little quotation here because he says this quite well. You want the Latin or the English? I only have the English, never mind. [LAUGHTER] "I have noticed that the irregularity of the rate of the change of the longitudes of the stars is not so considerable as Copernicus assumed. His erroneous ideas on this matter are a consequence of the incorrect observations of the ancients, as well as those of more recent times. Consequently the precession of the equinoctial point during these years is not so slow as he asserted. For in our times the fixed stars do not take a hundred years to move a degree but only 71 and a half years. This has practically always been the case, as appears when observations of our predecessors are carefully checked. In fact, only a small irregularity appears, which is due to accidental causes." So Ptolemy, I'm sorry, Tycho here would have gotten an "A" in the astronomy lab because he knew how to look at his data and estimate its reliability. Well, I stuck this on to this discussion of the 13th sign of the zodiac because I think that it's really interesting, these two issues are very closely coupled for astronomers. Trepidation, as silly as it kind of sounds, we get up to eventually 11 spheres all rocking each other around and stuff, that's a theory that was a response to evidence that they had before them. 

It's a rational, mathematical theory, an attempt to construct something that would allow you to make predictions like the positions of stars and things like that. Tycho disproved it on a completely rational ground because of his understanding of the nature of observational error. It didn't make good predictions, and so he rejected it. Tycho, as we said, showed that there was just one simple motion which theory had to explain. That's all about data. It's all about making predictions and finding out whether they work or not and learning how to interpret observational data. Just compare that to astrology. And I think I'll leave it right there. Thanks a lot. [APPLAUSE]