Vedic Cosmology Seminar 1

TRANSCRIPT:  Vedic Cosmology Seminar 1. ISKCON Philadelphia - July 7, 1986 / (061) 

In a sense this is a Bhāgavatam class. So I was asked to say a few words about Vedic cosmology and the structure of the universe. Just as a preface to that, in 1976 Śrīla Prabhupāda wrote a letter in which he said,

“Now all our PhD’s must collaborate and study the Fifth Canto to make a model for building the Vedic Planetarium.”  

And he makes a number of comments there and he says,

“Now all the PhD’s must carefully study the details of the Fifth Canto and make a working model of the universe. If we can explain the passing of seasons, eclipses, phases of the moon, passing of day and night, etc., then it will be a very powerful propaganda.”  

So that’s what Śrīla Prabhupāda said back in 1976. This was written to Bhaktisvarūpa Dāmodara Mahārāja.  

So, of course now it's 1986, but this Fifth Canto of the Śrīmad-Bhāgavatam has always been a cause of perplexity to many devotees and other people who have read it. This section of the Bhāgavatam describes the layout of the universe and it describes it in terms that are quite unfamiliar to a person with a standard western upbringing and background. So what I was going to do in these talks was to provide some explanation to clarify what the Fifth Canto is actually saying.  

So if you look at the... briefly at the Fifth Canto you will see that it is describing the earth, or what is translated there as the earth, in somewhat unusual terms. The word there used for the earth is Bhū-maṇḍala. So bhū means earth and maṇḍala is a Sanskrit word that basically means something round. Could be a circle or a ball or something like that. Actually the word maṇḍala has come into English via Tibetan Buddhism and things like that. A round figure with various designs on it is called a maṇḍala.  

So the earth is referred to as Bhū-maṇḍala, and one can understand from the text that this essentially is a reference to a disk, something shaped like a disk. And the radius of this disk is about, well the diameter is given as 50 koṭi-yojanas. This is a figure you get accustomed to pañcāśat-koṭi-yojanas (koṭi is ten million). So that would be five hundred million yojanas. And in the Bhāgavatam Śrīla Prabhupāda uses the figure of eight miles for a yojana. So five hundred million times eight miles gives you four billion miles. So imagine a disk four billion miles in diameter.

So that is what is referred to in the Fifth Canto as the earth. So naturally this is somewhat bewildering to people. So in the modern day and age we are accustomed to thinking, first of all that the earth is a globe, it’s a sphere, and we are certainly not accustomed to thinking that it’s as big as four billion miles in any of its dimensions. According to modern understanding, the earth is about 25,000 miles around the equator. So that’s the greatest distance you can travel on the earth without coming back to your starting point. So, 25,000 thousand miles – that’s fairly small distance. You can say it’s roughly about 8000 miles in diameter. So if pi is about 3, 3 times 8, it's about 24, so you can see 24, 25,000 miles in circumference and about 8000 miles in diameter.  

[4:48]

So that is tiny compared to a disk which is four billion miles in diameter. So this is the basic problem. Now we have a lot of experience in our modern society which tends to suggest the earth really is a globe. For example we have travel by jet airplanes, and devotees, at least quite a number of them, tend to be bonafide members of the jet set. Some of them even get free tickets on... from different airlines because they travel so much. So we have experience of traveling from city to city around the earth. We experience time zones; there is jet lag. You can go to India, and what is it, about a twelve-hour time shift? So... or going from here to Los Angeles, there is a three-hour time shift and so on. So all of these things make sense in terms of the idea that the earth is a globe.  

And of course if you look at the routes that you follow, if you travel, say, from London to New York and see where the plane is going, you will see that you come to land in North America first up in Labrador – some place like that – and you come down over Massachusetts, you fly over Boston, and eventually you get to New York. So if you look at an ordinary Mercator projection map, it seems you are going in a big arc to the north and then coming south. But if you look at a globe you will see that the shortest line between London and New York in fact goes over Labrador, northern New England and so forth.  

So we have all this experience that indicates that the earth is a globe. So then how can it be that the Fifth Canto is describing the earth as a disk four billion miles in diameter? So what’s really going on here? This is the real question that comes up with Fifth Canto, and in connection with that there are many other questions that go along with it. But in a way this is the basic question.  

So first point to note, then, is that this apparent conflict in understanding the Fifth Canto is not something new. And it is not a conflict between Vedic literature and modern scientific understanding. Actually there is a whole body of Vedic literature which describes the earth as a small globe. And this literature is what Śrīla Prabhupāda in His purports refers to as Jyotir-veda or Jyotiṣa Śāstras. So there is a whole body of literature like this.  

So just to indicate, and also as I was finding out recently commentators on the Bhāgavatam, including the commentators that Śrīla Prabhupāda referred to in writing His purports, have explicitly discussed this issue. So I will give you a quote. This is something which was recently translated by our Sukavak and myself. We were going over some of these commentators’ commentaries. This was written in Sanskrit by someone named Vaṁśīdhara. And we don’t yet know exactly who Vaṁśīdhara was, that is how he relates to various other figures that we know. His commentary appears right after Śrīdhara Svāmī’s commentary on the Bhāgavatam. But he makes the following interesting statement. He says:

Śrī Vyāsadev, for the purpose of confusing the asura janas, created apparent contradictions in the Jyotir-śāstra. But there is no contradiction in reality. Otherwise he would be obscuring the Vedas. This is the correct understanding. How then can the contradictions be resolved between the 100,000 yojanas size in Jambūdvīpa in the Purāṇas and the 5000 yojana size of the earth globe in the Jyotir-śāstra. The earth has two forms, one is a very big specific form, the śeṣa given in the Purāṇas and the other according to Jyotir-śāstra is a small globe.

And then he goes on to describe this in more detail. So, and he goes on to explain what’s going on here. So, just to briefly explain further, I mentioned that the earth is four billion miles in diameter according to the Śrīmad-Bhāgavatam, the Fifth Canto, and it is divided into different parts. One of those parts is Jambūdvīpa. And that is described as being a 100,000 yojanas across, which would be 800,000 miles. That’s about the size of the sun according to the modern ideas of the sun. So this Jambūdvīpa is normally identified with the region of the earth in which we are living. But I will be discussing that more later on.  

[10:35] 

So Vaṁśīdhara is here mentioning Jambūdvīpa which is 100,000 yojanas across, and he mentions the Earth which he gives a figure of 5000 yojanas. Well as a matter of fact, as I will describe later, the yojana has a somewhat variable measure. He is using yojanas that are five miles to the yojana. And there is other evidence indicating that this is the case. And if you multiply five by five thousand you get twenty five thousand. In other words, he is saying the earth is 25,000 miles in circumference. So he is talking about the same earth globe that we are talking about.

So it’s worth knowing that the traditional commentators on the Bhāgavatam also knew about the idea that the earth is a globe about 25,000 miles around. It’s not that they were unaware about this idea. In fact this is described in what is called this Jyotisa-śāstra. So I’ll say a little bit more about Jyotisa-śāstra. First point is to cite a purport in the Caitanya-caritāmṛta given by Śrīla Prabhupāda. This is a purport to a verse which describes some of the time units that are used in Vedic calculations. But in the purport Śrīla Prabhupāda says:

These calculations are given in the authentic astronomy book known as the Sūrya-siddhānta. This book was compiled by the great professor of astronomy and mathematics Bimal Prasād Datta, later known as Bhaktisiddhānta Sarasvatī Gosvāmī, who was our merciful spiritual master. He was honored with the title Siddhānta Sarasvatī for writing the Sūrya-siddhānta, and the title Gosvāmī Mahārāja was added when he accepted sannyāsa, the renounced order of life. (CC Adi 3.8)

So here Śrīla Prabhupāda refers to a book known as Sūrya-siddhānta. Now this is one of the books in this Jyotiṣa literature and indeed it turns out that Bhaktisiddhānta Sarasvatī was an expert in this field of the Vedic śāstra. Just to give an indication of this, we have some information here concerning Bhaktisiddhānta. It's described that in 1897 Bhaktisiddhānta opened a tole, or school, named Sarasvata Catuspati in Calcutta and it said here, “This is for teaching Hindu astronomy, nicely calculated independently of Greek and other European astronomical findings and calculations.” And at this time he also published two magazines on this subject. One called Jyotir-vid and the other was called Bṛhaspati. And in addition to that he has a whole list of publications on Vedic astronomy. There’s quite a long list here. For example, he translated Bhāskarācārya’s Siddhānta-śiromaṇi, and whole series of things with very long Sanskrit names here. It’s quite a list of things. So Bhaktisiddhānta was very much involved at one time with this Jyotisa-śāstra. So I am mentioning this to indicate that these literatures are definitely a part of the Vedic tradition and a part of our own line of disciplic succession.  

So what I thought I would do here is give a brief description of how the Sūrya-siddhānta describes the universe. And this will be useful not only for discussing the Jyotiṣa-śāstra but it will allow me to introduce some sort of practical fundamental knowledge of astronomy; because although in the modern day and age there is a highly developed science of astronomy, one hears of the Mount Palomar telescope and so on, most modern city dwellers never even look at the sky. The most they know about astronomy is that the sun rises in the east and sets in the west and you see stars at night, at least if you go out in the country. But that’s about as far as it goes.  

[15:24]. 

So I thought I would indicate some ideas first of all about what one sees. By the way, I don’t... I forgot to bring a watch. Maybe I can be warned of the passage of time in case I go on too long here. Ah! That’s good. How long should this go, for about, what do you think? ...Ok, I can cover a certain amount of material. Yeah?...Yes that’s one project. We want to do that. Oh yeah! One big project that we have now is to find those writings. Also to translate the commentaries of, various commentaries on the Bhāgavatam because, in fact, there is lots of material there on astronomy. So that is definitely something that has to be done.  

So let me first say a few words about what one sees in the sky if one looks. Of course, we know the sun rises and sets. So let me first define a standard orientation, that is, you are standing looking to the South. In fact, the best idea is that you are standing in India looking to the South. All the descriptions of what is going on in the sky that you find in the Vedic literature, as far as I can see, sort of take it for granted that this is your orientation. So with this orientation the sun rises to your left and goes up into the sky in an arc, moving to the right and then sets to your right. So this is pradakṣiṇa kurvan, is the word that they use, motion to the right. So, and you can also think of it as clockwise. If you hold a clock like this then the hands go round the same way the sun is going. So it’s described that this is one basic motion of the sun, clockwise or motion to the right, which is on a daily basis. It takes one day to go around.  

So of course during the daytime you can’t see stars but if you look at the stars at night and the moon and so on, you’ll see that they are also moving in the same way. They rise in the east and move around to the right and set in the west. And if you look towards the north you’ll find that there are some stars that never actually set. They go around in a circle in the sky and as you keep going to the north, the circle gets smaller and smaller... Well facing the South, the North is over your shoulder. It’s to your back. So you have to turn around. Of course, I am facing North right now. So you have to... everyone here actually is facing South. So you can apply these statements to yourself. But in that direction up to a certain angle in the sky you will see the circles in which the stars are moving on a daily basis, shrink down to a certain point occupied by a star we call the polestar. So the polestar tends to remain stationary, and all the stars seem to be circling around it in circles. And as the circles get bigger, finally they intercept the horizon of the earth and then as you go on, the stars seem to rise, go around in a circle, and set. And this takes place in a period of one day, that is one complete circle.  

Now it turns out though that the stars rise and set at a faster rate than the sun does. So there are two kinds of days: what is called a sidereal day and a solar day. So a sidereal day you can call it the star day, the time from the time a given star rises to the time it rises again. Whereas a solar day is the time from when the sun rises to when it rises again. So the stars go slightly faster than the sun. So the sidereal day is slightly shorter.  

[19:54]

So the way you can visualize this is to think of something called the celestial sphere. And maybe I will make a drawing here to indicate that. So what I have done here, the small sphere that you see is... represents the earth  And the large sphere around it represents just a big imaginary sphere drawn centered on the earth. So the earth’s equator is indicated in its axis, and then on the big sphere there is also an equator that matches the earth’s equator. That is just extended out on straight lines from the center. So the big sphere is called the celestial sphere. So if you are standing on the earth you can imagine all the different bodies that you see out up in the heavens to be projected as little dots on the surface of this sphere.  

So the first point is if you think of the stars projected on this sphere it is as though the whole sphere is rotating around this fixed axis. So the polestar is actually right where the axis passes through the sphere up to the North at the top. So as the sphere rotates, the pole star doesn't move and everything else moves in a circle. There are circles of varying sizes and you can see that if you are on the surface of the earth in say the Northern Hemisphere, you will be able to see some complete circles, but the earth will block your vision for some of the other circles. So they won’t be complete. So that’s how the stars move, once per sidereal day.  

So the next question, the next thing to bring up then, is the motion of the sun. So if we forget about the... if we just pay attention to the stars fixed on the sphere, we then see that the sun is moving relative to the background of stars. So of course during the day you can’t see the stars that are near the sun because it’s so bright. But if you could see that, you would see that on one day the sun was in front of a certain constellation. And as the days went by the sun would gradually drift across the sky, and it would pass from one constellation to another. And it would gradually go in a big circle all the way around this celestial sphere and come back to its starting point again. And it takes one year to do that. And the motion of the sun against the background of the stars is to the left. It is the opposite of the motion of the sun on its daily cycle.  

So as I say, the way then to visualize this is to imagine that you could look at the sky and see the stars as well as the sun. And imagine at a certain time of day, every day you looked, well, with each successive day the sun would be moving slightly in the leftward direction. Yeah, you are always looking at the same time. Say at noon every day you look at the sun and you can see, and this is sidereal noon (The important point about it being the sidereal noon is the same star will be, the stars will be in the same position at this time every day), so if you look at the sun every day and watch what it’s doing, you will see it is moving leftward across the sky. Eventually it will set in the East, and then will rise in the West and move around and in this way be moving counterclockwise.  

So this is the yearly motion of the sun. It takes one year to make a complete circle. And the sun follows a particular path against the background of stars. And there are various names for this. First of all there are constellations in the sky that are called, basically, the zodiac. Everyone’s probably heard of the zodiac. The sun follows a particular path which is called the ecliptic. I will make a drawing of what that is. This is a very crude drawing. What I have done is draw another circle, it’s called the Great Circle in the celestial sphere. And you notice it’s at an angle to the equator, the celestial equator. The angle is actually about 23 degrees. So what happens is over the course of the year the sun is moving on this circle counterclockwise. And you see the circle is at a tilt to the equator, so sometimes the sun is moving in a somewhat northerly direction as it goes around this circle until it comes to the highest point, and then it’s moving in a southerly direction until it comes to the lowest point, and then it goes back up North again.  

[25:11]

So when it reaches the most northern point that’s called the summer solstice. And that was just a few days ago. That’s the point in which the sun comes higher, furthest to the North. Now if you think about the daily motion of the sun, when the sun comes furthest to the North, that means the whole arch the sun travels during one day, it’s shifted the most towards the North. So that occurs during the summer time. And as that occurs the days get longer and longer until when the sun is at the northernmost point on this ecliptic path, the length of the daytime period is the longest and nights the shortest.  

So then as the sun continues around the ecliptic, it reaches a point where the ecliptic intersects the celestial equator. At that point the length of the day and the length of the night are equal. So that’s called the equinox. Then it keeps on going as you go into winter time until it reaches the southernmost point. So at that point the sun is the furthest South and the day is shortest. That’s called the winter solstice. That’s around in December. Then it comes back up to another equinox and up to the solstice again. So, pardon me? [unclear] Right, yeah, there was a pagan holiday at that time. So they shifted the celebration of Christ’s birth to that time. So anyway, that is how the sun basically moves.  

So it is described then there are two motions to the sun: this rightward daily motion, and the leftward yearly motion. And the rightward daily motion tends to go on one plane of rotation corresponding to this equator here. And the yearly motion is on another plane tilted at 23 degrees to that plane. So that’s the basic thing that one sees in the sky. And then I should mention the planets. So in the Vedic literature there are nine planets that are normally spoken of. These are, and this is somewhat different from the numeration of planets in the modern conception, so the nine planets are the sun, the moon, and then Mercury, Venus, Mars, Jupiter and Saturn, and Rahu and Ketu. Those are the nine planets in the Vedic system. So the sun and the moon are also called planets.  

So I have been describing how the sun moves. Now the perspective in the Vedic literature is what is called geocentric. That is, one takes the earth as being a fixed reference point. And one considers how everything is moving relative to the earth. So according to this idea, the sun is orbiting around the earth and so is everything else. The earth is fixed in this position. So we have been discussing orbit of the sun. All the orbits of the different planets can be plotted against the celestial sphere. Every planet has its daily east-west motion just as the sun does. Everyone can see this in the case of the moon. You’ll see that the moon also rises in the East and sets in the West. So each planet similarly rises in the East and sets in the West., but each planet has its own motion against the background of the stars. So to think of the motion of the planet, the easiest thing to do is to think of its motion against the celestial sphere, against the background of stars. So we have already described the orbit of the sun and that’s the circle I have drawn which is called the ecliptic.  

So one can also consider the orbit of the moon. Now it’s easy for us to see what the moon is doing against the background of stars because the moon isn't so bright. So you can actually watch it from day to day. But if you do that you’ll see that with each successive evening, say if you look at the moon at the same time, it has shifted quite a ways to the east. So this is easy to see; or in the morning you’ll see one morning, actually a few mornings ago the moon was full at about time of maṇgala-ārati. And then the next day if you looked at the same time it was not quite so full and it was quite ways up in the sky; when it was full it was on the horizon just about time of maṇgala-ārati. And a bit later it was well up in the sky moving towards the East, and right now it’s a thin sliver and it’s about to set in the West at that time.

[30:35] 

So the moon also has a motion to the left moving towards the West. But its motion is about twelve times as fast as the sun’s motion. However it follows nearly the same path as the sun, but not quite the same. It stays very close to this path called the ecliptic. And it has its own motion going around once in a month instead of once in a year. And the same thing is true of the other planets such as Mercury, Venus, Mars, and so forth. They all have their motions going towards the east or going to the left. And different planets have different motions.  

So the motion of the sun and moon is fairly simple to draw; it goes just in a circle. I have drawn a circle for the sun and for the moon; it’s a similar thing. Now for the other planets the motion is more complicated. And I’ll just give you an indication of what it looks like. This diagram indicates basically what the motion of the planets looks like. Now mind you I am presenting all this as a preface so that we can understand the Vedic outlook on the universe. It’s quite important to understand what you actually see in the sky. People today are taught that the various planets orbit around the sun in elliptical orbits and so on. But at least not very many people think of what this means in terms of what you actually see. Well, since the Vedic literature is describing what you see out there amongst other things, it’s important to know what that is. So this is the kind of motion a typical planet follows. I have drawn a line that loops back on itself.  

So typically what a planet will do is against the background of stars it moves towards the left along the ecliptic, close to it but not exactly on it, and it will move for a while, then it will reverse and go back towards the right again. That’s called retrograde motion. And then again it will move to the left and then again reverse and go to the right and then again to the left and so on. So the overall motion is to the left, but it keeps doubling back on itself. So that’s what the planets do. That’s their characteristic motion.  

So that’s the introduction. Here I have exaggerated how far it goes from the ecliptic. It really stays very close to it. These backward loops are very flat. So the Sūrya-siddhānta, which was translated into Bengali by Bhaktisiddhānta Sarasvatī, describes all of these orbits mathematically. Actually you can think of the Sūrya-siddhānta as a computer program for calculating exactly how these planets move through the sky. In fact, of course, it was written for people who didn't have computers and who just would calculate by themselves, but it’s written as a program. If you read the Sūrya-siddhānta you will find it says: write down this number, multiply it by that, add it to this other thing, look up this in a table, and multiply, and so on. It just goes on and on like that.  

So but what it does is it presents calculation so that if you know first of all the time, then you can calculate where each planet is on the celestial sphere. You can measure position on a celestial sphere by putting coordinates of latitude and longitude; they are just as you do on the earth. You know you have a grid of latitude and longitude coordinates on the earth. Similarly you can put that on this bigger globe, and thus you can give a position to every planet. So you can calculate those positions using the Sūrya-siddhānta. And in fact, it is interesting, you have to know the time from the beginning of Kali-yuga. So in fact it’s measured in days and fractions of a day. So if you know the time in days and fractions of a day from the beginning point of Kali-yuga you can use that to calculate where each planet is going to be on the celestial sphere at that moment. And conversely, if you know where the planets are at a given time, you can ask: at what time will the Sūrya-siddhānta give the planets in those positions? That must be the time we are at in Kali-yuga. And that’s why we say Kali-yuga begins 5000 years ago. Because in fact the precise time is about, well roughly speaking, it’s about 5000 years from the beginning of Kali-yuga till now. So that’s based on this Jyotiṣa literature. Yeah?  

[35:54]

Audience:  [unclear]

RLT:  Well in fact, these calculations are used by astrologers. You see a modern day astrologer will use something called an ephemeris, which is published by some convenient organization that we don't worry about. And in the ephemeris you just look up the positions of the planets as a function of time. But the Sūrya-siddhānta enables you to actually calculate the positions of the planets. And of course they did use this to make tables so that you could look up the positions as a function of time. So that’s what the Sūrya-siddhānta does.  

And the... I could mention some things about the Sūrya-siddhānta. It’s actually quite accurate; it works in describing these things, and it is based on what is called a system of epicycles. So I will describe briefly what that is just so as to relate this to the modern conception. Now everyone in the present day and age is raised according to the idea that the planets are orbiting around the sun. So I will make a diagram of indicating of what that looks like. In this diagram the sun is at the center here. We will call this S, V and E. We have the sun at the center, and then in a circle here we have Venus. So the idea is that Venus is orbiting around the sun in a circle, and in a larger circle we have the earth, and the idea that the earth is orbiting around the sun. Well, in the Sūrya-siddhānta you have the following picture. You will notice what I have done there is that I have drawn the earth, the sun and Venus in the same positions. I have drawn a different set of circles. So in one case the sun is at the center and the Venus and the earth are moving around in a circle. In the other case the earth is at the center, the sun is moving around the earth in a very large circle, which is only partially drawn here, and Venus is moving around the sun in a smaller circle. It actually should be the same size as the one in the first drawing. 

So if you think about it you can see that from the point of view of somebody standing on the earth, both of these pictures give you the same motion in the sky. It’s just a matter of what you want to take as the center of rotation. But from an observational point of view they are equivalent. So the Sūrya-siddhānta uses this picture. However the dimensions of these orbits are the same. That is, in the Sūrya-siddhānta, the size of the earth’s orbit and the size of the orbit for Venus are the same size, except of course I say earth’s orbit – it’s the sun’s orbit in the case of the Sūrya-siddhānta because it is the sun that is moving. Whereas it’s the earth’s orbit in the case of the modern heliocentric system. So that’s the relation essentially in simple terms between the Sūrya-siddhānta and the modern system.  

And I should relate these pictures to the ecliptic plane, or the circle, that I was drawing before. Of course, these pictures lie flat in the plane of the black board. But actually in space, either way you look at it, you have these things moving essentially in a plane, in a particular plane in space. Well in fact, that corresponds to the ecliptic that I was drawing before. So looked at from a heliocentric point of view, the plane of the ecliptic corresponds to the plane of the solar system, which is essentially flat. Or looked at from a geocentric point of view, well you can call it the... the earth centered system in which the sun is going around and the planets are all going around the earth essentially in the same plane or very close to it.  

[40:41]

So that’s the basic picture given in the Sūrya-siddhānta. Now there are quite a number of things one can say about the Sūrya-siddhānta. I’ll just say a couple of more things to wind up this lecture and in the next lecture we will begin discussing what the Bhāgavatam says. And then we will see how these things relate to one another. This is the background so that one can understand essentially what the Bhāgavatam is saying.  

So the final thing that I thought I would point out is that from a modern point of view one might think that the Sūrya-siddhānta is somewhat outmoded system, rather quaint and archaic. But I would suggest that there are indications of considerable sophistication in this description of the solar system. And here is one indication of that. In the Sūrya-siddhānta there is a table giving the diameters of the planets. This is a rather intriguing thing. The diameters are given as projected to the orbit of the moon. Now what that means, I should explain that. Imagine that someone is holding up a basketball at a distance. And at arm’s length someone holds up say a penny. And the penny perfectly matches the size of the basketball from his point of view. So that means that at arm’s length, the basketball size projected to arm’s length for that observer is the size of a penny. This is what I mean by projection.  

So obviously if a thing is of a certain size, if it is far enough away it will project down to any given size. So similarly, if you imagine a planet as a big globe out there in space, now projected down to the orbit of the moon, how big would it be when projected to the orbit of the moon? So the Sūrya-siddhānta gives a series of numbers for how big all the different planets are projected to the orbit of the moon. And these numbers vary as a function of time, by the way, because the distances of the planets vary as time passes. So using these figures and figures for the distances of the planets, you can calculate backwards and obtain figures for the actual diameters, the right numbers for the diameters of the planets, except in two cases you are off by a factor of two, which to me suggest that radii are being given instead of diameter somehow. There is some mistake in the text. But taking that into account the numbers you get come within 10% or even less of the present values for the diameters of the planets. And this is a rather interesting thing because you might ask: How could people could measure the diameters of the planets? Nowadays the way it’s done is you have to use a telescope, because if you look at a planet... for example many of you may have seen Venus which is sometimes called the morning star; it’s quite bright in the morning. But it looks like a star, and I think one would have to have a very good eyesight to even see that as a disk. And then to measure that disk is another thing! So it’s hard to see how anyone could do it. But yet the right figures are there.  

So how do they know? After all according to our modern history the telescope was invented by Galileo or at least first used for astronomy by Galileo back in 1600 something. And that probably wasn't, his instrument wasn't, adequate enough even to determine these diameters. You need more powerful telescopes. So people even in the Middle Ages in India presumable could not calculate such things. Yet the information is there. So that’s just an indication that there is something going on here. Some people actually knew something in the past there in India.  

[45:24]

So I’ll stop there for this evening. Anybody like to ask questions about the material so far? Yeah?  

Question:  [unclear]  

Answer:  What I was, about projection down to the orbit of the moon?

Q:  [unclear]  

A:  That’s not the method of parallax. It’s just a simple proportion. You know, if something at a given distance x has a certain size, then if you move it to 2x, it seems half as big. And if you move it to 3x, it seems a third as big, and so on. It’s just a matter of proportion. Yeah?

Q:  [unclear]  

A:  They have equations, yeah. That’s known as Newtonian astronomy. So there is the Newtonian system which provides equations for calculating how the planets move.  

Q:  [unclear]

A: The solar time, yeah.

Q:  [unclear]  

A:  That’s a different thing, called precession of the equinox. Yeah, that’s another topic. But the point of the equinox where it intersects the... where the ecliptic intersects the celestial equator, that shifts. But that’s another whole subject. It’s different from the... it doesn't have anything to do with the difference between the sidereal day and a solar day.  

Q:  [unclear]

A:  The equinox? Well, once again that’s a whole subject, but that is measured. It’s been observed over the last so many hundred years. But we will discuss that also in more detail. Yeah?

Q:  [unclear]

A:  Yeah, he said Vyasadeva put some apparent contradictions there to bewilder the asura janas.  

Q:  [unclear]

A:  One could take it that way. But anyway that’s what Vamsidhara said. But he said the contradiction is not real, just seems to be a contradiction. So we will discuss how that could be. You had a question?  

Q:  [unclear]

A:  Well there are always questions about how accurate is accurate. From what I understand, and I haven't checked the calculations myself, the Sūrya-siddhānta serves its intended purpose quite well. It does have to be adjusted to fit the positions of the stars from time to time. That is, it drifts off very slowly. But it works pretty well, and to give an idea of this I could cite some figures. I have much additional data in here that I haven't been mentioning because it would be a bit too much. But for periods, for example the Sūrya-siddhānta, the modern figure for the orbital period of the moon is 27.32166 days, just to give an example. And the Sūrya-siddhānta is 27.322. So it differs by 1, well actually it differs by 0.4 in the fourth decimal place. That gives an idea. For example the period of Venus is 224.701 days according to modern calculations. According to the Sūrya-siddhānta its 224.7, so it differs by 1 digit in the third decimal place. So things like that. So it’s not a bad system. Yeah?

[50:41] 

Q:  [unclear]

A:  Well, the method that they use today to measure that is the following: First you have to measure the distance of the planet. So for that you do use parallax. For example if you have observatories on two widely separated parts of the earth and you know the distance between those observatories, and you measure the angle to the planet, then you get two sides of a triangle and you know the side and the middle, so you calculate the distance. So using this kind of thing you can get the distances. Then you measure the apparent diameter using a telescope, and the apparent diameter and the distance enables you to calculate the actual diameter. So that’s how they do it today.  

Q:  [unclear]

A:  They take into account refraction. They have equations for it. That’s another thing they deal with. Yeah?

Q:  [unclear]

A:  Yeah, now this is an interesting thing, which also is an interesting thing to note. The Sūrya-siddhānta has figures for distances to the planets. These are somewhat different from the modern figures. And furthermore, the figures for the apparent diameters projected to the moon are different from what you would get from the modern figures, but the errors cancel out when you calculate the actual diameters, which is interesting.  

To give you an illustration of how that works: Suppose, let’s see, suppose that I had a basketball and I told you that the basketball was at a certain distance and at an arm’s length it seemed to have a certain diameter. Now from that you could calculate how big it was. But suppose the distance was wrong and the diameter was wrong. That is suppose the figure I gave you was too close and the diameter I gave you was too big. But, let’s say the figure I gave you, the distance was half of what it should be, for the sake of argument, and the diameter, apparent diameter, I gave you was twice what it should be. Well, if you then calculated the real diameter you would still get the right answer because the two errors cancel. Well, the odd thing is in the table of the numbers that they have the distances are off according to modern figures, the apparent diameters are off but if you calculate the real diameters you get the right numbers.  

So that is a mystery for the people to ponder as to why that might be so. One thing I would suggest is, it couldn't be accidental. At least it is highly unlikely that that would be an accident. So that’s…

Q:  [unclear] 

A:  No there is no indication. Yeah, according to modern ideas you need a telescope. There are some large observatories in India that at least date back to the Middle Ages in which there are fairly good methods for determining the angular position of a planet in the sky, that is in what direction it is located. Essentially what it amounts to is you have a sighting point and you have a very large curved wall. And then you cite along the location of the planet, let’s say, against that point, and you mark on the wall where the thing lies, and then by measuring distance along the wall you can determine the angle of the thing in the sky.  

[55:02]

Q:  [unclear]

A:  Yeah, in Delhi. Yeah, I saw the one in Delhi actually, but this will enable you to determine the direction in the sky but it won’t help you to determine, say, the diameter.

Q:  [unclear]

A:  You might be able to figure distance; diameter is still a problem because you have to somehow see the disk, unless people had very good eyesight. But, well, you never know how they might have found out. It’s not that they necessarily used the modern methods. There might be other methods. Well, a demigod might have come down and told them this is what it is. Mind you, that is what the Sūrya-siddhānta says, by the way. The Sūrya-siddhānta says this is a communication from Sūrya who is the sun-god. So that’s the version of the Sūrya-siddhānta. But…

Q:  [unclear]

A:  Well, he should know.  

Q:  [unclear]

A:  Yeah, traditionally that’s been used. And they would make tables called pañcakas which are like ephemerides, which give you positions of planets.

Q:  [unclear]

A:  Yeah, ephemeris, that’s what they are used for, and it’s a standard thing. And also it was mentioned in here that Bhaktisiddhānta Sarasvatī made a table of that kind, but he attached the names of Kṛṣṇa to everything. So he made a Kṛṣṇa Conscious pañcaka apparently.  

Q:  [unclear]

A:  Well, the same equations can be applied. Now it becomes a matter of controversy just how accurate things were back at the time of the beginning of Kali-yuga. Now the problem there is that there are no recorded observations except perhaps observations in the Vedic literatures themselves. But the earliest observations that are recognized by modern scientists were made by the Babylonians in about, maybe as early as the 7th century BC. They don't go back any further than that. So when we speak of different theories about what the planets were doing many thousands of years ago we should recognize that we don’t have any observational evidence.  

Q:  [unclear]

A:  Yeah, assuming that. It’s a big assumption. You see modern scientists will assume that everything was regular according to the Newton’s equations. But is that so? That’s outside of the bounds of observation. In fact some of the early Greek reports of eclipses of the sun are disavowed by the modern scientists because when they compute backwards using the Newtonian equation then they find that the eclipse must have occurred on a different date. So they will say that the Greeks were lying about when the eclipses occurred. They say that.

Q:  [unclear]

A:  Yeah, they actually say that Herodotus, the Greek historian, lied about the date of certain eclipses because they can calculate backwards and find out when that really happened and they know that it’s wrong. So...

Q:  [unclear]

A:  No, they couldn't see why he would lie about that. Well, they said Herodotus is the father of history and the father of lies. So they take refuge in that statement. You had a question?

Q:  [unclear]

[60:03]

A:  It’s different with the different planets. But the errors cancel out and you get the right diameters. So that’s curious. So, yeah?

Q:  [unclear]

A:  Well, it’s very similar, and this leads to a whole area of scholarly controversy. In Galileo’s time the geocentric model that was used goes back to a Greek, an Alexandrian Greek, named Ptolemy who, let me see, when did he live, around 200 AD or thereabouts. So modern scholars want to trace the Indian astronomical system such as Sūrya-siddhānta from this Greek system.That’s their idea.  

But then one should realize that the modern scholars also have a program of tracing practically everything in India back to the Greeks. I’ve even read in some places where they want to trace deity worship back to the Greeks, of all things. There are perhaps... one can argue that there may be some motives for this because in the West people have adopted the Greeks as their ancestors. Of course, most people of European descent really are descended from Goths and Vandals and Celts, another interesting people who went around sacking cities and so forth. At least the Northern Europeans are in that position, and these don't really constitute particularly honorable ancestors.  

So what people have done is adopted the Greeks as their ancestors. So there is a tendency to try and attribute everything to the Greeks and to glorify their position. So it’s a whole subject of controversy. The actual situation is that we don't have very much historical evidence telling us what went on with the ancient Greeks and their relations with India. The information is exceedingly fragmentary. In fact, I read a whole book on ancient Greek astronomy which supposedly outlined the history of it. And what it amounts to is that we have the book by Ptolemy which is called the Syntaxis, which is pretty complete, and we have fragmentary references by late Roman writers, people writing in say the 6th century AD, and these were people mainly who wrote in Latin who obviously didn't know what they were talking about. They made all kinds of gross errors. Apart from that there is practically no documentary evidence, just speculation. So who knows what the real history was! But anyway that’s a whole subject to look into. Yeah?

Q:  [unclear]

A:  Well as I was saying, the way I began the whole discussion was to say, on the one hand, in our modern experience we... our experience of the earth is that it’s a globe. In other words, the idea of the earth as a globe fits our experience, our gross sense perception. And in the Sūrya-siddhānta it says the earth is a globe. And the same is true of the other literatures known as Jyotiṣa-śāstra. They all say the earth is a globe. And they all give the size of that globe. And it comes out to be the same as the size that we think of the earth today, as I say, about 25,000 miles around. But in addition, the Bhāgavatam describes the earth in a different way. So the question now is what do these two descriptions have to do with one another? How do you relate them? Are they both true? Is one of them true and the other false? What’s going on?  

So I’ll really get into that in detail next time but what I was indicating here is that the idea of the earth as a globe is not something new in Indian tradition, or for that matter, in Vedic tradition. That’s been discussed for many – well in terms of what we definitely in black and white – it’s been discussed for many centuries. We would infer that it’s been discussed for much longer than that also, and the other point I made was that Bhaktisiddhānta Sarasvatī himself taught this Jyotiṣa literature which describes the earth as a small globe so that that can be considered.

[65:42] 

So the question is that if the earth is a small globe and the earth also is a gigantic disk, then how is that possible? What’s the proper understanding? What this Vaṁśīdhara said was there are apparent contradictions there. But no real contradiction. So ok, how is that? It looks like a contradiction! So what’s the answer? So I am going to discuss that. So, yeah?

Q:  [unclear]

A:  Well right at the moment we don't have what he wrote in detail about these subjects. We have a list of titles. We do have comments that he made in his Anubhāṣya commentary on Caitanya-caritāmṛta. Now in his purports, the verses in the Caitanya-caritāmṛta, from time to time he will just cite the Sūrya-siddhānta or the Siddhānta-śiromaṇi which is another of these literatures, and so on. He just cites them along with many other things that he cites. He doesn't say anything about whether this is valid or invalid but you assume that he wouldn't cite it if he thought it was invalid. He just cites it.  

Q:  [unclear]

A:  We don't have his commentary if he wrote one. We looked through to see if he wrote a commentary on the Bhāgavatam. We found translations of the Bhāgavatam that he wrote but no commentary. Either if he did write a commentary, that’s in some other book that is not in the Matsya collection. Since our source was this Matsya collection that Sukavak has. So it would nice to see what he had to say about the Fifth Canto, but I don’t know if he wrote anything.  

Q:  [unclear]

A:  Yeah, basically speaking, you'd say they show the same thing from a different reference point. The modern description uses the sun as the center of motion. Everything is orbiting around the sun, and the Sūrya-siddhānta uses the earth as the center of motion. The calculation saying where things will be as a function of time did not agree exactly but they are pretty close to one another. Of course modern scientists will say that the Newtonian calculations are exact and the Sūrya-siddhānta calculations are inaccurate. And that’s probably true in terms of, you know, the observational data. But anyway, they give essentially the same description. And one should keep in mind that you can do the Sūrya-siddhānta calculations with a pencil and paper. But nobody can do the calculations of the Newtonian astronomy that way unless they want to sit for many, many hours doing calculations. Of course, people used to do that a couple of centuries ago. But really, you need computers to do the Newtonian calculations. They are exceedingly complicated.  

So one can say the Sūrya-siddhānta is a simple system in which just by writing a few lines of calculations you can get the positions of the planets. So it’s a practical system also. In fact in South India there is a tradition in which people have memorized all the numerical data in the Sūrya-siddhānta and similar literatures, and by moving sea shells they can do all the calculations without even writing anything down. So they just sit down and move some sea shells around and they have all the information. So, yeah?

Q:  [unclear]

A:  Well, there were two practical applications of this in ancient Vedic culture.  

Q:  [unclear]

A:  Well, one was astrology, which was quite commonly known. The other was determining the dates of religious ceremonies of different kinds.  

[70:20]

Q:  [unclear]

A:  Ekādaśī for example, that’s based on the position of the moon. But there are many other things of this kind. Just for the sake of argument, I will quote you something from the Bhāgavatam just to give an idea of this. This tells about, something called the śrāddha ceremony. So it says:

“One should perform the śrāddha ceremony on the Makara-saṅkrānti, on the Karkaṭa-saṅkrānti. One should also perform it on the Meṣa-saṅkrānti day and Tulā-saṅkrānti day in the yoga names Vyatīpāta on a day in which three lunar tithis are conjoined during an eclipse of either the sun or the moon, on the twelfth lunar day and in the Śravaṇa-nakṣatra. One should…”

It goes on, actually I can read on for another five minutes here a list of different times you should perform the śrāddha ceremony. They are all astronomically determined. It all depends on whether the moon goes into a certain constellation and all kinds of things. The use of astronomy was a standard thing in determining times of religious performances. Yeah?

Q:  [unclear]

A:  Bhagavad-gītā describes karma of the individual. I don't believe the Bhagavad-gītā refers explicitly to astrology. One can reconcile the basic idea behind astrology with the doctrine of karma in the following way. Kṛṣṇa says that He places different souls into wombs that are appropriate based on their karma. So this indicates that a person is born in a situation which is appropriate depending on his past karma. Now the idea of astrology is that there are relationships between that karmic situation and the positions of planets and so on at the time of the person’s birth. Now the idea of karma could be correct even if astrology was completely wrong. But the idea of astrology is consistent with the idea of karma. If you just suppose that Kṛṣṇa, through His different agencies such as demigods and so on, is causing souls with particular karma to be placed in particular wombs so that they are born in particular times corresponding to the different planets being in particular positions. And it’s not necessarily a correct interpretation to think that the planets influence the individual fate. To give an example, consider the... what would happen if you observe a factory while watching a clock. You will see that when the hands of the clock point upwards suddenly a lot of people come pouring out the factory. Now you could say, is it that the metal hands on this clock influenced the people so that they came out at that time? Well, not exactly! It’s not that the clock hands had a strange mysterious influence that make people come out of the factories, but there is higher organized system in which people do things at certain times and the clock indicates the time.  

So similarly the motions of the planets are an indication of organized events going on in the universe. And just as behind the factory there is the management which determines the schedule and so forth, likewise behind the universe there are the demigods who are controlling the material affairs and so on. And ultimately beyond all of them there is the Supreme Personality of Godhead who is directing the whole thing.  

So that’s the idea of how something like astrology fits into the philosophy of Kṛṣṇa Consciousness.  

Q:  [unclear]

A:  Yeah they are like a sophisticated clock. And an interesting point by the way is that the clocks we have today started as planetariums, historically. It’s curious, in Europe back in the early Middle Ages people would build things that they called orreries, and these had hands representing the positions of all the planets as well as the time. Then gradually they just whittled things away and just came down to ordinary clocks. So that’s actually the history.  

So anyway I guess we should probably end there.  

All glories to Śrīla Prabhupāda!

Audience:  Jaya!