Astronomy Seminar 3
Thompson considers parallels between descriptions in the Srimad-Bhagavatam Canto 5 of the rings of Bhu-mandala, and the planetary orbits observed by contemporary astronomers. He then proposes that the mathematical closeness of fit of these features precludes coincidence and therefore suggests systematic astronomical knowledge. Thompson illustrates how numerous geographic descriptions found in this Puranic account could mirror a variety of complex modern constructs, such as quantum jumps, higher dimensions, and wave/particle duality.
TRANSCRIPT: Astronomy Seminar 3. VIHE Seminar: Gita Nagari, PA - 1990 / (207)
Yesterday we ended with the discussion of Bhu-mandala and so now we need to continue that. I should make some points concerning, we were discussing to some extent this appendix by Vamsidhara, so I should clarify a few points with regard to that. The view that I take on Vamsidhara’s presentation is given here. I say, “We should state clearly here that we do not think that his analysis is entirely correct.” So I say in the beginning here,
The main purpose in presenting this is to show that at a time before the advent of any European influence in India, the question of the earth as a small globe vs the idea of the earth given in Srimad-Bhagavatam as the Bhu-mandala disk was being discussed by Vaisnavas in our sampradaya.
So this Vamsidhara is an example of that, and as you can see in his presentation this was a controversial question at that time. People were perplexed about this. In fact, one of the solutions to this problem is that he mentions there is you should use the principle of anirvacaniya, which we have heard of in another context. He just mentions that as one of a list of different explanations. So the main point is that this issue is being discussed back in the early 1600s, which is the time when he was living. That apparently was the time of Visvanatha Cakravarti Thakura. Do we have any dates on Visvanatha Cakravarti Thakura? Yeah, just wondered what his exact dates might be.
So we were speaking about the cosmic scale of Bhu-mandala. So I want to do some presentation of that. Oh! It seems we have an artistic tesseract here. This is what it should look like: a four-dimensional cube or hypercube. We also have a one-dimensional simulation in space... Anyway, so what I want to do is give some idea of the scale of this Bhu-mandala, and I am going to try to do this with some drawings here. Let’s see how well this works. This is a cross section of Bhu-mandala and this is the center. So this is Jambudvipa right here. This is radially going out, so imagine that it extends on the other side also. So to get an idea of the dimensions, if we, from here out to here is about 250 million yojanas or about 2 billion miles using 8 miles per yojana. So that's the distance from here to the outer edge.
Question: That’s the radius of the Bhu-mandala disk?
Answer: That’s the radius of the Bhu-mandala disk. So, because the diameter would be 500 million yojanas or 4 billion miles. So half way there’s something called the Lokaloka mountain. Now everything in Bhu-mandala is arranged in circular form. So if this is Bhu-mandala and this is the center and the Lokaloka Mountain runs in a circle to the radius path, of the radius of Bhu-mandala. So it’s described that the region out here, between here and here, which is this region, that’s called Aloka-varsa. And it’s the region of perpetual darkness. There is no sunlight there and there are no inhabitants.
Comment: That’s what Aloka means, no people.
A: Yeah, so that’s Aloka-varsa. So this Lokaloka mountain is the boundary between the Loka and the Aloka. Hence it has that name. And it blocks the sunlight, that description is given. So there is no light in this region. So if we go in, so this has a distance of, this is another unit, 125 million yojanas. That’s that – it’s half of the radius. So then you go into about here, roughly speaking, and there is a region like this, this would be 82.2 million yojanas. This is the region of the Golden Land, it is called. There is an interesting description in the Bhagavatam. So that’s another circular region lying within here. This is also uninhabited. It’s described that the nature of this region is that everything is a blaze of light so that you can’t distinguish anything. And no one can live there. That’s the Golden land, it’s as though you are living on a surface of polished gold like a mirrored surface. And we can’t see anything because of all the light.
Now next we come to the, a region of inhabited land. Lets see, this, if we divide this up, it’s about this in proportion. This would be, okay, 15.75 million yojanas. This is the region from the outer edge of the clear water ocean to the beginning of the Golden Land, and that’s called inhabited land. That’s the description which is given. So that’s yet another circle. Then . . .
Q: Do you know what the Sanskrit terms for these are?
A: Yes, they’re all in the Bhagavatam. You can look them up. I don’t know them right off hand. So this right here is the beginning of the, this is the far shore of the clear water ocean. So now to describe what is going on inside here one has to expand out this diagram. So now this point becomes the same as this point – we have extended the scale. So within this radial region there is the seven dvipas and seven ring-shaped oceans. So the really important thing to note is that at a certain point here in the outer ring, which is called Puskara dvipa, there is a ring-shaped mountain called the Manasottara Mountain. So that would be here, another smaller ring. And this diagram is quite small now. And this is going to be of interest because this ring-shaped Manasottara Mountain is the path followed by the sun. So we are going to be talking about that in some detail.
A: No, it’s exactly in the middle of Puskaradvipa, which is inside the clear water ocean. So what you have is clear water ocean and then Puskaradvipa; and halfway across Puskaradvipa, radially, is Manasottara Mountain, which is a ring going all the way around. So going inwards you have successive oceans and mountains. And each one is half, as you go in each pair of oceans and mountains has half the width of the preceding one until finally you come down to Plaksadvipa, which is the smallest ring-shaped island. Within that is the salt water ocean, which is the smallest ring-shaped ocean. And then in the center of that is a circular island called Jambudivpa. And we were looking yesterday in the pictures, computer generated pictures in the book, which show what Jambudvipa looks like. So the main point is that on the scale of this picture, Jambudvipa here is very tiny. Just like a tiny region in the center of this large structure.
A: Yeah, I haven't drawn, yeah, I haven't drawn to scale. To give the figures correctly from Mount Manasottara which is here, to give the scale, is 9.6 million yojanas between Manasottara Mountain and outer edge of clear water ocean. And from Manasottara Mountain to the center of Jambudvipa, which would be the center of Mount Meru, there is once again 15.75 million yojanas. You can see this is, you know, about ⅔ of this. So I haven't drawn it to proper scale, but that is the arrangement.
So at this point there is an interesting observation to make concerning the scale of this system and that is that the Bhagavatam pretty much has the distance from the earth, which is at the center. We will be discussing how our location in Bharata-varsa and Jambudvipa, we would be located near the center of this whole structure. So the distance then from the earth to the sun, the earth as we know it to the sun, of course, I should emphasise in the Bhagavatam this whole thing is the earth. But the earth as a small planet as we experience, the distance from that to the sun would be given here as 15.75 million yojanas. Now if you use, as we have said the yojana is variable. But if you use 5 miles per yojana what you get, this comes out to 78.75 million miles, I’ll use that for million miles, and if you use 8 miles per yojana it’s 126 million miles. And also another figure for the yojana that I have seen is 6 miles, I’ll just put that one in for the sake of argument, you get 94.5 million miles. In any case, according to the modern science the distance from the earth to the sun is about 93 million miles. So it’s just interesting that the Bhagavatam seems to have the scale right as far as modern science goes. Yeah?
Q: What does the Jyotisa Sastra figure?
A: The Jyotisa Sastra, that’s a whole thing to discuss. It does not give a figure for the distance to the sun that agrees with the modern scientific figure.
Q: It should be the other way around if anything.
A: You might think. Now I would probably have to give whole lecture to properly discuss distances to the planets in the Surya-siddhanta, in the Jyotisa Sastra I would like to do that too, but I suspect that there are other more important things to cover first. But there are interesting issues there. Some of that is discussed in that first chapter you read, toward the end of this chapter. Yeah, so it’s interesting that the scale more or less agrees.
So this is the description of the Bhu-mandala. One thing I should point also with regard to Jyotisa sastra is that the historical astronomers who have written works in this field of Jyotisa Sastra have generally shown a lack of appreciation of the Fifth Canto description of the universe. For example, this Paramesvara said that the seven dvipas as were described in here are only for religious mediation. He said, “Well, they’re not real.” As for Mount Meru, he said that it is not acceptable to astronomers. And there are some other cases like that. This is the Siddhanta-siromani, this Bhaskaracarya, and he, for example, is describing here how they measured the circumference of the earth. This tells how they would actually do it in India. He is saying specifically that you would measure the distance from Ujjain to a point to the south of that and see the change in the angle of the sun. Ujjain, by the way, is the prime meridian used by the Indian astronomers. Just like Greenwich in England marks the prime meridian in modern astronomy. So you measure a distance going north-south and you see how much the angle of the sun changes if you cover that distance at a given date. And based on that we can calculate circumference of the earth.
The way it works is this: if this is the earth, it’s a sphere, and sunlight is coming down in parallel rays. So if you, this is the center, let’s say, the way I have drawn it right here the sun at this time would be right overhead. And here the sun at this time would be at this angle, which must be the same as this angle. If you measure this distance along the surface of the earth and you know this angle then you can find what the radius of the earth is. So that’s the method that they used. So he is describing that method and he gives the figure which agrees pretty much with the modern figure for the diameter of the earth. Then he says, “What reason then is there in attributing, as the Puranikas do, such an immense magnitude to the earth.” You see he is referring to this description of Bhu-mandala. So there is also a lack of understanding on their part of the situation of Bhu-mandala. So what I want to do today is go step by step to explain the situation of Bhu-mandala. So, yeah?
A: Yes, that’s seen most easily if you look at this picture, which is on page 52. So that is the picture of Jambudvipa and Mount Meru is the inverted cone-like structure that you see in the center.
Q: So what is Jambudvipa?
A: The whole thing is Jambudvipa, including Mount Meru.
Q: The whole thing, meaning what’s in that circle?
A: Everything in that picture is Jambudvipa, the whole totality of that picture.
Q: So Jambudvipa is the inner circle, the inner part of the disk of Bhu-mandala?
A: Yeah, the idea here is that you have these ring-shaped oceans and islands. Just to make another diagram, this just looks like a bullseye, but basically you have these rings getting smaller and smaller as you go in and finally in the very center there is a disk.
Q : That’s on the previous page, page 51.
A: Right, if you look on the previous page you get a perspective view, and you see Bhu-mandala [means Jambudvipa] situated within that series of rings. Yeah, so that’s the situation.
Q: The earth globe is where in relation to Mount Meru?
A: So that is what we want to now discuss. Now as I pointed out just at the very end of the class yesterday, to get an idea of scale, if you again look at the picture on page 53 you will see a mountain range that goes from A to B marked there. The height of that mountain range is about twice the diameter of the earth as we know it. It’s a mountain range that’s 2000 yojanas high. At 8 miles per yojana it's 16,000 miles high. The diameter of the earth is about 8000 miles. So that’s the height of that mountain range. So this Jambudivpa’s structure is enormous in comparison.
Now in order to understand Bhu-mandala, certainly our location has something to do with Bhu-mandala. That much you can say because in Bhu-mandala there is something called Bharata-varsa. And so there are nine varsas in Bhu-mandala which are divided by these different mountain ranges. And actually there’s this central square region that you can see that has Mount Meru growing up from it. That’s called the Ilavrta-varsa. And if you count the divisions made by these mountain ranges, counting that square as one of them you will see that there are nine, and Bhu-mandala [means Bharata-varsa] is shown more closely on page 55. It’s a sort of semicircular region on the southern side of this disk. So that is the description that is given.
Now in the Bhagavatam it’s described that the inhabitants of the varsas other than Bhu-mandala are all beings similar to demigods. It’s described that they are not quite demigods, actually they are persons who have nearly exhausted there karma on the heavenly planets – they were demigods. So having nearly exhausted their karma they come down to these other dvipas of, other varsas of Jambudvipa, but they still have basically good karma to exhaust. So they, it’s said that they live for ten thousand years and their bodies do not show symptoms of old age, and bad odour, and so on and so forth. Also these varsas are generally playgrounds to the demigods. All kinds of events involving the demigods take place there, including a lot of things mentioned in the Mahabharata for example. So these regions are not exactly earthly. They’re more like celestial domains; and it’s described that the Kali-yuga does not have a real impact in these other varsas. In general the Kali-yuga only affects Bharata-varsa to any severe degree. It just has a very slight effect in these other regions. Furthermore it’s described that Bharata-varsa is the region where one can accrue karma and where one can attain liberation. In these other regions typically one is simply exhausting the result of pious deeds done in the past. Generally they are just gradually gliding downward karmically. Yeah?
Q: Where is this that you are describing?
A: All the regions on this Bhu-mandala except for Bharata-varsa, which we described here, are what I am describing here.
A: You mean the innermost regions and these two side pieces? You know like, here and here, one of them is called Bhadrasva-varsa and so on. And these sort of more narrow strips here and on this side also, these are all regions in which basically the sort of like tail end of demigod life is being experienced.
There is a term that’s in the Bhagavatam known as Bhauma-svarga, which is interesting. It’s said that there are three kinds of heavens. There is Svarga proper which is the region Indra and the different demigods, Svarga-loka, so that’s an upper planetary system. Then there’s the Bhauma-svarga, which is the earthly heavenly region. So that consists of all the varsas of Jambudvipa plus the other six dvipas in Sapta-dvipa. So that is called the earthly heaven. And then there is something called Bila-svarga, which is the lower heavens. It’s interesting: there are lower heavenly regions which are inhabited by demoniac personalities who have a very high standard of material opulence. For example, Maya Danava lives in Bila-svarga and it’s described that he has very ideal material conditions, sort of like an ultimate in a wealthy suburb, sort of like La Jolla in San Diego actually.
But, so it’s interesting that these different regions apart from Bhu-mandala [means Bharata-varsa] are all referred to as heavens. So that means that we must be in Bhu-mandala [means Bharata-varsa] but there are some problems there. First of all, there is a problem of scale because the earth as we experience is very minute compared to the total size of Bharata-varsa. So the basic proposal that I am making is that the relationship between the earth globe of our experience and the structure of Jambudvipa is this higher-dimensional nature that I was discussing yesterday. So the idea is that the total system is higher-dimensional and one can experience it at different levels of perception.
Now in the Bhagavatam there are descriptions of correspondences between parts of Bharata-varsa as we know it (I keep saying Bhumandala!), namely India and so forth on this earth globe, and regions within Jambudvipa and Bharata-varsa in Jambudvipa. So these correspondences come up in various purports in Srila Prabhupada’s books in different places, and I have listed some of them in this chapter number three here. But what you’ll find, for example, is Srila Prabhupada describes that Bharata-varsa used to be the entire earth planet. That’s one thing that comes up in a number of different purports. In addition to that there are descriptions in several places that certain kings ruled all of Bharata-varsa, which in that case would include all of the earth planet. But then there are descriptions that some kings ruled all of Jambudvipa. And yet there are other descriptions of kings who ruled all the seven islands, Sapta-dvipa. And there is one case, namely Maharaja Priyavrata, in which it seems that he was ruling the entire universe. Srila Prabhupada said in one purport that it is very hard to understand where Maharaja Priyavrata was situated, because it seemed to be in the entire universe.
So the situation that you seem to have there is that in different periods of history there are different degrees of access. In one case you will have a king ruling in India who has access to all of Bhu-mandala, all seven dvipas. In other cases it’s just Jambudvipa, in other cases it’s just Bharata-varsa. So in the Kali-yuga of today there is a very limited scope of activity. But in other periods, different yugas and so forth, there was evidently much larger scope of activity to varying degrees. It’s also described that specific places on the earth correspond to places in the higher planets. By the way, Srila Prabhupada uses the term higher planets to refer to this general Jambudvipa system. For example he has spoken of Mount Meru as being on a higher planet. He has spoken of the Gandhamadana Hill, which forms one of the boundaries between two of these varsas, as being on a higher planet and so forth.
So let’s see here, just to illustrate some of this . . . interesting point here is that communication between the earth planet and the seven dvipas is still going on today according to the Caitanya-caritamrta. You can read there that human beings, not human beings but beings from the different dvipas of Sapta-dvipa, visited Lord Caitanya during His pastimes, disguised as human beings. So these kinds of things are going on. As far as this idea of the principle of correspondence is concerned, let’s see here, some of the things that I just mentioned are listed here or discussed on page 57. Where were these other things? One thing I wanted to discuss, was interesting to me, is the idea that rivers on earth have celestial counterparts. Srila Prabhupada in one place, this was in a purport in a section in Bhagavatam discussing the slaying of Vrtrasura. He pointed out that all of the major rivers flowing in India, not just the Ganges but the Narmada river and various others, have their counterparts in the heavenly planets. So there were descriptions of battles that took place on the heavenly planets along the shores of rivers, but those rivers are in India.
So the basic thesis that I would propose is that the total structure that you have here is this structure described briefly in the Fifth Canto, but this can be seen at different levels of perception in different ways. There are more limited levels of perception and more expansive levels, which depend then on the karmic situation of the individuals. And also the cycle of the yugas can be involved in this, this being Kali-yuga.
So in this way you have the earth being experienced by us as a small globe, but in a higher-dimensional sense, that is connected to this larger structure of Bhu-mandala. The basic thesis that I am proposing is that Bhu-mandala is a description of the universe as seen from the point of view of the demigods and rsis and so forth. And the small earth globe as we know it and as described in the jyotisa sastras corresponds to earth in the experience of the ordinary human beings like ourselves. Yeah, like in Kali-yuga. Yeah?
Q: So is this, are you saying that somebody’s karmic bank account, how much karma they have, kind of grows and prospers? It says that everyone on this planet experiences it as a sphere, so they must fall into the same category, a certain range of karma, that we have at this level of sense perception?
A: Yes that would be correct, there is group karma you might say, and it does go by quantums, quantum jumps, and the point where the quantum jump is made is when you die and get another body, because depending on the karma you have accrued in the course of one life time, at the time of death you could be promoted to a higher planet. So in effect you make a quantum leap at that point or you could be demoted to a lower one. So it’s not exactly that there is a continuum of possibilities. There are quantum jumps there. Yeah?
A: Yes, so the Bhagavatam describes all the varsas in terms of this basic geographical structure shown here. So I have made the point thus far that at least part of that, namely part of Bharata-varsa, can be experienced by its inhabitants as being a globe detached from everything else. Now it is interesting that Srila Prabhupada uses this kind of description for all of Bhu-mandala. And I collected together examples of that. Basically we see how Bhu-mandala is described in the Bhagavatam. That’s what we are discussing here. Srila Prabhupada describes it as a system of globes. And since that is an interesting point (let me look at the page reference where I have that discussed. I would have thought that I had good notes here. Here we go, 71-72 in the book), there is a section called “Planets as Globes in Space.” So Srila Prabhupada refers to the whole system in terms of globes in space and I have about seven different references here. Yeah?
Q: The idea that they are simultaneously globes in space and a plane, seems like the idea of an atom being simultaneously perceived as a particle and as a wave, two levels of . . .
A: Yeah, you can make an analogy like that, and that analogy is backed up in one sense because in order to explain the atom in that way, the physicists actually use a higher-dimensional scheme. As I was saying yesterday, in quantum mechanics you use higher-dimensional space to define atoms. So that whole wave-particle duality and all the different things you find in quantum mechanics is really expressed in terms of higher dimensions. So in any event, the idea from different points of view, you have either this structure as described in the Bhagavatam or you have systems of globes. That is there in Srila Prabhupada’s descriptions. Here is one, this is from the Krishna Book. I’ll just read this. This is where Arjuna and Krishna are going to visit Maha-Visnu. So it says, “Seated on His chariot with Arjuna, Krishna began to proceed north crossing over many planetary systems.”
I should, by the way, describe where they were travelling. north would mean towards the north pole star which is the direction of Satya-loka. And if you imagine Bhu-mandala then it is spread out beneath them as they travel upwards. So they get a panoramic view as they go up. So Srila Prabhupada says,
These are described [the planetary systems] in Śrīmad-Bhāgavatam as Sapta-dvīpa. [So that’s the Sapta-dvipa]. Dvīpa means ‘island.’ These planets are sometimes described in the Vedic literature as dvīpas. The planet on which we are living is called Jambūdvīpa. Outer space is taken as a great ocean of air, and within that great ocean of air there are many islands, which are the different planets. On each and every planet there are oceans also…
and so on. So there he is describing Sapta-dvipa in terms of islands in the ocean of air.
Here is another reference. This is from Caitanya-caritamrta, Madhya-lila is the reference here. By the way, in reading this book it’s useful if you look up these different references that I have in brackets because then you will see what Srila Prabhupada said in the original references. But here is another one. He says,
The planets are called dvīpas. Outer space is like an ocean of air. Just as there are islands in the watery ocean, these planets in the ocean of space are called dvīpas, or islands in outer space. [CC Madhya-lila 20.218]
Oh here is one, this one is interesting, number 4 here. I will just read a part of it. It says that, (this is in 5.1.31, Fifth Canto),
As Priyavrata drove his chariot behind the sun, he created seven different types of oceans and planetary systems, which altogether are known as Bhū-maṇḍala, or Bhūloka.
And there again he was saying, “Sometimes the planets in outer space are called islands.” And these are islands in the ocean of space.
So basically the idea here of a planet as an island floating in the ocean of air, the ocean of space. He explicitly refers to them as globes also. There are some other references here. So this gives, in a way this all adds up into a sort of unified picture of things. If you consider that you have the description of this Bhu-mandala system in Bhagavatam described in this way, including Jambudvipa, and that it is also understandable as a series of globes, or a system of planets, floating in space. So the idea then is that one can make sense out of this in terms of this higher-dimensional concept. Yeah?
Q: The geography of Bhu-mandala, with the circular rings, suggests the idea that this system of globes is nested together, one inside the other, with a common center . . . I’m sure you must have thought of that. . .
A: Well I thought of it, but what I thought was I can’t really do much more with it in the sense that I don’t have any information to go on there. But, you see, basically we have somewhat limited information. At least we have this much information here. But in terms of the details of how its all laid out, of course I don’t really know but, so let’s see.
I then wanted to go on to the descriptions in it. So we have this Bhu-mandala disk which I am claiming as higher-dimensional, and it can also be experienced as a series of globes. But as far as modern observation is concerned, if you look out into space from the earth you will see stars in all directions. You don’t see such a system of globes. Of course, there are certain other globes floating out there, but those are Mercury, and Venus, and Mars, and so forth, and the sun, the moon, there are just a few of them and they have names. They also are named in the Bhagavatam. So they are not Bhu-mandala, they are quite distinct from it because they are separately described in the Bhagavatam. So then where is this Bhu-mandala? So that’s what I wanted to discuss next.
So if you look into outer space you see stars in all directions.
Q: Are you saying that Mercury, Mars, and Venus are not part of Bhu-mandala?
A: Right, they are not, because they are separately described in the Fifth Canto. That is, it talks about Venus, Mercury, Mars, and so on, but they are not Bhu-mandala. They are something different, so they are all described. Their paths or orbits are described with reference to Bhu-mandala. And that’s what I want to come to. I think I’ll be able to get to it today.
Q: You have until 6:00.
A: I have until 6:00, right. Yeah?
Q: Are those planets described as globes?
A: Mercury, Venus, etc? Actually it doesn't explicitly say that they are globes, although I think it’s taken for granted. In the Surya-siddhanta they are definitely said to be globes.
Q: But the Surya-siddhanta accepts that in general...
A: Right. The Bhagavatam refers to them as graha. The word for those planets is graha. As I was saying before there are two words that Srila Prabhupada translates as planets generally. Loka is one of them and graha is the other. And as I was saying, that has astrological significance. It refers to the power of the planet to influence you. It grabs you, is the idea.
Q: What I’m thinking, in the Puranic view, there should be some consistency in how things are are seen, and the Jotisa Sastra has the consistency of seeing things as globes in space?
A: Yeah, well the Puranic system has more disks than just Bhu-mandala. There are fourteen of them.
Q: And there might be globes involved with them also?
A: Yeah, there could be. In fact Srila Prabhupada says that with regard to all fourteen of them. That’s the one I didn't read in this list here. He refers to all fourteen of these planetary systems in terms of globes in space, but basically in the Bhagavatam they are like planes, especially the lower ones. The lower planetary systems are all named -tala. There is Patala, Sutala, Mahatala. We have the word tala, is thali, a plate. So that’s what they are, disks, they’re plates.
A: Yeah. Well I don’t know, but tala definitely means a flat plate. And that is the etymology there as far as I am aware.
Q: Maybe I wasn’t clear. I mean, even from this higher-dimensional viewpoint, some of these things appear as globes? That’s what I’m asking.
A: Yeah. You see, especially for the higher planets, the Puranas don’t really say what shape it has, at least the Bhagavatam doesn’t. What is Indraloka like in terms of its layout? It doesn't really tell us or Svargaloka, actually that’s Indraloka, you know Maharloka, Janaloka, and so on. So what I am proposing basically is there are different ways of experiencing these things. Just to give some other examples: Just like we think of the earth as a globe and we experience it that way. But suppose you could actually go to Vrindavana and experience the whole Goloka Vrindavana present there – then you wouldn't be experiencing the earth as a globe. If you would be going there and seeing this infinite, unlimitedly expanded region which hardly would fit into the earth in the ordinary sense, so for that level of experience you wouldn't be experiencing the earth as a globe. So I am just proposing that in general that’s the way it is. Or to take a mundane example, if you take one of these yogis who can reach out with his prapti-siddhi. Let’s say he reaches, as Prabhupada says in the Nectar of Devotion there in the beginning, and touches the moon with his finger. So to him the moon is right there. So the whole structure of the things as he experiences it is different. And so the basic idea is that the total structure of reality is a sort of multi-level, multiply-connected, higher-dimensional system; and depending on how Krishna sets up your particular sensory situation, you can experience it in different ways.
Q: Yes, I understand that, but I’m just wondering if there is a certain level of consistency within the different ways of seeing things?
A: Yeah, beyond that I don’t know. This is as much as I know. Yeah?
A: Well that’s the, what happens with the advent of Kali-yuga. Well, the different living beings don’t grow as much. That’s the impression I have there, they become stunted in their growth. Yeah?
Q: Does Mount Sumeru go into any other mandalas?
A: It’s part of Bhu-mandala. It’s described as being a part of Bhu-mandala.
Q: Then the residences of the demigods on top of there are definitely distinct from their residences in the heavenly planets?
A: Yes, it’s like a king had a summer palace, as far as I can understand. Because for example, Brahma obviously is living in Brahmaloka and then he has his city on top of Mount Meru.
Q: Is there a significance that Mount Meru is cone shaped?
A: Well, it’s clearly different from an ordinary mountain. We call it Mount Sumeru but it certainly is not like any ordinary mountain.
Q: There is no significance to this?
A: There may be. There may be, I only know so much. It doesn't give a very clear account of how big the moon is.
So to continue, let’s see if I can get through to some of these points. If we ask where Bhu-mandala is we can think of it in this way: think of it again as a disk, which is the simplest image. Now we are at the center of that disk. Somehow that much is clear. And it’s a very big disk, it goes out two billion miles. So that means most of it is very far away from us out in space. So if you imagine sitting on a disk like that, that disk is going to be like a plane bisecting space into two halves. I talked to you the other day about the celestial sphere. So that would cut the celestial sphere in half along a great circle. So that means to say, where Bhu-mandala is, you would want to say, “What great circle on the celestial sphere does that correspond to?” That would be the way you would approach the question.
So there are different possibilities. The first one would be the, what you could call the ‘naive flat earth hypothesis.’ Now according to this idea Bhu-mandala must be on the plane of the horizon. The idea is that if people were thinking the earth was flat and it’s just a plane, so then that would be the plane of the horizon. So that’s what Bhu-mandala is. Now this won’t work, though, because ultimately the reason for that has to do with the motion of the sun. The sun moves along the plane of Bhu-mandala in a big circle. In fact I erased it, it moves on this Manasottara Mountain, which is a ring. So we’d be in the center and it moves on that ring. So if you think of that, that would mean the sun would be at some point of the horizon and it would just move around on the horizon. It would never go up. It’s a curious indication of the way people think. Bhaskaracarya criticises the Puranas on that very basis. He thinks that’s what they must be saying. So he says, “If this blessed earth were level like a plane mirror, then why is not the sun revolving above at a distance from the earth, visible at all times” etc. But the basic confusion is: that’s not what Bhu-mandala is. And of course another problem there is that the local horizon changes depending on your latitude because you are on the surface of the globe.
So there are two main possibilities for the location of Bhu-mandala: One of the them is the celestial equator, and the other is the ecliptic, which is the path of the sun. So I am going to talk about those. Now if you look at out into the sky at night, you see either one of these two possibilities, then that means Bhu-mandala is at a tilt compared to the plane where we are standing. That would be true anywhere you are on the earth. Depending on where you are on the earth the tilt would be different. But it tilts. So if you look at the sky at night that means that the plane bisecting the celestial sphere goes up at some angle and cuts across the sky like that. But of course, all we see when we look out into space is stars. We do not see any bisecting entity out there cutting the heavens in half. So the answer I would give to that objection for this whole Fifth Canto system is that, well for us then, Bhu-mandala is not visible because of its higher-dimensional nature. I would say that we have examples of that in other situations in the Bhagavatam. Kalapa-grama in the Himalayas is not visible to us. That’s also a material arrangement.
A: Kalapa-grama, that I mentioned the other day, is the place where the representatives of the sun dynasty and the moon dynasty are in yogic trance waiting for the end of Kali-yuga. And it’s there in the Himalayas. I have been told the location is defined in the other Puranas.
Q: Which Himalayas?
A: Ours. Remember Bhakta Prema Swami? Well, back when Srila Prabhupada was here, there was a Bhakta Prema Swami. He used to be a yogi. Initially he was called Prema Yogi, and, well, he told me he has been there. We can consider the source, but I think it’s fair to say that it’s known where these places are in the Himalayas. Yeah?
A: Yeah, let me clarify your example, because it still is there in that example. I gave this example in the book. I’ll explain at some length because that’s just the point that I’m making. I am proposing that something that is there in the higher-dimensional sense will also have a three-dimensional location. And in order to go to it you have to go to a two-dimensional location and travel to its higher-dimensional location. Now the example that I gave in the book is a two-dimensional example. So suppose you want to go to a certain office in New York city. So you’re given the street address. So lets say it’s a certain street, certain avenue. So if you go there on that two-dimensional grid to that address you may find that you can’t find the office. In order to reach the actual office you have to move in the third dimension, going up to, say, the 50th floor of the building, and then you find the office. So the point is it has a two-dimensional address, to get to it you have to first go to the two-dimensional address, and then go up. Of course you could go up in a helicopter, go across, and also reach it in that way. That’s also possible. But even there, there you are going in the third dimension first and then going to the two-dimensional address because you are still hovering over the same intersection, street and avenue, once you get there. So it has a two-dimensional address which you need in order to get to it and it has a third dimensional position. So to really get to it you have to move in the third dimension also.
Q: Is that like the rivers on this planet and the rivers on the higher planets having the same name?
A: Well, it is possible that a river on this planet can have a higher-dimensional existence. And of course we have examples where that would have to be true practically for the Vedic literature to work out. Take the Ganges: there’s the Ganges that we know that you can bathe in – that is coming down from the top of Mount Meru and it lands on the head of Lord Siva who is collecting the waters breaking its fall, and then tumbles down and comes down to the area where we can see it. Now in terms of our experience from what I understand the Ganges issues out of a spring or cave like region somewhere up in Himalayas. There was a BTG article about it once. So it looks from our perspective, you know, it’s certainly a river of this earth, with a source at a certain location that you can go to. But it’s described that it’s coming down from the top of Mount Meru. Prior to that it came down from the moon and prior to that it came down from the Sapta-loka planets, the seven rsis, and so on. That would have to be a higher-dimensional transformation in which finally it becomes manifest within our vision. So similarly with all of these things.
So the example, then, of the streets and the third-dimensional location of this office, if you apply that to the Bhu-mandala, the idea would be that Bhu-mandala would have its three-dimensional location, but to actually see what is there you have to travel in the third-dimensional as well, I mean a higher-dimensional as well. So that’s the idea, that it makes sense to talk about the three-dimensional position of the higher-dimensional system.
Q: But the sun is visible.
A: But the sun is visible.
Q: At the same distance above that Manosottara Mountain . . .
A: Yeah. So we have other examples of that. There are, well of course the I one already gave of Kalapa-grama, is one such example. The mountains that it’s on are visible to us – the place itself is not. It’s a spiritual example, of course that, Vrindavana as a place with its landscape is visible to us; we know where to go on the earth to reach it. But you have to go into a higher-dimension, so to speak, this time to the spiritual level, to see Goloka Vrindavana there, or the actual spiritual Vrindavana which is there. So and if you think of that example again as I far as I can see, you have to go to the three-dimensional place also in order to get there because otherwise one could say, well, you can go to Cincinnati and that would be Vrindavana too if you had the right level of realisation. But that’s not what you read in the scriptures. You are told, well, that the 32 krosas of land in one region, that’s where the spiritual Vrindavana is on the earth.
So the basic idea there is you can have a higher-dimensional system which also has a three-dimensional location. Another example which is interesting – we were talking about this last night – in the Fifth Canto of the Bhagavatam it describes that 100 yojanas above the level of the earth (of course when it says earth it means Bhu-mandala, but presumably 100 yojanas up would also mean 100 yojanas up for us. At 8 miles per yojana, that would be 800 miles up) there are worlds inhabited by a whole list of beings. These are Raksasas, Yaksas, and Bhutas, and Pretas, and so forth. They’re all rather demoniac types of beings. So they live about 800 miles up according to this. And if you go still further up, it doesn't say how far, but just a little bit further up you come to another strata inhabited by Siddhas, Caranas, and Vidhyadharas, and other beings like that. So to us, if you look up there, it seems like empty space, but they are living there. And living there means they have their own abodes, they have their vehicles, there are roads and houses and everything that you need in order to live. So that’s there, but we don’t see it. So that means given a three-dimensional location in the Bhagavatam so we can say, “Well, it’s up there at that distance, but it’s definitely not visible to us." So that would be another example. Yet another example would be the civilization on the moon. Of course that’s a whole issue – did we go to the moon or not?! But the same thing could be applied there. I’m going to talk about the moon later on, though. So let me continue with this. Yeah?
Q: Would this be like the example of, I think Abbott, who wrote Flatland?
A: Well, he had some interesting ideas there. We can use his analogies. There’s this book called Flatland which, it was actually a political satire I think pretty much. But you have this two-dimensional world with two-dimensional beings living in it, and they can only understand two-dimensions; and it describes what happened when a three-dimensional being visited that world. The three-dimensional being was described as a sphere, just for simplicity. So when he visited that world it looked as though a point suddenly appeared and then expanded into a circle. And then when he left, the circle shrank down into a point again and vanished. So from the point of view of the beings in Flatland, this circle-being seemed to have amazing powers because it appeared at one place then disappeared and then appeared in another place. But from the point of view of the sphere-being, who was three-dimensional, he was just moving around like that. So there are analogies like that. Of course we have so many appearances and disappearances in the Vedic literature. Let’s see.
A: UFO’s and all that. We’ll discuss that – that will come up later – we have some material on that also. So what I want to do now is discuss the path of the sun in the Bhu-mandala. So in the Fifth Canto, I have brought this along here, I am not going to try to discuss all the details that are there in the book. That we can read gradually. But I wanted to discuss a couple of interesting verses which refer to the movement of the sun. So this one verse says the following thing – actually these aren’t really verses, the Fifth Canto is mainly in prose – so it says,
The chariot of the sun-god has only one wheel, which is known as Saṁvatsara. The twelve months are calculated to be its twelve spokes, the six seasons are the sections of its rim, and the three cātur-māsya periods are its three-sectioned hub. One side of the axle carrying the wheel rests upon the summit of Mount Sumeru, and the other rests upon Mānasottara Mountain. Affixed to the outer end of the axle, the wheel continuously rotates on Mānasottara Mountain like the wheel of an oil-pressing machine.” [SB 5.21.13]
So I will try and make a drawing of what this is saying. If you look at, well, let’s see, the best thing to do I guess is to look at this from the side. So this ellipse would be the ring of Manasottara Mountain seen from the side. Jambudvipa is the center (I am drawing this completely out of scale!), this Mount Sumeru would be in the center there. So what you have is an axle going from there to a wheel. So this is a wheel and the axle goes out like that. So the idea is that this wheel is rotating on top of Mount Meru and going around in a circular track. And the axle is supported by the wheel at this end and at the top of Mount Meru at the other end. So that’s the description that’s given. So this is compared here to an oil pressing machine called a taila-yantra. So I have never actually seen one. Has anyone seen one of these? You have seen? Yeah, but if you see what the oil pressing machine is, it consists of a heavy wheel with an axel going through the central stabilizer. And oxen will pull that, and it goes around in a continuous circle. And you put say, something you want to press oil out of…. sesame seeds. So it just keeps them crushing as it goes around in a circle. And in this way you get the oil from the seeds.
So that’s how it’s being described. And the sun is located here. How exactly it is situated in respect to the wheel I am not sure but it’s out at this end of the axle. So the idea is that this goes around, it carries the sun around. Now if you look at it in terms of the proper scale the thing to notice is that in the Bhagavatam you will find that the sun is above the plane of Bhu-mandala by a 100,000 yojanas – that’s how high it is above that plane. And this distance from the center up to where the sun is, that is up to Manasottara mountain, was 157,500,000 yojanas. A hundred thousand is a lakh of yojanas. So the point is, the distance out to the sun is much greater than the distance from the sun to Bhu-mandala. And we are up at the center, somewhere in here. So that means that to us the sun has to be very close to Bhu-mandala, because you can imagine, let’s say, if you have a rod 157 feet long and the wheel kept a light bulb one foot up and thing was rotating on a plane, it would be practically on the plane. So that’s the scale of this situation. So that means that to know where Bhu-mandala is, you have to ask where the sun is because the path the sun follows is right next to Bhu-mandala, like this. So the basic idea then is that this verse….
Q: What is the height of Sumeru again? 80,000?
A: 84,000 yojanas. Yeah, it fits in basically in terms of the dimensions of these things. So what this does is support the idea that the Bhu-mandala disk corresponds to the path of the sun. So there are two ways in which the sun moves (we have fifteen minutes here), two basic motions, and one of these is the daily motion that you see from sunrise to sunset and back around again; and the other is the yearly motion, which I described, against the background of the celestial sphere. So if you take this motion to be the yearly motion, then what you get is the, this thing goes around in one year on this circle, where the sun is where Bhu-mandala is, the sun goes around the ecliptic once in a year. So that if you think about it, it pins down Bhu-mandala to be in the plane of the ecliptic. That’s where Bhu-mandala would have to be. So that would be how you figure the location. Now there are descriptions here, which, it’s a little bit more complicated than this though.
A: That would be where the plane of Bhu-mandala is.
A: Well, gravity is another whole topic: how you relate all these things to questions of gravity. By the way, there is a whole section in the book later on, on the whole subject of gravity, which is a whole issue.
Q: What about the idea of the earth going around the sun?
A: Ah, that is what we discussed on the first day here, namely the heliocentric versus the geocentric viewpoint. Actually in that discussion I was pointing out, of course, that the jyotisa sastra presents things from a geocentric perspective. So the earth is the fixed point and things move around it, the sun, the moon, and so forth, whereas modern astronomy takes the heliocentric viewpoint. And the main reason intuitively that people tend to be convinced that the earth must be going around the sun rather than the other way around is that the sun is so massive compared to the earth that if the sun is going around the earth it’s like the tail wagging the dog basically. It makes more sense to think that the tiny earth is going around the big sun.
A: Now you can sort of see here some indication as to why the same argument would favor the geocentric point of view in the context of the Bhagavatam, because here the sun, big though it is, is relatively small compared to this earth structure that we are talking about. Of course, then comes the question of gravity. If you take a naive model and you fill out all the space in the plane between the earth and the sun with mass, just like they have some incredible gravitational field, and in terms of ordinary physics things just wouldn't work out.
A: Yeah, that’s another whole topic. Srila Prabhupada says some things about gravity. Huh?
A: Well, he makes a number of comments. I could look this up – it’s later on in the book. Basically the point Srila Prabhupada makes is the, the greatest concession he makes to the law of gravity is that, what’s really happening is not according to the law of gravity – but you can name it as such if you want. But the thing that’s really going on is something quite different. Of course it’s described that the Ananta Sesa is holding the planets and so forth. Well, there are two basic descriptions of what is causing the planets to move in their particular orbits. One is the idea of Ananta Sesa; the other is the idea of things being moved by wind. It’s something called the pravaha wind which is moving the planets around. Srila Prabhupada refers to both of those. Yeah?
A: So that is one, let’s see. The next thing I had is . . . okay, I will turn to this . . . 302. On page 302 of the Bhagavatam there is another long description here and basically Srila Prabhupada says in the purport, which is actually shorter than the section of text itself, he says, “The sun orbits around Mount Sumeru for six months on the northern side and for six months on the southern. This adds up to the duration of day and night of the demigods in the upper planetary systems.” So that’s what Srila Prabhupada says there. By the way, the Bhu-mandala has a system of directions like this. If this is Jambudvipa in the center and you have north, and south, and east, and west like this. In other words, the center point we still have directions going out from it – north, south, east, and west.
Q: But in the Krishna Book section that you read, it said that north was going up?
A: Yeah, I said that. There is north to the pole star, and it stands to reason that Arjuna and Krishna were going through Satyaloka toward the pole star.
A: Yeah, the surface of our earth is at an angle, but the point I am making here is that Bhu-mandala itself, that plane, has its own system of directions and it’s arranged like this. So on the earth globe the system of directions changes depending on where you are. If you are at the north pole then every direction is south and so if you are a little bit south on one of those lines then north is toward the north pole. If someone goes south the other way, north is still toward the north pole. So there, norths go at one another. If you can see, in very northern countries, north for them points over right on top of the globe toward one another. So that the way it is on the globe. You have a different coordinate system for directions at different points, but Bhu-mandala is given one coordinate system for north, south, east, and west.
A: The point I made prior to that, I did this to illuminate the purport of Srila Prabhupada that I read where he said, “The sun orbits around Mount Meru for six months on the northern side and six months on the southern side.” That was the point there.
So, what I would finally like to get to, well, we will probably talk about this more on other days, is the other planets. So in the Srimad-Bhagavatam, apart from the sun and the moon, there is Mercury, Venus, Mars, Jupiter and Saturn, and Rahu. And other Vedic literatures describe Ketu also, but the Bhagavatam doesn't as far as I can see. But in any case, Uranus, Neptune, and Pluto aren't mentioned. This is also the case with Jyotisa Sastra. The same planets are there without Uranus, Neptune, and Pluto. Curiously enough, this Bhu-mandala disk, if you take it all the way out, it goes out two times the radius of orbit of Saturn according to modern calculations, but it wouldn’t include Neptune, Uranus, and Pluto, curiously enough.
Anyway, discussion of distances is another whole topic to go into. But what I want to talk about now is where these planets Mercury, Venus, and so forth are located. So the basic description given in the Bhagavatam is that these planets are at various heights above Bhu-mandala. So let’s make a horizontal picture again. If this is Bhu-mandala, then the planets are given as having various heights above it, and there is a table in the book, which is on page 85, in which these heights are given. Now it would appear that in the Fifth Canto as we have it, there are some misprints there concerning these heights and I mention that in this table. These particular numbers in this table 8 are given based on the following considerations: In the Bhagavatam the earth-sun distance, the height of the sun, is given as 100,000 yojanas above Bhu-mandala. So that’s also confirmed in various other places. Then in different verses it gives the height from one planet to the next going up. So then if you then add those numbers one upon another, you get the values here. By the way, in this table I am just using 8 miles per yojana. So you see the first figure here is 800,000 miles and so forth. So you have this sequence of planets and the lowest one here is the sun, the next one is the moon, and then we have Venus, Mercury, Mars, Jupiter, and Saturn.
Q: Does the figure for the moon correspond to modern calculations?
A: Not exactly. And I am going to show, though, a very interesting thing that emerges if you look at all the planets as a group. The figure for the moon does not particularly correspond to any of the modern figures. But you find some very interesting things though, nonetheless. And I’ll just build up to that.
So this is the system. It’s like a sack of horizontal levels, like phonograph records on a stack. Basically, if you look at these numbers, the highest one is Saturn, which is 11 million miles roughly. Now keep in mind the distance from the center out to where the sun is was 126 million miles. That’s the radius from the center up to the Manasottara Mountain. So yeah, here it is, we’re using this figure right here because we’re using 8 miles per yojana. So from the center out to the sides is 126 million miles and as you can see in this table, Saturn, which is the highest one, is 11 million miles, which is small compared to that. So they are really close to this plane – they don’t go very far above it. So that’s what you get from the Bhagavatam.
Now on the next page I have another calculation, which is kind of interesting. This is based entirely on modern astronomy. What I did was the following thing: take the plane of the ecliptic and ask how far each planet goes away from the plane of the ecliptic in the course of its orbit. Now the thing to realise here is that the planets move in different orbits and these correspond to different planes. Just as from a geocentric point of view the sun’s orbit around the earth, that makes one plane; the moon’s orbit around the earth makes a different plane and that tilts with respect to the first plane. And the same is true of all the different planets.
And I was describing actually on the first day how the Surya-siddhanta also discusses this. It gives for that second epicycle, it gives the tilts of the different planes. So since the plane for a given planet tilts compared with the plane of the ecliptic, and the planet is moving in a roughly circular orbit in the ecliptic. Now using modern astronomy this is actually an ellipse, elliptical orbit. That means the planet is going to go to the furthest point away from the plane of the ecliptic in the course of its orbit. And so what is that value? You can calculate that using the orbital data that they have. So in table 9 on the next page, page 86, you see the results of that calculation. And we have a table of the planets in the increasing order of distance according to those calculations. The thing that is interesting is that although these figures are not exactly the same as the figures you see on table 8 on page 85, they’re in the same ballpark, they are in the same order of magnitude. And the order that you get from the distances of the planets from the ecliptic is the same as the order that you get in the Bhagavatam, namely it’s the sun, the moon, Venus, Mercury, Mars, Jupiter, and Saturn. You get that same order.
A: Yep, Mercury and Mars, isn’t close, but it is the same order, that’s true. So Saturn goes further south, actually 38 million instead of 11 million. But then Jupiter is 11 million and over here its 9.6 million. So it’s rough, but it’s in the same ballpark basically. So what I am suggesting is, then, the basic picture in the Fifth Canto is consistent with the picture of how the planets are related to the ecliptic in modern astronomy. Now it’s not exactly the same because in the Bhagavatam it just says these planets are different heights above Bhu-mandala. Whereas in modern astronomy it gives all these tilted orbits – they go above and below as they go around and so they cross over at a certain point. So it’s somewhat different but at the same time there is this basic agreement.
But what I am calculating in table 9 is in fact the distances reached from the plane of Bhu-mandala. Not from the plane of Bhu-mandala, rather, but from the ecliptic. Here’s how it is done: if here is the earth and here is the sun, this is the way you do it in the Western system, and another planet goes on a plane…we are supposed to end. We really should end. We will resume tomorrow.