Astronomy Seminar 2
The second presentation of the Vrindavan Institute for Higher Education seminar on astronomy focuses upon “the nature of matter.” Thompson begins by examining a number of mathematical relatively sophisticated constructs found in Vedic texts, such as the Pythagorean theorem, accurate estimates for pi, and complex algebraic and trigonometric calculations. He then expands the discussion with a review of Vedic accounts of multi-dimensional space that sound more reminiscent of Einstein’s analysis of curved space, and as such appear in marked contrast to the limited experience of matter as “little bits of 3D stuff.”
TRANSCRIPT: Astronomy Seminar 2. VIHE Seminar: Gita Nagari, PA - 1990 / (206)
The Surya-siddhanta, I know that’s a little bit mathematical, its orientation, but then astronomy is like that. Astronomy is the most ancient tradition of mathematical science actually. And that’s true in India also. As I was pointing out, a lot of mathematics that we have today comes originally from India, that’s an interesting point. For example, the so-called Pythagorean Theorem is found in the Silpa-sastra which is a part of Atharva Veda. And it’s a general form of the theorem. Sometimes they will say that, “Well, certain ancient people had special cases – they didn’t have the theorem in its general form.” But in the Silpa-sastra it gives the most general form of the Pythagorean Theorem. So they had geometry and they could solve all kinds of complicated geometrical problems. These were involved in building sacrificial altars. Apparently they would want to do such a thing, well they had, say, an altar in the shape of an eagle, very precise shape defined geometrically, and there would be the problem of making an altar of the same shape but with twice the area. Now how would you solve that? You had to double the area. But they could do it using their geometrical constructions. So that’s in the Silpa-sastra.
Then algebra really comes from India. We get it from the Arabs, but it’s there in India and trigonometry as I mentioned yesterday. And while I am on the subject, in the very last part of the book, I’ll mention something which is kind of interesting, this business of calculating π to many decimal places was a favourite pastime in India. So there’s a 14th century Indian mathematician named Madhava and he gave the following approximation for π. It’s 3.14159265259 and he lived in South India sometime in the 14th century.
So in any case, the purpose in discussing the Surya-siddhanta was to lay the groundwork for understanding the Fifth Canto of the Srimad-Bhagavatam. Because in order to understand the Fifth Canto it’s important to have an idea of where the different structures are that are mentioned in the Fifth Canto. I am going to talk about the Fifth Canto proper tomorrow, but when I go over that we will be discussing such things as Mount Meru, Jambudvipa, Bhu-mandala and so forth; and we’ll be interested in knowing where they are in the universe. So this introduction involving the Surya-siddhanta will help us in identifying where these different structures are so we can get an idea of what the Fifth Canto is really saying.
Before coming to that there is some additional preparatory work which is important for understanding the Fifth Canto. And that involves understanding the nature of matter. So that’s what I want to talk about today. So in the book, this corresponds to the second chapter which I call “Vedic Physics: The Nature of Space, Time, and Matter.” So the basic point to make is that in the Vedic literature the universe has many levels of experience. In effect they are what should be called parallel worlds so that you may have experiences on one level. So you see a certain world and have certain experiences and this was based on your karma, a particular arrangement of your senses. However, by altering the arrangement of your senses you can experience another world which in effect is in the same place. So in the book I used the term ‘higher-dimensional’ to refer to this. In Vedic literature as far as I am aware there is no Sanskrit word that corresponds to this term ‘higher-dimensional’. It’s a modern mathematical term. However, it’s a useful word for referring to certain basic properties of space and time which are implicit in the Vedic literature. So I’ll give you a few examples of what I’m talking about and then we can consider the general principles involved.
So one example of what you could call a parallel or higher--dimensional reality is provided by Vrindavana – it’s a rather essential example. We are told the entire spiritual world is there in Vrindavana. Now if an ordinary person goes to Vrindavana he sees an ordinary earthly village with buildings, and streets, and people, and so forth. But if the person is at a higher level of spiritual awareness then he can see the actual reality of Vrindavana. There’s the whole Brahma-vimohana lila in which Krishna revealed to Brahma the reality of Vrindavana and Brahma was totally astonished by what he saw, so much so that he actually fainted. So the point then is that the ordinary world is there in Vrindavana that we see and experience and this transcendental world is also there. And it’s a question of the level of consciousness of the individual as to which world you can experience. So you might say well this is an entirely spiritual example. There are material examples also. For example, in the Himalayas there is a place called Kalapa-grama which is mentioned, I think, mainly in the Eighth Canto of the Bhagavatam. So this is the place where the representatives of the surya-vamsa and soma-vamsa are waiting out the Kali-yuga. The idea is that these are dynasties of kings descending from the sun-god and the moon-god. And they are referred to quite a bit in the Bhagavatam.
And you can see that these dynasties go through many different yugas, yuga cycles, but it is also described in the Bhagavatam that these dynasties become degraded and die out during the Kali-yuga. I think it’s, which Canto is it? One of the, Twelfth may be, yeah, one of the later Cantos describes the remaining members of the surya-vamsa in the Kali-yuga and it comes down to within about a thousand years of our own time if you add up the ages or periods of reign of these different kings. And then the dynasty peters out; but there are representatives of these dynasties who are staying in a place called Kalapa-grama and they are said in the Bhagavatam to be in a, they are practising yoga to slow down the functions of their body so that they can essentially go into a state of suspended animation and wait out the Kali-yuga. Then in the next Satya-yuga they will become kings again. So they are there, but who can see them? And that’s in the Himalayas. So that’s a more material or mundane example of parallel reality. Another interesting transcendental example is provided by Navadvipa. If you look at the Navadvipa Mahatmya you’ll see it’s described that there is a transcendental city in Navadvipa and it’s there right now. But people with ordinary vision can’t see it. So there is sort of a multi-level aspect to the universe. These are a few examples.
What I want to do is describe some of the basic principles which will enable us to get a grasp of this multi-level feature of the universe. So the thing to do to explain this is to start with the position of Krishna. Of course in this class on the catuh-sloki there is that verse in which we learn that before, during, and after the creation there is nothing but Krishna. So that means then that in some sense, namely in the sense of acintya-bhedābheda-tattva, the material energy is Krishna. Now this has important implications concerning the nature of matter. We don't usually look at it that way. In fact there may be a tendency to think that matter is the ordinary stuff we conceive of on the basis of our general education – three dimensional, made up of little molecules and particles, and so forth – and Krishna somehow is all-pervading within that; one might have an impression like that. So in effect what one visualises is this: one takes one’s image of matter and space and then one adds Krishna, and you add Him everywhere, and then you say, “Well, that’s very hard to conceive of, so we’ll say that’s inconceivable.” So you could think of it in that way. It’s natural to think of it in that way. But that’s not actually the proper understanding, because if you adopt that approach to understanding the position of Krishna then you are making Krishna relative to space and matter; whereas Krishna is the absolute source of everything and space and matter are relative to Krishna.
So in order to understand the actual nature of matter, the thing to do is to start with Krishna. Actually, when I was in Vrindavana once a man gave me an argument in favour of the Mayavadi doctrine based on this idea that Krishna is in ordinary space. So he pointed to a picture of Krishna on a poster. He said, "Well this cannot be the Absolute Truth and here’s why. You see here is Krishna’s arm, ok? And go a little bit beneath His arm, there’s empty space. And go further down, there’s His foot; go a bit further down, well, there’s more space. So Krishna is relative. So how could He be the Absolute Truth?" This was his argument. But of course this is based on a misconception.
So in the Brahma-samhita there is a fairly succinct description of Krishna’s position which is very interesting. here are two verses in particular which I would like to read. The first one is,
I worship Govinda, the primeval Lord, whose transcendental form is full of bliss, truth, substantiality and is thus full of the most dazzling splendor. Each of the limbs of that transcendental figure possesses in Himself, the full-fledged functions of all the organs, and eternally sees, maintains, and manifests the infinite universes, both spiritual and mundane. [BS 5.32]
So this provides a sort of basic axiom describing the nature of Krishna’s form. And you can see that it’s not like material form. A material form as we normally conceive of it is made up of a number of little parts that are just juxtaposed next to one another. The idea in physics there are some kind of forces that pull these parts together, not very strong though. If you take an ordinary human body, these parts are temporarily stuck together, and they tend to come unstuck unfortunately. And in a sense the body then is unreal because the only things that are really there are the parts. That’s what we were talking about in connection with the simulated worlds and so forth. But Krishna’s body is not like that. We find that Krishna’s body has parts – limbs, head, arms, fingers, and so forth – but each part of Krishna’s body is the totality of Krishna. Now materially this is inconceivable, but then this is not supposed to be a description of matter. This is the starting point for understanding Krishna. So that is the... you can say the initial axiom: that Krishna has variegated form but He is perfectly unified because each part of that form is the totality of Krishna.
So believe it or not, this is going to tell us something about the nature of space and matter. And actually that’s not so hard to understand because space and matter are produced by Krishna. So to get to the topic of space and matter, we go to another verse. This one says,
He is an undifferentiated entity as there is no distinction between potency and the possessor thereof. In His work of creation of millions of worlds, His potency remains inseparable. All the universes exist in Him and He is present in His fullness in every one of the atoms that are scattered throughout the universe, at one and the same time. Such is the primeval Lord whom I adore. [BS 5.35]
So this verse is making a rather interesting statement because it is saying that the universes exist in Krishna. So alright, here is Krishna, you can imagine a universe in Him. Now imagine taking one atom in that universe. Well, Krishna is fully present in that atom. So there is Krishna and there is the universe in Him and the atom in the universe and He in His fullness is present within the atom. So you say, “Well, that’s materially impossible!” But once again it’s an axiomatic situation. This is the situation of Krishna. Srila Bhaktisiddhanta Sarasvati in his purport emphasises this point. Let’s see where is this. Yeah, he says,
Again His abode is beyond human conception since all worlds, limited and spiritual, exist in Him and He resides simultaneously in His fullness and entirety in all the atoms in all the worlds.
So that is the situation of Krishna. So . . . which text? Oh these! Well, this is text 35 that I was just reading. and the one before was text 32 in the Brahma-samhita. So you can see then that this idea that Krishna is situated in space is not the correct idea. Actually space is defined by Krishna and all the space in the universes is within Krishna and Krishna is present at every point within space.
So this idea of Krishna being present in space can be looked at in another way, and that is by saying that Krishna has direct access to every point in space – every location is where Krishna is. That’s just another way of saying that Krishna is situated in every location because Krishna is one. Just like in the Bhagavad-gita also it is said, stated, the Supersoul appears to be divided but actually He is situated as one. So it’s not really that there are lots of little Supersouls in all of the different atoms. There is one Supersoul and He is everywhere simultaneously. So that means in a sense all the points in space are in the same place, at least from the perspective of Krishna. And because of that He doesn't have to travel in order to go anywhere. There are many examples of that. For example, when the embryo Pariksit in Uttara’s womb was being burned and Krishna appeared to save him, Srila Prabhupada commented in the purport that Krishna didn't have to travel in order to appear there. He was actually already there and so on.
So this says something then about the nature of space. Basically if space and matter in the ultimate issue are Krishna, as that catur-sloki verse is saying, then matter must have potency beyond what we ordinarily think of and what we ordinarily experience. In fact, all the potency that Krishna has must be there. So this leads to all kinds of possibilities. To give an idea of what it implies, I am going to read for you a passage from the Caitanya-caritamrta that always very much intrigued me. And I have it in the book here. This tells about a visit of Brahma to Krishna in Dvaraka. So it’s quite intriguing. Brahma came to see Krishna and he was waiting, apparently there were lots of important demigods waiting to see Krishna, and so Krishna’s secretary told Brahma, well he came out and said, “Krishna wants to know which Brahma has come to see Him!” And Brahma was immediately a bit surprised at this. He thought, “Well, I am the only Brahma of the universe! What’s he talking about?” So when Brahma came in to see Krishna finally the following conversation took place. So Krishna said, or rather Brahma said to Krishna,
“Why did you inquire which Brahma had come to see You? What is the purpose of such an inquiry? Is there any other Brahma besides me within this universe?”
Upon hearing this Sri Krishna smiled and immediately meditated. Unlimited Brahmas arrived instantly. These Brahmas had different numbers of heads: some had ten heads, some twenty, some a hundred, some a thousand, some ten thousand, some hundred thousand, some ten million, and others a hundred million. No one can count the number of faces they had. There also arrived many Lord Siva’s with various heads numbering one hundred thousand and ten million. Many Indra’s also arrived and they had thousands of eyes all over their bodies.
When the four-headed Brahma of this universe saw all these opulences of Krishna he became very bewildered and considered Himself a rabbit among many elephants. All the Brahmas who came to see Krishna offered their respects at His lotus feet. And when they did this, their helmets touched His lotus feet. No one can estimate the inconceivable potencies of Krishna. All the Brahmas who were there were resting in the one body of Krishna. When all the helmets struck together at Krishna’s lotus feet there was a tumultuous sound. It appeared that the helmets themselves were offering prayers unto Krishna’s lotus feet.
With folded hands all the Brahmas and Sivas began to offer prayers unto Lord Krishna saying, “O Lord, You have shown me a great favour. I have been able to see Your lotus feet.” Each of them then said, “It’s my great fortune, Lord, that You have called me, thinking of me as Your servant. Now let me know what Your order is so that I may carry it on my head.” Lord Krishna replied, “Since I wanted to see all of you together I have called all of you here. All of you should be happy. Is there any fear of the demons?”
They replied, “By Your mercy we are victorious everywhere. Whatever burden there was upon the earth You have taken it away by descending on that planet.”
This is the proof of Dvaraka’s opulence. All the Brahma’s thought that Krishna is now staying in my jurisdiction. Thus the opulence of Dvaraka was perceived by each and every one of them. Although they were all assembled together no one could see anyone but himself.
So this is the final point here that all of these different Brahmas were summoned by Krishna but each Brahma, except for our Brahma, thought that he was alone with Krishna. So that means each Brahma went to see Krishna in his own universe in Dvaraka. So Krishna was manifesting Dvaraka in all those different universes simultaneously. So Krishna and Dvaraka in that one room within Dvaraka were in all the universes all at once. And our Brahma could see that but each of the other Brahmas could only see himself with Krishna. So this indicates what I mean by higher-dimensional space. I use the word higher-dimensional space to refer to this kind of thing. Yeah?
Answer: For all we know there, he just was discussing our Brahma, I mean as far as we are told. But in this passage right here we are told explicitly, of course, that He was speaking to all these different Brahmas. And He was speaking to them all individually. And our Brahma was given the vision to see all of that. That’s similar to Arjuna being given the vision to see the universal form. So here we have the situation, which in terms of three-dimensional space, is not possible. Now you might say, "Well, this is a particular example involving Krishna in Dvaraka and so forth. But it also involves Brahma, the different Brahmas and their universes, and so on. In other words, it involves the total picture of reality. So we see that there is this, what I refer to as multi-dimensionality of space. As I said, I am using that term, the term evolved from mathematics, but it’s a convenient term to refer to this kind of thing.
Now there are some more things you can say about it. Let me first of all let me indicate something about the mathematical analogy. It’s only an analogy. You can define, in mathematics, you see historically there’s what they call Euclidean geometry, which you may study in school. So that has a very long history and people have tended to think of space in terms of Euclidean geometry in the West, simply as a matter of tradition. So in Euclidean geometry you have planes and points and lines and so forth, and different axioms. So people tend to think of space in those terms. But in more recent times in mathematics so called higher-dimensional spaces have been studied and there are all kinds of different things that you can do. For example, if you think of this piece of paper as a plane, you can bend it in another dimension – namely the third dimension – and bring two points together. And in that case those two points are very close together because of the bending of the paper, whereas they were widely separated initially. That is, initially you would have to go from here to here, between those two points, but when its bent like this you can cross over directly. So if you can bend something in a higher-dimensional space all kinds of different transformations become possible.
Now it turns out that there are things called mystic siddhis that we read about, mystic powers, and they also shed some light on this issue. For example, there is the prapti siddhi. Srila Prabhupada gives a couple of interesting examples of that. One of them is in the early part of the Nectar of Devotion. He says with the prapti siddhi a yogi who has this power could reach out his hand, let’s say he is in New Delhi, let’s say, reach out his hand to some place in Afghanistan and take some pomegranates and they will appear in his hands there in New Delhi. So in effect he has been able to reach to a distant place and take a physical object. So this isn't simply a matter of some kind of subtle out-of-body travel or astral travel because he is moving real physical pomegranates. And they were in Afghanistan and now they’re there in New Delhi. So that is an example of something, which at least by analogy we can think of, in terms of the example of the paper. At least such a thing is not possible in ordinary three-dimensional space. But the idea of higher-dimensional space at least gives an idea of how that could be possible. In any case, the Vedic literature describes that this kind of thing is going on.
So the basic point that I want to make then is that these mystic potencies also imply something about the nature of space. Now the interesting thing is that the mystic potencies are obtainable by borrowing Krishna’s potency. In other words, all these different mystic potencies are actually the potency of Krishna manifested in the given individual person to a limited degree. So if Krishna is everywhere at once and Krishna gives you a little bit of His potency then you can also transcend the ordinary limits of space and go to some other place instantaneously. Also, there is the possibility of changes of scale. Krishna is not just there everywhere at once, but He exists at all possible size levels. He exists as being smaller than the smallest and also greater than the greatest. So by borrowing the potency of Krishna you can also experience space in the same way. So that’s described in some detail in the Bhagavatam. I thought I would read you a few examples of that because it’s kind of interesting. For example, here Krishna is saying, Krishna is speaking to Uddhava here, this is in the Eleventh Canto. It’s in Chapter Fifteen actually. So He says here,
One who worships Me in My atomic form pervading all subtle elements, fixing his mind on that alone, obtains the mystic perfection called aṇimā. [SB 11.15.10]
So aṇimā is the mystic power to become smaller than the smallest. So according to this, if you meditate on Krishna’s feature as smaller than the smallest you can acquire that power from Him. In that case you can become very minute and enter into the atoms and so forth. Or conversely,
One who absorbs his mind in the particular form of the mahat-tattva and thus meditates upon Me as the Supreme Soul of the total material existence achieves the mystic perfection called mahimā. By further absorbing the mind in the situation of each individual element such as the sky, air, fire, and so on, one progressively acquires the greatness of each material element. [SB 11.15.11]
So here is the case where this mahimā siddhi is the power to expand oneself enormously. So these can be looked at as indications of the nature of space as understood in the Vedic literature. Perhaps the first way one would think about these things is to think of space as being a fixed framework given by Euclidean geometry and imagine somehow these things can take place within space. But actually we see here these potencies are obtained by acquiring a small amount of Krishna’s potency. And Krishna has the feature that He is everywhere in space, He is simultaneously includes all the universes within Him and He is also within every atom within the universes. So by borrowing Krishna’s potency the individuals also experience space in this way.
So the basic point then is that space and time have properties that are somewhat different from what we normally experience. So the Vedic literature contains all kinds of stories which implicitly make use of this understanding. All kinds of things happen which would be rather difficult to understand in terms of ordinary three-dimensional space. To give another example, which is material, consider the demon Banasura, who had a thousand arms. You can consider that one. It was described that with his thousand arms he was working five hundred bows simultaneously and firing arrows at Krishna in that big battle which they had. So if you think about that you can see there could be some problems with that description because, well, you may say that the arms are somehow subtle so they can pass through each other but what about the bows! If you have got five hundred bows, 360 degrees in a full circle, with 500 bows you have less than one degree per bow if you went around in a complete circle. But actually he was aiming them all in one direction. So why didn't the bows get in the way of one another? And you might say, “Well, they pass through each other,” but why didn't the bow strings pass through the arrows? It’s a little bit hard to make the whole thing work because you could say, “Well, a given arrow has to be propelled by its bow string, but it has to pass through all the other bow strings that were there.” Things would get in the way of each other. And the arrows, presumably once they are launched, they will make definite holes in people, but they have to pass through things, so how could it be?
But you can see, though, if you have higher-dimensional space such a thing becomes possible. And of course in this description that I just read about the different heads on the body of Lord Brahma, you can see problems there also. Rather large numbers of heads were being mentioned, ten millions and hundreds of millions and so forth. So how do you work that out anatomically. But again if you can have higher-dimensional space then that becomes possible.
A: Yeah, have to be pretty big teeth! How do you have five hundred arms coming out one shoulder? Make them as thin as hairs? Actually you can see that in paintings. Artists have a lot of trouble with some of the different pastimes.
A: Yeah, for example there is the Kaliya serpent. I have seen paintings in which you see this enormously thick trunk and then these very thin heads coming out in order to fit all those heads onto one basic trunk. But in any case there are many different things like this. So the idea is there’s a multi-dimensionality of space which is implicit in the Vedic literature. And there is the idea of parallel worlds and connections between worlds and so forth. So that was the basic idea that I wanted to convey in this whole subject of the Vedic Physics. Yeah?
Q: We are conditioned to see this world as three-dimensional, the world we see, and it doesn't talk like that in Vedic literature. Is it actually….some other way of considering, they didn't see the three-dimensionality of it, didn't take notice of it, why….or were they seeing something different from what we are seeing?
A: I think the people saw the same thing that we see under normal circumstances. After all, you also all read of the ten directions in the Vedic literature and those are North, South, East and West and then combinations, North East, North West and so on. That makes eight, and then up and down. So those are the ten directions. So that seems pretty three-dimensional. But there’s all kinds of references also to what we might call mystical operations which many people in Vedic times, let’s say, were able to perform.
Another example that comes to mind is this matter of travelling to a distant place by entering into a river such as the Ganges. Srila Prabhupada has said that even today there are some yogis who can enter into the Ganges somewhere up near Haridwar and they emerge for the Kumbha-mela, I guess near Allahabad; and it’s not that they swam underwater all the way. Somehow you just enter into the river at one point and emerge at another point, which is again a higher-dimensional type of thing, similar to that prapti siddhi it would seem. You might ask what is the role of the river in that? I don't really know. Maybe it's’ a sort of guiding beacon or something. There are descriptions in the Bhagavatam that this method can be used to travel from the higher planets to the lower planets, which described that the four Kumaras were in Satyaloka and they went to visit Ananta Sesa. So they entered the Ganges, went down to the lower planets, found where Ananta Sesa was, and emerged; and their hair was wet when they came out of the Ganges. So there are all kinds of descriptions of, you might say, higher-dimensional experience, you know many different things of that sort. This for example, when Indra was stealing the sacrificial horse from Maharaja Prthu and Maharaja Prthu’s son went chasing after Indra and he just automatically flew through outer space chasing him. So it seems that people sort of had ordinary experience some of the time walking around on the earth in an ordinary way but then in the case of this person, he just took off into the ether.
Oh by the way, another interesting point is that Srila Prabhupada very often, especially in the Krishna Book, refers to travelling in outer space, and one might get the impression that this is something like the astronauts going up into outer space. But as far as I can see it really means travelling in the ether, the element of ether. It doesn't mean that you have to go up through the atmosphere, up to the ionosphere and so on up and then travel to space, and come back down. For example there is that story in which what was it, Aniruddha was kidnapped by that mystic yogini Chitralekha. So without even waking him up she flew through space and picked him up and took him to this city Sonitapura or something hundreds of miles away from Dvaraka; and so then there he was. So this appears to be an ability to move through the ether.
Another interesting point in this Bhagavatam, by the way, stresses that you can move gross bodies this way. I just saw this, one of those that I have labelled here. I have a whole series of them. Yeah, this is it. This is text 22  in Chapter 15, it says,
The yogī who completely absorbs his mind in Me, and who then makes use of the wind that follows the mind to absorb the material body in Me, obtains through the potency of meditation on Me the mystic perfection by which his body immediately follows his mind wherever it goes. [SB 11.15.21]
Q: [unclear] . . . Hanuman, when he was little, tried to grab the sun and flew pretty close to it.
A: Oh yeah, there are so many descriptions of these things. What’s described here is that you can move your gross body to another part of the universe going at the speed of the mind and so forth. Yeah?
A: Yeah, apparently so. Another way to look at it is that the laws that we know of in our ordinary experience are special cases of more general laws. So when these kinds of things are done presumably the more general laws are being invoked. We have experience of that kind of thing. If you consider the fact that nowadays we have electronics, so we can do all kinds of things with electricity. So the potency of electricity was always there in matter but until about hundred years ago nobody ever did anything with it, at least within our historical period. So all that potency was there but nobody knew anything about it. Now we know about it and so we have radio, television, electric lights, and so on. So similarly, these would be potencies that are there in matter, in the material universe, but we don’t know how to take advantage of them. But then there are other personalities that do. Yeah?
Q: You talked about so many things, like so many shoulders mounted, or heads, that becomes possible in the higher-dimensional space because you are saying we can have more than one thing in what we would consider the same place, but somebody else doesn’t consider it the same place.
A: Yeah, that’s right. In fact, you can even make a computer model of a, in four dimensions of a four-armed form. I tried this. It was pretty crude actually – I only had a 64K computer to do that with so I just used blocks to make it. So I used four-dimensional blocks. People know about these things. Did you ever see a four-dimensional block? So, I will make a drawing for you.
A: Well, a fourth dimension can be a spatial dimension. You take an ordinary box like this and then we need to extend each of these lines and connect them like this. Oops, I forgot two extensions . . . there we go. Yeah, this is a hypercube. It’s called a tesseract also. I just have to connect all the lines now. Have to stand back from this, to see where they all are. Let’s see, not quite, I misconnected some lines here I am afraid. Wait a minute, where does this go . . .
A: Well basically, you can do this with mathematics. You can have four-dimensional cubes, it’s a hypercube. Just as you can take ordinary three-dimensional cubes and put them together to make a figure – somewhat crude blockish looking figure – you can take four-dimensional hypercubes and put them together in four-dimensional space; and you can make a figure using a computer just as you saw with those computer graphics. You can take a three-dimensional model of something generated in the computer and project that on the two-dimensional screen and you see it as a two-dimensional representation of a three-dimensional thing. Well, you can do the same thing with a four-dimensional object. You can also project it unto a screen and you can rotate in four dimensions and look at it from various angles. So I tried that out. You get some quite remarkable looking pictures, but I arranged the thing with two arms coming out of each shoulder. So it would be interesting, by the way, to make a more realistic model of that. There are more powerful computers. Actually people do this kind of thing. There are a number of videos showing higher-dimensional surfaces projected onto 2D and then rotated in higher-dimensional space. These are used in some mathematics classes. And what you see on the screen are all these amazing transformations taking place that really corresponds to the rotation of the higher-dimensional surface.
So it’s because of that sort of thing that I really adopted this term ‘higher-dimensional’ although I should stress it’s only really a metaphor for the actual reality. And there are lots of things involved here in which I don’t really understand how they work. For example I don’t really know how the prapti-siddhi works, that is, how a yogi can reach for an object at a distance. But the basic principle, though, behind it, is easy enough to understand: namely if Krishna is a unified being who at the same time has diverse features, and He is simultaneously at all points in space and actually is the very definition of all points in space, then these kinds of things are possible. And then the detail, of course, you know, would be a vast subject known only to Krishna ultimately. Of course, yogis at different levels of advancement would know the whole system at different levels of detail beyond what we are aware of. So that is a basic foundation then. Is there any other questions? Yeah?
A: Yeah, that’s then answered I think in a purport here: it mentions that one can obtain a perverted reflection of these siddhis also and the demons are allowed to do that. So Krishna is facilitating their sense gratification. It’s an educational experience to be a demon.
A: Yes, that’s an interesting point. I should mention something about modern science, because you might say these, this idea of higher-dimensional space is really rather far out – but in modern science you find these kinds of ideas. First of all, in mathematics generally subjects such as linear algebra and so on are presented in terms of n-dimensional space. They don’t even bother with three-dimensional, they make it n, where n could be anything. But then in physics, where they are talking about the real world, it turns out first of all that quantum mechanics assumes, really the necessity of, an infinite-dimensional space, simply to define atoms. A lot of people aren't aware of this. But if you take, say, a carbon atom which has [audio break]... that’s the way you define one quantum, one carbon atom in quantum mechanics. You need that. If you try to do it just in three-dimensional space it wont work. All the physics breaks down. Yeah?
A: Quantum mechanics is an amazing subject. That’s a good question. What you have are, well the whole thing to go into in quantum mechanics, but yes you have... actually, just to sum up the debated point, I was once speaking to this British physicist Sir Brian Pippard at the Cavendish Laboratory, and he said to me that, “The moment you think of two electrons you’re lost.” So it’s a total misconception to think that there are two electrons. In effect there is one electron. I spoke of a carbon atom and I said, “Well you need 18-dimensional space.” Now guess what you need to have two carbon atoms? That’s right, you need 36-dimensional space to talk about the electrons in two carbon atoms. So all the electrons in two carbon atoms, that’s really one electron so to speak moving in 36-dimensional space. Now if you go to three, four, etc. carbon atoms you just keep multiplying the numbers of spatial dimensions. So quantum mechanics is defined in terms of what is called Filbert space, which is infinite-dimensional space. That’s the way quantum mechanics works. So the point can be made that if in physics, and one should keep in mind quantum mechanics isn’t just some strange esoteric theory but it’s the foundation of modern chemistry; and chemical reactions are understood in those terms.
A: If you look at the actual theory it’s all wave and there’s no particles. But the really mysterious thing is that the wave suddenly reorients itself by jumps and the jumps correspond to what they speak of as particles. I have to give you some descriptions to clarify that, that’s a pretty obscure statement, but it’s a really remarkable theory. The strange thing about that is that it works.
A: Yeah, sometimes it’s like that of a particle . . . yeah, I’d have to draw a whole bunch of diagrams to explain how that works out. But the basic point to make there is they are dealing with higher-dimensional space just to define atoms and molecules. So already then that means this whole idea has been introduced into modern science. The Vedic literature is going much further than that, but the ideas are there.
Q: What are they waves of?
A: Well no one would be able to say what they are waves of. That’s the question I asked when I first studied this. Actually I was in high school and I studied this thing, so I said, “Well, what is this wave oscillating in?” That’s totally the wrong question to ask. Just take it as an axiomatic starting point. You start with this wave. You don’t ask what it is oscillating in or what it’s made of. That’s not a fruitful question. So one shouldn't laugh at that though. It's actually a valid approach because it’s the same approach that I was just advocating for understanding Krishna. That is, in the Brahma-samhita you have the description of the way Krishna is – that each part of His transcendental body is identical to the totality. Now you could say, “Well how are we to understand this. What is His body made up of anyway?” But the answer would be that that’s the wrong question. Actually this is the starting point. Krishna is like this and other things could be understood in terms of this. This is what they call the axiomatic method. And in fact it’s quite ancient and respectable.
For example I mentioned Euclidean geometry. Euclidean geometry is defined in terms of axioms: two points determine one straight line and so on and so forth. So how do you know that these axioms are true? Well you don’t. Actually it’s interesting, the history of geometry. For many years people thought that these axioms of Euclidean geometry are somehow intuitively obvious, that is, they are obviously true. You can just tell that by looking at it. But then somebody came along and defined geometry with different axioms and it was just as good as Euclidean geometry, the so-called non-Euclidean geometry. Then they realised those axioms are not obviously true because you could have something different which may be just as good.
So the basic idea is that the axioms are starting points and if you have the right starting point then you will be able to draw the right conclusions. The whole idea of logic, logic has to start with something that is never proven, because if you start at a certain point and reason and finally come back to your original conclusion – that’s called circular reasoning, which is invalid. Now if it’s not circular it has to start somewhere. And where it starts, that’s the point where there is no proof preceding that. So that’s the nature of logic. And that fits in nicely with the idea of a descending system for knowledge. In other words if you are given from some absolute source some initial axioms that are actually correct, then you can safely apply logic and you will get right conclusions all the way down the line. Whereas by the ascending process you also have to have axioms, but where do you get them? So what scientists do using the ascending process is they say, “Well ok, we need axioms,” so they just try something out. They guess a certain set of axioms, and then they work out the conclusions and see how well the conclusions hold up. If they hold up pretty well they say, “Well, we chose some pretty good axioms.” So the trouble is eventually they come to believe that the axioms are absolute because it’s natural for the people to think that way.
Like I mentioned the other day, the problem with the scientists is they are using the parampara system and the thing is, it’s a parampara system that isn't coming from an absolute source. It’s just coming from a guesswork originally. So . . .
A: You better ask me later because now I am supposed to have ended the class five minutes ago but…oh I misread the clock. Ok, you can ask one question.
A: The difference though is, yes you can point the TV camera at the screen and you can get an infinite regress of cameras and screens. But those are all images. But in this case, it is the actual reality. You see this pastime in which Mother Yasoda looked into Krishna’s mouth, because she heard He ate the dirt, she saw the universes and she even saw herself in there – she was actually seeing herself. And that’s an illustration of that verse in the Brahma-samhita where Krishna says that the universes are within Him. So mother Yasoda looked into Krishna’s mouth and saw herself, presumably looking into Krishna’s mouth.
A: Everything is ultimately spiritual. You see this is also the discussion in that class on the catuh-sloki, namely, that everything that is seen to be separate from Krishna has no actual reality. Because everything that is actually real is not separate from Krishna, it is intimately part of Krishna and ultimately it is Krishna. That is the acintya-bhedabheda-tattva. So the point then is that matter, we see it as being separate from Krishna. That’s the... another point that’s made here: Krishna’s illusory energy has the power to make us see things as being separate from Krishna. So it’s by Krishna’s power that we are seeing the absence of Krishna, and we are just seeing matter wherever we look. But Krishna is actually there everywhere. So actually all the potencies of Krishna are actually present everywhere in space.
A: There is no indication that there are any more Sadaputas. Brahma, by the way, is a post. Just like there are many presidents. There is only one, you know, Bush, or whoever it may be. But there are many different presidents, so there are many different Brahmas.
A: Yeah, so you can run wild in the imaginary field of these ideas, but the point is, in the Vedic literature you do have these different aspects of the universe. Now, yeah?
A: Go beyond Krishna to understand Krishna!
A: Well yes, by realisation. You see when you are talking about axioms and deductions and so on, you are talking about logic, reasoning, simple manipulation. Of course, the real way to understand Krishna is ultimately by realisation. You get to meet Krishna and then you really know to the fullest extent what is possible for the jiva. So that’s the ultimate way to know about Krishna. But meanwhile one can look at it in terms of the framework of ideas. And that’s useful for understanding the Vedic literature.
So I could, let’s see, for the next time the thing to read is this third chapter. This gets into the actual subject matter of the Fifth Canto. And I’ll say a little bit about it now since we have some time. But you can look this over. I know there is a lot of material here and you don’t have to, you know, consider that you have to absorb all of this. It’s just a good idea to get an overview. You know, you can skim it over and just get an idea of what’s there. So what I am going to be doing then is discussing this material. So the starting point for the discussion of the universes described in the Fifth Canto is the earth, and so the earth is described in the Fifth Canto as Bhu-mandala. And I translated this here as ‘middle earth’ because it is a middle planetary system. This Bhu-mandala is described in the Fifth Canto of the Bhagavatam essentially as a disk which is fifty koti yojanas in diameter. Koti is ten million. So its 500 million yojanas, and Srila Prabhupada consistently uses the figure of 8 miles for one yojana. So that comes out to 4 billion miles in diameter.
So that is the earth as is referred to in the Srimad-Bhagavatam. So this of course can be a little bit perplexing because you can say, "So what does that correspond to, you know, in our experience?" Because we tend to think of the earth as a globe; so how does this disk 4 billion miles in diameter correspond to a globe? So one idea that one might have is that, well, the Vedic literature is not even accepting the idea of the earth as a globe. But that’s one of the points regarding this description of the Surya-siddhanta that I was giving yesterday because the Surya-siddhanta describes the earth as a globe. And in fact it describes it as a globe of about the right size. There we use the figure of 5 miles per yojana and the earth is a globe which is about 25,000 miles around the equator, which is the right value according to modern understanding.
A: The reason I would select 5 is that there are various distances mentioned in the Surya-siddhanta. There’s the diameter of the earth, there is the distance to the moon, the diameter of the moon, and diameter of different planets. And if you adopt 5 miles per yojana then all of these agree with modern numbers. So that’s the reason for thinking it’s 5 miles. Now in the Siddhanta-siromani, that’s another one of these Jyotisa Sastras, written by Bhaskaracarya, the figure is, I think, 7.55, if you calculated it in the same way, namely, by matching all these distances. So those are two different scales, and as I mentioned yesterday, this astronomer Paramesvara comes right out and says there are two different scales used by the astronomers for the yojana. So the 8 mile figure which Srila Prabhupada uses is closer to the Siddhanta-siromani figure. I have also seen references to a 6 mile yojana and so forth.
So that’s the question then. We have on the one hand the earth globe described in terms of yojanas as having a diameter of 1600 yojanas, and this 500 million yojana disk referred to as the earth in the Bhagavatam. So what is the relation between the two? Now I was interested in checking to see what commentators on the Bhagavatam explicitly had to say on this subject and I found some material which is contained here in the appendix of this book, specifically the first appendix – there are a two appendices. What I have here is a translation, pretty much commentary and part translation, of some remarks made by a commentator on the Bhagavatam named Vamsidhara. Now this was obtained from the volumes that Srila Prabhupada used for Bhagavatam commentary, the large green volumes that he would consult, which had each I think, they had eleven different commentaries by different authorities. Yeah?
A: I say explicitly in the book that actually I don't think it’s necessarily bonafide. What my purpose…
A: Yes it’s in this appendix. Have you read the appendix? Well perhaps I didn't make it suitably clear, but I definitely said it in here. The, I say, where do I say it, that basically he’s speculating. But you might say then, “What is the value?” The value of it is that it shows what Vaisnavas were thinking about the Fifth Canto as opposed to the Jyotisa-sastra in that time period, which was before the European invasion. This Vamsidhara was active in 1642. I don’t know any other dates concerning his life but according to what I was able to find he was writing things, so he was mature in 1642 AD.
Yeah, it’s after Lord Caitanya. Another point to make is that in the Fifth Canto Srila Prabhupada at one point quotes verbatim a very large chunk of Sanskrit which he attributes to, what’s his name, that name just escaped my mind . . . yes, Visvanatha Cakravarti Thakura. So there’s a large block of Sanskrit that he quotes there. In fact there is a commentary by Visvanatha Cakravarti Thakura in which that passage in Sanskrit is to be found. Vamsidhara has word for word the same passages as part of his larger passage. Now that means that one of them is quoting the other but I don't know who is quoting whom.
A: Well they would seem to be. So that’s as much as I know. But the section in this appendix I present a translation of the section which is found both in Vamsidhara and Visvanatha Cakravarti Thakura, that’s in the beginning part of the appendix. Basically what that is, is a detailed calculation of the diameter of Bhu-mandala which refines, you might say, the Bhagavatam figures, because there are slightly different figures than those contained in the Bhagavatam. They explain why. Actually the explanation given is that, you see, just to jump ahead a little bit, this 4-billion-mile-diameter disk is sitting within a spherical shell 4 billion miles in diameter. That’s the description given. That means it goes right out to the edge of that shell. So what they did was to give a little leeway between the edge of the disk and the shell. And they did that by adding up in detail the distances of different sub-components of Bhu-mandala going radially outward. I won’t go into that, but you can read it here. It’s fairly complicated and so they wound up, what was it, the gap how big was that gap?
Comment: 16 lakhs.
A: Yeah, and they pointed out that allowed the earth to sink down into the Garbhodaka Ocean. This by the way is an interesting point. Lord Varaha of course then lifted the earth from the Garbhodaka Ocean, that’s what is mentioned in this section of Sanskrit that we are talking about. Now you’ll see portrayals in our books showing Lord Varaha lifting the earth globe from an ocean, but in fact Bhu-mandala is the entity being lifted from the ocean. And they describe here that by allowing some leeway around the edges, Bhu-mandala can move up and down. So therefore it can go into the ocean. So it wasn't just the little earth globe.
A: Well you wonder, they may get a little bit squashed. I guess they must be carried down with the Bhu-mandala, they must go into the ocean also. It’s like stacking phonograph records. That’s what he says, both Visvanatha Cakravarti Thakura and Vamsidhara, because the identical Sanskrit is in each one’s commentary.
Comment: The globe is being described as being on Varaha’s tusks.
A: Well, Bhu-mandala, the earth, is held on Varaha’s tusk. But it turns out it’s the whole Bhu-mandala disk which is involved here. That’s the earth which is being lifted. That’s what they say at any rate. So He can hold more than just a little globe on His tusk also.
A: Well that was the other question. Presumably when the earth goes down they had to be flooded also. It makes sense they would have to be. So I am going to be explaining a lot of these things: where is this ocean, how do we relate back to the world as we know it? So right now I am just giving some introductory material concerning this particular purport or commentary by Vamsidhara. So Vamsidhara is a commentator on the Bhagavatam. After this section which he has in common with Visvanatha Cakravarti Thakura he goes on to give a much more detailed account. Basically he first comes right out and says that there’s a problem that people are confronting, namely there seems to be two descriptions of the earth in the Vedic literature. One is the earth as a small egg of clay, and he specifically gives its diameter in yojanas. He uses the circumference, and pariveṣṭana is the word, so 5000 yojanas is the circumference, that’s 25,000 miles around. So he says, there is a small 5000-yojana earth which is an egg of clay he says, and then there is this big earth, Bhu-mandala, and that’s 50 koti yojanas across. So how are we to understand that? He raises this question. Let us see.
Let’s see if I can quickly find . . . yeah, here it is. This is one place where he says it,
Well then, how can one explain the contradiction between the Bhagavata and the Jyotisa-sastra or astronomical science? In the Bhagavata Jambudvipa is said to measure 100,000 yojanas (Jambudvipa is just part of Bhu-mandala), whereas the astronomical science states the entire earth to be measuring only 5000 yojanas. The solution is given in the Goladarsa. According to that, some brief explanation is given below.
So that’s what he says. He goes on to give his explanation. I assume Goladarsa is a book that he wrote or at least it’s some kind of book; but I have no access to that book. So he then goes to give his understanding of how you relate the Bhu-mandala disk to the earth globe. So as I do say here, I think that he is mistaken in certain respects about what he is saying. And that’s part of the whole discussion within this book. Basically what he does is he says that the Bhu-mandala disk is a reflection of the earth globe. He resolves the apparent contradiction with what he calls this pratibimba-tarka. Pratibimba means a reflection. And he argues that – it’s fairly complicated – it’s presented in this appendix. But he argues that this large disk Bhu-mandala is some kind of reflection. This creates a bit of a problem, because of course according to the Bhagavatam this Bhu-mandala is inhabited thought out its whole extent. So we have the problem of an inhabited reflection. So that’s the situation there.
Well, of course there could be various ways in which we could interpret the term reflection. Also by the way, he cites some Vedic evidence concerning the position of the Jyotisa Sastra. Since I am, I hadn't exactly planned to speak about this, I am just looking for where I have quotations here, but he mentions the Vedic quotation describing this, let’s see where we have, oh yeah. At one point he says,
Not indeed has the Jyotisa Sastra or science of luminaries started contravening the Puranic statement that Vyasa is Narayana Himself, nor could Vyasa also have proceeded in contravention of the science of luminaries which is the very eye of the Vedas as expressed in the statement that astronomy is declared to be the eye of the Veda.
Astronomy here is the Jyotisa Sastra. I found what I think is that statement, the Sanskrit matches up. There is verse number 1.4 Narada-samhita which says,
The excellent science of astronomy comprising siddhanta, samhita, and hora as its three branches is the clear eye of the Vedas.
So that statement is there. So he is pointing out that we seem to have this contradiction, which he wants to resolve. So the basic question then is this: we have this disk of Bhu-mandala and we have the earth globe. Now to go further I should describe Bhu-mandala in greater detail. Ultimately the key to understanding what Bhu-mandala is, and where it is, is based on the description of the subdivisions of the Bhu-mandala. So I have a series of pictures in the book, computer generated. In the center of Bhu-mandala there is a structure called Jambudvipa. So Bhu-mandala is 4 billion miles across. This Jambudvipa is in the very center of it and it’s 100,000 yojanas across. So it’s fairly small, and because it is so small it’s practically a speck compared to the total size of Bhu-mandala.
So I have a series of pictures illustrating that beginning on page 49. What you see first is a picture of the plane of Bhu-mandala from a distance of 600 million miles from the center. Imagine you are in a spaceship and you are up at 45 degree angle above that plane, 600 miles out, that picture shows what you will see. It looks sort of like a bullseye with concentric rings. These rings are alternating islands and oceans. So the islands are called dvipas, it’s a word for island, and these all have different names. As you go out from the center each successive dvipa becomes twice as big as to one within. You can see pretty much how that goes in the diagram, and also each successive ocean becomes twice as wide as to one that is within it. So if you turn to the next page, now we look at the same thing from a distance of about 150 million miles and in the very center you can barely see what is called Jambudvipa. So to see Jambudvipa better you move in again, so figure 5 you see Bhu-mandala from 15 million miles. And you begin to see what the structure of Jambudvipa looks like in the center of that picture.
And then finally figure 6 on the next page, page 52, you get a close up picture of Jambudvipa. This is a computer generated picture. It’s based on all of the, it’s entirely based on dimensions given in the Fifth Canto of the Bhagavatam. So everything is drawn to scale according to that description. Some things are left out, namely different mountain ranges and lakes and so on, for which no dimensions are given. So because there were no dimensions, I wouldn't know where to put them in the picture exactly. But essential features for which dimensions are given are presented here. This Jambudvipa is divided into nine regions called varsas. And these are separated by mountain ranges. In the center this inverted cone that you see sticking up is called Mount Meru. That is 84,000 yojanas high from top to bottom and there are various other structures here.
One last comment I will now make, because it’s getting late. In figure 7 you will see a mountain range stretching from a to b. So the height of that mountain range is about twice the diameter of the earth as we know it. That gives you an idea of the scale of the picture.
Q: Could you say that again?
A: This mountain range goes from a to b, if you look at the height of that, that’s about the twice the diameter of the earth as we know it, of the earth globe. That’s just to give you an idea of the scale of that picture. Yeah?
A: Well the, I think the most coherent understanding of the Bhagavatam is that these dimensions relate to one another in three-dimensional space because they are so described. Because they are described in terms of north, east, west, up, down, and so on. So the whole description relates these different dimensions to one another in three-dimensional terms. So it seems most reasonable to assume that it is intended that way.
A: Yes, that’s right.
A: Not on the earth planet exactly. So this is indeed a good question. This is indeed a good question and that’s what I am going to be discussing tomorrow.
Stay tuned tomorrow and we will try to tie it all together.