"Calculation of Time from the Atom" (SB 3.11.1)
Thompson analyzes calculations described in this chapter of the Srimad-Bhagavatam that reference motion of an “ultimate particle, which is indivisible,” called the paramanu, or atom. For example, time attributed for the integration of six of these minute particles is considered a truti, or 1/1687.5 of a second. These basic units are then combined to form days, months, years, and yuga cycles lasting 4,320,000 years. One thousand yuga cycles is considered a kalpa, or 4,320,000,000 years. Thompson describes these numbers as corresponding to the time it would take for a celestial body traveling at the speed of the Moon, to travel around the circumference of the Puranic cosmos.
TRANSCRIPT: Srimad-Bhagavatam, Canto 3, Chapter 11, Text 1. “Calculation of Time from the Atom.” Alachua - 1995-10-31 / (522
...is called the atom. It exists always as an invisible entity, even after the dissolution of all forms. The material body is but a combination of such atoms but it is misunderstood by the common man.
Purport by Srila Prabhupada:
The atomic description of the Srimad-Bhagavatam is almost the same as the modern science of atomism, and this is further described in the Paramanu-vada of Kanada. In modern science also, the atom is accepted as the ultimate indivisible particle of which the universe is composed. Srimad-Bhagavatam is the full text of all descriptions of knowledge, including the theory of atomism. The atom is the minute subtle form of eternal time.
cakṣur unmīlitaṁ yena
tasmai śrī-gurave namaḥ
śrī-caitanya-mano-'bhīṣṭaṁ sthāpitaṁ yena bhū-tale
svayaṁ rūpaḥ kadā mahyaṁ dadāti sva-padāntikam.
So the translation:
The material manifestation's ultimate particle, which is indivisible and not formed into a body, is called the atom. It exists always as an invisible entity, even after the dissolution of all forms. The material body is but a combination of such atoms, but it is misunderstood by the common man.
So, this is the first verse of the famous chapter on “Calculation of Time from the Atom.” And in this chapter it is described that the material manifestation is made up of particles called atoms. In Western science, the concept of an atom is coming from the Greeks. It is commonly said that an ancient Greek named Democritus created the idea of the atom. It's quite possible that he got this idea from India. It is known that there was Indian influence in ancient Greek thinking. For example, the doctrines of Pythagoras have many elements which come from India including the idea of reincarnation, the idea that you should be a vegetarian, and even the so-called Pythagorean theorem. The Pythagorean theorem is a famous theorem of mathematics about the squares on the sides of the right triangle: the sum of the areas of the two squares on the sides equals the area on the hypotenuse, the square of the hypotenuse. Well, this is commonly called the Pythagorean theorem after Pythagoras, but it appears in the Sulvasutras in India. These are mathematical texts, which have the practical purpose of designing altars for fire sacrifices and they contain a great deal of what we call geometry. And the Pythagorean theorem is also stated there. So, it's quite possible that this concept of the atom came into the ancient Greek world from India.
Among the Greeks and Romans, atomism was associated with an underlying philosophy of materialism. For example, Democritus claimed that nothing really exists except atoms and the void. So, that means, in fact he specifically denied the reality of sensations, conscious perceptions. He said these are just conventions in human society, but what really exists is nothing but atoms in the void. There was also a Roman philosopher named Lucretius who expounded the theory of atomism and he was also very much a materialist. So atomism has been associated with materialism and of course the modern scientific theory of the atom is also connected with materialism. Interestingly enough the philosopher Kanada in India is basically presenting a materialistic viewpoint. So, here the Bhagavatam is mentioning the atom, but even in India discussion of atoms has been connected with materialistic philosophy to a very large extent.
So, the atom is a very mysterious entity. Of course, the word ‘atom’ from Greek means indivisible. So the idea is the atom is the smallest particle into which things can be divided and an atom cannot be divided further. However, the atom of modern chemistry can be divided. So basically, the word atom is simply used to apply to it. So basically, the history of physics in the 20th Century has been, you might say the search for the ultimate atom because it was found that the atom of chemistry can be divided into electrons, protons, neutrons. But then, are these the ultimate particles? At one time it was thought that these particles could not be divided further, but now it's believed that a proton can be divided into quarks. Actually, the names for these different particles became a little bit humorous after a while, so the quarks are said to have properties such as strangeness, charm and color. So, this is all tongue-in-cheek of course.
The idea of the atom in physics is ultimately dependent on the concept of a quantum. There's a whole subject in physics called quantum mechanics, which is understood on a formal level in the sense that the physicists can do calculations with it, but it's not understood philosophically. Even today there's a great deal of controversy over just what quantum mechanics means and no one has really figured it out yet. So, the atom is something quite mysterious. Here Srila Prabhupada says that the atom is “the minute subtle form of eternal time.” So it would be nice if we had more information about that. It's certainly interesting, but I don't really know what it means. A bit further here we have a verse which says that:
Atomic time is measured according to its covering a particular atomic space. That time which covers the unmanifest aggregate of atoms is called the great time.
So, that is also interesting but nonetheless mysterious. In any case, we have the idea here that somehow matter is made up of small units. Now the size given for atoms in the Bhagavatam is a bit large from the point of view of modern science. Text five states that six atoms can actually be seen “in the sunshine which enters through the holes of a window screen.” So back in the 1970’s, there was some… when this chapter first came out there was some discussion of whether one could actually see this. There were some devotees were looking at window screens. Some say they can see it and some not. I must admit I never saw anything. But something that could be seen is much bigger than the atom of modern science, so that factor is there.
Then again the rate at which atoms interact it is given in the Bhagavatam it is rather slow. It is stated here, the time duration needed for the integration of three trasarenus is described in this previous verse as a group of six atoms. So, this is called the truti. So, an account is given of what a truti is and if you do the calculation you find that if you divide a second into 1687.5 parts, that is one truti. So that is said to be the time needed for the integration of three trasarenus. But this is quite slow from the point of view of the modern scientific idea. Operations involving many atoms go much faster than that. For example, in computers you talk about millions of instructions per second or nips, but one computer instruction involves a lot of complicated operations in the computer, and you can have millions of those in a second. Whereas, here we're talking about 1700 operations in a second. So, it's not clear exactly why this is, but certainly the basic concept of the atom is there in the Vedic literature.
There are also different values given for the truti. The value I just mentioned is given here in the Bhagavatam, but in for example the Surya-siddhanta, a figure is also given for the truti and that's one 20th the length of the truti given in the Bhagavatam. So, there are different values for these different figures. So, the various time durations in Vedic literature are summed up here in this chapter starting with the truti and working all the way up to the kalpa, or day of Brahma. So, these are interesting units. From the point of view of ordinary life it's hard to see what the value would be for the truti, namely a 17,000th of a the second, or 1700th of a second rather, is not a measurement that has any practical value in ordinary life, but nonetheless it's there in the Vedic calculations.
On the other hand the largest units of time in the Vedic system come to about 4,320,000 years. So that's also quite a large period of time. This verse that describes the atomic time is suggestive of an interesting point mentioned in the Surya-siddhanta. It said here that the time which covers the unmanifest aggregate of atoms is called the great time. In the Surya-siddhanta the... let's see, one kalpa is taken to be the time of what is called the orbit of heaven or the orbit of the Brahmanda. So different orbital periods are given and the orbital period for the Brahmanda is the time that it would take a planet moving at the speed of the moon in its orbit to travel the circumference of the universe. So, this calculation is given in the Surya-siddhanta, that comes out to one kalpa or one day of Brahma. So, that's at least suggested by this statement about time covering the unmanifest aggregate of atoms because of course the time to go all the way around the universe… [break] ...all of the atoms, but of course, that's not by any means definite. The main problem that we are faced with, we don’t have very many details to go on.
So after giving a bit on atoms, there's a description of various lengths of time… [break] ...is the prana, which is 4 seconds in terms of our time measure. Prana literally means, would be the time of one breath. It turns out that this... from a geocentric viewpoint you can say the sun goes all the way around the earth in one... is the time it takes the sun to move one minute of arc. So in this way, your lifetime is draining away, from each breath the sun moves a minute of arc and that's one minute... [break] ...are mentioned here coming up to the laghu which is two minutes. Two dandas make one muhurta, or Brahma muhurta. There are different muhurtas in the course of the day and actually they all have the… [break] ... Jyotisa Sastra is that in one day of 24… [break] ...two ghatikas is a muhurta and that tells you that in the muhurta there are 48… [break] ...so that's somewhat less than an hour.
So one day and night, 24 hours, is of course mentioned; and 15 days is called a paksa and two days... two paksas is one month. So it is said that... this means a month of 30 days. So this is a solar month. And it is said that the time of one day and night on the Pitrloka, the planet of the forefathers, is in fact one month of 30 days. So their day time period is 15 days and their nighttime period is 15 days. Then it turns out that 12 of these months is said to be one year which means that a year lasts 360 days, which is an interesting statement because apparently the year lasts 365 and a quarter days. So, if you're off by five and a quarter days in the length of the year then you can see that for example over 10 years you'd be off by, well about 50 days. So that's quite a big discrepancy.
So, it's interesting that in various ancient cultures in the world the tradition used to be that the year last 360 days. For example, the Babylonians, the Egyptians and the ancient Chinese all had a year of 360 days. But at a certain point maybe two or three thousand years ago, they changed and adopted a year of 365 days. So, that's a curious thing – one wonders if the length of the year underwent a shift. Of course, we don't know but that is the tradition. Actually, if you look in the Bhagavatam you'll find a year is always given as 360 days and you don't find mention of 365.
So, let's see… Going up from the year various lengths of time are given. There's an interesting point made on relative lengths of time. I mentioned Pitrloka, in the Bhagavatam it's also said that one year is the day of the demigods. So 360 days would be one day of the demigods which means that their time scale is different.
Now, if you go up to still higher planets – demigods would be in the inhabitants of Svargaloka – if you go up to still higher planets you find that the time units are still longer. So, one day of Brahma comes out to 4,320,000 years. So this period of time is divided into yuga cycles. So, it's described that... Let's see, the structure of the yuga cycles is interesting. The basic unit for kali-yuga is 1000 years of the demigods. And at the beginning and end of this, you add one-tenth of that period and that's called the yuga sandhya. So that adds another 200 years of the demigods. So the kali-yuga comes out to 1200 years of the demigods. But if you want to convert that into our years, you have to multiply by 360 and that gives you 432,000 years for the kali-yuga. So then two times the kali-yuga is the dvapara-yuga. Three times the kali-yuga is the treta-yuga and four times is the satya-yuga. And if you add up satya, treta, dvapara and kali that gives you one yuga cycle. So four plus three plus two plus one is 10. So that means 10 times the length of the kali-yuga is one yuga cycle.
So, the sandhya are there for the other yugas also. So the length of the sandhya for, let's see kali-yuga would come out to 36,000 years. And it's described that in the yuga sandhya periods different religious activities are typically performed. So we're now actually in the yuga sandhya of the kali-yuga, of this particular kali-yuga.
So, the really severe manifestation of the Age of Kali hasn't begun yet. So for those of you who really enjoy our present state of human society, you can know that it's going to get much worse. Actually, it's interesting that the Golden Age of Lord Caitanya occurs during the yuga sandhya. Srila Prabhupada has referred to this as lasting ten thousand years. And in fact, in the Brahma-vaivarta Purana it is described that after 5,000 years of kali-yuga there will be a 10,000 year period in which Krsna's devotees are very prominent on the earth. So, that's one shastric reference for this Golden Age of 10,000 years. Since about 5,000 years of kali-yuga have now elapsed that means that this 10,000 year golden age is about to begin or has just begun. So, that indicates that from a spiritual point of view things should be very auspicious for the next 10,000 years. But after that one shouldn't want to be around on the earth planet.
So let's see, those are some observations on time. I'll just mention there are also sandhya periods in connection with the yuga cycles. Each, oh well I mentioned those, and I was going to mention that 71 yuga cycles constitutes one age of Manu, a manvantara period. And there are 14 manvantara periods in one day of Brahma. But if you multiply out 14 times 71, you'll see that it doesn't come out to 1000 yuga cycles. But the detail there is that at the beginning and end of each manvantara there's another sandhya of the length of one satya-yuga. So if you add those in then it comes out to 1000 yuga cycles. So that's the situation there. So a few observations on time in the time and the atom. Any questions? Yes.
Question: I need to take that statement of atoms in the Bhagavatam, sort of a generic description of what is the smallest indivisible unit, as opposed to what we learned as atoms which consists of protons, neurons, elections.
Answer: Well, all we know from the description here is...of course Srila Prabhupada translates this first text to say that the atom is indivisible. Now actually in the Sanskrit... unless ultimate is taken to mean indivisible, which logically it really does, because if you can divide it then how can you say that it's the ultimate particle? So it seems to me that indivisible is taken from the word ultimate here, carama. And then of course, there's the very name which is paramanu and para means the most, the super most and anu would be this particle, little particle. So the ultimate particle then is the atom. So if you ask then, what do atoms correspond to say in modern science, it couldn't be the atom of chemistry. Now when you come to protons and the quarks that supposedly make them up, the trouble is if you go into what is called particle physics you find a huge array of different kinds of particles. For example quarks are held together by gluons. Yes, they say that the physicists are becoming a little bit humorous. And so on and so forth. But basically we have the idea of a little quantized units of things.
Interestingly enough the soul is even called cittana means consciousness. And again you see ana which is like that word anu. So the soul in a sense is an atom of consciousness. And of course the soul cannot be divided. So that is there. Any other questions? Yes.
A: The axiomatic truths that the scientist must accept in physics?
Q: They can't prove but they must accept it.
A: Well, indeed there are so many things that the scientists cannot prove. And basically what you have in physics is the system of formulas which work nicely. Now the reason that they work, you can say in practical terms, is that lots of people have been adjusting them and fixing them up over the years so that they do work. In other words if they find they don't work in some way then they correct the formulas until they do work. So you have a system of formulas that work. Now it's amazing that they work as well as they do. Even some physicists have written about that. They're astonished.